Eurock 2012 Page 1 Design aspects for concrete lined vertical shafts for hydropower constructions H.Wannenmacher & M. Bauert Amberg Engineering AG. Sargans, Switzerland F. Amann ETH Zürich, Geological Institute, Zürich, Switzerland Abstract: Hydropower plants are of great relevance for European energy production. Vertical shafts in comparison to inclined shafts may serve as a cost alternative in case of favourable ground conditions. Vertical shafts have a higher ground coverage compared to surface parallel inclined shafts. The increased rock mass cover and therefore higher in-situ stress magnitudes (e.g. decreasing risk for hydro-fracturing) may allow unlined solutions instead of cost intensive steel lining (providing that water losses are economically acceptable). Both, concrete lining and rock mass are subjected to transient loading conditions during operation. Depending on strength and thickness of the concrete lining, unreinforced concrete tends to crack more easily and intense upon exceeding a critical effective internal water pressure. The structural integrity is associated with the number of hydraulically induced cracks and the crack width at a given internal water pressure. The design of reinforcement depends on the bedding of the lining (e.g. deformability of the rock mass), the hydraulic conductivity of the rock mass in relation to the concrete lining, the external and internal water pressure, and the in-situ state of stress. The paper presents a procedure to determine the stress state within a concrete liner and the surrounding rock mass. Furthermore, the reliance and application of the European Standard (Eurocode EC 2) for the geotechnical and structural design of concrete lined pressure shafts is discussed. Theme: Design Methods Keywords: Hydropower Construction, Shaft Lining, Eurocode, Analytical Solution
Transcript
Eurock 2012 Page 1
Design aspects for concrete lined vertical shafts for hydropower constructions
H.Wannenmacher & M. Bauert Amberg Engineering AG. Sargans, Switzerland F. Amann ETH Zürich, Geological Institute, Zürich, Switzerland
Abstract: Hydropower plants are of great relevance for European energy production. Vertical shafts in comparison to inclined shafts may serve as a cost alternative in case of favourable ground conditions. Vertical shafts have a higher ground coverage compared to surface parallel inclined shafts. The increased rock mass cover and therefore higher in-situ stress magnitudes (e.g. decreasing risk for hydro-fracturing) may allow unlined solutions instead of cost intensive steel lining (providing that water losses are economically acceptable). Both, concrete lining and rock mass are subjected to transient loading conditions during operation. Depending on strength and thickness of the concrete lining, unreinforced concrete tends to crack more easily and intense upon exceeding a critical effective internal water pressure. The structural integrity is associated with the number of hydraulically induced cracks and the crack width at a given internal water pressure. The design of reinforcement depends on the bedding of the lining (e.g. deformability of the rock mass), the hydraulic conductivity of the rock mass in relation to the concrete lining, the external and internal water pressure, and the in-situ state of stress. The paper presents a procedure to determine the stress state within a concrete liner and the surrounding rock mass. Furthermore, the reliance and application of the European Standard (Eurocode EC 2) for the geotechnical and structural design of concrete lined pressure shafts is discussed. Theme: Design Methods Keywords: Hydropower Construction, Shaft Lining, Eurocode, Analytical Solution
Eurock 2012 Page 2
INTRODUCTION
Modern pump storage schemes allow immediate production of peak current upon demand. Due to the availability of modern shaft construction methods, vertical penstocks may serve as an alternative to common inclined shaft solutions with steel lining. In general, vertical shafts have a higher ground coverage compared to surface parallel inclined shafts. The increased rock mass cover and therefore higher in-situ stress magnitudes favour unlined shaft constructions instead of cost intensive steel lining solution. Even though, economic considerations may favour the implementation of a concrete lining in order to minimize head losses and thus allow smaller excavation diameters and the abdication of a rock trap.
Such a decision requires a detailed ground investigation program, which is in particular focused on in-situ stress estimates, the sensitiveness of erosion and alteration of the rock mass due to water flow, and the hydraulic conductivity of the rock mass to account properly for the long-term performance of the shaft during operation. The pending decision to incorporate a concrete lining in favour of an unlined solution often depends on the cost effectiveness of constructional aspects such as reduced excavation diameter, minimized head losses, and maintenance of a rock trap. Economic considerations may be in favour of a reinforced concrete lining for pressure shaft construction. The reinforcement is hereby considered to evenly distribute hydraulically induced cracks, and to limit crack width. The design of concrete lining can be facilitated with either numerical approaches or analytical solutions, which account for transient loading conditions of the concrete lining and rock mass during operation (Schleiss 1997, Fernandez 1997). In this paper the applicability of different analytical design approaches are compared, which allow determining the crack development in a concrete lined pressure shaft.
