Cycle d'études postgrade en aménagements hydrauliques 1999 - 2001 ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE
Diploma Project
December 7, 2001
Chimay : Rock trap at chainage 4+992 m
Hydraulic head losses in an unlined pressure tunnel of a high head power plant Theoretical approach and comparison with the measured values
Pertes de charge en galerie non-revêtu d’un aménagement haute chute Calcul théorique et comparaison avec les résultats mesurées
Diploma project report by Project guide Jury
Manoj Kumar GARNAYAK Dr. Jürg SPEERLI Prof. Dr. Anton SCHLEISS Prof. Dr. Peter EGGER
Preface
The Postgraduate Course in Hydraulic Structures, 1999-2001, at the Federal Institute of Technology, Lausanne, Switzerland, and the practical works as a Student-Trainee at Electrowatt-Ekono, Zürich, during this period has further diversified my own interest, in construction of underground works before the course, by the addition of hydraulic and hydro-geological aspects involved in the design of such structures after the course and the training. I sincerely thank the course management for an excellent coverage of the related topics. At the same time my earnest thanks goes to the management of Electrowatt Ekono who supported my study and provided with an excellent professional working atmosphere at their office with a practical exposure to real life problems related to hydraulics. The diploma project work on ‘Hydraulic head losses in an unlined pressure tunnel of a high head power plant- Theoretical approach and comparison with the measured values’, has been another step in the study of the hydraulic aspects of the underground works of Chimay Project, Peru. This diploma work has improved my knowledge on overbreaks, hydro-geology, head loss calculations and how to simplify complex problems with simple analytical thought. The meetings with Professor A. Schleiss and his encouragement to know something more about the unlined rock tunnels was a very good stepping stone for this project. My guide, instructor, and friend Dr. Jürg Speerli has identified this project work, and has extended full support, advice, and review during its progress. Especially, his experience that reading and writing should go simultaneously was very valuable and saved time. The help and support with a team spirit, both directly and indirectly, from Mr. M. Nater and Mr. M. Aemmer, in providing data and sharing relevant information in time has been instrumental in completing the report. The management and administrative support from Mr. Sigg, Mr. Ruoss and Mr. Derungs has been positive and tremendous. Literatures from Dr. Boillat were the source of initial study about the Drill & Blast and TBM excavated tunnels.
Manoj Kumar Garnayak
Hydraulic head losses in an unlined pressure tunnel 1 Theoretical approach and comparison with the measured values
Summary Area and shape of the cross sections in an unlined drill & blast tunnel vary randomly. Flow in such a tunnel is not fully developed. However, the rough pipe flow relation is used to calculate the head loss. The roughness of the tunnel can be described by two distinct phenomena: one due to the area variation, called macro-roughness; and the other, due to geology, grain sizes of the rock, rate of progress, excavation direction etc., known as micro-roughness. Friction coefficient of an unlined tunnel is, therefore, project specific.
Cross section areas of Chimay Project, Peru, have been studied to determine the friction losses in accordance with various methods proposed in the literature. Evaluated friction factor changes from one stretch to another in the same tunnel. Equivalent roughness of a cross section having composite roughness arising due to the application of shotcrete and invert lining is dealt with.
Friction head losses, and singular head losses due to bends, transitions, expansion and contraction etc. in the system are identified separately. Losses due to friction are more significant, which account for nearly 90% of the total losses. It is difficult to calculate singular losses in an unlined drill & blast tunnel, but the available theories have been applied.
In a TBM excavated tunnel, there are area variations due to different types of supports provided within the excavated diameter. However, the flow in a TBM excavated tunnel shall show a developed pattern.
Calculated results are discussed and compared with the measured values at site for the design discharge. Since the friction losses come from both TBM and drill & blast tunnel, an indirect comparison has been made to know the extent of losses only in the drill & blast stretch.
The results are discussed.
Out of the several methods available for calculation of the head losses in an unlined drill & blast tunnel, the most suitable one, which can be used during preliminary hydraulic design stages, has been identified.
Hydraulic head losses in an unlined pressure tunnel 1 Theoretical approach and comparison with the measured values
Contents
Preface
Summary
1 INTRODUCTION 5
2 BASIC HEAD LOSS EQUATION FOR PRESSURE FLOW 7
2.1 Darcy-Weisbach’s friction head loss equation 7 2.2 The friction coefficient 8
3 GENERAL DESCRIPTION OF CHIMAY PROJECT 10
3.1 Headwork 10 3.1.1 Diversion weir 10 3.1.2 Intake and intake channel 10 3.1.3 Earthfill dam 11 3.1.4 Inlet canals to desilting system 11 3.1.5 Desilting system 11 3.1.6 Head-pond 12 3.2 Water conductor system 12 3.2.1 Layout of the water conductor system 12 3.2.2 Tunnel excavated by Drill & Blast (D&B) method 12 3.2.2.1 Rock classification and tunnel supports in D&B excavation 13 3.2.3 Rock trap I 14 3.2.4 Tunnel bored by Tunnel Boring Machine (TBM) 14 3.2.5 Construction adits for the low pressure tunnel 14 3.2.6 Rock trap II 14 3.2.7 Surge tank 14 3.2.8 Vertical pressure shaft 15 3.2.9 Horizontal high pressure tunnel 15 3.2.10 Construction adit for the horizontal high pressure tunnel 15 3.2.11 Powerhouse 15
4 CROSS SECTION SURVEY AND HEAD LOSS DATA FROM CHIIMAY SITE 16
4.1 Cross section survey of D&B tunnel 16 4.2 Tunnel invert level data 17 4.3 Relevant as-built drawings of the water conductor system 18 4.4 Geological mapping during construction 18 4.5 Head losses measured at site 19 4.6 Calculation of hydraulic properties of D&B tunnel section based on the site data 19 4.6.1 Correction in calculation 19 4.7 Cross sections in TBM tunnel 20
Hydraulic head losses in an unlined pressure tunnel 2 Theoretical approach and comparison with the measured values
5 LITERATURE REVIEW FOR HEAD LOSSES IN UNLINED DRILL & BLAST TUNNELS 21
5.1 Origin of pressure losses 21 5.2 Suggested methods from the literatures 21 5.2.1 Rahm’s method (1953) 22 5.2.2 Modification of Rahm’s method by Hellström (1955) 23 5.2.3 Colebrook’s method (1958) 23 5.2.4 Approach by Morris (1958) 24 5.2.5 Huval’s method (1968) 25 5.2.6 Priha’s method (1968) 26 5.2.7 Reinius’s Method (1970) 26 5.2.8 Wright’s method (1971) 27 5.2.9 Johansen’s method (1974) 28 5.2.10 Solvik’s method (1984) 29 5.2.11 Ronn’s IBA method (1997) 30 5.3 Review from the laboratory modelling carried out in Sweden and recommendations by Czarnota (1986) 32 5.4 Discussion on the literature study 33 5.5 Conclusions on literature study on unlined D&B tunnels 33
6 APPLICATION OF THE AVAILABLE METHODS TO CHIMAY PROJECT DATA 34
6.1 Statistical analysis 34 6.2 Calculation of average friction factor 38 6.2.1 Application of Rahm’s method 39 6.2.2 Application of Colebrook’s method 41 6.2.3 Application of Huval’s method 41 6.2.4 Application of Priha’s method 42 6.2.5 Application of Reinius’s method 42 6.2.6 Application of Wright’s method 43 6.2.7 Application of Johansen’s method 43 6.2.8 Application of Solvik’s method 45 6.2.9 Application of Ronn’s IBA method 45 6.2.10 Application of Czarnota’s recommendation 46 6.3 Discussion on the results 46 6.4 Correction to be applied to the calculated friction coefficient 48
7 CALCULATION OF HEAD LOSSES IN TBM EXCAVATED TUNNEL 49
7.1 Influence of supports on the flow area 49 7.2 Longitudinal invert slope of the tunnel excavated by TBM 50 7.3 Estimated friction head losses in TBM excavated tunnel 51 7.3.1 Influence of area variation on head loss 51 7.3.2 Influence of area variation on friction coefficient f 51 7.3.3 Friction losses in TBM excavated tunnel 51 7.3.4 Comparison of Manning-Strickler’s coefficient K and friction factor f 52 7.4 Singular head losses due to expansion and contraction in TBM tunnel 53 7.4.1 Head loss due to expansion 53
Hydraulic head losses in an unlined pressure tunnel 3 Theoretical approach and comparison with the measured values
7.4.1.1 Discussion on the results 54 7.4.2 Head loss due to flow contraction 55 7.4.2.1 Discussion on the results 56 7.5 Estimated average roughness values of TBM excavated tunnel of Chimay 56
8 FRICTION HEAD LOSSES IN THE LINED PART OF THE WATER CONDUCTOR SYSTEM OF CHIMAY PROJECT 58
8.1 Low pressure tunnel 58 8.2 Shaft and high pressure tunnel 58 8.3 Calculation approach 59 8.4 Friction head losses in Rock Trap I 60 8.5 Friction head losses in the transition between D&B and TBM tunnel 60
9 SINGULAR HEAD LOSSES DUE TO BENDS IN THE WATER CONDUCTOR SYSTEM OF CHIMAY 61
9.1 Flow regime 61 9.2 Bend losses 61 9.2.1 Identification of the bends 61 9.2.2 Calculation procedure 62 9.2.3 Bend loss results 64 9.2.4 Interference of bends 64 9.2.5 Discussion on the results 64
10 SINGULAR HEAD LOSSES IN THE WATER CONDUCTOR SYSTEM DUE TO ENTRANCE, AREA VARIATION, OBSTRUCTION, BIFURCATION, COMBINATION AND OTHER LOCAL CAUSES IN CHIMAY 65
10.1 Entrance and area variation 65 10.1.1 Entry losses at tunnel intake 65 10.1.2 Expansion or contraction losses where geometry is defined (except for TBM stretch) 65 10.2 Loss due to flow bifurcation and combination 66 10.2.1 At adit # 1 67 10.2.1.1 At the end of the TBM tunnel 67 10.2.1.2 In the penstock 68 10.2.2 Local losses in the rock trap I and II due to obstruction by steel beams and concrete walls 68
11 FRICTION HEAD LOSSES IN THE UNLINED DRILL AND BLAST TUNNEL OF CHIMAY 70
11.1 Equivalent tunnel length with shotcrete 70 11.2 Effect of lined invert on composite friction factor 72 11.3 Effect of shotcrete on friction losses 72 11.4 Calculated friction losses in unlined tunnel 73 11.5 Comparison with the measured values 74 11.6 Discussion on the results 76 11.6.1 Calculated and measured head losses by each method 76 11.6.2 Relevance of measuring roughness of a TBM tunnel at site 78
Hydraulic head losses in an unlined pressure tunnel 4 Theoretical approach and comparison with the measured values
11.6.3 Influence of composite roughness of a D&B tunnel 78 11.6.4 Equivalent average friction coefficient of D&B tunnel 79 11.6.5 Effect of invert lining on head losses in D&B tunnel 79 11.6.6 Effect of shotcrete on friction head losses in D&B tunnel 79 11.6.7 Comparison of head losses in TBM tunnel 80 11.6.8 Comparison of friction head losses and singular head losses 80 11.6.9 Distinction of macro and micro roughness 80 11.6.10 Friction head losses per metre length 81 11.6.11 Refinement of the assumptions 81
12 SUGGESTED DESIGN GUIDELINE 82
12.1 For unlined drill & blast tunnels 82 12.2 For a TBM bored tunnel 84 12.3 Some suggestions for unlined tunnels 84
13 CONCLUSION 85
Symbols, subscripts and abbreviations used in equations
Bibliography
Appendix A to H
Hydraulic head losses in an unlined pressure tunnel 5 Theoretical approach and comparison with the measured values
1 INTRODUCTION Unlined rock tunnels, excavated either by drill & blast (D&B) or by tunnel boring machine (TBM) or by both in different stretches of the same tunnel, are constructed in areas where the geology is favourable, and excellent tunnelling conditions are expected (in rocks like sound granodiorite, sandstone, granite, basalt, dolomite, etc.). Elimination of the lining, enables an early power generation by reducing the construction time of such a tunnel. However, due to the restriction of flow velocities in unlined rock tunnels, the area of excavation shall be comparatively more than that of a lined one. Energy economics and the risk mitigation play an important role to decide the choice between a lined and an unlined tunnel. Partial lining of the tunnels is also an alternative study.
An unlined tunnel is economical, but may require more construction maintenance due to the problems arising from rock falls (sudden or progressive), squeezing rocks and leakage of water to underground.
Suggested flow velocity in an unlined rock tunnel, excavated by drill & blast method, is around 2 m/s, which is prescribed to inhibit growth of slime on the surface, to prevent deposition of the falling rocks on the invert, and also to restrict migration of fines from an invert prone to erosion. Theoretically, due to a larger cross section of D&B tunnel than the nominal area, the flow velocity decreases and this results in reduction of head losses. Increased area gives an increased equivalent diameter, and hence further reduction of energy loss due to friction can be expected. In reality, the roughness elements in an unlined drill & blast rock tunnel are quite large, which create more turbulence that contributes to a greater head loss due to friction in a system, despite decrease of flow velocity.
The purpose of this project work is to study and to evaluate “hydraulic head losses in an unlined drill & blast pressure tunnel” based on the measurable real dimensions which have been established at a site during construction. For a turbulent flow with high Reynolds number, the most important measurable dimensions from hydraulic point of view are: cross section area, wetted perimeter and the equivalent roughness of the elements over the perimeter which offer resistance to the flow. The first two quantities can be measured to a greater degree of accuracy, whereas it is very difficult to make site measurements of the last parameter, namely the physical roughness. This is because, even after maintaining an exact drill & blast pattern for a theoretical shape, each measured cross section of a tunnel after blasting shall have different areas and shapes. This inevitable happening is due to the properties of the natural rock mass which change from point to point inside a tunnel. Also, for example, if the rock mass is homogeneous in a small stretch, and the drilling pattern and explosive charges are identical, the rock will not blast off exactly in the same way everywhere. Therefore, the roughness will change at each point on the surface.
Methods based on statistical analysis on the measurable dimensions are being used to evaluate equivalent hydraulic roughness of such drill & blast unlined tunnels. Measured cross sections and perimeters of an unlined D&B tunnel of 2x72 MW Chimay hydropower project, Peru, have been studied in this project work to determine equivalent hydraulic roughness of the tunnel. Total length of the tunnel is 9’161.43 m,
Hydraulic head losses in an unlined pressure tunnel 6 Theoretical approach and comparison with the measured values
of which 56% of length has been excavated by D&B method, and balance 44% by a TBM.
Out of several approaches available in the literature to estimate the hydraulic roughness or the friction coefficient, the ones that fit to the case of Chimay project, within the acceptable range of calculated values, have been identified. Head losses in the entire water conductor system at the design discharge (Q=82 m3/s) have been recorded at site. From the recorded head losses of the water conductor system, how much should be the losses in the D & B stretch of the tunnel are calculated indirectly.
Geological mapping drawings have been referred to know the type of rock supports provided in the D&B tunnel, as well as the TBM tunnel. This has helped in calculating hydraulic properties of the tunnel, like cross section area and wetted perimeter. The invert of the D & B tunnel has been concreted over 80% of its length. The roof and the walls of the tunnel are either fully or partially shotcreted at different locations. Attempt is made to recognise the influence of the lined invert and shotcrete on the estimated head losses. Based on the findings from this project, one of the approaches has been identified for hydraulic design of the unlined drill & blast tunnels.
Hydraulic head losses in an unlined pressure tunnel 7 Theoretical approach and comparison with the measured values
2 BASIC HEAD LOSS EQUATION FOR PRESSURE FLOW A drill & blast (D&B) tunnel under pressure flow is treated as a rough pipe to calculate the head losses due to friction. Standard engineering materials like steel, concrete, PVC etc., used as pressure pipes, have geometrically defined shapes and estimated friction resistance to flow. Natural rock surface after drill & blast neither has a defined shape nor an analytically estimated friction coefficient. Therefore, the approach is simplified by using the approach of pressure flow in a pipe.
The pressure flow regime in a pipe can be laminar, transitional or turbulent defined by Reynolds number. In hydraulic engineering practices, mostly turbulent flow conditions are encountered. The flow is said to be turbulent when the value of Reynolds number Re, is greater than 5⋅103.
When a pipe is of constant diameter, after certain length from the entry, the flow becomes fully developed, i.e. it has a single pattern of velocity profile. However, in the region after the entrance, the flow is in a developing stage. During the development of the flow velocity profile, more head losses occur than when the flow is fully developed. In a D&B unlined tunnel, due to axial and lateral asymmetry of the cross sections, a developed flow never occurs.
2.1 Darcy-Weisbach’s friction head loss equation The head loss in a pipe flow due to friction is given by Darcy-Weisbach’s equation
v 2 L h = f ⋅ ⋅ (2.1) f 2 ⋅ g D
Where
hf = head losses due to friction expressed in metre of water column, [mwc]
f = friction coefficient, [-]
L = length of pipe, [m]
v = average flow velocity, [m/s]
g = acceleration due to gravity, [m/s2]
D = equivalent hydraulic diameter of the pipe, [m]
The friction coefficient f depends on Reynolds number Re, relative roughness of the pipe wall all around k/D, and the cross sectional shape described by the equivalent hydraulic diameter D. The above approach is applicable when the pipe length is sufficient to have a pattern of developed flow. Choosing the value of f for any hydraulic calculation needs sound judgment and experience, if not determined from laboratory model tests.
Hydraulic head losses in an unlined pressure tunnel 8 Theoretical approach and comparison with the measured values
To demonstrate the influence of D on the friction head losses, average values of Chimay project are considered. In Chimay, average cross section area of the D&B tunnel increases by 15% when compared to the nominal area, and the perimeter increases by 8.7%. Assuming that the friction coefficient f remains practically constant, the head loss should decrease by 30%. However, if the tunnel is unlined the effect of the relative roughness on the friction coefficient is so large that the friction head losses can be as high as 2.5 times when compared to that of a concrete lined tunnel of the same nominal area.
In an unlined D&B tunnel the cross sections, the roughness elements both in size and concentration, and the flow alignment vary constantly. Due to this reason there is no fully developed flow. However, above equation (2.1) is applied for practical purposes. The value of f is then taken as an average value. The main uncertainty is to ascertain the value of f. At high Reynolds numbers (Re>106), an error of 100 % in roughness values causes about 30% of error in the friction coefficient.
The roughness in an unlined tunnel varies due to the fractures in the rock, the angularity and size of the rock crystals, rapid or slow progress of the work, advance along or against the flow direction, accuracy in drilling and blasting, length of a round etc., and these are all project specific. The prediction of the friction coefficient f is, therefore, restricted to an initial estimation. As the work progresses, after taking elaborate measurements at site, the friction coefficient can be revaluated with better accuracy.
2.2 The friction coefficient Colebrook-White relation to calculate the friction coefficient for a turbulent flow is implicitly given by equation (2.2) which was developed from the experiments with respect to mixed roughness (equivalent), and not on uniform sand grains.
1 D 2.51 = 2 ⋅ log(3.7 ⋅ + ) , Re>5’000 (2.2) f k Re⋅ f
To avoid the iteration from Colebrook-White equation (2.2), a non-iterative explicit relation with similar accuracy (within 1%) is used to estimate the value of f and is given by equation (2.3) [Miller et al]:
0.25 f = 2 (2.3) k 5.74 log + 0.9 3.7D Re
Equation (2.3) is used throughout this report for the calculation of the friction coefficient f or indirectly the roughness k, wherever necessary.
Alternatively, having known the relative roughness k/D and Reynolds number Re, the friction coefficient can be read from Moody Diagram (enclosed in Appendix H-3).
Hydraulic head losses in an unlined pressure tunnel 9 Theoretical approach and comparison with the measured values
The equivalent diameter concept D, in a pressure flow is valid until an aspect ratio (width/height) of 10 for a rectangular cross section. At higher aspect ratios the friction losses are underestimated when equivalent hydraulic diameter concept is considered.
Turbulent dissipation is at minimum in a smooth or a straight pipe (constant cross section) or passage (of any shape). Turbulence is enhanced by roughening the walls, or by turning or diffusing the flow. In regions where the fluid is accelerated, the static pressure is converted to velocity pressure which is a stable and low energy dissipation process. Where the flow is decelerated, velocity pressure is converted back to static pressure, and intense turbulence is generated.
In turbulent flow the boundary conditions do not define the flow uniquely (like the assumption that there is no flow across a pipe). On microscopic level and at any instant the flow conditions are unique, not repeated. Turbulent eddy sizes in the industrial flow system typically extend down to 10-4 m in diameter. An order of 1012 calculations per second per cubic meter of system volume is required, if the turbulence is to be studied analytically [Miller et al].
Where random change in the area and the direction of flow occurs, large scale turbulence spreads through the flow to equalise the energy distribution. Fluid may turn back causing rapid decay of the turbulence. The literatures and the laboratory experiments indicate that the flow in a rock tunnel is quasi- steady.
The loss coefficients in a pressure flow can be:
1. Definitive (checked through many research programmes),
2. Adequate for normal design (from isolated research),
3. Suggested values (very little information available, unlined rock tunnels fall into this category).
The head losses can increase with time if there are rock falls that obstruct the flow in a D&B unlined tunnel, in which case the safety and reliability of power system is in question. Partial concrete lining in difficult geology is suggested.
Strickler coefficient in unlined D&B tunnels varies from 23 to 37 m1/3s-1 and that for unlined TBM tunnels varies from 50 to 67 m1/3s-1[Solvik, 1984].
Hydraulic head losses in an unlined pressure tunnel 10 Theoretical approach and comparison with the measured values
3 GENERAL DESCRIPTION OF CHIMAY PROJECT The 2 x 72 MW Chimay hydropower project is situated on the Tulumayo river at the eastern side of the Andes in central Peru. The catchments area at the dam site is 2’364 km2. The mean annual discharge of the river is 80 m3/s. The design discharge of the power plant is 82 m3/s at a gross head of 218.5 m.
The hydropower project is a run-off-the-river scheme with a daily regulation reservoir having an active storage of 1.5 M m3 in order to generate peak power during the dry season.
The features of the project can be divided into four distinct categories. These are:
• Headwork
• Low pressure tunnel
• High pressure shaft and the penstock
• Powerhouse
Relevant layout drawings of the project are included in Appendix A.
3.1 Headwork The headwork consists of the diversion weir, the earth fill dam, the intake, the intake channel, the desilting system and the head-pond. The diversion weir is across the main river closing the right side valley, while the earth fill dam closes the left valley. The water intake, placed in between both these structures, is located towards the left bank of the natural river.
3.1.1 Diversion weir The diversion weir is a concrete structure of 75 m x 68 m in plan, having six opening bays. Three bays towards the intake are equipped with sluice gates at a sill elevation of 1’314 m asl, and remaining three towards the right bank are equipped with radial gates over an ogee shaped crest with the sill at 1’323 m asl. The first bay from the left is monolithic with the intake structure and has a divide wall that runs upstream. The dimension of the openings of the sluices is 8.0 m x 4.5 m (width x height), and those over the crest are 8.0 m x 7.95 m each. The diversion weir has been designed for 3 Q10’000 year flood of 2’300 m /s. The design flood water level is 1’331.00 m asl. Top of the weir is at 1’331.50 m. The openings of the sluices and the overflow weirs are operate by radial gates of 8.0 m x 4.5 m, and 8.0 m x 6.0 m size, respectively.
3.1.2 Intake and intake channel The entrance of the intake is inclined at 105 ° to the axis of the diversion weir and has two openings, each measuring 5.0 m x 4.5 m, separated by a central pier. The sill level
Hydraulic head losses in an unlined pressure tunnel 11 Theoretical approach and comparison with the measured values
of the intake coincides with the upper level of the under sluice openings. The intake structure is 18 m high with a free board of 0.5 m above the design flood water level. The intake openings are provided with inclined trash racks. After a short length downstream, the intake structure makes a right turn at an angle of 57.2°. At the end of the turn, the intake channel starts. The intake is supplemented with a stone trap to collect the bed load that enters the channel through the trash rack. The collected stones are ejected downstream of the diversion weir periodically. Two roller gates control the flow into the intake. The control room of the intake is at the top of the superstructure. Water flows through a 270 m long rectangular open channel of 7.0 m wide and 5.2 m wall height. The bed slope of the channel is 1 in 1’000. Over a length of 30 m, the intake channel becomes a box culvert in order that its deck functions as a superpass for an existing stream.
3.1.3 Earthfill dam When the diversion weir was under construction, the river was diverted through the available space on the left valley (which is relatively flat). The foundation of the central core of the earth dam is on rock. To prevent seepage below the foundation, primary and secondary grout curtains have been placed. The zoned earth dam is 160 m long at crest with a maximum height of 20 m. The crest elevation is same as those for other structures i.e. at 1’331.50 m asl. The central core of the earth fill dam is constructed from TBM excavated tunnel materials. On the upstream face of the central core a rock fill has been placed, followed by an 80 cm filter zone, and a rip-rap protection of 1.0 m thick. Immediately on the downstream face of the central core 1.5 m thick graded filter layer has been placed followed by a random rock fill, and finally protected by a 0.5 m thick random filter material (non-graded). The crest width of the dam is 8.0 m, the upstream slope is 2H : 1V and that at downstream is 3H:1V.
3.1.4 Inlet canals to desilting system The intake canal of 7.0 m base width has been divided symmetrically into two smaller canals each of 3.26 m wide by a pier nose. The flow from the bigger channel gets divided equally into the smaller ones. Then the flow is in a mild horizontal curve in plan over a length of 41 m. Each divided channel is again subdivided into two smaller channels by a nose. Each subdivided channel has a width of 2.5 m over a length of around 20 m. Thus the original headrace channel is divided into four smaller channels before entering into the desilting system.
3.1.5 Desilting system A group of four chambers constitute the desilting system, each chamber connects to one of the subdivided channels. Stoplog grooves are provided at each inlet. At the entrance, the sill level is 1’318.20 masl. Each desilting chamber is divided into two parts, the first part where the flow diffuses from a width of 2.5 m to 12.4 m over a length of 19.02 m. Simultaneously, the bottom elevation dips from 1’318.20 m asl to 1’312.20 m asl. This zone is intended for slowing down the velocity of incoming water. In each chamber, four numbers of calming racks are provided in this zone. The second part of each chamber is 72 m long with a varying depth from 10.62 m at the beginning to 12.06 m at the end. The top of the desilting basin is at 1’322.80 m. Each
Hydraulic head losses in an unlined pressure tunnel 12 Theoretical approach and comparison with the measured values
chamber has a 4.5 m deep hopper bottom. The lowest level of the hopper is connected to the silt-flushing canal. A sliding gate (1.3 m W x 1.5 m H) at the entry to the silt ejecting canal controls the flushing operation.
3.1.6 Head-pond Over the crest shaped downstream walls of the desilting chambers at an elevation of 1’321.14 m asl, water flows into the head-pond structure. Head-pond has the same width of 55.62 m as that of the desilting chambers at their common interface. The sidewall of the head-pond towards the river is 78.46 m long. Part of this length, namely 49.6 m, works as an overspill crest to let out excess water from the head-pond to the river at 1’321.0 m asl. From this elevation, water drops by 9 m vertically into the energy dissipater apron. The third and the fourth sides of the head-pond, parallel and perpendicular to the flow, respectively, have inclined surfaces that slope at 2H:1V. The sloping sides are covered with a layer of concrete. Extensive drainage arrangement has been provided at the bottom of the head-pond to drain out the seeping water. There is a provision for emptying the pond whenever required. The head-pond creates a maximum water level of 1’321.0 m asl for power generation. From the fourth side of the head-pond, as described above, the water conduction system starts.
3.2 Water conductor system The invert level of the head-pond at the location of the tunnel intake is 1’316.35 m asl. The intake structure, with an overall dimension of 29.3 m x 10.9 m (L x Bin plan), is an open construction that remains completely inside the head-pond. The elevation of intake invert at the entrance to the tunnel is 1’306.8 m asl. A sloping apron at 45° connects the elevation difference between the head-pond floor and that of the tunnel invert. At the end of the tunnel intake, a stoplog groove is provided. The stoplog is operated from the intake platform at an elevation of 1’322.8 m asl. At the entry into the intake, a trash rack slot also has been provided. A smooth concrete transition piece of 10 m long connects the intake and beginning of the D&B tunnel. The water conductor system starts after this transition piece.
3.2.1 Layout of the water conductor system Total length of the low-pressure tunnel is 9’161.43 m. Its invert varies from 1’305.5 m asl to 1’247.952 m asl. Initial 5’130 m of it has been excavated by conventional drill & blast method. Stretch of the tunnel excavated by TBM is from ch.5+130 m to ch.9+161.43 m, and has a length of 4’031.43 m.
3.2.2 Tunnel excavated by Drill & Blast (D&B) method The theoretical cross section of the tunnel excavated by conventional D & B method is of D-shape, with 7.0 m width at the invert level and a height of 6.15 m. The alignment of the tunnel is in northwest direction almost in a straight line, except for a local detouring towards the right side in plan view, which realigns back to the original alignment (appendix A-1 and A-2). The tunnel has variable invert slopes for the first 2’607.59 m as given below:
Hydraulic head losses in an unlined pressure tunnel 13 Theoretical approach and comparison with the measured values
Ch.0+000 m to ch. 0+800 m 1.0908 %
Ch. 0+800 m to ch.1+648.819 m 1.08 %
Ch. 1+648.819 m to ch. 2+107.681 m 1.12 %
Ch. 2+107.681 m to ch. 2+607.586 m 0.50%
From ch.2+607.586 m onwards 0.49%
The theoretical tunnel invert varies from 1’305.5 m asl to 1’267.643 m in the flow direction over the D&B stretch only.
3.2.2.1 Rock classification and tunnel supports in D&B excavation Four different rocks, type I (RMR>65), II (RMR 45 to 65), III (RMR 25 to 45) and IV (RMR< 25) are geologically classified in the stretch excavated by conventional D&B method. The support system for the rock is summarized in table 3.1. In this table RMR is an abbreviation for Rock Mass Rating, and Q is the abbreviation for Tunnelling Quality Index (refer Appendix A-5 to A-8).
Rock Support type RMR Q Support description type I A1 >65 >10 Spot rock bolting Plain shotcrete 5 cm I A2 >65 >10 thick II B1 55 to 65 5 to 10 Rockbolts at 1.5 m Rockbolts at 1.5 m, wire mesh, first layer of II B2 45 to 55 1 to 5 shotcrete 3 cm, second layer of shotcrete 7 cm thick Rockbolts, shotcrete 10 III C1 30 to 45 0.5 to 1.0 cm thick Rock bolt, first layer shotcrete 3 cm, wire III C2 25 to 35 0.1 to 0.5 mesh, second layer of shotcrete 7 cm Steel ribs in 25 cm thick IV D1 15 to 30 0.05 to 0.1 shotcrete Steel ribs with 35 cm IV D2 <15 <0.05 thick shotcrete Micropiles at the crown, steel ribs, three layers of IV D3 < 15 <0.05 shotcrete of 40 cm thickness. Table 3.1: Chimay, Rock type and supports in the D&B excavated tunnel
Hydraulic head losses in an unlined pressure tunnel 14 Theoretical approach and comparison with the measured values
3.2.3 Rock trap I The first rock trap (rock trap I) is placed near the end of the D&B excavated tunnel stretch, and it starts at ch.4+992 m. The tunnel invert slopes down at 13% over the next 20 m. The rock trap is 68 m long, divided into two chambers each of 34 m long, with an invert slope of 0.49%. Then the invert level goes up at a slope of 12% from ch.5+080 m to ch.5+100 m after which the invert slope reverts back to the usual slope of the tunnel at 0.49% till the end of the drill and blast zone at ch.5+130 m. The transition length between the conventional zone and the TBM zone is 10.0 m (refer Appendix A-10).
3.2.4 Tunnel bored by Tunnel Boring Machine (TBM) The tunnel after the first 5’130 m length (from ch.0+000 m to ch.5+130 m by D&B method) has been excavated by a TBM. The TBM advanced in the opposite direction i.e. from ch.9+161.43 m to ch.5+130 m. The shape is circular with a diameter of 5.7 m. The straight alignment of the drill and blast tunnel changes from northwest to nearly north. The invert slope of 0.49% continues (refer Appendix A-1 and A-2).
3.2.5 Construction adits for the low pressure tunnel There had been two work adits for the construction of the low-pressure tunnel, one for the D&B stretch, and the second is for the TBM stretch.
The adit for D&B excavation is placed at an intermediate location on the alignment of the tunnel through which 2’095.45 m length of the tunnel on upstream of the adit junction, and 3034.55 m length of the tunnel on the downstream direction have been excavated. The adit is plugged and has a Y shape junction with the alignment to the main tunnel (refer Appendix A-9).
Initial lengths of the second construction adit have been excavated partially by conventional D&B method to be used as the installation space of the TBM. This is also plugged after construction.
3.2.6 Rock trap II The 25 m long second rock trap (rock trap II) is at the end of the TBM bored section of the tunnel, and is created by deepening the invert by 2.87 m. Bottom of the rock trap slopes at 0.497% in the direction of flow. It is completely concrete lined. The crown of the trap chamber is semicircular with a radius of 2.5 m, and its sides and the bottom form a trapezium below the springing line. This trap chamber also works as a transition between the tunnel and the vertical pressure shaft. The surge tank is connected to rock trap II through another branch gallery (refer Appendix A-11).
3.2.7 Surge tank The surge tank is approximately 136 m high, 8.5 m in diameter, open at the top. It is connected to the main tunnel by a gallery of 40 m long which starts from rock trap II. The shape of the connecting gallery is a semicircle at the crown with the bottom and the sides forming a trapezium below the springing line, whose height gradually
Hydraulic head losses in an unlined pressure tunnel 15 Theoretical approach and comparison with the measured values
reduces from an elevation of 1’244.88 m asl to 1’248.80 m asl over a length of 23 m. This is followed by a circular section of 5.2 m in diameter for the remaining length of 17 m till it connects to the surge tank with an upward transition bend. The bottom of the surge tank has a conical hopper shape, the diameter of which varies from 5.2 m to 8.5 m within a height difference of 5 m. The surge tank is concrete lined.
3.2.8 Vertical pressure shaft After a horizontal transition piece of 9.65 m long from rock trap II, the vertical pressure shaft of 4.5 m internal diameter begins. With a vertical bend of 9.0 m radius the shaft changes its alignment from horizontal to vertical at an elevation of 1’240.92 m asl. The vertical shaft is 111.7 m long. Until the elevation of 1’129.22 m asl, the shaft is concrete lined.
3.2.9 Horizontal high pressure tunnel Towards the end of the vertical pressure shaft, the concrete line is thickened to form a transition piece of 5 m long reducing the diameter of the vertical shaft from 4.5 m to 3.8 m. The horizontal pressure tunnel, which is steel lined, starts from an elevation of 1’129.22 masl. A vertical bend of 12.0 m diameter changes the alignment of the shaft from vertical to near horizontal. The 3.8 m diameter steel lined high-pressure tunnel continues at an invert slope of 2% over a length of 213.2 m till the bifurcation.
After the bifurcation the diameter of each branch of the penstock becomes 2.65 m. The initial stretch of 17.11 m from the point of bifurcation of each branch continues at a slope of 1.8%. This is followed by a bend at a radius of 7 m which aligns the shaft at 45° downward over an inclined length of 17.04 m. Again another reverse bend of 7 m radius makes the shaft horizontal for a length of 23.99 m that connects to the turbine. Few metres from the entry to the turbine, the penstock has a diameter of 2.5 m.
3.2.10 Construction adit for the horizontal high pressure tunnel The adit for the construction of the horizontal pressure tunnel starts near the left bank of the Tulumayo river, and is located upstream of the powerhouse. The adit joins the horizontal pressure tunnel some metres upstream of the bifurcation. Construction of the pressure tunnel has been achieved through this. Finally the tunnel has been plugged.
3.2.11 Powerhouse The surface powerhouse of 41 m long x 23 m width x 37 m high houses two turbines each of 72 MW capacity.
Hydraulic head losses in an unlined pressure tunnel 16 Theoretical approach and comparison with the measured values
4 CROSS SECTION SURVEY AND HEAD LOSS DATA FROM CHIIMAY SITE The recorded data from Chimay site include:
• Cross section survey in the drill & blast portion of the tunnel at certain intervals (refer table 4.1),
• Invert levels at 10 m intervals,
• As-built-construction drawings of the water conductor system,
• Geological mapping of the D&B and TBM tunnel which give fair idea about the supports provided in the tunnel, and
• Measured head losses at the inlet to the turbine by the electromechanical contractor at various discharges.
From the drawings and information available, necessary database for the project work have been created in Microsoft excel in order to calculate hydraulic head losses in the system.
4.1 Cross section survey of D&B tunnel Nominal cross section area of the D&B tunnel is 37.792 m2, and the perimeter is 23.296 m.
The contractor for civil construction has measured and made records of the cross sections of D&B tunnel at intervals of 5 m and 10 m along the tunnel axis for different stretches. Out of total length of the D&B tunnel of 5’130 m, initial 1’035 m has no invert lining, whereas the remaining length of 4’095 m has a concrete lined invert.
The cross sections of the excavated tunnel have been measured at a distance of around 50 m to 100 m behind the face of advance. This implies that preliminary supports like rockbolt and shotcrete were in place when the cross section data were recorded.
Theodolite has been used for making survey of the actual excavated cross sections to know how they vary from the theoretical nominal area. For this comparison, while recording the data, a systematic cylindrical co-ordinate system (r,θ) has been regularly followed. For each cross section measurement, there has been only one instrument station. The centre of the instrument is co-planar with that of the cross section measured. The survey instrument has been set up on the invert such that its vertical axis, and the longitudinal axis of the theoretical tunnel intersect each other at right angle. From the centre of the instrument, radial distances of the blasted circumference of the D&B tunnel have been measured. Any radial line from the instrument centre to a point on the circumference has certain angular value with respect to the vertical axis of the instrument. Such radial distances have been measured at 10° intervals for the walls and the crown of the excavated surface. There are very few records where the
Hydraulic head losses in an unlined pressure tunnel 17 Theoretical approach and comparison with the measured values
radial distances were measured at 5° angular intervals. Generally, the measurement has been recorded starting from the crown exactly over the instrument (0°), then while rotating the instrument in a clockwise direction the distances of the rock surface are measured with respect to the instrument centre. Moving thus, approximately at 107° (±), the line of sight meets the right corner between the wall and the invert. Radial distance measurement on the tunnel invert has not been made at this regular interval of 10°. It has been assumed that the invert has been a straight line. At some stations, the next line of sight from the right corner is the point exactly below the instrument (180° rotation with respect to the crown). Otherwise, in usual cases, the next line of sight, after the right corner, has been the left corner where the left wall and the invert meet, and is described by an angle approximately at 253° (±). The radial distance measurement for the left wall and the left half of the crown again proceeds up at 10° intervals till the starting point has been reached (360°). It is assumed that the blasted rock projections on the surface between two successive points on the circumference have negligible effect on the net area. The method adopted for the measurement will not give any idea about the surface roughness of the excavated rock.
As mentioned above, the area measurements were taken 50 to 100 m behind the working face. There was movement of the construction equipment inside the tunnel. As such, it can be noted that a layer of muck, over the blasted invert, always existed to facilitate such movement. This implies that the measured cross section area shall be lesser than the real cross section, and the measured invert level shall have a higher elevation than the real value. Real elevation of the invert is briefed in section 4.2.
A sample survey data sheet at a particular chainage is attached in appendix B-6. Data for any other cross section are similar.
The split up of the number of cross sections available in the data bank is summarised in table 4.1. Around 92% of the D&B tunnel length has been covered for which a measured cross section is available. On the other hand, if one assumes uniform data at 5 m intervals, then around 82% length of the tunnel has been covered.
4.2 Tunnel invert level data Initially it was not envisaged to do concrete lining in the invert of the D & B tunnel. After the cleaning of the muck from the invert it was noticed that there were big potholes. Site changed the decision to go for an invert lining from ch.1+035 m to ch.5+130 m. Initial stretch from ch.0+16.5 m to ch.1+035 m has an unlined invert.
The reduced level of the invert is available from direct survey at site after the muck was cleaned properly, and after the concrete was placed on the invert for most of the stretches mentioned above.
The elevation of the invert after the final concreting is available at 10.0 m intervals until ch.4+620 m. The geological mapping information described in section 4.4, listed the invert levels at 60 m intervals. After ch.4+620 m, the values from geological mapping drawing were taken in the database.
Hydraulic head losses in an unlined pressure tunnel 18 Theoretical approach and comparison with the measured values
Stretch in chainage Length Number of cross Interval between [m] [m] sections cross sections [m]
0+010 to 1+115 1’105 222 5
1+125 to 1+215 90 19 5
1+225 to1+850 625 126 5
1+860 to 2+005 145 30 5
2+120 to 2+210 90 10 10
2+220 to 2+240 20 5 5
2+305 to 2+550 245 50 5
2+600 to 2+795 195 40 5
2+905 to 3+205 300 61 5
3+215 to 4+690 1’475 296 5
4+700 to 5+129 429 44 10
Total 4’719 903
Table 4.1: Chimay; Available cross sections in the studied stretch of the D&B tunnel
4.3 Relevant as-built drawings of the water conductor system As-built construction drawings of the water conductor system showing layout of the scheme, and cross sections of various elements were studied for the calculation of hydraulic properties of different components. They include the intake, lay out of the tunnel, rock trap I, rock trap II, shaft, penstock and type of supports provided in the tunnel. For reference, these drawings are attached in Appendix A.
4.4 Geological mapping during construction Geological mapping of the tunnel after excavation is available for the entire stretch of the D & B and of the TBM tunnel. The mapping is recorded on a grid of 1 m intervals, both in length and perimeter of the theoretical excavated surface of the tunnel. These data, in an electronic form, provides the base to ascertain the type of supports provided along the tunnel. The mapping covers the sidewalls and the crown for the D- shaped D & B tunnel, whereas it covers the entire circumference of the TBM tunnel. Sample copies of the geological mapping drawings are enclosed in Appendix A-16 and A-17.
Hydraulic head losses in an unlined pressure tunnel 19 Theoretical approach and comparison with the measured values
The available mapping data are from ch.0+000 m to ch.5+130 m for the drill & blast stretch, and from ch.5+130 m to ch.9+380 m for the TBM stretch. In this study, the mapping data up to ch.9+161 m for the TBM tunnel are considered.
4.5 Head losses measured at site Measurement of head losses in the entire water conductor system at variable discharges was recorded through instrumentation provided by the electromechanical contractor near the turbine inlet (refer Appendix A-14). The measured results are for varying discharges from 11.33 m3/s to 90.32 m3/s. The measured values are given in appendix G-1. There have been only one recorded measurement for most of the discharges, but several measurements for the design discharge. In this report, we are only referring the head losses to the design discharge of 82 m3/s.
4.6 Calculation of hydraulic properties of D&B tunnel section based on the site data From the hydraulic calculation point of view, in order to make use of different methods for assigning a friction coefficient to D&B tunnel, it is necessary that the cross section area, as well as the wetted perimeter are calculated from the available data base. Calculation was performed for each cross section which involved assigning co-ordinates to each measured point on the excavated perimeter in Cartesian system; determining the invert level during survey, arriving at the right-half and left-half of the area; right-half and left-half of the perimeter; and the wetted perimeter at the invert. Approximately, 40% of the survey data were available in electronic form. Manual entry of the remaining 60% of the data was done to convert these into electronic form. The manual data were once again checked for their accuracy, and each cross section is now available as an individual work sheet in Excel.
4.6.1 Correction in calculation Calculated areas and perimeters in section 4.6, give values as per the survey records. As seen in section 4.2, the real invert levels did differ when either the muck was removed or the concrete invert was placed. Second step of calculation was carried out for each section to make allowance for the changing condition.
The real invert level is either higher, or lower, or same as those arrived in cross section survey data. If the final invert level were higher than the surveyed level, there would be reduction in cross section area, as well as some reduction in wetted perimeter. The reverse is true when the final invert level is lower than the surveyed elevation. There would be no change when the invert levels in both the cases match each other.
The correction to the measured cross sections were applied in the following way:
• Base width of the invert at a cross section was assumed to remain same as those measured during survey
• The difference between the real invert and the surveyed invert was found out
Hydraulic head losses in an unlined pressure tunnel 20 Theoretical approach and comparison with the measured values
• If the difference is negative, there will be addition to the area by an amount given by invert width times the difference in elevation. The addition to the wetted perimeter is twice the difference.
• If the difference is positive, there will be subtraction from the area by an amount given by invert width times the difference in elevation. The reduction from the wetted perimeter is twice the difference.
The sample calculation method is attached in appendix B-6.
The areas were calculated separating the right-half and the left-half at each cross section with respect to the vertical line passing through the theoretical tunnel axis. The perimeter was calculated for the right, for the left and for the bottom at each cross section.