VERTICAL PRESSURE SHAFT IN A DENSE ROCK MASS
A vertical pressure shaft with sufficient ground coverage was utilized to investigate the influence of different design approaches (Table 1) on cracking of the lining. This example is based on an actual hydropower project and was modified for the purpose of this study. The rock mass is considered to be isotropic, homogeneous and continuous, and thus the influence of discontinuities on the lining design is neglected. The layout of the pump storage scheme is shown in (Figure 1); the pressure shaft is about 600 m in length. The excavation diameter of the pressure shaft is do = 6.6 m. The lining consists of reinforced concrete with a thickness of 30 cm. The rock mass support (e.g. shotcrete lining) was neglected for the design consideration in this study. The maximum transient hydraulic pressure (dynamic pressure ratio = 1.25) at the bottom of the shaft is 75 bar.
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600
m
PRESSURE TUNNEL
SURGE SHAFT
CAVERN STRUCTURE
Pre
ssu
re S
haft
Ø =
6.0
m
SURGE SHAFTGROUNDWATER TABLE
Figure 1. Longitudinal section along the water conduit
DESIGN APPROACH
In general the rock mass serves as an integral part of the lining design. The design approach considered in this study consits of a composite 3-layer system involving the concrete lining, the rock mass influenced by seepage flow, and the rock mass which is not affected by seepage flow (Figure 3). All three layers of this system are faced to various stress states which were analysed in terms of two different design approaches (Table 1). In principle both design approaches are only relevant when the hydraulic conductivity of the lining is lower than the hydraulic conductivity of the rock mass.
Table 1. Comparison of design approaches
Design Approach I Birckenmaier (1983)
Design Approach II EC 2 (2005)
Primary Stress State -
Secondary Stress State Feder and Arwanitakis (1976) Feder and Arwanitakis (1976)
Internal Water Pressure acting
on Concrete Lining and Rock
Mass
Schleiss (1997) Birckenmaier (1983)
Schleiss (1997) EC 2 (2005)
Tertiary Stress State Sum of secondary stress state and internal water pressure action
on concrete lining and rock mass
Primary Stress State
The primary state of stress is typically influenced by the topography, the tectonic history, landform developement and the elastic properties of the rock mass. The stress ratio is considered to be K0 = 1 in this study. The vertical stress at the bottom of the shaft is 21.6 MPa. The rock mass parameters considered are given in Table 2.
Eurock 2012 Page 4
Table 2. Characteristic Rock Mass Properties
Young’s modulus: Erock 34’000 [MPa]
Poisson’s ratio: νrm 0.3 [-]
Specific weight: γrm 27.0 [kN/m3]
Friction angle: ϕrm 42.0 [°]
Cohesion: crm 10.0 [MPa]
Stress ratio K0 1.0 [-]
Hydraulic conductivity: krm 8E10-7 [m/s]
Secondary Stress State
As a consequence of excavation a secondary stress state evolves. The radial and tangential stresses were determined using the analytical solution of Feder and Arwanitakis (1976). The total tangential and radial stresses within the rock mass are shown in Figure 2. Although stress redistribution takes place as a consequence of the excavation, the rock mass in this study behaves elastic due to it’s high strength.The elastic state of the rock mass allows for a direct superposition of the subsequent stress states during operation. In case of undesired zones of weakness the rock mass must be treated to achieve the desired conditions with regard to deformation behaviour and hydraulic conductivity (e.g. grouting).
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
Str
ess
[MP
a]
Distance from Tunnel Centre [m]
Radial Stress (σr)
Tangential Stress (σt)
Radial Stress (σr)
Tangential Stress (σt)
Figure 2.: Radial and tangential stresses after Feder and Arwanitakis (1976).
Internal Water Pressure acting on Concrete Lining and Rock Mass
The shaft lining faces a high static internal water pressure, which is superimposed by dynamic loads during operation. When the internal water pressure exceeds the sum of the tangential stress and the tensile strength of the concrete lining, cracking will occureinstantaneously.
The positive effect of the external pressure (groundwater pressure) counteracting the internal water is not considered in this study to account for the drawdown of the watertable during construction (conservative approach). The transient recovery of the fluid pressure in the rock mass after excavation depends on the internal water pressure, the water losses of the pressure shaft (e.g. hydraulic conductivity of the concrete lining) and the hydraulic properties of the rock mass. The characteristic properties of the concrete lining including notation for the reinforcement are given in Table 3.