Variation of the invert elevations (surveyed, real and theoretical), and the elevation at the crown along the drill & blast tunnel is enclosed in Appendix B-7. Appendix B-8 summarizes graphically the change of the base width.
4.7 Cross sections in TBM tunnel There has been no survey to calculate the area in the TBM portion of the water conductor system. It is therefore assumed that the boring diameter of 5.7 m remained constant throughout, and there has been no geological overbreaks any where along the tunnel during the progress of the work. The bottom levels of the TBM tunnel were taken from geological mapping drawings at 60 m intervals. It shows that the tunnel alignment is practically on a single slope of 0.49%, but in reality, at some stretches there are local variations of slope. This is graphically presented in Appendix D-3. At some places the TBM has moved horizontally, even at some others the slope is more than double of the theoretical slope. In reality, there might have been local over- breaks, some change in the invert, area convergence and divergence due to the gripper pads, may be there have been some local changes in the horizontal (in situation plan) alignment too. These possible changes are neglected in the calculation assuming their effect is insignificant.
The TBM tunnel has different types of supports depending on the rock mass classification (see Appendix A-7, A-8, D-1). Geological mapping of the excavated surface has been done at 1 m grids. This gives a good guideline to see the changes in the final cross section area of the TBM tunnel due to the presence of the supports. The thickness of shotcrete, wherever applied, is assumed to be uniform. The net flow area of the tunnel is arrived at after deducting the area of shotcrete or of the steel ribs wherever they have been placed. Based on this the variation of cross section area along the TBM tunnel is represented in Appendix D-2. It can be concluded that the area variation in TBM section also influences the hydraulic properties and the associated head losses.
Hydraulic head losses in an unlined pressure tunnel 21 Theoretical approach and comparison with the measured values
5 LITERATURE REVIEW FOR HEAD LOSSES IN UNLINED DRILL & BLAST TUNNELS
There has been continuous effort to study and find out the head losses in unlined D&B tunnels. All approaches are observational based, leading to the conclusions from measurements and monitoring of the existing unlined tunnels, either excavated by drill & blast or bored by TBM. Early works started in Sweden and Norway.
In hydraulic design the following methods are usually adopted, 1) analytical method – when enough data is available for the analysis of a physical process, 2) observational method- with dealt with measurements and monitoring, 3) empirical method – based on the experience gained
The study in this report combines the empirical methods and the observational methods to make a comparison.
The symbols used in the equations may have different meanings according to different investigators. When such cases arise, the meaning of the symbol shall be briefly described under that particular equation.
5.1 Origin of pressure losses In a pipe flow of constant cross section area, the friction coefficient, f, in Darcy- Weisbach equation (2.1) is described as a function of Reynolds number of flow Re, and the relative roughness k/D.
The functional relation is expressed as
k f = F Re, (5.1) D
In an unlined rock tunnel excavated by drill & blast, due to variation of the cross section area ∆A, along the length ∆X, the value of f also depends on these two additional factors and is functionally related as
k ∆A f = F Re, , (5.2) D D ⋅ ∆X
5.2 Suggested methods from the literatures There have been many unlined tunnels in Norway, Sweden, USA and Australia. Based on the works done on these projects, different methods have been suggested by the investigators for the hydraulic design of such tunnels. These methods are briefly touched upon in this chapter. The earliest methods started with the cross section areas of the tunnel being the sole parameter defining equivalent roughness of the unlined D&B tunnel surface. In later years, the roughness component was divided into two:
Hydraulic head losses in an unlined pressure tunnel 22 Theoretical approach and comparison with the measured values
namely roughness due to variation of area, and roughness due to walls. The former is known as macro-roughness, and the latter as micro-roughness. This is followed by laboratory investigations to establish velocity distribution, pressure distribution, boundary shear stresses, influence of a lined invert on the total head loss, and the influence of shotcrete and invert concrete on the head loss.
5.2.1 Rahm’s method (1953) This method was suggested on the observation of 9 Swedish unlined D&B tunnels to establish the friction loss coefficient on the measurable dimensions of the actual D&B unlined tunnel. In a construction site, the measurable dimensions of an unlined D&B tunnel are the cross sections and the wetted perimeter that vary considerably from one cross section to another.
The method assumes that:
• Pipe flow as per Prandl- von Karman equation is valid for rough turbulent flow.
• Measured cross section areas can be plotted in a standard distribution curve.
• Frequencies of cross section area from 1 to 99 percent (i.e. A99 and A1) are considered for practical purposes.
The variation of the cross sections, termed as “relative overbreak”δ is defined in equation (5.3):
A − A δ = 99 1 ⋅100% (5.3) A1
The relative equivalent roughness in the rock tunnel can be expressed through equation (5.4)
15 δ −0.5 = 0.105⋅ log (5.4) k / R
The relationship between f and δ is empirically given by equation (5.5)
f = 2.75⋅10−3 ⋅δ (5.5)
According to Rahm, friction losses shall be greater with the increasing relative overbreak even though the cross section area becomes more. It is intended to limit the overbreak.
The method does not take into account when the tunnel invert is lined. For the same areas, both in the case of a fully unlined and invert-lined D&B tunnel, the method would give equal values of f from the overbreak concept.
Hydraulic head losses in an unlined pressure tunnel 23 Theoretical approach and comparison with the measured values
Once the relative overbreak δ is known, the approximate head losses due to friction, hf, are calculated by equation (5.6)
L ⋅Q 2 δ h f = 73⋅ 2.5 ⋅ 2.5 (5.6) At ()δ + 200
Where
2 At = theoretical area of the cross section, [m ]
Q = discharge, [m3/s]
According to Rahm, equation (5.6) can be used to calculate approximately the head losses before filling in the tunnel with water, and necessary modifications can be done to δ in order to limit the head losses as desired.
5.2.2 Modification of Rahm’s method by Hellström (1955) Hellström concluded that the friction coefficient obtained from equation (5.5) of Rahm’s method is valid only whenδ >17%, and f >0.047.
For an average roughness k of 10 cm, and relative variation of cross sectional area δ of 3% a minimum value of f=0.03 has been assigned by the author, and this value joins Rahm’s straight line with a curve (refer Appendix H-1).
This method has not looked into the aspect when the invert is concrete lined.
5.2.3 Colebrook’s method (1958) Rahm’s method is accepted by the author as far as the relative overbreak is concerned.
1 D The author supports use of the rough pipe flow relation = 2 ⋅ log(3.7 ⋅ ) f k
in case of an unlined rock tunnel with high Reynolds number.
The author proposes the formula for the friction co-efficient f as:
1.5 tm ⋅ R f = 0.55 ⋅ 2.5 (5.7) (R + tm )
Where
tm = normal overbreak= 0.5⋅(Dm-D1), [m]
Dm = mean hydraulic diameter, [m]
D1 = hydraulic diameter with 1% frequency, [m]
Hydraulic head losses in an unlined pressure tunnel 24 Theoretical approach and comparison with the measured values
R = theoretical hydraulic radius. [m]
The author points out that the normal overbreak is caused by the outward splay of the ring drills. The roughness k is a function of the normal overbreak. The maximum value of roughness is equal to tm as per equation (5.8).
kmax = tm (5.8)
According to Colebrook, roughness of the horizontally bedded homogeneous rock can vary from 4.32 cm to 30.5 cm, the average being 15.25 cm, and that for the diagonally bedded slate, it can be up to 61 cm. Using these roughness values, the friction factor can be obtained from equation (5.9)
1 R = 2 ⋅ log(14.8⋅ ) (5.9) f k
In case of a partly lined tunnel, total resistance to water flow is equal to the sum of the individual resistances offered by the lined part and that by the unlined part. It has been suggested that for an unlined tunnel, having wall and crown perimeter Pw with an associated friction factor fw, and for the lined invert the same parameters being Pb and fb, respectively, the equivalent friction factor f of the composite section which practically gives acceptable results can be linearly related by equation (5.10):
P f + P ⋅ f f = w⋅ w b b (5.10) Pw + Pb
With the invert lined with concrete, a reduction in friction losses amounting to 28% is reported.
5.2.4 Approach by Morris (1958) The methods stated in 5.2.1, 5.2.2 and 5.2.3 represent the friction coefficient by a single parameter or an equivalent dimension. It is argued by the author, that peripheral and longitudinal spacing, radial height and curvature of the roughness elements influence the friction coefficient which cannot be described by a single factor.
The author describes various turbulent flows regimes:
1) smooth turbulent flow,
2) normal turbulent flow,
3) semi-smooth turbulent flow,
4) hyper-turbulent flow,
5) quasi-smooth flow.
Hydraulic head losses in an unlined pressure tunnel 25 Theoretical approach and comparison with the measured values
The approach needs that the roughness geometry and the flow regime should be known precisely. Actual dimensions are needed instead of the equivalent sand grain diameter.
It is practically difficult to make such measurements at site.
5.2.5 Huval’s method (1968) It is based on the field data collected for 42 tunnels. The shapes of the tunnels investigated were horseshoe type. Based on these investigations hydraulic design criteria of unlined D&B tunnels has been established.
Suggested maximum velocities in unlined D&B tunnel are:
• Power tunnels without penstock and turbine v < 3 m/s
• Tunnels with penstock and turbine v < 1.5 m/s
• Diversion flow tunnels v < 6 m/s
The measure of overbreak is equated with the equivalent roughness k, defined to be the difference between the minimum allowable and the actual average tunnel dimensions and is given by equation (5.11):
4 k = D − D = ⋅ ( A − A ) (5.11) m n π m n
Where
Dm = actual average equivalent diameter
Dn = nominal tunnel equivalent diameter
Am = actual average cross section area
An = nominal cross section area
The overbreak is equal to the equivalent sand-grain diameter as per Nikuradse. Prandtl – von Karman fully developed rough flow is valid. The friction factor is calculated with equation (5.12).
1 D = 2 ⋅ log m +1.14 (5.12) f k
The dimension of k is approximately twice the mean overbreak thickness.
Combination of local geology and the method of construction vary from project to project. The amount of overbreak varies from about 25 cm in the best granite to 46 cm in very blocky or laminated shale and sandstones.
Hydraulic head losses in an unlined pressure tunnel 26 Theoretical approach and comparison with the measured values
For a preliminary design of an unlined D&B tunnel with average rock and blasting conditions, the following Manning coefficients have been suggested:
• n= 0.033 m-1/3s for the mean driven area of the D&B tunnel, (K= 30.3 m1/3s-1)
• n= 0.027 m-1/3s for the nominal area of the D&B tunnel, (K= 37.0 m1/3s-1)
5.2.6 Priha’s method (1968) This method was developed based on small unlined tunnels for water supply in Finland. Relative variation of the cross sections is the main influencing factor, as per Rahm (section 5.2.1).
The method requires that additional width and height measurements should be taken at site to define the relative roughness. Recommended intervals for measuring the cross section areas is between 5 m to 10 m. Width and height measurement of each cross section at 25 cm intervals should be taken.
The value of f is given by equation (5.13)
0.5 −3 A1 f = 3.30 ⋅10 ⋅δ ⋅ 0.5 (5.13) (A1 + 9)
The author’s experiment with air cavities in the roof showed that there is a diminishing influence on the head loss.
5.2.7 Reinius’s Method (1970) Tunnels constructed in the direction of flow had more head losses than if the excavation is in the opposite way. If the drilling is fast with heavy equipments, the serration will be large, and the difference in head loss between the drilling along and against flow will be small. The investigation was done in open flume whose bottom was serrated.
Relative overbreak δ cannot be treated as the only factor for the roughness. Value of δ shall remain the same irrespective of the drilling direction. Parameters like the wall roughness and the direction of advance also play a role to define the friction coefficient. Allowance for the modern tunnelling methods like contour holes around the drilling periphery are incorporated in the recommendation for tunnels excavated by D&B method after 1946.
For a normal excavation the friction factor f is described by:
f = 0.02 + 0.0016 ⋅δ (5.14)
For a careful excavation the friction factor is:
f = 0.03 + 0.00085⋅δ (5.15)
Hydraulic head losses in an unlined pressure tunnel 27 Theoretical approach and comparison with the measured values
And, for a rapid excavation, the friction factor is:
f = 0.01+ 0.0027 ⋅δ (5.16)
5.2.8 Wright’s method (1971) The method suggests the hydraulic resistance of both unlined and an invert lined D&B tunnel. Resistance to flow can be correctly described by Darcy-Weisbach equation. The friction coefficient f is calculated as per Prandtl- von Karman equation. It is impossible to represent the complex roughness of a D&B tunnel. However, Nikuradse’s equivalent sand roughness can be used.
The author states that the friction coefficient f is not a linear function of δ, as described by Rahm (section 5.2.1). Wright’s method gives a lower value of f with increasing δ .
The author defines the ‘natural overbreak’ tn of the rock as per equation (5.17):
A50 − A1 tn = (5.17) 0.5⋅ (P50 + P1 )
Where
A50 = area of the mean cross section
A1 = area of the minimum cross section
P50 = wetted perimeter of the mean section
P1 = wetted perimeter of the minimum section
Graphical presentation of ‘relative overbreak’ δ, and f are made for both unlined and lined-invert tunnels. The relationship is not a straight line, but is a curve (refer Appendix H-2).
The measured friction coefficient for a tunnel whose invert is lined is around 30% less than that for a completely unlined tunnel.
The author suggests a design procedure which involves following steps:
• Assumption of an average hydraulic radius R50 corresponding to the average cross section of the unlined tunnel is made.
• From the graph (Appendix H-2) normal overbreak tn is ascertained.
• Calculation of δ is done as per equation (5.18)
t 1 δ = 2 ⋅ n ⋅ ⋅100% (5.18) R t 50 (1− n ) 2 2 ⋅ R50
Hydraulic head losses in an unlined pressure tunnel 28 Theoretical approach and comparison with the measured values
R • Form factor of a particular tunnel shape ψ = is calculated. A
• For a given head loss hf, desired mean hydraulic radius is calculated from equation (5.19)
f ⋅ Q 2 .ψ 4 ⋅ L R50 = 5 (5.19) 8 ⋅ g ⋅ h f
• Above steps are repeated to arrive at a better agreement.
• Once R50 is known, the average area can be back calculated.
During the construction of a D&B tunnel supervision of the tunnel is required to keep the head loss within the designed value. The author suggests the following guideline:
• Cross sections shall be measured at 1 m intervals for 100 m long stretches
• At least 10% of the total length of the tunnel must be included in the measurements
• It is required to exercise control over A50 and δ
• Tunnel size shall be adjusted to have the control over A50 and δ
5.2.9 Johansen’s method (1974) The method is based on 18 D&B unlined tunnels in Norway. It was found that Rahm’s method (section 5.2.1) did not fit to these cases. This method for the calculation of the friction coefficient is based on the relative variation of two adjacent cross section areas.
The absolute roughness for a cross section is defined by equation (5.20).
∆Ai ki = α + β ⋅ (5.20) Ai
For m measured cross sections along the tunnel stretch, the absolute roughness is
1 m ∆A k = α + β ⋅ ⋅ Σ i (5.21) 1 m Ai
Where
th Ai = i cross section area
Ai+1 = adjacent downstream cross section area
Hydraulic head losses in an unlined pressure tunnel 29 Theoretical approach and comparison with the measured values
∆Ai = Ai − Ai+1 = difference between two adjacent cross sections
α = experimentally determined value = 0.15
β = experimentally determined value = 0.37
For the investigated tunnels, k value varied from 0.2 to 0.4 m.
The friction factor f is related to k by equation (5.22)
k 2 f = 0.49 ⋅ ( ) 3 (5.22) 4R
or in terms of area only by equation (5.23)
10.7 2 f = 0.029 ⋅ (1+ ) 3 (5.23) A0.5
The design procedure suggested by the author has following steps:
• Initially the friction coefficient f is approximately anticipated from equation (5.23) based on the nominal area.
• As the portion of the tunnel excavation is completed, measurements are taken.
• Absolute roughness k and the friction factor f are calculated by using equations (5.21) and (5.22).
• If the calculated friction factor is more than the anticipated friction factor, then the corrected cross section area is calculated from equation (5.24)
f 2 A = A⋅ ( k ) 7 (5.24) k f
where the subscript k is for the corrected values.
• The interval of cross section measurement is suggested as 10 to 20 m.
5.2.10 Solvik’s method (1984) The method is slightly different from Johansen’s method described in section 5.2.9. Each measured cross section has an equivalent roughness relative to the adjacent cross section described by the expression in equation (5.25).
Ai − Ai−1 ki = (5.25) Pi
Where
Hydraulic head losses in an unlined pressure tunnel 30 Theoretical approach and comparison with the measured values
ki = equivalent roughness
Ai-1 = upstream cross section area
Ai = adjacent downstream cross section area
Pi = perimeter of the downstream cross section
The average area roughness of m numbers of cross sections is calculated thus:
1 m k avg = ∑ ki (5.26) m i=1
Total roughness of the tunnel, k = wall roughness (kw) + area roughness (kavg)
The author from his investigation on 20 numbers of unlined tunnels in Norway, suggests that the wall roughness kw= 0.15 m is appropriate.
Darcy-Weisbach’s friction coefficient f is calculated after k is known by using the relation
0.667 k f = 0.49 ⋅ (5.27) 4 ⋅ Ravg
Where
Ravg = average hydraulic radius of the measured cross sections
5.2.11 Ronn’s IBA method (1997) The method is based on a statistical approach for the wall roughness and area roughness by calculating root mean square for both.
This method is valid when the cross sections for area and longitudinal distances for wall are measured very closely. The author has suggested minimum number of measurement for wall roughness is 50. The distance between measurements is 25 cm to 50 cm. The stretch of the tunnel where measurement is being done should have at least 4 rounds of blasting. Minimum 3 longitudinal lines along the tunnel wall parallel to the tunnel axis must be identified. Roughness of the wall also depends on the geological conditions and the changes in excavation method.
The method suggests to take a line parallel to the tunnel axis as a reference line. A minimum tunnel excavated length equal to or more than 4 rounds is taken to define the wall roughness. Minimum three longitudinal lines are drawn on the excavated surface, all of them being parallel to the reference line. For example, one longitudinal line on each of the side walls, and one line on the roof of the excavated tunnel. At 25 cm intervals on the reference line, the distance of the longitudinal lines on the blasted surface is measured from it. The root mean square (rms) value of r measurements on a particular line j is calculated by equation (5.28).
Hydraulic head losses in an unlined pressure tunnel 31 Theoretical approach and comparison with the measured values
r 2 ∑ (xi − x) rms = i=1 (5.28) j r
Where
x = average distance between the reference line and the line j on the excavated surface
xi = distance from the reference line to the surface line
r = number of measurements
After calculating rms of each line, rms of the wall, from m number of longitudinal lines, is calculated as shown in equation (5.29).
m 2 ∑(rms j ) rms = j=1 (5.29) wall m
The cross section roughness is calculated from the variation of the cross section areas. The cross sections shall be measured at an interval of 0.5 m to 1.0 m intervals, over a length of at least 25 m continuously. Minimum 50 measurements for the tunnel section must be made. The rms value of area is calculated using equation (5.30).
r 0.5 0.5 ∑ (A j − A ) rms = 0.53⋅ j=1 (5.30) Ai r
Where
Aj = area of a cross section j
A = average area of the cross sections in the stretch Ai
r = number of cross sections
For m numbers of stretches where cross sections are measured, the rms of all the cross sections is
m (rms ) 2 ∑ Ai rms = i=1 (5.31) A m
Total roughness of the tunnel is obtained by adding both the wall and the area roughness, as shown in equation (5.32).
Hydraulic head losses in an unlined pressure tunnel 32 Theoretical approach and comparison with the measured values
k = rmswall + rms A (5.32)
After the equivalent k value is obtained, Colebrook’s equation for turbulent rough pipe flow can be used to determine the friction factor.
5.3 Review from the laboratory modelling carried out in Sweden and recommendations by Czarnota (1986) A tunnel (Bolmen tunnel of ≈8 m2 area in Sweden) was taken for a general study at a scale of 1:10. Photographs of the prototype tunnel were taken to represent the macro- roughness and were reproduced in the model. The undulations in the prototype were disregarded.
Height of the individual roughness elements varied from 10 to 100 mm, in exceptional cases up to 200 mm. The influence of these roughness elements is too less on the cross section area of the tunnel. They do not change the macro-roughness, but represent the micro-roughness. Crushed rock was glued to represent this roughness in the model. Plexiglas was used at the bottom to represent a lined invert. Cement layer was used over the crushed rock to represent the application of shotcrete.
From the model study it was concluded that the flow in an unlined D&B tunnel is three-dimensional. A central core of similar velocity distribution exists at all cross sections, which occupies approximately 75% of the area and is bound by an isovel of 0.85 times the average velocity. Flow near the wall varies considerably. Central core conveys 85% of the discharge. The flow field is complex to be described analytically. Location of the maximum velocity changes from one section to another. Pressure distribution in the tunnel is asymmetric.
Total head in the flow is less at the boundary that increases towards the centre. The distribution is not symmetrical. It may resemble the boundary contours in some of the sections.
The piezometric heads show pressure variation over a cross section. Extreme variations occur near the walls and roofs where the boundary shapes change. Negative pressure region may be possible. The pressure increases near a concave boundary, and decreases at a convex boundary. Shear stress distribution across the width at the bottom is asymmetric. Longitudinal distribution of the shear stress at the bottom is more or less as theoretically predicted.
The flow also produces longitudinal turbulence due to macro-roughness. Higher turbulence at the central core is also observed.
Friction coefficient due to macro-roughness is constant and is independent when Re> 0.5 x 106.
Macro-roughness calculated based on sudden expansion and sudden contraction of areas gives around 55% higher values than the observed results. The cross section changes cannot be classified as abrupt. The contribution of the macro-roughness towards the total head loss may vary from 15% to 30%.
Hydraulic head losses in an unlined pressure tunnel 33 Theoretical approach and comparison with the measured values
The representative friction coefficients for the model were:
• The friction coefficient of the drill & blast rock f = 0.0730
• Average friction coefficient with the invert lined f = 0.0623
• Average friction coefficient with unlined invert and shotcrete on wall and roof f = 0.0519
• Average friction coefficient with lined invert and shotcreted on wall and roof f = 0.0411
5.4 Discussion on the literature study Most of the earlier methods base the calculations on the assumption that the cross sections are normally distributed. When we look at the sample distribution, in fact, they are not really so (refer chapter 6.1).
The methods did not discuss on the reduction in head losses due to application of shotcrete. The method by Wright indicated the reduction in head losses when the invert is lined. The composite roughness of a cross section has been dealt by Colebrook.
All the methods have tried to find out the head losses in an unlined D&B tunnel that is already excavated and cross section measurements are taken. These methods, however, cannot be used directly for the estimation of head losses during the design stage or to what accuracy the head losses can be estimated at this stage.
5.5 Conclusions on literature study on unlined D&B tunnels The flow in an unlined D&B tunnel is complex. Assigning an absolute hydraulic roughness is difficult. There will be generally two types of roughness: micro and macro. The former is due to the grain sizes of the blasted surface, and the latter is due to the area variation from one point to another along the D&B tunnel. Statistical methods based on the measurements done at site are the best guideline to assign an equivalent roughness of the blasted rock surface. The least required measurement is the cross section area at regular intervals of 5 to 10 m. If the measurement of the cross sections is done at closer intervals, a better statistical distribution can be obtained.
Hydraulic head losses in an unlined pressure tunnel 34 Theoretical approach and comparison with the measured values
6 APPLICATION OF THE AVAILABLE METHODS TO CHIMAY PROJECT DATA The methods to calculate the friction coefficient as described in sections 5.2.1, 5.2.3, 5.2.5, 5.2.6, 5.2.7, 5.2.8 and 5.2.11 require a statistical analysis of the cross section area and perimeter recorded from the site measurements (refer section 4.6.1). It has been assumed that the cross section areas vary randomly, and that they follow a normal distribution curve. The statistical requirements are the mean area, mean perimeter, area with 99% frequency, area with 1% frequency, and perimeter with 1% frequency in order to describe the relative overbreak δ or the equivalent absolute roughness k.
Initial few metres of Chimay D&B tunnel, immediately downstream of the intake structure, are completely lined, i.e. from ch.0+000 m to ch.0+016.5 m. From ch.0+016.5 m to ch.1+035 m, the D&B tunnel is totally unlined on invert, on sides and on crown. Around 56% of this length is without shotcrete, while the rest 44% length has a shotcrete layer.
The invert of the tunnel is concrete lined from ch.1+035 m to ch.5+130 m. At the rock trap I, the tunnel invert is deepened to collect and store the fragmented or loose rocks that fall into the flow. For this reason, the cross section of the tunnel has been changed intentionally from ch.4+992 m to ch.5+100 m in rock trap I.
In the available databank, local lateral enlargement on to right, possibly for a niche in the tunnel, at ch.4+140 m and ch.4+145 m is recorded. The change of cross section at these two locations is considered to have been done with intention.
Before making a statistical analysis, the excavated cross sections that have been altered with motive, are deleted from the data list.
6.1 Statistical analysis There are 903 cross sections recorded all together in the D&B of 5’130 m long. Deleting the cross sections where the area enlargement was intentional, the analysis is made over the remaining 888 stations.
The calculated cross section areas are arranged in ascending order. Percentage variation of area at each cross section is calculated with respect to the nominal area of the theoretical cross section of 37.792 m2. Frequency of sampling was done with a successive interval of ± 2% with nominal area as the base. The sampling is done for every km, and presented in table 6.1. For abbreviation in the table the following lengths are shortly designated as:
Ch. 0+016.5 m to ch.1+035 m km 1
Ch. 1+035 m to ch.2+000 m km 2
Hydraulic head losses in an unlined pressure tunnel 35 Theoretical approach and comparison with the measured values
Ch. 2+000 m to ch.3+000 m km 3
Ch 3+000 m to ch.4+000 m km 4
Ch. 4+000 m to ch.5+130 m km 5
Full length of tunnel all
Area all km 1 km 2 km 3 km 4 km 5 variation [no. of [no. of [no. of [no. of [no. of [no. of (%) samples] samples] samples] samples] samples] samples]
-6 to -4 2 1 0 1 0 0 -4 to –2 2 0 1 0 1 0 -2 to 0 4 0 0 2 2 0 0 to 2 12 0 0 8 3 1 2 to 4 25 0 2 9 8 6 4 to 6 49 3 3 18 18 7 6 to 8 69 6 17 12 22 12 8 to 10 69 6 12 18 23 10 10 to 12 101 10 19 19 34 19 12 to 14 100 12 27 13 27 21 14 to 16 90 16 24 11 18 21 16 to 18 80 25 27 3 10 15 18 to 20 79 29 23 4 7 16 20 to 22 57 17 13 4 8 15 22 to 24 37 15 8 1 3 10 24 to 26 25 12 5 1 2 5 26 to 28 31 19 5 1 3 3 28 to 30 21 14 2 1 2 2 30 to 32 16 7 1 0 4 4 32 to 34 7 4 0 0 3 0 34 to 36 5 5 0 0 0 0 36 to 38 3 2 0 0 0 1 38 to 40 1 1 0 0 0 0 40 to 42 2 0 0 0 1 1 42 to 44 1 0 1 0 0 0 Total 888 204 190 126 199 169 Table 6.1: Chimay; Frequency distribution of the measured cross section areas with respect to the nominal area of 37.792 m2
The graphical representation of the above sample distribution is presented at figure 6.1. It is seen that total of all the sections can be approximated as a normal distribution. In reality it is a skew to left. However, individual kilometre data are not normally distributed.
Hydraulic head losses in an unlined pressure tunnel 36 Theoretical approach and comparison with the measured values
110
100 km 1
90 km 2 80
70 km 3
60 km 4 50
40 km 5 Number of samples 30
20 all
10
0 -5 0 5 10 15 20 25 30 35 40 45 variation of area over the nominal area %
Figure 6.1: Chimay; Area distribution of D&B tunnel
If all data are assumed to have a normal distribution function, the following statistical values are obtained for the cross section areas (see table 6.2). It is seen from the table that for every km, A99% is less than the maximum area in that particular km. However, A1% is not always more than the minimum area in the particular km: it is in fact less for the distribution at km 4 and km 5, the reason being that the distribution curves in reality have more skew to left.
Statistical all km 1 km 2 km 3 km 4 km 5 parameters [m2] [m2] [m2] [m2] [m2] [m2] Average 43.474 45.476 43.565 41.500 42.455 43.628 area (A50%) Minimum 35.590 35.590 36.992 35.987 36.650 38.117 area Maximum 54.009 52.534 54.009 48.987 53.038 53.586 area Standard 2.874 2.766 2.275 2.271 2.699 2.658 deviation A99% 50.161 51.912 48.858 46.783 48.733 49.812
A1% 36.788 39.041 38.272 36.217 36.178 37.444
Table 6.2: Chimay; Statistical parameters of the excavated area in drill & blast tunnel
Similarly, the perimeter distribution is done to know if they have normal distribution characteristics. Variation of perimeter is also calculated at ± 2% intervals with the
Hydraulic head losses in an unlined pressure tunnel 37 Theoretical approach and comparison with the measured values
nominal perimeter as 23.296 m of the D&B tunnel as the base. The calculated frequency distribution is presented in table 6.3. % all km 1 km 2 km 3 km 4 km 5 variation of [no. of [no. of [no. of [no. of [no. of [no. of perimeter samples] samples] samples] samples] samples] samples] -2 to -1 1 0 0 1 0 0 -1 to 0 1 1 0 0 0 0 0to 1 5 0 1 2 2 0 1to 2 9 0 0 5 3 1 2 to 3 18 1 2 5 6 4 3 to 4 38 1 10 11 13 3 4 to 5 65 4 13 15 21 12 5 to 6 76 12 10 19 22 13 6 to 7 90 10 20 16 28 16 7 to 8 84 11 17 15 30 11 8 to 9 101 19 23 18 22 19 9 to 10 88 24 26 4 15 19 10 to 11 83 28 25 4 6 20 11 to 12 67 21 19 4 7 16 12 to 13 52 16 9 4 9 14 13 to 14 39 21 4 2 4 8 14 to 15 19 11 4 0 0 4 15 to 16 23 13 4 0 4 2 16 to 17 16 6 2 1 4 3 17 to 18 6 1 0 0 2 3 18 to 19 3 3 0 0 0 0 19 to 20 1 0 1 0 0 0 20 to 21 2 1 0 0 0 1 21 to 22 1 0 0 0 1 0 Total 888 204 190 126 199 169 Table 6.3: Chimay; Frequency distribution of measured perimeter with respect to nominal perimeter of 23.296 m of D&B tunnel
Figure 6.2 shows the graphical view of the frequency distribution of actual perimeter in D&B tunnel. If the figures 6.1 and 6.2 are compared, it is seen that the distribution in both the cases are similar in terms of skew.
Hydraulic head losses in an unlined pressure tunnel 38 Theoretical approach and comparison with the measured values
110 km 100 1 90 km 2 80 km 70 3 km 60 4 50 km 5 40 all
Number of samples of Number 30 20 10 0 -2 2 6 10 14 18 22 variation of perimeter %
Figure 6.2: Chimay; Frequency distribution of perimeter
The statistical parameters of the perimeter distribution are summarized in table 6.4. Statistical All km 1 km 2 km 3 km 4 km 5 parameters [m] [m] [m] [m] [m] [m] Average 25.334 25.810 25.340 24.810 25.073 25.451 perimeter (P50%) Minimum 22.961 23.105 23.444 22.962 23.486 23.590 perimeter Maximum 28.363 28.038 27.824 27.031 28.363 28.079 perimeter Standard 0.844 0.791 0.733 0.707 0.819 0.760 deviation P99% 27.298 27.65 27.047 26.456 26.981 27.218
P1% 23.375 23.971 23.64 23.166 23.167 23.684
Table 6.4: Chimay; Statistical parameters of perimeter in drill & blast tunnel
6.2 Calculation of average friction factor Average friction factor for each kilometre of the drill & blast tunnel is calculated by using the suggestions put forward by different investigators as outlined in chapter 5: literature review for head losses in unlined tunnel. The results of the analysis and the numerical values of the friction factor are dealt with in this section.
Hydraulic head losses in an unlined pressure tunnel 39 Theoretical approach and comparison with the measured values
6.2.1 Application of Rahm’s method Suggested equations of section 5.2.1 are used, and their results are summarized in table 6.5. Statistical all km 1 km 2 km 3 km 4 km 5 parameters A [m2] 99%, 50.161 51.912 48.858 46.783 48.733 49.812
A [m2] 1%, 36.788 39.041 38.272 36.217 36.178 37.444
δ, [%] 36.351 32.968 27.659 29.175 34.703 33.030 R, [m] 1.714 1.761 1.718 1.672 1.692 1.713 k, [m] 0.677 0.579 0.398 0.433 0.614 0.566 f, [-] 0.1000 0.0907 0.0761 0.0802 0.0954 0.0908 Table 6.5 : Chimay; Friction coefficient according to Rahm
For the above k values in table 6.5, f values calculated using modified Colebrook- White equation (2.3) yield similar results.
Rahm also has defined that the average cross section area is a function of the relative
overbreak and is given by:Am = A1 ⋅ (1+ 0.005⋅δ ) (6.1)
Table 6.6 compares the results. Statistical all km 1 km 2 km 3 km 4 km 5 parameters
δ , [%] 36.351 32.968 27.659 29.175 34.703 33.030 2 A1%, [m ] 36.788 39.041 38.272 36.2167 36.178 37.444 2 Am, [m ] 43.475 45.477 43.565 41.500 42.456 43.628 2 A50, [m ] 43.474 45.476 43.565 41.500 42.455 43.627 Table 6.6: Chimay; Average area as per Rahm and statistical area comparison
The average areas from statistics A50, and Am calculated by Rahm’s formula (6.1) have very close convergence, so to say practically no difference.
The calculated head losses using equation (5.6) is presented in table 6.7. The same is compared with the values calculated by using Colebrook-White simplified equation (2.3) and Darcy-Weisbach friction head loss equation (2.1).
Hydraulic head losses in an unlined pressure tunnel 40 Theoretical approach and comparison with the measured values
Calculated all km 1 km 2 km 3 km 4 km 5 parameters L, [m] 5005.50 1018.50 965.00 1000.00 1000.00 1022.00 V2 avg, 3.60 3.29 3.57 3.94 3.77 3.57 [m2/s2] δ, [%] 36.351 32.968 27.659 29.175 34.703 33.030 Re, [-] 1.13⋅107 1.11⋅107 1.13⋅107 1.15⋅107 1.14⋅107 1.12⋅107 fRahm, [-] 0.1000 0.0907 0.0761 0.0802 0.0954 0.0908 k, [m] 0.677 0.579 0.398 0.433 0.614 0.566 fcolebrook, [-] 0.1009 0.0915 0.0767 0.0810 0.0963 0.0917 h f, Rahm, 11.84 2.27 1.91 2.05 2.30 2.28 [mwc] h f, Darcy, 13.40 2.20 1.94 2.41 2.71 2.47 [mwc] Table 6.7: Chimay; Comparison of head losses calculated according to Rahm and Darcy-Weisbach
Friction head losses calculated by Rahm’s method for the full tunnel is 11.84 mwc, while the individual stretches add up to 10.81 m, and both are not equal. Friction head losses in individual stretches, calculated by Darcy’s equation, add up to 11.73 mwc, while that for the full tunnel is considerably higher at 13.4 mwc. The statistical parameters vary from stretch to stretch. Friction factor f for km 1, km 4 and km 5 are comparable in magnitude, while the same for km 2 and km 3 are lower by 13% to 18%. The friction coefficient of the full tunnel depends on the minimum and the maximum area (which influence the distribution), and both may occur only in one of the individual stretches. This will overestimate the friction factor for the entire tunnel as a whole. Therefore, addition of friction losses of individual stretches would give better accuracy.
Without doing a normal distribution, if areas closest to A99% and A1% are picked up from the samples (refer table 6.1), the following values are obtained which indicate that the relative roughness for km 1, km 2, km 4, and km 5 decrease by around 2.5 % to 12%, while the same increases by around 18% for km 3.
Stretch A99% A1% δ variation
[m2] [m2] [%] [%]
all 50.934 37.968 34.15 -6.05
Km 1 51.50 39.624 29.97 -9.09
Km 2 49.095 38.99 25.92 -6.29
Km 3 48.348 35.987 34.35 +17.74
Km 4 50.345 37.62 33.83 -2.52
Km 5 49.868 38.629 29.09 -11.93
Hydraulic head losses in an unlined pressure tunnel 41 Theoretical approach and comparison with the measured values
Generally, it cannot be concluded which area should be taken into consideration, whether the values obtained from normal distribution function, or the real ones corresponding to the closest cumulative frequency. However, as followed by the author, fictitious areas from the normal distribution shall be retained in the report.
6.2.2 Application of Colebrook’s method Calculations are performed for the complete tunnel and also for individual km based on the proposed equations in section 5.2.3, and the results are given in table 6.8.
Calculated all km 1 km 2 km 3 km 4 km 5 parameters R50%, [m] 1.714 1.761 1.718 1.672 1.692 1.713 R1%, [m] 1.573 1.624 1.609 1.555 1.563 1.593 tm, [m] 0.284 0.274 0.218 0.234 0.257 0.240 D [m] t, 6.489 6.489 6.489 6.489 6.489 6.489
fColebrooke,[-] 0.0621 0.0596 0.0517 0.0554 0.0587 0.0555 hf, [mwc] 8.321 1.444 1.322 1.664 1.667 1.506 Table 6.8: Chimay; Friction coefficient and head losses in D&B tunnel according to Colebrook
The sum of head losses in individual stretches is 7.60 mwc which is lesser than the value obtained by assuming the whole tunnel as one stretch. The reason is that the absolute roughness, which is equal to tm, is higher for the full tunnel as per the statistical analysis.
6.2.3 Application of Huval’s method Application of the suggested formula in section 5.2.5 has been made. Influence of alternative evaluation of k value is also briefly touched upon.
A) Based on the mean area, table 6.9 summarises the results:
Calculated all km 1 km 2 km 3 km 4 km 5 parameters 2 A50%, [m ] 43.474 45.476 43.565 41.500 42.455 43.628 2 At, [m ] 37.792 37.792 37.792 37.792 37.792 37.792 k, [m] 0.503 0.673 0.511 0.332 0.416 0.516 D , [m] 50% 7.440 7.609 7.448 7.269 7.352 7.453
f, [-] 0.0826 0.0948 0.0832 0.0685 0.0757 0.0836 Table 6.9: Chimay; Friction coefficient according to Huval based on average area
B) If the value of the friction coefficient is calculated based on the mean hydraulic radius of the cross sections, reduction in friction coefficient from 6% to 17% is noticed in table 6.10. Therefore, alternative calculation method than that suggested may not yield desired results.
Hydraulic head losses in an unlined pressure tunnel 42 Theoretical approach and comparison with the measured values
Calculated all km 1 km 2 km 3 km 4 km 5 parameters R50%, [m] 1.714 1.761 1.718 1.672 1.692 1.713 Rt, [m] 1.622 1.622 1.622 1.622 1.622 1.622 k, [m] 0.368 0.553 0.384 0.198 0.278 0.362 D50%, [m] 6.857 7.042 6.873 6.687 6.767 6.851
f, [-] 0.0739 0.0891 0.0753 0.0567 0.0653 0.0733 % change -10.6 -6.05 -9.5 -17.25 -13.67 -12.32 Table 6.10: Chimay; Friction coefficient with Huval’s method based on mean hydraulic radius.
C) On the other hand, if the suggested formula is used to find out the mean of the difference between each cross section’s hydraulic diameter and that of the nominal hydraulic diameter, the equivalent roughness values shall be greater by approximately 42% than those calculated from the mean area (refer table 6.9).
6.2.4 Application of Priha’s method This method is not directly applicable to Chimay. It is due to the fact that as required by this method, width and height measurement of each cross section has not fulfilled the criteria of 25 cm interval (refer section 5.2.6). However, it is presumed that the friction coefficients so calculated with the present available data shall indicate results of some order of magnitude, and are presented in table 6.11. Calculated all km 1 km 2 km 3 km 4 km 5 parameters 2 A99%, [m ] 50.161 51.912 48.858 46.783 48.733 49.812 2 A1%, [m ] 36.788 39.041 38.272 36.217 36.178 37.444 2 A50%, [m ] 43.474 45.476 43.565 41.500 42.455 43.627 δ, [%] 36.352 32.968 27.659 29.175 34.703 33.030 R, [m] 1.714 1.761 1.718 1.672 1.692 1.713 f, [-] 0.1075 0.0981 0.0821 0.0862 0.1025 0.0979 Table 6.11: Chimay; Approximate friction coefficient according to Priha
6.2.5 Application of Reinius’s method Suggested formulae from section 5.2.7 summarize the friction factor in table 6.12. Calculated all km 1 km 2 km 3 km 4 km 5 parameters δ,[%] 36.352 32.968 27.659 29.175 34.703 33.030 fnormal, [-] 0.0782 0.0728 0.0643 0.0667 0.0755 0.0729 fslow, [-] 0.0609 0.0580 0.0535 0.0548 0.0595 0.0581 frapid, [-] 0.1082 0.0990 0.0847 0.0888 0.1037 0.0992 faverage, [-] 0.0824 0.0766 0.0675 0.0701 0.0796 0.0767 Table 6.12: Chimay; Friction coefficient calculated by Reinius’s method
Hydraulic head losses in an unlined pressure tunnel 43 Theoretical approach and comparison with the measured values
For further calculation, the average friction factor is retained, even though the concept of averaging is not found in this method. Friction coefficient for normal excavation is approximately 5% less than the average, for slow excavation it is 25% less than the average, and for rapid excavation it is 28% higher than the average.
6.2.6 Application of Wright’s method Recommendations by the author, described in section 5.2.8, have been followed, and the values are entered in table 6.13. Friction coefficients for the unlined invert and for the lined invert are scaled out from the graphs by Wright (enclosed in appendix H-2). Comparison is made as how the composite friction coefficient decreases when the invert is lined.
Calculated all km 1 km 2 km 3 km 4 km 5 parameters 2 A99%, [m ] 50.161 51.912 48.858 46.783 48.733 49.812 2 A1%, [m ] 36.788 39.041 38.272 36.217 36.178 37.444 2 A50%, [m ] 43.474 45.476 43.565 41.500 42.455 43.627 P99%, [m] 27.298 27.651 27.047 26.456 26.981 27.218 P1%, [m] 23.375 23.971 23.640 23.166 23.167 23.684 P50%, [m] 25.334 25.810 25.340 25.810 25.073 25.451 tn, [m] 0.2746 0.2585 0.2161 0.2202 0.2602 0.2517 R50, [m] 1.714 1.761 1.718 1.672 1.692 1.713 δ, [%] 37.85 34.21 28.67 30.20 36.11 34.24 Invert Mixed unlined lined lined lined lined condition fcomposite, [-] 0.0838 0.0452 0.0457 0.0476 0.0467 frock only, [-] 0.0838 0.0738 0.0767 0.0867 0.0838
Table 6.13: Chimay; Friction coefficient according to Wright
In the table 6.13, two friction coefficients are shown, the first line with the values corresponding to the actual invert condition (lined or unlined). The second line of f values corresponds to the condition as if there has been no lining in the invert. Other methods described in this chapter calculate friction factor for the exposed rock. For all comparison purposes, the f values for the exposed rock are considered in this report.
It is noted that, with the invert lined, the composite friction coefficient is lesser by 39% to 45% than for the exposed rock.
6.2.7 Application of Johansen’s method Absolute value of the area difference between two adjacent cross sections is considered in the calculation.
Adjacent measured cross sections within 5 m or 10 m intervals have been chosen. If the adjacent recorded cross sections are spaced at higher intervals, they have been omitted from the calculation.
Hydraulic head losses in an unlined pressure tunnel 44 Theoretical approach and comparison with the measured values
Average area between two adjacent cross sections is considered to represent the area mean way between the sections.
The results are shown in table 6.14.
Calculated all km 1 km 2 km 3 km 4 km 5 parameters
∆Ai ∑ ,[m] 255.733 57.571 52.691 38.354 58.083 49.033 Ai N 881 203 190 122 199 167 k, [m] 0.257 0.255 0.253 0.266 0.258 0.259 7 7 7 7 7 7 Re, [-] 1.13⋅10 1.11⋅10 1.13⋅10 1.15⋅10 1.14⋅10 1.12⋅10 R50, [m] 1.714 1.761 1.718 1.672 1.692 1.713 f, [-] 0.0549 0.0536 0.0542 0.0571 0.0555 0.0551 Table 6.14: Chimay; Friction coefficient according to Johansen
In this method 0.15 m is taken as the micro-roughness of the rock grains. Macro- roughness can be found by subtracting 0.15 m from the value of k presented in table 6.14.
However, Johansen gives another formula (equation 5.23) to determine the friction coefficient in which area of the cross section is the only parameter.