Eurock 2012 Page 5
Table 3. Characteristic Properties Of The Concrete Lining
Nominal steel coverage: cnom 5.0 [cm] Diameter steel bars: D 14 [mm] Spacing: a 15 [cm] No. reinforcement layers: n 2.0 [-]
Displacements and effective stresses within the rock mass and concrete lining were calculated using the theory of the thick wall cylinder considering three different layers (Schleiss, 1986). Figure 3 illustrates the three different layers with concrete lining, the rock mass around the tunnel which is influenced by seepage flow, and the rock mass which is not affected by seepage flow.
r i
ro
Rpi
u(ro)
u(R)po
pF(ro)
12
3
pF(R) pR
pF(R)..
PR……..
pF(ro)..
po……
R…….
ri…..…
ro…….
pi…….
u(ro)…
u(R)…
Contact stress at boundary of seepage
External water pressure
Contact stress acting at the joint concrete
to rock mass
Hydraulic water pressure acting at the
interface of concrete to rock mass
Radius of seepage induced zone
Radius internal
Radius external
Internal water pressure
Displacement at the joint concrete to rock
mass
Displacement at boundary of seepage
Figure 3.: Layered lining system (concrete lining / rock mass) under internal and external water pressure (Schleiss, 1986)
This system comprises three unknown parameters po, pF(ro) and pF(R) (see Figure 3), which can be determined by three equilibrium conditions as stated by Schleiss (1986). The equilibrium conditions hereby consider:
Equal displacement at the interface (outer radius ro) of the concrete lining and
rock mass. Equal displacement at the boundary at distance “R” from the tunnel, which
separates the zone affected by seepage flow from the zone not affected by seepage flow.
Identical water flux through the liner depending on the number of cracks (cracks) and crack widths (2a) and the rock mass influenced by seepage flow.
ioww
oiLiner rr
cracksappq
12
2 3
(1)
ow
rmRoMassRock
rRg
kppq
ln
2
(2)
Eurock 2012 Page 6
The determination of the number of cracks (cracks) and crack widths (2a) is based on two different design approaches:
Design Approach I: according to Birckenmaier (1983); this model was
suggested by Schleiss (1997) for the general design of reinforced concrete lining.
Design Approach II: according to EC2 (2005). Figure 4 and Figure 5 show the effective stress in the liner and rock mass affected
by the internal water pressure considering a linear water pressure decrease in the liner and a logarithmical water pressure reduction in the rock mass, which is influenced by seepage flow. The effective radial stress component can be expressed by equation (3). Crack initiation within the lining leads to an abrupt loss of the tangential stress component accompanied by an increased hydraulic conductivity of the lining (see table 4). The increased conductivity of the lining considers a linear water pressure distribution along the cross section, expressed by (4).
)(1)(
1
11
13
2)(
2
2
22
2
2
2
22
2
oFo
io
ioF
o
i
oo
io
i
c
iocr
rpr
r
rr
rrp
rr
rr
r
r
rr
rppr
(3)
io
iooi
rr
rrprrprp
)( (4)
The effective radial and tangential stresses in the rock mass, which is influenced
by seepage flow were derived using equation (5) and equation (6). Assuming axisymmetric conditions the water pressure distribution along a cross section of the rock mass, which is influenced by seepage flow was calculated using equation (7).
)(1)()(
ln
ln1
12)(
2
2
22
2
2
2
22
2
Rpr
R
rR
rrpRp
rR
rR
r
R
rR
rppr
Fo
ooFF
oo
o
rm
oRr
(5)
)(1)()(
ln
21ln1
12)(
2
2
22
2
2
2
22
2
Rpr
R
rR
rrpRp
rR
rR
r
R
rR
rppr
Fo
ooFF
o
rm
o
o
rm
oRt
(6)
rR
rrpr
Rprp o
Ro
ln
lnln)(
(7)
Eurock 2012 Page 7
-12.0
-10.0
-8.0
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
3 3.3 3.6 3.9 4.2 4.5 4.8 5.1 5.4 5.7 6
Str
ess
[MP
a]
Distance from Tunnel Centre [m]
Datenreihe und weite
Datenreihen3
Datenreihen5
Radial Stress (σr)
Tangential Stress (σt)
Water Pressure (p)
Figure 4.: Effective stresses in the liner and rock mass, which are affected by the internal
water pressure according to Birckenmaier 1983).