If this equation (5.23) is applied at each cross section (not on average area), different values of average f are obtained for each stretch. Similarly, assuming that k values calculated by Johansen’s method are correct, and applying Colebrook-White simplified equation (2.3) another set of friction factor values is obtained. This is shown in table 6.15. Calculated all km 1 km 2 km 3 km 4 km 5 parameters k, [m] 0.257 0.255 0.253 0.266 0.258 0.259 7 7 7 7 7 7 Re, [-] 1.13⋅10 1.11⋅10 1.13⋅10 1.15⋅10 1.14⋅10 1.12⋅10 f as per equation 0.0667 0.0648 0.0665 0.0686 0.0676 0.0665 5.23 f as per equation 0.0629 0.0619 0.0623 0.0645 0.0633 0.0630 2.3 Table 6.15: Chimay; Friction coefficient from individual area, and comparison with Colebrook formula
Incidentally, both the f values in table 6.15 show good agreement. It means, that friction coefficient of the unlined D&B tunnel can be known only by measuring individual areas. However, this is a doubtful speculation. Well, the value of k remains in the range from 0.2 to 0.4 as investigated by Johansen. But the equations (5.22) and (5.23), suggested by the same author, yield results which have difference of around 22% between them.
Hydraulic head losses in an unlined pressure tunnel 45 Theoretical approach and comparison with the measured values
6.2.8 Application of Solvik’s method Recommendations of section 5.2.10 are incorporated in form of numerical values in table 6.16.
Absolute area difference between two adjacent cross sections ∆Ai, is considered when the cross sections are situated at 5 or 10 m intervals between them. If spaced at higher interval, the area difference has not been included in the calculations. The perimeter P1-i, of the upstream cross section appears in the computation.
Calculated all km 1 km 2 km 3 km 4 km 5 parameters ∆A 0.076 0.074 0.072 0.082 0.076 0.076 i , [m] P1−i k’, [m] 0.15 0.15 0.15 0.15 0.15 0.15 k, [m] 0.226 0.224 0.222 0.232 0.226 0.226 7 7 7 7 7 7 Re, [-] 1.13⋅10 1.11⋅10 1.13⋅10 1.15⋅10 1.14⋅10 1.12⋅10 R50, [m] 1.714 1.761 1.718 1.672 1.692 1.713 f, [-] 0.0502 0.0492 0.0497 0.0520 0.0507 0.0504 Table 6.16: Chimay; Friction coefficient according to Solvik
The method accounts for 0.15 m as the micro roughness, and the balance, after subtracting micro roughness from the computed k, represents macro-roughness.
6.2.9 Application of Ronn’s IBA method This method is not directly applicable to data series available for this project. The requirement is that data should be available at half a metre intervals. However, this method is tried keeping in mind that the cross section variation in an unlined tunnel is random. Whatever randomness is expected for the data series at 5 to 10 m intervals, the same is assumed to occur hypothetically for 0.5 m intervals. The area roughness can be calculated from the recommendations given in section 5.2.11 directly. For the wall roughness calculation, at least three longitudinal lines parallel to the tunnel axis are required. In the created data base (refer sections 4.1 and 4.2) the elevation of the crown has been calculated. Similarly, the elevation and distance of both the corners at invert are also calculated. A line at the theoretical centre of the invert is taken as the reference line. Distance from this reference line to the crown, to the right corner of invert and to the left corner of invert satisfy the requirement of at least three longitudinal lines measured from a reference line.
The numerical values of this method are presented in table 6.17. The value of friction coefficient has been calculated using equation 2.3.
Hydraulic head losses in an unlined pressure tunnel 46 Theoretical approach and comparison with the measured values
Calculated all km 1 km 2 km 3 km 4 km 5 parameters 2 (rms) right 0.064 0.0518 0.0877 0.069 0.049 0.068 2 (rms) left 0.069 0.051 0.066 0.098 0.057 0.088 2 (rms) crown 0.138 0.201 0.102 0.131 0.123 0.126 2 (rms) area 0.013 0.018 0.008 0.015 0.014 0.011 N 888 204 190 126 199 169 2 (rms) wall 0.091 0.101 0.085 0.099 0.076 0.094 (rms)wall 0.301 0.318 0.292 0.315 0.276 0.306 (rms)area 0.115 0.134 0.091 0.123 0.116 0.106 k, [m] 0.416 0.452 0.382 0.439 0.392 0.412 R, [m] 1.714 1.761 1.718 1.672 1.692 1.713 7 7 7 7 7 7 Re, [-] 1.13⋅10 1.11⋅10 1.13⋅10 1.15⋅10 1.14⋅10 1.12⋅10 f, [m] 0.0784 0.0806 0.0752 0.0815 0.0767 0.0781 Table 6.17: Chimay; Friction coefficient f as per Ronn’s IBA method
In this method the macro-roughness aspect is included in area variation given by (rms)area, and the micro-roughness aspect by (rms)wall. It should be noted that, individual roughness calculated may be additive, but arithmetical addition of individual friction factor for area and the wall are not allowed, since friction factor is a logarithmic function. Arithmetical addition, in this method, will give 43% more values of f.
6.2.10 Application of Czarnota’s recommendation In his laboratory model, Czarnota has found out the friction coefficient of the rock, walls and roof with a layer of shotcrete, and for a lined invert. The values of the friction coefficient have been mentioned at section 5.3.
6.3 Discussion on the results The methods of Rahm, Colebrooke, Rheinius etc., depend on the calculation of the relative overbreak factor δ. The assumption is that all the data are normally distributed. The results are very sensitive, when there is a geological overbreak. For example, it is assumed that there is one cross section in each stretch whose area becomes nearly double of the nominal area (say 74 m2) due to a geological overbreak. And assuming that other areas are not changed, the overbreak will change the normal distribution parameters significantly. The distribution will become more skewed causing A99% becoming more, and A1% becoming less. The value of δ shall be more. This is shown in table 6.18.
Hydraulic head losses in an unlined pressure tunnel 47 Theoretical approach and comparison with the measured values
Stretch Value of δ is more by km 1 26% km 2 39% km 3 72% km 4 33 % km 5 36% Table 6.18: Chimay; Change of δ if a cross section area becomes double of the nominal area
Therefore, the friction value shall be proportionately higher. This is one of the limitations that a real estimate of the friction factor is greatly influenced by a single section. Similar shall be the case, if a cross section becomes too small. Cross sections where rock falls are found should not be taken into the analysis.
In view of the above point, the methods using average area approach are expected to yield better results which will be closer to accuracy than the formulas based on extreme areas.
Methods of Priha, Reinius and Wright recommend the value of the friction coefficient f. To arrive at the equivalent roughness k, equation 2.3 is used.
The following graph (figure 6.3) indicates how the values of k calculated by each method vary. Here each kilometre of tunnel stretch is considered.
0.8 Rahm 0.6 Colebrook 0.4 Huval k [m] Wright 0.2 Johansen 0 Solvik 12345IBA km
Figure 6.3 : Chimay; Comparison of k obtained from different methods
The comparison of the friction coefficient f can be seen in figure 6.4.
Hydraulic head losses in an unlined pressure tunnel 48 Theoretical approach and comparison with the measured values
Rahm 0.12 Colebrook 0.1 0.08 Huval 0.06 Priha f [-] 0.04 Reinius 0.02 Wright 0 Johansen 12345Solvik IBA km
Figure 6.4: Chimay; Comparison of f obtained from different methods
6.4 Correction to be applied to the calculated friction coefficient The friction coefficients obtained through different approaches in this chapter are for the exposed rock surface in the D&B tunnel. There are shotcrete layers of varying thickness and of surface coverage inside the tunnel. Also, the invert is lined in 80% of its length. The different surfaces now bring in the composite aspect of the roughness. Suitable corrections will, therefore, be applied to the calculated f values in later chapters, and equation (5.10) shall be used.
Hydraulic head losses in an unlined pressure tunnel 49 Theoretical approach and comparison with the measured values
7 CALCULATION OF HEAD LOSSES IN TBM EXCAVATED TUNNEL
The length of the TBM bored tunnel in Chimay water conductor system, measured from the end of the transition after the unlined portion (ch.5+140 m) to the beginning of the bend before the rock trap II (ch.9+161.43 m), is 4’021.43 m.
Generally, the TBM excavated diameter of a tunnel is more or less constant. However, depending on the geological conditions, there can be local overbreaks at limited places during the work progress due to the presence of fissures, cracks and faults in the native rock. From the project data available, further information about such localised overbreaks could not be interpreted. Therefore, it is assumed that the bored cross section of the tunnel under study remains constant, which is equal to the theoretical diameter of 5.7 m.
Another assumption is that all the steel ribs are covered with shotcrete as shown in the support drawings, and they are not exposed directly to the flow. Otherwise the flanges of such beams will create more eddies, and hence more head losses. Also, it is considered that the small projection of rockbolt ends, if any, does not influence the head loss.
7.1 Influence of supports on the flow area In Chimay project, there have been six types of rock supports in the TBM section of the tunnel. The supports those affect the effective flow area and the wetted perimeter are:
• Partial shotcrete of uniform or variable thickness,
• Complete shotcrete over the perimeter, and
• Steel ribs covered with shotcrete.
The excavated diameter of the tunnel in TBM stretch remaining more or less constant, the application of these supports will reduce the cross section area when compared to the nominal area. Most significant area reduction in the TBM tunnel comes when whole excavated surface is shotcreted or there are steel rib supports in the tunnel. As the supports vary from point to point, there shall be variation of area from one stretch to another. Types of supports used in various stretches are approximately identified and attached in Appendix D-1 (refer section 4.7 also).
To have an idea about the cross section area, the geological mapping drawings are referred to. It has been found that different support types (refer Appendix A-7 and A-8) used in the tunnel, influence the cross section area as follows:
A1, B1 No shotcrete. No area reduction.
A2, B2, B2 alt Shotcrete partially over the perimeter. Area reduces.
Hydraulic head losses in an unlined pressure tunnel 50 Theoretical approach and comparison with the measured values
C1, C2, C2 alt Shotcrete over complete surface. Area reduction.
D1, D1 alt Steel ribs covered with shotcrete. Area greatly reduces.
There are stretches where the application of shotcrete is in small patches. When the patches are only few and very wildly scattered (covering less than 2% of the surface area of the stretch under consideration), the reduction in flow area is presumed to be negligible, and hence not taken into the calculations. When the patches have significant coverage over a stretch (>2% of the surface area), their effect is taken based on the assumption that there is a continuous strip of shotcrete of the same thickness having an equivalent constant width that gives the same surface area coverage of the shotcrete over the stretch in question. Thus one finds there are stretches having cover up of 2.5%, 9%, 12%, 15%, 20%, 30%, 33%, 39%, 40%, 42%, 43%, 45%, 50%, 56%, 59%, 61%, 75%, 78%, 100% of the total surface area with shotcrete.
With a certain thickness of shotcrete which covers some percentage of the excavated surface, the net flow area of the TBM stretch are calculated and summarized in Appendix D-1 and D-4.
The area variation in the TBM stretch is graphically plotted in Appendix D-2.
Maximum area in the TBM section is same as that of the nominal area with 5.7 m diameter. Statistical average and minimum area are stated below:
• Maximum area 25.518 m2 (100%)
• Minimum area 20.63 m2 (81%)
• Average area 24.57 m2 (96%)
Equivalent length of TBM tunnel where the perimeter rock is directly exposed to the flow (complete length with A1 & B1 supports + proportionate length in which partial shotcrete is applied in A2, B2, B2 alt type supports) is approximately 71% (= 2860 m) of the total length of the TBM portion. Balance length of around 1161 m is covered with shotcrete or combination of steel rib and shotcrete.
7.2 Longitudinal invert slope of the tunnel excavated by TBM It is assumed that the alignment of the TBM tunnel in plan follows the theoretical layout. While comparing the records from geological mappings and plotting the invert elevation of the TBM tunnel at 60 m intervals, it is noticed that the TBM does not move absolutely at the defined slope. There are local changes in the slope of the TBM. The change of elevation can be seen in Appendix D-3. A possible reason could be that the TBM was old and refurbished, and most of the time, during its operation, it was not able to develop full power.
Hydraulic head losses in an unlined pressure tunnel 51 Theoretical approach and comparison with the measured values
7.3 Estimated friction head losses in TBM excavated tunnel Head losses in TBM portion of the tunnel are in accordance with the rough pipe flow. Local contraction and expansion is expected due to change of cross section area as explained in section 7.1 and evaluated in section 7.4.
Usually, suggested range of the roughness of the rock elements in a bored tunnel is 7±3 mm [Czarnota, 1986]. The measured values by some investigators are graphically presented in Appendix D-5. Strickler coefficient for an unlined TBM bored tunnel is typically 62 m1/3s-1, and that for the shotcrete lining is 64.5 m1/3s-1 [Lecocq, 1986]. These values correspond to an absolute roughness of the order of 4 mm. Therefore, it is presumed that the absolute roughness of the TBM bored tunnel with or without shotcrete is of the same magnitude and this presumption is uniformly applied throughout the tunnel length irrespective whether the surface has exposed rock or is shotcreted.
7.3.1 Influence of area variation on head loss The weighted average area of the TBM tunnel is 24.84 m2, which means an overall reduction of around 2.66 % of the original area, resulting in increase of velocity by the same magnitude. There is 1.3% decrease in hydraulic radius. This amounts to more than 6.8 % increase in head losses if the friction factor remains constant.
From the statistical average, the area reduces by 3.7%, hydraulic radius decreases by 1.87%, as a result there can be 9.6% more head losses, when compared to the values with nominal dimensions, if the friction factor remains constant.
7.3.2 Influence of area variation on friction coefficient f As area changes, the relative roughness also changes. This too has an impact on the friction factor f according to equation (2.3). However, this is very negligible in the TBM excavated length, and need not be accounted. For the statistical average area, value of f increases by 0.44% to 0.49% for a k value varying from 4 mm to 10 mm, when compared to those for the nominal dimensions. Similarly, for the weighted average area, the influence is still less and it varies from 0.31% to 0.35%.
7.3.3 Friction losses in TBM excavated tunnel Friction losses in TBM excavated tunnel are studied by varying the value of k from 4 mm to 10 mm. The k value is kept same for the exposed rock and also for the shotcrete cover. Area of each stretch is calculated by the shotcrete cover it has. The equivalent diameter at each stretch depends on the effective area at that stretch. Equation (2.3) is used to determine the value of f for each stretch. Individual stretch has been treated separately. The results for a design discharge of Q= 82 m3/s are summarized in table 7.1.
Hydraulic head losses in an unlined pressure tunnel 52 Theoretical approach and comparison with the measured values
v Re
Average 3.35 m/s 1.63⋅107
Maximum 3.97 m/s 1.77⋅107
Minimum 3.21 m/s 1.59⋅107
Nominal 3.21 m/s 1.59⋅107
k [m] f [-] fmax [-] fmin [-] hf [mwc]
0.004 0.0182 0.0185 0.0181 7.24
0.005 0.0191 0.0195 0.0190 7.63
0.006 0.0200 0.0204 0.0199 7.97
0.007 0.0208 0.0212 0.0207 8.28
0.008 0.0215 0.0220 0.0214 8.57
0.009 0.0221 0.0226 0.0220 8.83
0.010 0.0228 0.0233 0.0226 9.07
Table 7.1: Chimay; Calculated friction losses in TBM excavated tunnel for various roughness values varying from 4 mm to 10 mm
The mean value of f is 0.0206 for the TBM portion of the tunnel, and the most expected linear head loss is average of the calculated results in table 7.1, and is estimated to be 8.23 m of water column.
7.3.4 Comparison of Manning-Strickler’s coefficient K and friction factor f Having known Manning’s coefficient from the literature, the equivalent friction factor f in Darcy-Weisbach’s equation (2.1) can be calculated by the relation established from equal head loss:
8 ⋅ g ⋅ n 2 f = 1 (7.1) R 3
Also, Strickler’s coefficient is calculated from the mean roughness size or the grain size diameter by the relation
26.61 K = 1 (7.2) k 6
Hydraulic head losses in an unlined pressure tunnel 53 Theoretical approach and comparison with the measured values
1 n = (7.3) K
The value of f calculated from the above equation (7.1) and Colebrook-White’s equation (2.3) do not yield the same result. The f value calculated with Colebrook- White’s equation gives around 16% higher result in this case. Since, the co-relation is made with the Manning equation for an open channel flow without any reference to relative roughness, the f values calculated according to the rough pipe flow regime will be retained throughout the calculations of the head losses. This conclusion can be seen in the following table 7.2 where f1 is the friction factor calculated from Strickler’s relation, and f2 is that with Colebrook’s equation.
D Q v Re k K f1 f2 %difference [m] [m3/s] [m/s] [-] [m] [m1/3s-1] [-] [-] 5.7 82 3.2135 1.59⋅107 0.004 66.788 0.015 0.0181 15.68 6 5.7 82 3.2135 1.59⋅107 0.010 57.330 0.021 0.0226 6.73 2 Table 7.2: Chimay; Comparison of friction factors by using pipe flow equation and Manning’s equation
7.4 Singular head losses due to expansion and contraction in TBM tunnel Considering the observations in section 7.1, it is found that the cross section areas vary from one stretch to another. However, they remain constant for a particular stretch. Between the stretches either there is contraction or expansion which gives rise to local losses. While evaluating the singular losses due to expansion and contraction, it is assumed that the changes are gradual (due to shotcrete) at angles θ varying from 20° to 45° (some literatures suggest an angle of 20° to 60°).
From geological mapping information, it has been found that the steel rib supports have been placed at 16 locations in the TBM tunnel, and in one location there is shotcrete of 25 cm thick. Corresponding to rock mass classification RMR > 15 and Q(Tunnelling Quality Index)>0.05, steel rib supports are either of class D1 or class D1 alternative types. No support of D2 and D3 type has been encountered.
There is combination of expansion-contraction, expansion-expansion, contraction- expansion, contraction-contraction, or no change in areas between the adjacent stretches. The effective area for a stretch is taken as the area average over that stretch. The area variation is not random, but can be defined through a proper geometrical shape and can be said as predetermined. No interference effect due to combination of expansion and compaction is considered in the calculations.
7.4.1 Head loss due to expansion
The coefficient of head loss due to expansion ζe, as defined by Borda-Carnot has been applied in this report. Value of the coefficient is given by equation (7.4)
Hydraulic head losses in an unlined pressure tunnel 54 Theoretical approach and comparison with the measured values
2 A 1 ς e = Φ e ⋅ 1− , 0≤ζe≤1 (7.4) A2
Where
2θ φe= Coefficient of correction =α ⋅ + sin 2θ for θ≤π/6 π
5 θ =α ⋅ − for π/6≤θ≤π/2 4 2π
α = shape factor of the conduit = 1 for circular, 0.75 for open channels
A1 and A2 are the areas upstream and downstream of the expanded flow.
While calculating head loss due to expansion, it is assumed that the transition angles θ, vary from 20° to 45°. Shape factor of 1 for a circular conduit has been adopted.
The head loss for expansion he in the TBM portion is calculated using the relationship
v 2 h = ς . , where v is the velocity in the upstream section (7.5) e e 2g
The head loss values are given in table 7.3.
Transition angle, θ [°] Number of locations Head loss due to expansion of expansion [mwc]
20° 57 0.22
25° 57 0.27
30° 57 0.31
35° 57 0.30
40° 57 0.29
45° 57 0.29
Average expected 57 0.28
Table7.3: Chimay; Head loss due to expansion in TBM excavated tunnel
7.4.1.1 Discussion on the results The estimated singular head losses due to expansion at 57 locations are around 3.4% of the estimated linear head loss. The ratio of flow area where steel supports are
Hydraulic head losses in an unlined pressure tunnel 55 Theoretical approach and comparison with the measured values
provided is quite high and is of the order of 1.11 to 1.21 times of the upstream cross section area. Where steel rib is not provided, maximum area change is only 1.04 times. The steel supports cover around 10% of the length (16 locations out of 57). However, they are responsible for around 93 % ÷95% of the head losses due to expansion. If the number of discontinuous locations of steel supports is more, there would be more head losses. Area variation due to shotcrete accounts for around 5%÷7% of the head losses due to expansion, and can be neglected in practical design.
7.4.2 Head loss due to flow contraction Head loss arising due to gradual contraction of flow in the TBM tunnel is calculated using the relation
v 2 h = ς . , where v is the velocity in the downstream section (7.6) c c 2g
The coefficient of contraction,ζc, is obtained from the relation given by Gardel as
2 1 ς c = 1− (7.7) µ
Where
1− ()1− a ⋅ (1.032 ⋅ b +1.38 ⋅ a1.48 ⋅ b 0.7 )⋅ (1.495 − b 0.49 ) µ = 1.03 − 0.03⋅ b
A a = ratio of downstream area to upstream area = 2 A 1
θ ° b = 180°
In the similar line as described in the preceding section 7.4.1, the variation of transition angle is selected between 20° to 45° where flow contraction is expected.
Estimated singular head loss due to contraction alone is presented in table 7.4.
Hydraulic head losses in an unlined pressure tunnel 56 Theoretical approach and comparison with the measured values
Transition angle, θ ° Number of locations Head loss due to of contraction contraction [mwc]
20° 54 0.13
25° 54 0.15
30° 54 0.17
35° 54 0.20
40° 54 0.22
45° 54 0.24
Average expected 54 0.19
Table7.4: Chimay; Head loss due to contraction in TBM excavated tunnel
7.4.2.1 Discussion on the results Head loss due to contraction is around 2.3% of the linear losses in the TBM portion. The ratio of the flow areas at the location of steel supports is minimum and it varies from 0.8 to 0.90. Around 76% to 86% of the head loss due to contraction occurs only at the locations of discontinuous steel supports which account for 16 locations only.
The local head loss due to contraction goes on increasing with the transition angle contrary to the trend calculated for the expansion. It is due to the fact that, for the same flow area ratio, maximum head loss coefficient for expansion will occur at 30°, while that for contraction increases with increasing angle.
7.5 Estimated average roughness values of TBM excavated tunnel of Chimay Excluding the losses due to expansion and contraction in the TBM excavated tunnel, with the average head loss of 8.23 mwc in it, average friction coefficient of the surface is interpreted as below:
Davg = 5.591 m
2 2 2 v avg = 11.246 m /s
f = 0.02
k = 6.03 mm (from equation 2.3)
K = 59.24 m1/3s-1
k = 8.2 mm (from equation 7.2)
Hydraulic head losses in an unlined pressure tunnel 57 Theoretical approach and comparison with the measured values
If the losses due to expansion and contraction are included in the friction head loss, then total head losses in the TBM tunnel shall be 8.7 mwc. This will result in the following friction coefficient values:
f = 0.0211
k = 7.48 mm (from equation 2.3)
K = 57.67 m1/3s-1
k = 9.65 mm (from equation 7.2)
Hydraulic head losses in an unlined pressure tunnel 58 Theoretical approach and comparison with the measured values
8 FRICTION HEAD LOSSES IN THE LINED PART OF THE WATER CONDUCTOR SYSTEM OF CHIMAY PROJECT
8.1 Low pressure tunnel Few locations in low pressure tunnel are lined with concrete. These locations are (refer Appendix A-3, A-11, A-12, and A-13):
• Tunnel intake: the rectangular tunnel intake until its junction, with the D&B tunnel at ch.0+000 m, has a length of 25.04 m, which is concrete lined. This is a single intake in plan. The friction losses for this section are not calculated separately. Intake entrance loss coefficient is assumed to include the friction losses, entry losses, gate groove losses, expansion or contraction and friction losses in the connecting piece to the tunnel.
• Tunnel from ch.0+000 m to ch.0+016.5 m: the first entry length of the tunnel is concrete lined for a length of 16.5 m. Cross section geometry changes are there. Taking this into account the linear losses are calculated.
• Transition curve connecting TBM tunnel and rock trap II: this curved section of bend radius of 30 m, extending an angle of 49.04° at the bend centre, is assumed to be concrete lined.
• Rock trap II: this part measuring 26.65 m long is concrete lined. While calculating it is assumed that there is no rock collected in the trap.
• Transition after rock trap II: the transition joins from low pressure tunnel to the bend at top of the pressure shaft. The transition has a bend radius of 13.5 m extending an angle of 40.96° at the bend centre. It is concrete lined.
8.2 Shaft and high pressure tunnel To calculate friction losses in shaft and high pressure tunnel, the following components in this system are identified (refer Appendix A-12, A-13 and A-14). The chainages mentioned in this section are not with respect to the D&B tunnel. However, the chainages are with respect to the pressure shaft ( refer Appendix A-14 for chainage marking):
• Upper bend of the vertical shaft: this is a 4.5 m internal diameter concrete lined bend of 90° at a radius of 9.0 m
• Vertical shaft: 4.5 m constant diameter concrete lined shaft, 116.7 m long, from elevation 1’240.92 m asl to 1’124.22 m asl
• Transition between concrete and steel: Just above the beginning of the lower bend of the shaft, a concrete lined transition piece of 5.0 m long with a varying diameter from 4.5 m to 3.8 m.
Hydraulic head losses in an unlined pressure tunnel 59 Theoretical approach and comparison with the measured values
• Lower bend of the vertical shaft: steel pipe of 3.8 m diameter, with a bend angle of 88.85° and a bend radius of 12.0 m
• High pressure tunnel: 3.8 m diameter, steel lined tunnel of 201.29 m (ch. 0+036.99 m to ch. 0+238.28 m) long till the bifurcation.
• Penstock: 2.65 m diameter steel lined penstock each of 56.74 m long (ch. 0+238.28 m to 0+295.02 m, refer Appendix A-14)
• Penstock entry piece to turbine: 2.5 m diameter, 6.4 m long steel piece (ch. 0+295.02 m to ch. 0+301.02 m, refer Appendix A-14)
8.3 Calculation approach Each lined part, as separated above, whether straight or curved in alignment, has either a constant area of cross section or a varying cross section. For curved parts loss due to friction is calculated without considering the effect of bends (effect of bends is treated separately in section 9.2 as singular losses). For varying cross sections, average flow area is taken into consideration while calculating friction losses.
Absolute roughness for the concrete lined parts is assumed to have three different values, 0.5 mm, 0.75 mm, and 1mm.
Absolute roughness of steel lined part is assumed to have four values: 0.025 mm, 0.050 mm, 0.075 mm and 0.1 mm.
Head loss results are summarised in table 8.1 and 8.2. Detail table of calculation is attached in Appendix E-1 and E-2.
k [mm] of concrete hf [mwc]
0.50 0.57
0.75 0.62
1.00 0.654
Average 0.62
Table 8.1: Chimay; Friction head loss in concrete lined part
Hydraulic head losses in an unlined pressure tunnel 60 Theoretical approach and comparison with the measured values
k [mm] of steel hf [mwc]
0.025 1.87
0.050 2.01
0.075 2.12
0.1 2.21
Average 2.05
Table 8.2: Chimay; Friction head loss in steel lined part
8.4 Friction head losses in Rock Trap I Calculation of friction head losses in rock trap I is treated separately since its cross section areas gradually go on increasing until the deepest part (ch.4+992 to ch.5+036.), then remain almost constant over a certain length (ch.5+036 to ch.5+080), and finally decrease gradually back to the usual shape (ch.5+080 to ch.5+100).
In the rock trap chamber (from ch.5+036 m to ch.5+046, and from ch.5+070 to ch.5+080 m), there is obstruction to flow by concrete walls and removable covers. While calculating, it is presumed that the trap is filled with 1 m height of rock deposit whose top elevation is 1’266.722 m asl.
The area of the concrete walls and of the beams above the muck level, which obstruct the flow, is approximately estimated at 1.5 m2. This area is reduced at relevant cross sections while analysing the friction losses. Effect of the small concrete walls, covering 20 m long of the rock trap, on the friction coefficient is neglected. The absolute roughness values k for rock trap are tested with the range obtained for D&B tunnel described in section 6.2.
It is calculated that head losses due to friction in the rock trap I will be of the order of 0.14 mwc. (Refer Appendix E-3).
8.5 Friction head losses in the transition between D&B and TBM tunnel The transition piece of 10 m long from ch.5+130 m to ch.5+140 m changes from D-shape of the D&B tunnel to circular shape of TBM. The area varies from 41.445 m2 to 24.615 m2. The transition is shotcreted completely. Assuming an average roughness of 15 mm in this zone, the estimated head loss is very minor, and has a value of the order of 0.02 mwc.
Hydraulic head losses in an unlined pressure tunnel 61 Theoretical approach and comparison with the measured values
9 SINGULAR HEAD LOSSES DUE TO BENDS IN THE WATER CONDUCTOR SYSTEM OF CHIMAY In the layout of the tunnel, there have been curves, bends, transitions, expansion and contraction, flow obstructions at the rock traps, bifurcation and combination of flow at various locations. The losses due to these elements are calculated separately and are attached in Appendix F. This chapter treats head losses due to bends only. Other singular head losses are taken up in chapter 10.
9.1 Flow regime Head losses have been measured in the water conductor system at different discharges varying from a minimum of 11.329 m3/s to a maximum of 90.318 m3/s. The design discharge for the power plant is 82 m3/s. For a general note on the flow regime, the lowest and the design discharges are chosen for the unlined D&B tunnel.
Q Re max Re min Re avg vmax vmin vavg
[m3/s] [-] [-] [-] [m/s] [m/s] [m/s]
82 1.24⋅107 1.01⋅107 1.13⋅107 2.304 1.518 1.894
11.329 1.72⋅106 1.39⋅106 1.56⋅106 0.318 0.210 0.262
Table 9.1: Chimay; Flow regime in D&B tunnel
In engineering system, the flow is turbulent if Reynolds number, Re> 5⋅ 103. As seen from table 9.1, and chapter 7.3.3, the flow regime is rough-turbulent for both D&B and TBM excavated zones.
The value of the kinematic viscosity ν of water at 15° C is taken as 1.15 x 10-6 m2/s for the calculation of Reynolds number Re in this report. The bend loss coefficients have been derived for circular pipes of constant diameter, at high Reynolds number. If the bends are spaced more than 30 times the equivalent tunnel hydraulic diameter, the interaction effect is neglected.
9.2 Bend losses The location of the bends in the water conductor system can be seen in the layout drawings attached in Appendix A-1, A-2, A-11, A-12, A-13, and A-14. The bends are identified by the abbreviations denoted herein.
9.2.1 Identification of the bends There are 15 bends present in the alignment of the water conductor system. These are identified as below:
Hydraulic head losses in an unlined pressure tunnel 62 Theoretical approach and comparison with the measured values
• Five horizontal bends in the D&B zone (named TBP2-TBP4, TBP5-TBP7, TBP8-TBP10, TBP11-TBP13, TBP14-TBP18 in the flow direction)
• One horizontal common bend between D&B, rock trap I, transition between D&B and TBM portion, extending into TBM portion (named TBP17-TBP19)
• One horizontal bend in TBM section alone (TBP20-TBP22)
• One horizontal bend between TBM and the rock trap II (V3T4)
• One horizontal bend-cum-transition connecting the rock trap II and the upper bend on the vertical shaft (TP8-TP9)
• Upper bend of the vertical shaft (TP9-PDP)
• Lower bend at the bottom of the shaft (BPDP)
• One horizontal bend in high pressure tunnel before the bifurcation (TP1-B5)
• One horizontal bend on each branch of the penstock (B3-B1)
• One vertical bend on each branch of the penstock at 0+255.39 (B255.39)
• One vertical bend on each branch of the penstock at 0+272.43 (B272.43)
9.2.2 Calculation procedure Head loss calculation at the bends is done assuming that each bend has a constant cross section area, and the walls are concentric. This is not really the case in case of the D&B portion of the tunnel. The relative roughness k/D, is higher than what has been experimented in the laboratory. Areas of the cross sections in a bend in D&B tunnel keep on changing randomly. Therefore, when a bend has variable cross sections, the average area of the measured cross sections in that particular bend is approximated as the effective cross section area. This approximation is regarded to give acceptable results due to the fact that higher velocity concentration in the D&B tunnel remains towards the central core, and that the flow will pass over the roughness elements due to edge effect.
Following recommendation for the calculation of bend losses are adopted:
5 For rough walls, k>0, and Re > 2⋅10
The head loss co-efficient at a bend is given by ζb and is defined by Idel’cik as
ς b = α ⋅ β ⋅ς m (9.1)
ς m = x ⋅ y ⋅ z (9.2)
Where
Hydraulic head losses in an unlined pressure tunnel 63 Theoretical approach and comparison with the measured values
x = F()θ , deflection angle of the bend
R y = F 0 , ratio of radius of curvature of the bend and the equivalent hydraulic D diameter of the tunnel
h z = F , ratio of height and width of the cross section of the tunnel w
The value of x is taken from the table 9.2
θ ≤ 70° 90° ≥100°
x 0.9⋅ sinθ 1 0.7+0.35⋅θ/90°
Table 9.2: Bend loss coefficient x
The value of y is found from equation 9.3.
0.21 y = (9.3) R0 D
The value of z = 1 for a circular or square section is adopted for TBM excavated tunnel, vertical shaft, high-pressure tunnel, and the penstock. On assuming that the drill and blast section is an equivalent rectangular section with a statistical average area of 43.474 m2 and an average base width of 7.606 m, one obtains h/w ratio as 0.751. For this ratio the value of z is 1.2, which is used to calculate the head losses.
k The coefficient α is a function of Re and the relative roughness . For D k k k Re > 2 ⋅105 and 0< ≤0.001, α = 1+ ( ) 2 ⋅106 , and for ≥0.001, α = 2 D D D
The coefficient β =1 is used for the flow Reynolds number in this project.
For a stretch in the D&B tunnel and the TBM tunnel, the average area, and the average hydraulic diameter are taken in the calculation.
Head loss at a bend is given by
v 2 h = ς ⋅ (9.4) b b 2 ⋅ g
Hydraulic head losses in an unlined pressure tunnel 64 Theoretical approach and comparison with the measured values
9.2.3 Bend loss results Detail calculation sheet for head losses at the bends is attached in Appendix F-1. Without considering the interference, total head loss due to the bends is estimated at 1.5 mwc which is taken in the report.
9.2.4 Interference of bends Bend loss coefficients according to chapter 9.2.2 are valid if the adjacent bends so placed are independent of each other. When two consecutive bends are placed at a distance less than 30 times the hydraulic diameter between them, the flow disturbances caused by the upstream bend do not return to a fully developed flow the moment it enters the downstream bend. For this reason, the effective loss coefficient for the combination of bends will be less than the arithmetic sum of those for the individual bends.
In the drill & blast section of the tunnel, the distance between two consecutive bends exceeds 30 times the hydraulic diameter criteria. Therefore, the bend-bend interference is not applied in this stretch. It is to be noted that the flow in an unlined tunnel is not fully developed at any moment. Applying the same principle, the bend loss coefficient for an unlined tunnel may be less when compared to the results obtained assuming uniform cross section and concentric walls. Similarly, there is no interference of the bends in the TBM excavated tunnel.
It is seen that the bends in the shaft, high pressure tunnel and penstock do interfere. On applying the interference coefficient, the estimated head loss can be around 9% lesser than the results obtained in section 9.2.3 (refer Appendix F-2).
9.2.5 Discussion on the results It is noticed that most of the head losses at the bends is in the stretch from the top of the pressure shaft to the end of the penstock. In this stretch of 428 m long, there are only 6 bends which account for 92 % of total head losses due to bends. The reason is that there are sharp bends with lower R0/D ratios, and higher flow velocities in this stretch. The D&B and the TBM tunnel with 9 bends over a length of 9’161 m long stretch contribute to 8% of the head losses due to bends.
For practical design estimation, head losses for bends with R0/D ratio more than 50, and a flow velocity up to 5 m/s in the bend can be neglected since they do not have significant influence. Interference of the bends in a hydropower scheme also need not be considered in preliminary estimation of head losses.
Hydraulic head losses in an unlined pressure tunnel 65 Theoretical approach and comparison with the measured values
10 SINGULAR HEAD LOSSES IN THE WATER CONDUCTOR SYSTEM DUE TO ENTRANCE, AREA VARIATION, OBSTRUCTION, BIFURCATION, COMBINATION AND OTHER LOCAL CAUSES IN CHIMAY If one looks at the random area variation in the D&B tunnel, one would expect continuous expansion and contraction of flow. It is difficult to treat such erratic behaviour through relations developed based on ideal conditions. The friction co- efficient obtained by using suggested procedures of different investigators is already presented in section 6.2, which has an in-built component of friction losses due to macro-roughness (area variation) in it. In the TBM excavated tunnel, there is also change in cross section areas arising due to the supports, but the flow pattern is not erratic, this is treated in sections 7.3 and 7.4.
Besides these, there are few geometrically defined features such as entrance, gate grooves, change in cross section areas (expansion and contraction), transitions, flow division, and flow combination which will give rise to singular losses. The locations of these components are identified in the following sub-chapters. Obstruction due to protrusion of the rockbolt, if any, in the tunnel, has been neglected.
10.1 Entrance and area variation Entry loss at an intake is project specific and can be accurately determined from the prototype or model test. In absence of these, the recommendation from the literature is followed. Losses due to area variation are calculated as per the procedure outlined in sections 7.4.1 and 7.4.2. There are some transition geometry on curves for which the bend losses have been included in section 9.2.3. Effect due to area variation is assumed to be independent of curve.
10.1.1 Entry losses at tunnel intake The floor of the head pond is at 1’316.35 m asl and that for the intake invert is at 1’306.80 m asl. The flow dives down at an angle of 45° and then becomes horizontal while entering into the intake structure. The intake is a single tube rectangular opening of 5.0 m x 4.5 m size with a smooth transition to guide the flow. The intake losses include trash rack, entrance, gate slot, transition, and friction losses throughout the intake section. An average coefficient of ζi=0.16 is adopted from literature.
v 2 The intake head loss is taken as h = ς ⋅ (10.1) i i 2.g
10.1.2 Expansion or contraction losses where geometry is defined (except for TBM stretch) Expansion and contraction in the TBM tunnel has been dealt with separately in section 7.4. Besides this, there are few locations in the water conductor system where the geometry has been already defined. These locations are identified for the calculation of head losses due to expansion or contraction.
Hydraulic head losses in an unlined pressure tunnel 66 Theoretical approach and comparison with the measured values
At the following locations in the water conductor system change of flow area is noted:
• Transition of 10 m long in the intake from rectangular to D-shape tunnel through gradual expansion. However, the head loss due to this is already included in entry loss at chapter 10.1.1.
• Ch.0+000 m to ch.0+001.1 m, a gradual contraction piece at the tunnel entrance.
• Ch. 0+006 m to ch.0+008 m, a 2 m long contraction near the tunnel entry with respect to the effective flow areas.
• Ch. 0+015 m to ch.0+016.5 m, gradual expansion from the lined concrete part to the unlined tunnel.
• Ch.4+992 m to ch.5+012 m gradual expansion at rock trap I at the end of the unlined tunnel (assuming no muck deposit).
• Ch.5+080 m to ch.5+100 m gradual contraction at rock trap I (assuming no muck deposit).
• Ch. 5+130 m to ch.5+140 m gradual contraction from unlined D&B tunnel to TBM excavated tunnel.
• Ch. 9+161.43 m to end of curve V3-T4, a gradual contraction.
• End of curve V3-T4 to rock trap II, an abrupt expansion.
• End of rock trap II to TP8, an abrupt expansion.
• From TP8 to TP9 gradual contraction.
• Gradual transition from 4.5 m diameter to 3.8 m diameter in vertical shaft.
Calculation table for all the above area variation is attached in Appendix F-2. Estimated head losses due to these are 0.32 mwc.
10.2 Loss due to flow bifurcation and combination There are three locations in the water conductor system, where the flow is either divided or combined inside the water conductor system:
• First location is where construction adit # 1 meets the D&B tunnel.
• Second location is where the flow is directed from the TBM tunnel end towards the pressure shaft through a curve, the straight tunnel passing through the surge chamber creates another branch which is plugged at the end.
• Flow bifurcation in the penstock.
Hydraulic head losses in an unlined pressure tunnel 67 Theoretical approach and comparison with the measured values
The calculation of head losses due to flow division and combination are at table 2 of Appendix F-2.
10.2.1 At adit # 1 The construction adit # 1 meets the D&B tunnel with a Y junction (refer Appendix A-9), the left and right limb of Y connects to upstream and downstream, respectively. No measured cross section area is available for this stretch. A plug is placed little below the junction of the limbs. This will cause a flow division locally at the upstream meeting point with the tunnel, and a flow combination downstream where the other limb joins back the main tunnel.
Since cross section areas at these locations are not available, through an approximate analysis, based on the theoretical area of the main tunnel and the limbs, head losses are calculated. Equal friction coefficient in both the parts has been assumed. The flow is in two loops, first loop is the main tunnel, and the second is the adit. The basic principle adopted is that head losses between the point of separation and the point of combination for each of the loops shall be same. The adit loop of 60 m long shall have friction loss, as well as some loss due to its configuration which creates a bend of around 90° angle. The main tunnel loop of 42 m long shall have only friction losses.
R For 0 <1.5, and with a deflection angle of 90°, the bend loss coefficient is estimated D to be 0.73.
Based on this assumption, it is found that the design discharge of 82 m3/s shall divide itself in both the loops as given in table 10.1.
Loop Area theoretical Perimeter Velocity Discharge [m2] theoretical, [m] [m/s] [m3/s] Main 37.79 23.30 1.46 55.1 Adit 24.83 19.07 1.08 26.9 Table 10.1: Chimay; Division of discharge in the main tunnel loop and the adit loop
Approximately, for a 45° flow division, the head losses at the point of division are practically negligible (-0.002 m), while the head loss at the flow combination point is +0.03 m. Thus there is a net head loss of 0.03 m in this system.
10.2.1.1 At the end of the TBM tunnel At the end of the TBM tunnel (ch.9+161.43 m), there are two branches (refer Appendix A-11). Through a transition curve on right, the flow branches itself in the direction of the vertical shaft. The straight alignment of the tunnel passes below the surge shaft, which has again an interconnection to rock trap II.
Since the tunnel is plugged on the straight branch, which creates a dead water zone, it is assumed that there will be negligible flow in this branch, and that entire discharge will pass through the curved branch.
Hydraulic head losses in an unlined pressure tunnel 68 Theoretical approach and comparison with the measured values
Again assuming that the curve meets the tunnel at 15° angle, the head loss coefficient for branching off of the flow is 0.038, an estimated singular loss of 0.02 m at this location can be expected.
10.2.1.2 In the penstock The design discharge of 82 m3/s gets divided into two equal branches of 41 m3/s each. The junction angle is 60° (refer Appendix A-15).
The entry velocity is 7.23 m/s. The velocity after the bifurcation is 7.43 m/s. The area at entry is 11.34 m2, the area of both the branches added together after the bifurcation is 11.03 m2. It is assumed that the area before the flow division is approximately equal to the sum of the flow areas after the flow division. The loss coefficient ζd is 0.1. The net head loss at the bifurcation is 0.27 m.
10.2.2 Local losses in the rock trap I and II due to obstruction by steel beams and concrete walls Steel beams have been placed at two locations in the deepened part of the rock trap I to shear the flow above the top of the beams in order that the deposited materials do not get lifted by turbulence and do not enter the turbine (refer Appendix A-4).
The beams are supported on the concrete walls. The area of the concrete walls and the beams exposed to the flow direction will obstruct the flow causing local losses.
It is also assumed that some rock has moved inside the tunnel and is trapped in the deeper part of the structure. The loss is calculated for one chamber and is doubled to take care of two chambers. The loss coefficient is read out from the graphs corresponding to the ratio of the free area to the area of the total passage. As suggested by the literature [Miller], a coefficient of 0.1 is added to the coefficient read out from the graphs to take care of the redevelopment of the flow. This may be a little conservative, since the second chamber is situated almost immediatly downstream of the first chamber. The following alternatives are studied and presented in table 10.2 for rock trap I. Detail calculation can be found at Appendix F-3.
Area of Muck Area of Area of Area of Ratio of Loss Local passage height muck concrete beams areas coefficient losses [m2] [m] [m2] [m2] [m2] [-] [-] [mwc] 60.145 0 0 2.75 0.614 0.943 0.25 0.053 60.145 1 6.26 2.75 0.614 0.839 0.35 0.094 60.145 2 12.52 2.75 0.614 0.735 0.73 0.256 Table 10.2: Chimay; head loss at rock trap I due to obstruction to flow
The alternative with 1 m high deposited muck in the rock trap is considered in the evaluation of the results.
For rock trap II similar exercise is done. However, no muck deposit is assumed there. The head loss is around 0.003 m and its influence is neglected (refer Appendix F-3).
Hydraulic head losses in an unlined pressure tunnel 69 Theoretical approach and comparison with the measured values
Taking both the rock traps into consideration, a head loss of 0.1 m is expected in the system.