-12.0
-10.0
-8.0
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
3 3.3 3.6 3.9 4.2 4.5 4.8 5.1 5.4 5.7 6
Str
ess
[MP
a]
Distance from Tunnel Centre [m]
Datenreihe und weite
Datenreihen3
Datenreihen5
Radial Stress (σr)
Tangential Stress (σt)
Water Pressure (p)
Figure 5.: Effective stresses in the liner and rock mass affected by the internal water
pressure (according to EC2).
The critical internal water pressure leading to systematic cracking in this study was found to be 14.3 bar. Cracking of the lining due to shrinkage prior to watering up as well as a temprature decrease due to watering up was not considered.
The number of hydraulically induced cracks, the crack width and average crack spacing calculated from the two different design approaches (e.g. BM and EC2) are summarized in Table 4. The calculation of the hydraulic conductivity of the cracked concrete is based on the initial hydraulic conductivity of the uncracked concrete (k = 10e-8 m/s) superimposed by the hydraulic conductance of individual cracks (e.g. number of cracks and crack width).
The calculation based on EC2 revealed a slightly higher crack spacing and a lower crack intensity. The total tangential elongation of 5.8 mm was calculated after Schleiss (1986) in both design approaches. The higher the crack spacing at equal elongation, as
Eurock 2012 Page 8
derived within the EC2 approach, as higher is the crack widths and the hydraulic conductivity.
Table 4. Comparison of crack characteristics after EC2 and BM
EC2 BM Units
Number of cracks - 46 54 [-] Average spacing between cracks sr 43.0 36.7 [cm] Average crack width 2a 0.13 0.11 [mm] Hydraulic conductivity (cracked concrete liner): kc_cracked 4E10-6 3E10-6 [m/s]
Tertiary Stress State
The tertiary stress state evolves during watering up of the pressure shaft. Due to the linear elastic behavior of the rock mass, a point-symmetric modeling was utilized to calculate the tertiary stress state in this study. Figure 6 shows both, the effective stresses in the concrete and the rock mass in vicinity of the pressure shaft. The effective tangential stress in the rock mass is reduced by the amount of the pore pressure.
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
3 3.3 3.6 3.9 4.2 4.5 4.8 5.1
Str
ess
[MP
a]
Distance from Tunnel Centre [m]
Sec Radial Stress…..… Sec Tangential Stress ..
Ter Radial Stress-------- Ter tangential stress
Datenreihen5
2nd Radial Stress (σr)
3rd Radial Stress (σr)
Water Pressure (p)
2nd Tangential Stress (σt)
3rd Tangential Stress (σt)
Figure 6.: Final effective stresses in the liner and the rock mass based on the combined
model of Feder & Arwanitakis (1976) with Schleiss (1997).
Eurock 2012 Page 9
INFLUENCES OF HYDRAULIC CONDUCTIVITY AND GROUND WATER TABLE
The Operational Phase
During operation, water losses through the lining highly depend on the hydraulic conductivity of the rock mass and the concrete lining, as well as on the height of the groundwater table. Figure 7 shows the proportional water loss within the rock mass in comparison to the ratio of the hydraulic conductivity lining / rock mass.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0.001 0.01 0.1 1 10 100
Pro
po
rtio
nal
Wat
er L
oss
wit
hin
th
e R
ock
Mas
s
Ratio of the Hydraulic Conductivity Lining / Rock Mass [-]
V = 5
V = 10
V = 15
V = 20
Figure 7.: Proportional Water Losses within Rock Mass
Within a ratio of the hydraulic conductivity lining / rock mass lower than 0.01 the losses depend solely on the lining. Exceeding a ratio of 0.1 the losses are solely governed by the rock mass. Within the transition zone with a ratio, ranging from 0.01 to 0.1 the dependence of the loss is a mixed mode. (Gysel 1984, Schleiss 1997, Fernandez 1997, Seeber 1999). According to Gysel, (1984) a water loss of 1 l/skmbar is torable for pressure shafts and tunnels. Table 5 summarizes the coherence of the rock mass conductivity (krm= 8E10-7 m/s) considered, in regard to the groundwater table and the conductivity of the lining. Furthermore, for each examined combination of the lining conductivity and groundwater table, the desired rock mass conductivity for acceptable water losses is given.
Table 5.: Compilation of water losses in addiction to concrete conductivity and groundwater table.