Hydraulic head losses in an unlined pressure tunnel 70 Theoretical approach and comparison with the measured values
11 FRICTION HEAD LOSSES IN THE UNLINED DRILL AND BLAST TUNNEL OF CHIMAY Calculation of friction coefficients using various approaches put forward by the investigators has been discusses in chapter 6. The friction coefficients so calculated are believed to be for the exposed rock surface of the blasted tunnel, except for that in Wright’s method at section 6.2.6 in which influence of the lined invert has been made. In practice, the rock surfaces of the unlined tunnel are not completely exposed, often part of the rock tunnel is covered by shotcrete as required at site. This will have an influence on the friction factor.
11.1 Equivalent tunnel length with shotcrete The unlined part of the tunnel has different types of supports. Summary of the actual supports performed at site are provided under Appendix C. There are quite a number of locations where shotcrete has been applied only to a part of the surface. Part of the surface covered by shotcrete and the remaining exposed rock surface are accounted separately and are expressed in terms of equivalent length of the tunnel which is either completely covered by shotcrete or completely exposed. Apportioning is done linearly. For example, considering a stretch of 50 m long of the tunnel which is covered by a layer of shotcrete on 30% of its surface only, the stretch is considered to have two equivalent parts: first part with full surface exposed rock of equivalent length 50 m x 70% = 35 m, and the second part with equivalent shotcrete cover of 50 m x 30%=15 m.
For a stretch, when the complete perimeter is covered with shotcrete (walls and the crown), the linear length under shotcrete is same as the length of the stretch. Similar analogy for the completely exposed rock surface also has been made.
When there are two different thickness of shotcrete in a particular stretch, the length in that stretch is linearly apportioned for each thickness of shotcrete. For example, in a stretch of 50 m long, the crown is covered by 8 cm and the walls by 5 cm thick shotcrete. The crown accounts for 69% of the shotcrete surface area. The proportioned stretch under 8 cm thick shotcrete will be 50 m x 69% = 34.5 m, and the balance of 15.5 m will fall under the category of 5 cm thick shotcrete. This is done approximately to identify the length of the tunnel with a particular thickness of shotcrete. However, such division does not have final implication on the friction coefficient. There can be some modification to the friction coefficient if two or more layers of shotcrete are applied in a drill & blast unlined tunnel.
Such division of supports is necessary to accommodate the recommendation that in case the tunnel invert is lined with concrete or asphalt concrete, there could be a reduction in head loss up to 30% of the fully exposed tunnel. Also, due to the application of shotcrete, on the walls and roof, the angularity of the rock roughness is hidden under the layer, which reduces head loss once more, may be by around 20% of the original value compared to that of an unlined D&B tunnel.
Hydraulic head losses in an unlined pressure tunnel 71 Theoretical approach and comparison with the measured values
Since the equivalent roughness in a pressure tunnel, having composite roughness values on the wetted perimeter, is expressed by a simple proportional relation as given in equation 5.10, the proportional linearity is assumed to remain valid for the concrete lined invert, and shotcrete on walls and roof.
A second layer of shotcrete reduces the area of flow to some extent. However, the net effect is that there will be still reduction in head losses as compared to a single layer of shotcrete. Application of two layers of shotcrete is very negligible in Chimay, therefore, it is altogether ignored in the calculations. The adjusted friction coefficient for a stretch is assumed to remain uniform and homogeneous for a single layer of shotcrete.
The tunnel has been divided into 5 stretches (km 1, km 2, km 3, km 4, and km 5) for simplicity in calculation. The first stretch (km 1) of 1’018.5 m long has an invert which is unlined. The successive stretches have a concrete lined invert.
It is assumed that the concrete invert has an absolute roughness of 3 mm. Average Reynolds number (Reavg), average area (A50%), average perimeter (P50%) and average hydraulic radius (R50%) associated with a particular stretch are taken into consideration while calculating the friction head losses.
The estimated surface cover in the unlined D&B tunnel is summarised in table 11.1. Linear losses in the rock trap I has been dealt with separately in section 8.4; therefore, its length of 108 m (equivalent to 66.6 m exposed rock, 9.9 m with 10/12 cm thick shotcrete, 24.6 m with 8 cm thick shotcrete, and 6.9 m with 5 cm thick shotcrete) is reduced from km 5 (ch. 4+000 to 5+130 m).
Type of All km 1 km 2 km 3 km 4 km 5 surface [m] [m] [m] [m] [m] [m] Exposed 2751.86 574.46 451.08 578.20 394.88 753.24 rock (55%) Shotcrete 3.50 3.50 25 cm (0%) Shotcrete 139.70 73.00 35.00 31.70 10/12 cm (3%) Shotcrete 846.94 238.93 192.04 131.05 204.92 80.00 8 cm (17%) Shotcrete 1167.5 201.61 227.88 290.75 290.2 157.06 5 cm (23%) Steel ribs 96.00 21.00 75.00 with (2%) shotcrete Table 11.1: Chimay; Covering over the excavated surface of D&B tunnel
Around 55% of the excavated surface (wall and crown) of the D&B tunnel remains without any surface treatment. Reduction of friction factor will not apply to this. Balance 45% of the surface is covered with at least a layer of shotcrete to which reduced friction factor shall be applicable.
Hydraulic head losses in an unlined pressure tunnel 72 Theoretical approach and comparison with the measured values
11.2 Effect of lined invert on composite friction factor Approximately 20% length of Chimay D&B tunnel invert is unlined. The friction factor of the natural rock will apply in this case. For balance 80% of length, the invert is lined. Appropriate friction coefficient for concrete will apply to the invert.
As seen in chapter 6.2, value of k varies from one method to another. For an average D&B tunnel of Chimay, the bottom invert covers 30% of the total wetted perimeter. Assuming the linear relationship (equation 5.10), and varying the tunnel wall roughness from 0.2 m to 0.8 m, and the concrete lined invert with an absolute roughness of 3 mm, it was found that the composite surface shall reduce the friction factor by 20% to 26% as compared to the exposed rock roughness. Therefore, an average reduction of 23% in friction coefficient seems appropriate (further discussed in section 11.6.5).
When invert concrete is placed, the irregularities of the rock on the invert are completely eliminated. If entire wetted perimeter is concrete lined, with the same analogy (without reducing area), around 77% percent of the head loss can be reduced.
11.3 Effect of shotcrete on friction losses A layer of shotcrete neither eliminates completely the irregularities of the rock, nor is it as smooth as the concrete lining is. It is therefore difficult to ascertain how much head loss reduction shall be there if shotcrete is applied.
It is believed that the cross section measurement was taken after the application of shotcrete, and hence there should not be any reduction in the macro-roughness in case of Chimay. There will be definitely the reduction in micro-roughness.
From theoretical calculations, if we apply a layer of 5 cm shotcrete over the walls and crown of the nominal perimeter of the D-shaped drill & blast tunnel, it is seen that area reduces by 2%, perimeter by 1%, hydraulic radius by 1%, velocity increases by v 2 2%, term increases by 5.4%. 2 ⋅ g ⋅ D
Similarly, if 8 cm thick shotcrete is applied on the nominal surface (on walls and crown only), area reduces by 3.4%, perimeter by 1.77%, hydraulic radius by 1.66%, v 2 velocity increases by 3.5%, and term increases by around 9%. 2 ⋅ g ⋅ D
The model test by Czarnota (refer section 5.3) concludes that, there is substantial v 2 reduction in head losses when shotcrete is applied, despite an increase in 2 ⋅ g ⋅ D term. Since, there is no laboratory model test for the unlined tunnel of Chimay, it is assumed that the results of Czarnota’s model test can be judiciously applied while evaluating the friction coefficient in the shotcreted zone of the drill & blast tunnel. The inference from the model is drawn in the following way:
Hydraulic head losses in an unlined pressure tunnel 73 Theoretical approach and comparison with the measured values
• The result of the friction factor f, when the tunnel walls and roof are unlined, has a value of 0.0730. With prototype area of the tunnel as 8.607 m2, equivalent hydraulic radius works out to be 3.31 m. By applying equation 2.3, equivalent roughness of the rock tunnel works out to 17 cm.
• When the model is tested with one layer of shotcrete on the walls and roof, the equivalent roughness of the rock tunnel is calculated at 7.8 cm.
• This implies that with the application of one layer of shotcrete, the reduction in equivalent roughness of the full section is of the order of 9.2 cm. This amounts a net reduction of 11.7 cm in roughness on the shotcreted surface only, while the roughness of the invert remains same at 17 cm.
• When compared with the friction coefficients with a lined invert with and without shotcrete on the walls and roof, a reduction of wall roughness by 10.9 cm is computed for the shotcreted part.
• On average a reduction of wall and crown roughness by 11.3 cm has been considered in Chimay project, where shotcrete is applied.
Through different methods in chapter 6, equivalent roughness values of the unlined tunnel has been calculated, or k values have been determined through equation 2.3, once f values are known. Now to take into account the effect of one layer of shotcrete, average wall and roof roughness is reduced by 11.3 cm, and appropriate new friction factor values are calculated. These values are presented in Appendix G-2.
11.4 Calculated friction losses in unlined tunnel After taking into account the influence of invert lining and shotcrete, wherever applicable, theoretically expected friction head losses for every km is furnished in table 11.2 and graphically shown in figure 11.1.
Head loss (mwc) 012345678910
RAHM HUVAL PRIHA REINIUS WRIGHT IBA CZARNOTA MEASURED COLEBROOK JOHANSEN SOLVIK
Figure 11.1: Chimay; Comparison of estimated friction losses in D&B tunnel
Hydraulic head losses in an unlined pressure tunnel 74 Theoretical approach and comparison with the measured values
Method km 1 km 2 km 3 km 4 km 5 Total [mwc] [mwc] [mwc] [mwc] [mwc] [mwc]
Rahm 2.13 1.38 1.72 1.89 1.79 8.91
Colebrook 1.34 0.88 1.18 1.13 1.10 5.63
Huval 2.23 1.53 1.48 1.51 1.66 8.41
Priha 2.31 1.50 1.87 2.06 1.92 9.66
Reinius 1.78 1.22 1.51 1.59 1.52 7.62
Wright 1.96 1.35 1.66 1.73 1.66 8.36
Johansen 1.41 1.12 1.39 1.24 1.25 6.41
Solvik 1.04 0.83 1.09 0.92 0.99 4.87
IBA 1.87 1.37 1.77 1.53 1.55 8.09
Czarnota* 1.55 1.30 1.60 1.41 1.54 7.40
Table 11.2: Chimay ; Friction head losses in the D&B tunnel calculated by various methods after applying correction
*only recommended friction factors from the model test (refer section 5.3) considered.
11.5 Comparison with the measured values There is no site measurement made directly to know the head losses only in the tunnel excavated by drill & blast method. Head losses in the system as a whole have been measured at the inlet to the turbine. Calculation of head losses in TBM tunnel, shaft, penstock, bends, transitions and other special features are individually treated in chapters 7, 8, 9 and 10, and are summarised in table 11.3 in this section. The measured average head losses at design discharge of 82 m3/s are 21.80 mwc in the entire water conductor system (refer Appendix G-1).
Major part of the head losses in the system is in the TBM and the drill & blast tunnel. Other losses in the defined geometry and singular losses may not change so much.
Head losses in the TBM are calculated with assumed equivalent roughness. Any change in the assumed roughness value of TBM tunnel will change the head losses in it to a great extent.
Hydraulic head losses in an unlined pressure tunnel 75 Theoretical approach and comparison with the measured values
Losses at Type of loss Minimum Maximum Average [mwc] [mwc] [mwc]
TBM tunnel friction 7.24 9.07 8.23
TBM tunnel singular, 0.22 0.29 0.28 expansion
TBM tunnel singular, 0.13 0.24 0.19 contraction
Concrete lined friction 0.57 0.65 0.62 portion
Steel lined friction 1.87 2.21 2.05 portion
Bends singular 1.5 1.5 1.5
Expansion / singular 0.32 0.32 0.32 contraction
Flow singular 0.32 0.32 0.32 bifurcation / combination
Rocktraps friction 0.14 0.14 0.14
Obstruction in singular 0.09 0.09 0.09 flow
Transition friction 0.02 0.02 0.02 between drill & blast and TBM
Total 12.42 14.85 13.76 computed losses
Table 11.3 : Chimay; Minimum, maximum and average computed losses in the tunnel other than the friction losses in D&B section
If we suppose that the minimum equivalent roughness of 4 mm in TBM tunnel is valid, then the friction head losses in the D&B section shall be around 9.38 m. If the maximum equivalent roughness of TBM tunnel is 10 mm, then, the friction head losses in the D&B section shall be 6.95 m, means the results can vary within a range of 35% above the minimum value. Generally, there is no randomness of the cross section areas in the TBM, and linear head losses in it can be calculated more accurately once the roughness of the rock surface and the shotcrete surface are
Hydraulic head losses in an unlined pressure tunnel 76 Theoretical approach and comparison with the measured values
measured at few locations along the tunnel. The comparison of the results, therefore, depend mainly on the TBM tunnel losses in case of Chimay due to the fact that its length is 44% of the total tunnel length. However, maintaining an average approach, most expected friction head loss in the D&B section shall be of the order of 8.00 m (36.9% of the total loss, 42.3 % of the friction loss).
11.6 Discussion on the results The average expected results stipulated in chapter 11.5 are taken into consideration for further discussion on the results. The friction coefficients are various, each method giving rise to a new coefficient.
11.6.1 Calculated and measured head losses by each method
Rahm’s method based on statistical parameters of A99% and A1%, which are fictitious areas computed from an ideal normal distribution curve, and after applying corrections for the invert lining and shotcrete, calculates a head loss which is 10.8% higher than the measured values in the D&B stretch of Chimay. It is not known if the method included other minor losses in its approach. It is shown later in this section that other minor losses account for approximately 12.5% of the total losses (2.72 mwc of 21.8 mwc measured) in the water conductor system. This method, which deals nearly with extreme areas, is to be judged judiciously, since a single cross section having an area twice that of the nominal (say due to geological overbreak) can skew the normal distribution and may result in higher values of the relative overbreak and the friction coefficient. The method can be used after eliminating unusual cross section areas. The k value so obtained is for the rock surface. Correction is required for invert lining and shotcrete. If normal distribution curve is not assumed and actual areas of the cross sections corresponding to approximately 99% and 1% cumulative distribution are chosen the f values can be either more or less than those calculated from normal distribution curve, as seen in the case of Chimay. It is, therefore, suggested to go for the normal distribution function. The approach shall give different f values for each independent stretch. In the case of Chimay, if independent stretches are not treated separately, and all the cross sections are taken as one sample, it results in a likely overestimation of f value by more than 15% of the average in each stretch. A minimum of 150 to170 numbers of cross sections per kilometre of D&B tunnel at regular intervals appears appropriate for describing the normal distribution function.
Colebrook’s method did not fit well to Chimay. However, it gives a head loss of 7.61 m if the corrections due to invert lining and shotcrete are not applied. Logically, the results after correction are under estimated by 30% than the real head losses. This approach may not be suitable to all cases. The lower results are due to lower estimation of k value as per the definition in this approach.
Huval’s method based on statistical parameters of mean area and nominal area, estimates the head loss at 4.6% more than the values measured. This method has been tested with many tunnels of horseshoe or modified horseshoe shapes, and has been Corps of Engineer’s guideline for the design of the unlined D&B tunnels. Though it is closer to the expected values in Chimay, there are great scatters of f values in the original graphical presentation of the method. Roughness k must be calculated with
Hydraulic head losses in an unlined pressure tunnel 77 Theoretical approach and comparison with the measured values
respect to the mean area. If calculated with respect to individual cross sections, the k value will be overestimated by around 40%. Corrections for invert lining and shotcrete are to be applied to arrive at effective f values. It is interesting to note that the value of absolute roughness k as per Huval is approximately twice of that defined by Colebrook.
Priha’s stipulated conditions were not satisfied in the statistical analysis, which needs width and height measurements at 25 cm intervals. This could be the reason why the results are over estimated by 20 %. The method can be tested when the collection of the data are made according to the recommendations.
Reinius’s method uses Rahm’s statistical parameters. In case of Chimay, the average of slow, normal and rapid friction coefficients, in terms of work progress, are considered, which will probably happen in combination at a construction site. The normal condition is very close to the average figures, while the slow progress will lower the friction coefficient by around 30%, whereas in rapid construction it would increase by around 30% when compared to the normal condition. The final results are very close the measured values with an underestimation of 5.2%.
Wright’s method is a modification of Rahm’s method by introducing area, perimeter and hydraulic radius. It overestimates the head loss by 4% (lowered by ≈7% from Rahm’s). The design chart from Wright (appendix H-2) grossly underestimates the head losses for an invert lined tunnel. Therefore, design values have been taken assuming an unlined tunnel, and corrections have been applied as appropriate for the concrete invert and the shotcrete surface.
Johansen’s method, which takes care of the surface roughness (micro) and area variation (macro), underestimates the results by 20%. This method is not based on statistical values.
Solvik’s method is a slight modification from that of Johansen’s, and it grossly underestimates the results by 39%. This method is also not based on statistical mean value.
IBA method, which estimates the area and wall roughness, based on statistical mean values, gives the closest approach to the expected head loss overestimating by 0.6 %. This method appears to describe macro (area) and micro roughness (walls) concepts individually. Corrections due to invert lining and shotcrete layer in the tunnel are to be applied on the estimated k values.
From the explanations above, it is inferred that Huval (+4.6%), Reinius (-5.2%), Wright (+4%) and IBA (+0.6%) methods, based on statistical input, are the most suitable approaches which predict the head loss in the project to a greater accuracy (i.e. within ±5%). The methods based on individual area variation like the ones proposed by Johansen and Solvik, grossly under estimate the values. Rahm’s method, based on statistical parameters, is also acceptable, but it gives results which are more than 10% of the expected values.
Hydraulic head losses in an unlined pressure tunnel 78 Theoretical approach and comparison with the measured values
The method proposed by Colebrook, though based on statistical parameters somehow deviates and does not properly describe the head losses due to lower assumption of k value.
11.6.2 Relevance of measuring roughness of a TBM tunnel at site Calculation of head loss in a pressure pipe flow at high Reynolds number (>106), k depends mainly on the evaluation of the equivalent and relative roughness. If ratio D increases by 100 times, the friction factor will increase by 6 times. In an unlined D&B tunnel measuring the value of k is very difficult, but this can be measured in a TBM tunnel by modern optical measuring devices. When, D&B and TBM tunnels are in combination in one project, and there is no separate head loss measurement for D&B and TBM tunnel independently, roughness measurement of the TBM section shall be a good reference to indirectly calculate the head losses in the unlined portion. In the case of Chimay, where roughness of the TBM tunnel is not available, the evaluation of measured head losses in D&B stretch became coupled with the TBM tunnel. Therefore, an indirect approach was followed to determine the most expected losses in D&B section.
11.6.3 Influence of composite roughness of a D&B tunnel For a composite roughness on the tunnel wetted perimeter, for example, partly exposed rock, partly shotcrete, and the lined invert, a linear relationship, as suggested in the literatures, has been followed in this report, and it agrees with the measured head losses. In open channel flow, the equivalent roughness of a section having composite roughness is calculated by drawing isovels and orthogonals. This approach was not successful in a D&B tunnel having a random shape: application of this approach may require further research as how to draw the isovels in a cross section of random shape.
If it is assumed that the D&B tunnel with the excavated average area is concrete lined with a k value of 3 mm, at the design discharge, the head lossed in the D&B tunnel would have been only 2.20 m. It means, by making an unlined tunnel, there has been 5.84 m of more head loss. This difference is on the lower side, since 80% of the tunnel has an invert lining, and 45% of the wall and crown are covered by shotcrete. Had the rock surface been completely exposed, approximately, total estimated head losses in D&B tunnel would have been around 10.9 m, increasing the difference to around 8.7 m. Partial invert lining and shotcrete has reduced the head loss by approximately another 2.86 m, the invert lining contributing to around 83% of this.
If theoretical shape of the D-shape tunnel (A=37.792 m2) would have been maintained with a concrete lining of 3 mm of absolute roughness, a head loss of 3.12 m would have been expected in the D&B tunnel section. This means, head loss has in fact increased to 258% of the ideal lined cross section, just by leaving it unlined.
Hydraulic head losses in an unlined pressure tunnel 79 Theoretical approach and comparison with the measured values
11.6.4 Equivalent average friction coefficient of D&B tunnel In actual site conditions, the friction coefficient for each stretch in the tunnel shall be different. If we assign an average value for Chimay project, the value of friction factor f for the composite section (shotcrete, invert lined, and exposed rock), shall be f = 0.0600 (K = 33.06 m1/3s-1, k = 273 mm as per equation 7.2, and k = 234 mm as per equation 2.3). Had there been no composite section (only exposed rock), average value of the friction coefficient would have been around f = 0.0813 (K = 28.41 m1/3s-1, k = 675 mm as per equation 7.2, and k = 454 mm as per equation 2.3). Therefore, Strickler’s value for an invert lined rock tunnel shall be around 33 m1/3s-1 and for an unlined rock tunnel it would be around 28 m1/3s-1. Since equation 2.3 has been applied in calculations throughout, average equivalent absolute roughness of Chimay tunnel is 234 mm. Without invert lining and shotcrete, the same would have been around 454 mm. Assigning an absolute equivalent hydraulic roughness is formula dependent as seen in this case. On referring to Moody diagram in Appendix H-3, values of f in the chart corresponding to k/D ratios (k calculated as per equation 2.3) of 0.066 and 0.034, the friction coefficients are 0.08 and 0.06, respectively, for Re > 107.
11.6.5 Effect of invert lining on head losses in D&B tunnel Some of the literatures propose that the saving in head loss due to an invert lining is of the order of 30%. This appears to be correct. In Chimay there is a saving in head of 2.38 m when 80% of the invert is lined. This corresponds to a reduction of around 27% of the head losses when the entire invert would be lined. However, Wright’s method recommends a greater reduction of around 40%, which could not be verified in Chimay. Therefore, for invert lined rock tunnels, the friction coefficient read from the graphs provided by Wrights (Appendix H-2) shall underestimate the results. The reduction will depend on other geometrical dimensions of the tunnel too.
11.6.6 Effect of shotcrete on friction head losses in D&B tunnel By providing 45% length of the tunnel with shotcrete, around 0.5 m (equivalent to 4.5% of reduction of total loss had the tunnel been completely unlined) of reduction in head losses is calculated. If the entire D&B tunnel would have been shotcreted on the walls and the crown, an expected savings of 10% of the total head losses is possible when compared to that of an unlined tunnel. This is contrary to the recommendation in the literature that shotcrete can reduce around 27% of the head losses. The literature recommendation was based on a model test of a tunnel of 8 m2 area, in which the k relative roughness played an important role. In case of Chimay, net reduction in D absolute roughness of 11.3 cm due to application of shotcrete did not play a dominant role in the value of the relative roughness. Therefore, it gives a lower reduction.
It can be emphasised that, for the tunnels of Chimay size, head losses can be reduced more effectively by lining the invert, than shotcreting entire surface.
Application of two layers or more of shotcrete practically does not exist in Chimay. Influence of this on the head loss could not be verified. However, in future projects, model tests of Czarnota may serve as a reference guideline.
Hydraulic head losses in an unlined pressure tunnel 80 Theoretical approach and comparison with the measured values
11.6.7 Comparison of head losses in TBM tunnel In the TBM section, if the tunnel would have been of uniform diameter, and is lined with concrete of absolute roughness of 2 mm, theoretical friction head losses in that section should have been only 5.82 m. On the otherhand, if the diameter remained uniform and the abosolute roughness varied from 4 mm to 10 mm, a head loss of 7.71 mwc could be expected. Due to the supports in Chimay TBM tunnel, the effective area has decreased, velocity has increased, and there is local expansion and contraction, which increased total head losses to 8.7 mwc ( 8.23 m friction + 0.28 m expansion + 0.19 m contraction). The head loss has jumped to 150 % when compared to a concrete lining, and to 113% when compared with shotcrete and exposed bored rock.
11.6.8 Comparison of friction head losses and singular head losses Head losses only due to friction are 19 mwc of the measured result of 21.8 mwc, accounting for around 87% of the total. The minor losses are only 13% of the total head losses. Therefore, it is important to predict the friction losses as correctly as possible.
Flow obstruction in rock traps may give rise to minor losses in the system. But its component will be negligible, say around 0.7% of the total loss.
By concrete lining both the D&B and TBM tunnel, with the theoretical areas, friction head losses could have been reduced by 50% of the total 19 m.
11.6.9 Distinction of macro and micro roughness Macro-roughness of the unlined D&B tunnel could not be studied separately. However, if reference is made to Johansen’s and Solvik’s methods described in sections 6.2.7 and 6.2.8, respectively, it can be seen than the contribution to macro- roughness varies from 8 cm to 11 cm. The micro-roughness has been estimated at 15 cm. If these values are compared with those in IBA method (section 6.2.9), the macro-roughness due to area variation is of the similar order, but the micro-roughness estimation is almost double of what is specified by Johansen and Solvik.
Despite the discussions in the preceding paragraphs, it is not known as how to separate macro-roughness and micro-roughness. On reverting back to IBA method, it is seen that this method describes a wall roughness and an area roughness. Since areas were measured after the preliminary supports were in place, it can be assumed that the roughness only due to area variation remains constant, and that the wall roughness changes due to the invert lining and shotcrete. If the wall roughness is considered as primary, and area roughness as secondary, head losses due to wall roughness is of the order of 6.08 mwc and that due to area roughness is 2.01 mwc. This indicates that the head loss due to area roughness is around 25% of the total head losses in the unlined portion. This may not be true. If the roughness are reversed, that is the area roughness is treated as primary and the wall roughness as secondary, then head losses due to area is around 6.13 mwc (76%), while that for wall is 1.96 mwc. On the other hand, if sudden expansion and contraction between the cross sections is assumed, head losses due to this is of the order of 0.75 mwc (calculated for cross sections at 5 m intervals
Hydraulic head losses in an unlined pressure tunnel 81 Theoretical approach and comparison with the measured values
and proportioned over the full length of the D&B tunnel) which is around 9% of the total losses in the D&B tunnel. If gradual expansion and contraction between adjacent cross sections is approximately taken, then the head loss can be around 0.22 mwc (around 3% of total losses). From these observations it is difficult to say what could be the head loss only due to area variation. It is appropriate not to separate the roughnesses, but to denote all roughness as one integrated value in an unlined D&B tunnel. The head losses due to macro-roughness can vary from 15% to 30% of the total head losses in D&B tunnel [Czarnota].
11.6.10 Friction head losses per metre length If we look at the friction head losses per meter of the tunnel (excluding the singular losses associated with the area variation) it is estimated that, the drill & blast tunnel has an average linear losses of 1.60 mwc per 1000m (excluding rock trap I and the initial lined part). Similarly the friction losses in TBM tunnel are 2.05 mwc per 1000 m. The head losses per 1000m in TBM tunnel is 28% higher than that in the unlined tunnel. It is due to the fact that the average friction coefficient in the D&B is around 3 times higher than that of a bored tunnel, but the ratio of velocity 2 v TBM 11.25 squares 2 = , which is around 3.12 times; and the ratio of equivalent v D&B 3.60 D 5.59 hydraulic diameters TBM = , which is around 0.81 times, are mainly responsible DD&B 6.86 for more friction head losses per linear meter in the TBM stretch.
11.6.11 Refinement of the assumptions The reduction of the rock roughness due to application of one layer of shotcrete is based on the literature reference on one laboratory experiment. Further tests or references may be required to establish if the assumption of reduction in roughness fits well to other projects.
Various methods to estimate friction coefficient were developed and applied to the then existing D&B tunnels (refer section 5.2). It is not clear whether the then existing tunnels had a layer of sotcrete or guniting over the surface, or the friction coefficients were derived for the exposed rock surface. According to Reinius, tunnels excavated before 1946 give a higher value of friction coefficient, and D&B tunnels excavated after that give reduced friction coefficient due to development in mining technology. It is assumed in this report that the existing methods apply to the exposed rock.
If instrumentation that measures head losses at intermediate points could be installed inside the tunnel (for example in Chimay the calculation is done for every km, therefore, installation of instrumentation at each km) a better comparison of the results could be made.
Hydraulic head losses in an unlined pressure tunnel 82 Theoretical approach and comparison with the measured values
12 SUGGESTED DESIGN GUIDELINE The suggested design guideline to make preliminary estimation of the head losses in an unlined D&B tunnel with or without invert lining, with or without shotcrete is derived from the application of the data of Chimay project in preceding chapters.
12.1 For unlined drill & blast tunnels It is seen from the preceding chapter that the methods proposed by Rahm, Huval, Reinius, Wrights, and IBA closely predict the expected head losses in an unlined D&B tunnel. The method of Rahm, Reinius, Wrights and IBA can be used only when the work is in progress and statistical parameters are made available from the measurements made at site. Without these, the relative overbreak factor δ, or the root mean square values (rmswall or rmsarea), as required, cannot be estimated.
Also the method of Rahm, Reinius, and Wright will require many cross sections (in case of Chimay at least 175 cross sections at 5 m intervals per km in average) before a real statistical normal distribution is possible. The practical guideline that the sections should be measured at 5 m intervals in a tunnel is adoptable at sites. If the cross sections at closer intervals over a long stretch of the unlined D&B tunnel are obtained, a better distribution of the results shall be achieved with more data in hand.
The IBA method (section 5.2.11) can be adopted after a short excavation of the tunnel has been undertaken, subject to rigorous measurements at very close intervals.
However, for preliminary hydraulic design of the unlined D&B tunnels, the method of Huval (section 5.2.5) seems to be more appropriate. This approach needs an average area and the nominal area of the cross section. Though this method investigated horseshoe or modified horseshoe tunnels, it has shown reasonable acceptance of the results for a D-shape tunnel in Chimay. From the literature, it is found that the average area of an excavated D&B tunnel has almost a linear relationship to the nominal area. This graph is presented in figure 12.1. Selecting the nominal area of the tunnel, expected average cross section of the blasted section can be found out from the graph. Following the approach by Huval, the relative roughness can be obtained through Prandtl-von Karman’s rough pipe flow (equation 5.12) or from Colebrook –White rough pipe flow (equation 2.3). This will give a close estimation of the rock surface roughness before the real excavation work starts.
Correction factors must be applied to the basic absolute roughness so obtained to take care of shotcrete in identified stretches as per geological investigation. For preliminary hydraulic design, roughness reduction of 10 cm than what obtained from Huval shall be appropriate, for application of one layer of 5 to 10 cm thick shotcrete.
The stretch where concrete invert lining is required shall be determined from site investigation. Composite roughness formula (equation 5.10) for the pressure flow shall be used to determine the equivalent friction coefficient of the cross section.
Hydraulic head losses in an unlined pressure tunnel 83 Theoretical approach and comparison with the measured values
By changing the nominal and the excavated areas, stretch of shotcrete, lined invert, unlined invert, and the exposed rock, different alternatives to arrive at the head losses can be attempted.
Nominal area versus excavated area of a drill and blast unlined tunnel
240
230 220 210
200
19 0 18 0
17 0
16 0
15 0
14 0
13 0
12 0 110 10 0
90
80 70
60
50
40
30
20
10 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
Nominal area, m2
Figure 12.1: Nominal area versus average excavated area
To verify the expected head loss, cross section measurements at site must be taken. The cross section measurement shall include the type of supports, lining and shotcrete placed in the tunnel. All the five suggested methods (chapters 5.2.1,5.2.5,5.2.7,5.2.8, and 5.2.11), as far as possible, shall be tried to evaluate the probable friction losses that may occur.
Hydraulic head losses in an unlined pressure tunnel 84 Theoretical approach and comparison with the measured values
Singular head losses in the system depend on the layout which can be estimated as per existing approaches.
Adjustment to the area of excavation shall be done to limit the head losses.
12.2 For a TBM bored tunnel Expected type of supports can be marked approximately on the layout drawing as per geological investigations or based on judgement. The important locations are the steel ribs, if these are places within the excavated diameter.
Effective cross section areas of the tunnel can be estimated after knowing the type of supports.
In the event there is difficulty in deciding the supports, an assumption to include 5% of the friction losses towards expansion and contraction appears reasonable.
Surface roughness of shotcrete or the roughness of the bored tunnel surface can be assumed as 4 to 10 mm for preliminary design.
If rock roughness and shotcrete roughness are different, application of the composite friction formula (equation 5.10) is suggested.
To compare the results, type of supports and linings actually used in the tunnel shall have to be marked. Roughness of shotcrete and rock surface must be measured at few locations along the tunnel as accurately as possible in practice.
Colebrook-White friction formula for a rough pipe flow can be used to estimate the friction coefficient.
12.3 Some suggestions for unlined tunnels With the advent of electronic mapping and closer measurements, simulation of the tunnel surface in computer with a numerical analysis may be possible for a small stretch to determine the friction coefficient for an unlined tunnel. The computed results can be verified with a model test.
Bend loss estimation in developing flow in an unlined D&B tunnel needs further laboratory research.
Measurement of head losses in an unlined tunnel can be taken at few years interval to know the influence of the deposits in rock traps, growth of slime on the walls, deposition of fine sediments on the rough walls where dead flow zones are created.
Hydraulic head losses in an unlined pressure tunnel 85 Theoretical approach and comparison with the measured values
13 CONCLUSION Flow in a drill and blast unlined tunnel is non-uniform and not fully developed. The head losses are calculated by Darcy-Weisbach relation assuming one dimensional linear flow. In a TBM bored tunnel of sufficient length the flow will be completely developed. Modified Colebrook-White friction formula is useful to determine the value of the friction coefficient f.
Statistical variation of area or longitudinal lengths with respect to a reference line is the main parameter to assign the roughness to an unlined tunnel. Therefore, systematic data collection at site is a prime requirement to compare the estimated versus the actual head losses. Friction coefficient can vary from one stretch to another. Recording of cross section data at 5 m intervals is reasonable for most of the methods. For IBA method, the cross sections have to be taken at 0.5 m intervals.
Statistical methods proposed by Rahm, Huval, Reinius, Wright and IBA give a close approximation of the estimated absolute roughness k and the friction factor f. All these methods are to be tried at site as and when enough data from the excavated cross sections are available. When both TBM and drill & blast tunnels are in the same system, roughness measurement at few locations of the TBM stretch shall be a good reference.
Steel supports in a TBM tunnel cause expansion and contraction of flow.
Only the method of Huval is appropriate to estimate the head loss during preliminary design.
The micro-roughness in a drill & blast tunnel is greater than the macro-roughness. When the invert is lined and shotcrete is applied on the walls and crown, the macro- roughness and the micro-roughness may become equal.
An invert covering 30% of the average wetted perimeter of a drill & blast unlined tunnel can reduce head losses by 27%, while one layer of shotcrete on the walls and roofs can reduce head loss by around 10% for a tunnel of around 40 m2 area. Reduction of micro-roughness due to application of 1 layer of shotcrete of 5 to 10 cm thickness is around 10 cm. Lining the invert has more hydraulic advantage.
Equivalent roughness of an unlined drill & blast tunnel is around 45 cm. Strickler’s roughness coefficient is around 28 m1/3s-1. This corresponds to f value of 0.0813. By lining 80% of the invert with concrete and shotcreting on 45% of the surface average equivalent roughness can be brought down to 23.5 cm, and the Strickler coefficient to 33 m1/3s-1. This corresponds to f value of 0.0600.
For a preliminary design of a rock tunnel of around 40 m2 area, the method by Huval, or f values from Czarnota or f values from Chimay will give a satisfactory estimation.
Hydraulic head losses in an unlined pressure tunnel 86 Theoretical approach and comparison with the measured values
Head loss per linear meter in TBM tunnel can be more than that in a drill & blast tunnel. Measurement of roughness in the TBM section is to be made to have a good reference.
If the tunnels are concrete lined, up to 50% of the head losses due to friction can be saved in unlined D&B tunnel and TBM together. This needs another power economics study to decide for a lined or an unlined tunnel.
Hydraulic head losses in an unlined pressure tunnel 87 Theoretical approach and comparison with the measured values
Symbols, subscripts and abbreviation used in the equations
Symbols
α [-] Coefficient β [-] Coefficient δ [-] Relative overbreak coefficient (in decimal or percentage θ [-] Angle µ [-] Parameter for contraction loss δ [-] Relative overbreak (in decimal or percentage) ψ [-] Shape factor ζ [-] Co-efficient for singular head losses ∆A [m2] Area variation ∆X [m] Length variation a [-] Ratio b [-] Ratio f [-] Friction factor / friction coefficient g [m/s2] Acceleration due to gravity (9.81 m/s2 hL [mwc] Head loss general hf [mwc] Head loss due to friction hb [mwc] Head loss due to bends and curves he [mwc] Head loss due to expansion hc [mwc] Head loss due to contraction hi [mwc] Head loss at intake k [m] Equivalent absolute roughness k’ [m] Form roughness of the rock n [m-1/3s] Manning’s coefficient t [m] Overbreak v [m/s] Velocity x [-] Ratio y [-] Ratio z [-] Ratio A [m2] Area D [m] Diameter or hydraulic diameter F Functional relation K [m1/3s-1] Strickler’s coefficient L [m] Length N [-] Number of samples P [m] Wetted Perimeter Q [m3/s] Discharge R [m] Hydraulic radius Re or Re [-] Reynolds number R0 [m] Radius of curvature
Hydraulic head losses in an unlined pressure tunnel 88 Theoretical approach and comparison with the measured values
Subscripts d division k corrected values m mean, average max maximum min minimum n normal / natural / nominal i,j,m,r integer variables t theoretical
Abbreviations avg Average ch. Chainage D&B Drill and Blast H:V Horizontal : Vertical slope log Logarithm function to base 10 m asl Metre Above Mean Sea Level mean Arithmetic mean mwc Metre of water column Q Tunnelling Quality Index RMR Rock Mass Rating TBM Tunnel Boring Machine Theory Theoretical value
Hydraulic head losses in an unlined pressure tunnel 89 Theoretical approach and comparison with the measured values
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Hydraulic considerations (Section 6) – describing method [Solvik, 1984] for unlined pressure tunnels, received from Kukule Ganga Hydropower Project, Sri Lanka.
I.E. Idel’cik- coefficients de pertes de charge singulièrs et de pertes de charge par frottement, traduit par Mme. Meury, 1979.
Lecocq R. et Marin G. – Evaluation des pertes de charge des galleries d’amnee d’eau forees au tunnelier et non revetus, 1986 (collected from Prof. Schleiss, EPFL, Laussane).
Metcalf J.R. and Jordaan J.M.- Hydraulic roughness change in the Orange-Fish Tunnel: 1975-1990, The Civil Engineer in South Africa, August 1991.
Miller D. S.- Internal flow systems. BHR publication. ISBN0-947711-77-5.
Nord G.- Drilling Accuracy in Underground Construction, World Tunnelling, December 2000.
Pennington M.S- Hydraulic roughness of bored tunnel. Paper on internet, IPENZ Transactions, Vol.25, No. 1/CE,1998.
Hydraulic head losses in an unlined pressure tunnel 90 Theoretical approach and comparison with the measured values
Petrofsky A.M.- Contractor’s view on unlined tunnels, Journal of the Power Division, Proceedings of the American Society of Civil Engineers, October 1964.
Polycopie du postgrade aménagement hydrauliques, Laussane, 2001-2003 – Pertes de charge singulièrs.
Polycopie du postgrade aménagement hydrauliques, Laussane 1999-2001; Basic Hydraulics of Natural Water Courses
Reinius E. – Head losses in unlined rock tunnels; Water Power July / August 1970.
Ronn and Skog – New method for estimation of head loss in unlined water tunnels. Hydropower 1997.
Solvik O. and Tesaker E.- Floor paving in unlined hydropower tunnels, Hydropower 1997.
Spencer R.W.- Unlined tunnels of the Southern California Edison Company, Journals of the Power Division, Proceedings of the American Society of Civil Engineers, October 1964.
Hydraulic head losses in an unlined pressure tunnel 91 Theoretical approach and comparison with the measured values
Appendix A
Reference drawings
Identification Description of drawing Drawing number
A-1 General layout of water conductor system 300-GE-001-G
A-2 Longitudinal profile of the tunnel 310-GE-001-F
A-3 Intake structure, plan and sections 255-EN-002-C
A-4 Rock trap I- sections 310-DE-011-A
A-5 Rock support type A, B, and C in drill & blast 310-EX-002-F tunnel A-6 Support type D in drill & blast tunnel 310-EX-003-C
A-7 Rock support type A, B, and C in TBM 310-EX-005-F excavated tunnel A-8 Rock support type D in TBM excavated tunnel 310-EX-006-E
A-9 Junction of construction adit # 1 with drill & 320-EN-007-A blast tunnel A-10 Rock trap I 350-DE-019-A
A-11 Location of surge tank and the concrete plug 350-EN-013-A
A-12 Vertical shaft 370-EN-010-A
A-13 Transitions to vertical shaft 370-EN-011-A
A-14 Layout of penstock 370-EX-004-C
A-15 Bifurcation of penstock 370-EX-007-B
A-16 Sample geological mapping of the drill & blast 390-GE-008 tunnel A-17 Sample geological mapping of TBM tunnel 390-GE-093
Hydraulic head losses in an unlined pressure tunnel 92 Theoretical approach and comparison with the measured values
Appendix B
Calculated area and perimeter of cross sections in drill & blast tunnel
Ch. 0+010 to ch. 1+000 m Appendix B-1 Pages 1 to 3
Ch. 1+000 to ch. 2+000 m Appendix B-2 Pages 1 to 3
Ch. 2+000 to ch. 3+000 m Appendix B-3 Pages 1 to 3
Ch. 3+005 to ch. 4+000 m Appendix B-4 Pages 1 to 3
Ch. 4+000 to ch. 5+129 m Appendix B-5 Pages 1 to 3
Sample survey and cross Appendix B-6 Pages 1 to 4 section area calculation for two sections at ch. 0+940 and ch.3+455 m
Elevations of the invert and Appendix B-7 Pages 1 to 5 crown of the drill & blast tunnel
Invert width of the drill & blast Appendix B-8 Pages 1 to 5 tunnel
Hydraulic head losses in an unlined pressure tunnel 93 Theoretical approach and comparison with the measured values
Appendix C
Rock Supports in Drill & Blast tunnel
Ch. 0+016.5 to ch. 1+035 m Appendix C-1 Pages 1 to 2
Ch. 1+035 to ch. 2+000 m Appendix C-2 Pages 1 to 2
Ch. 2+000 to ch. 3+000 m Appendix C-3 Pages 1 to 2
Ch. 3+000 to ch. 4+000 m Appendix C-4 Pages 1 to 2
Ch. 4+000 to ch. 5+130 m Appendix C-5 Pages 1 of 1
Hydraulic head losses in an unlined pressure tunnel 94 Theoretical approach and comparison with the measured values
Appendix D
TBM excavated tunnel: Rock supports, net flow area, invert level, roughness of surface
Support typed in TBM Appendix D-1 Pages 1 to 4 excavated tunnel
Effective flow area in TBM Appendix D-2 Pages 1 to 4 excavated tunnel
Invert level of TBM excavated Appendix D-3 Pages 1 of 1 tunnel
Net flow area of the TBM Appendix D-4 Page 1 of 1 tunnel after placement of supports
Wall roughness of TBM Appendix D-5 Page 1 of 1 excavated tunnel
Hydraulic head losses in an unlined pressure tunnel 95 Theoretical approach and comparison with the measured values
Appendix E
Friction head losses in lined portion of the water conductor system + rock trap I
Linear losses in concrete lined Appendix E-1 Pages 1 to 3 part of the water conductor system
Linear losses in steel lined part Appendix E-2 Pages 1 to 2 of the water conductor system
Friction losses in rock trap I Appendix E-3 Pages 1 of 1
Friction losses at drill & blast Appendix E-4 Pages 1 of 1 and TBM tunnel transition
Hydraulic head losses in an unlined pressure tunnel 96 Theoretical approach and comparison with the measured values
Appendix F
Singular head losses in water conductor system
Singular head loss due to bends Appendix F-1 Pages 1 to 2 (with and without interference)
Singular head loss due to Appendix F-2 Pages 1 of 1 expansion and contraction, flow division and combination
Local head losses at rock traps Appendix F-3 Pages 1 of 1 due to obstruction
Hydraulic head losses in an unlined pressure tunnel 97 Theoretical approach and comparison with the measured values
Appendix G
Measured head losses in water conductor system
Head loss measured at site Appendix G-1 Page 1 to 3
Friction coefficient of each Appendix G-2 Page 1 to 1 stretch after correction
Hydraulic head losses in an unlined pressure tunnel 98 Theoretical approach and comparison with the measured values
Appendix H
Design charts from literature
Hydraulic resistance of unlined Appendix H-1 Page 1 of 1 rock tunnels after Rahm and modified by Hellström
Hydraulic resistance of unlined Appendix H-2 Page 1 of 2 and invert lined rock tunnels after Wright
Moody Diagram Appendix H-3 Page 1 of 1
Hydraulic head losses in an unlined pressure tunnel 99 Theoretical approach and comparison with the measured values
APPENDICES