Concrete Lining
Conductivity Concrete
Conductivity Rock Mass
Groundwater Table
Water Loss Desired R.M.
Conductivity for accept. Water Losses
[m/s] [m/s] [m] [l/skmbar] [m/s]
cracked 3E10-6 8E10-7 0 22 3E10-8
uncracked 1E10-8 8E10-7 0 5.2 4E10-8
cracked 3E10-6 8E10-7 700 1.9 4E10-7
uncracked 1E10-8 8E10-7 700 0.4 -
oio
i
r
R
rr
rV
Eurock 2012 Page 10
Obviously the water losses exceed the proposed limit of Gysel (1984) in the case of a cracked lining considering a groundwater table, and in case of a uncracked lining considering no groundwater table.Ground improvements (e.g grouting) must be considered to achieve the desired rock mass conductivity and thus acceptable water losses.The desired rock mass conductivity is in the range of 3E10-8 m/s in case of a
cracked concrete lining, and 4E10-8 m/s for an uncracked concrete lining. The water losses decrease markedly when an external groundwater table exists. Nevertheless the criteria for the water losses are not yet met with a cracked lining, neglecting natural sealing over time. The desired rock mass conductivity for the cracked lining is in this case 4E10-7 m/s.
The Dewatering Phase
Any ground water pressure acting on the lining during a dewatering phase leads to compression of the concrete lining. The compressive stress (σc) within the lining depends on the height of the groundwater table and on the ratio of the hydraulic conductivity of the lining / rock mass. A ratio of ~ 0.11 is demanded for the given groundwater table of 700 m and a design strength of the concrete lining of fcd = 20 MPa in this study, to avoid damage of the concrete lining. Figure 8 illustrates the design process, which results in a minimum hydraulic conductivity of 1E10-7 m/s, which is only met by a cracked concrete lining. Controlled cracking of the concrete lining is therefore demanded to avoid substantial failure of the shaft lining during a dewatering phase.
Figure 8.: Design Chart for Dewatering of Concrete Lined Shaft
10 oio
i
r
R
rr
r
Eurock 2012 Page 11
DISCUSSION
As soon as the internal water pressure exceeds the sum of the tangential stresses and the tensile strength in the concrete lining, cracks will be initiated. The hydraulic conductivity of the lining increases as a consequence of systematic cracking, but is of subordinate relevance, since the hydraulic conductivity of the rock mass and the actual groundwater table fluctuation govern the overall water losses from the shaft. Nevertheless, the methods for computing crack development are of importance for the problem statement, especially in case of an overall drawdown of the groundwater table, a very low groundwater table and in case of a very low hydraulic conductivity of the rock mass. The reinforcement is relevant for the lining stability to in terms of a limited crack development (e.g. number of cracks and crack width). The design process of a concrete lined shaft demands for cracked lining to avoid substantial failure of the shaft lining during a dewatering phase. Nevertheless, the crack development must be balanced to comply with acceptable water losses during operation.
REFERENCES
Birckenmaier, M. 1983. Über Nachweise im Gebrauchszustand, Schweizer Ingenieur und Architekt , No6.
Feder, G. and Arwanitakis, M. 1976. Zur Gebirgsmechanik ausbruchsnaher Bereiche tiefliegender Hohlraumbauten (unter zentralsymmetrischer Belastung), Berg- und Hüttenmännnische Monatshefte, H.4
Fernandez G. 1994. Behavior of Pressure Tunnels and Guidelines for Liner Design, Journal of Geotechnical Engineering. Vol 120, No.10
Gysel, M. 1984. Bestimmung der Felsdurchlässigkeit aufgrund von Stollenabpressversuchen, Wasser, Energie, Luft 76, H. 7/8.
Schleiss, A. 1997. Design of reinforced concrete linings of pressure tunnels and shafts, Hydropower and Dams, Issue Three.
Schleiss, A. 1985. Bemessung von Druckstollen, Teil I, Literatur, Grundlagen, Felshydraulik insbesondere Sickerströmungen durch Auskleidung und Fels. ETHZ, VAW, Mitteilung 78
Schleiss, A. 1986. Bemessung von Druckstollen, Teil II, Einfluss der Sickerströmung in Betonauskleidung und Fels, mechanisch-hydraulische Wechselwirkung, Bemessungskriterien. ETHZ, VAW, Mitteilung 86
Seeber G. 1999: Druckstollen und Druckschächte – Bemessung– Konstruktion – Ausführung. Stuttgart: Enke im Thieme Verlag.
