Groundwater Seepage Rate (GSR) A New Method For Prediction of Groundwater Inflow Into Jointed Rock Tunnels 1-s2.0-S0886779816308902-Main
Groundwater Seepage Rate (GSR) A New Method For Prediction of Groundwater Inflow Into Jointed Rock Tunnels 1-s2.0-S0886779816308902-Main
Groundwater Seepage Rate (GSR) A New Method For Prediction of Groundwater Inflow Into Jointed Rock Tunnels 1-s2.0-S0886779816308902-Main
A R T I C L E I N F O A B S T R A C T
Keywords: The main purpose of this research is to introduce a new method for estimating the groundwater inflow rate into
Groundwater Seepage Rate (GSR) tunnels excavated in rock environments. The Groundwater Seepage Rate (GSR) is a novel analytical method that
Groundwater inflow has the capability to assess the rock mass potential in conducting the groundwater into tunnels. Geological and
Hydraulic conductivity hydraulic parameters and radius of the tunnel are the main parameters used in the GSR method. In this method,
Fracture and joint sets
geological parameters are defined based on the characteristics of the joint sets including the strike, number,
3D dimensional
spacing and aperture of joints of each joint set. In addition, hydraulic head and hydraulic conductivity are other
Elastic behavior
principle inputs of the proposed model. In GPR method, the rate of groundwater inflow has been evaluated in 3D
dimensions and efforts were made to obtain acceptable values by creating rational correlations among input
data. The taking account of joints condition in tunnel and the direct effect of tunnel radius, the separate study of
the joint sets and the role of fracture systems in the groundwater conductivity into excavated openings are the
main advantages of this model. According to the results of this study, GSR method can provide better estimations
of the inflow volume for rock masses with elastic behavior in which fracture systems have been developed.
Finally, in the end this paper for validation of GSR values, the results of this method were compared with the
obtained results of empirical methods and observed groundwater inflow in various geological units of the Zagros
tunnel in Iran. Additionally, the calculated value of groundwater inflow based on GSR method shows good
compatibility with empirical methods.
⁎
Corresponding author. Tel.: +98 914 400 3015; fax: +98 21 88768555.
E-mail address: Mahdi.Rasouli@yahoo.com.
http://dx.doi.org/10.1016/j.tust.2017.10.006
Received 25 December 2016; Received in revised form 17 September 2017; Accepted 18 October 2017
Available online 02 November 2017
0886-7798/ © 2017 Elsevier Ltd. All rights reserved.
M. Rasouli Maleki Tunnelling and Underground Space Technology 71 (2018) 505–517
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M. Rasouli Maleki Tunnelling and Underground Space Technology 71 (2018) 505–517
Fig. 1. The orientation, spacing and number of joint sets with respect to tunnel axis.
spacing as another geological parameter is used to determine the Where C is the ellipsoid circumference (m); a and b are the one-half
number of joints in each joint set in the whole tunnel path which is of the ellipse’s major and minor axis (m), respectively.
defined using Eq. (1) as follows. In GSR method, to calculate a parameter, can be used Eq. (4) and b is
equal to radius tunnel (m).
L sin(α ) ⎤ L sin(α ) ⎤ L sin(α ) ⎤
NJ 1 = ⎡ , NJ 2 = ⎡ . .. NJn = ⎡ 2
⎢ SJ 1 ⎦
⎣ ⎥ ⎢ SJ 2 ⎦
⎣ ⎥ ⎢
⎣ SJn ⎦ ⎥ (1) 1 2 1 ⎛ 2r ⎞
a= (L + 2r 2)0.5 = ⎜ + 2r 2⎟
2 2 ⎝ sin(α ) ⎠ (4)
Where NJ is the number of joints; SJ is the spacing of joints (m); α is the
angle between strike of joints and tunnel axis (°); L is the length of each Where a is the one-half of the ellipse’s major axis (m); L is the length
zone (m) and J1, J2… Jn are the joint sets. of each zone (m); r is the tunnel radius (m) and α is the angle be-
tween the strike of joint and tunnel axis (°).
3.1.4. Aperture of joints (AJ) c. In case the joint strike is parallel to the tunnel axis (α ∼ 0), i.e. if the
According to the proposed GSR method, the distance between the angle between joint strike and tunnel axis is smaller than the critical
walls of joints known as the aperture is directly related to the rate of angle (α < θ), (Eq. (5)), the formed shape from their intersection
water inflow into the tunnel. In this model, it is presumed that the total will not be elliptical any more. Instead, a rectangular shape is cre-
aperture surface area in tunnel circumference equals to the cross-sec- ated in which one side has been excavated. Therefore, its cir-
tion from which water flows into the tunnel. Accordingly, considering cumference can be calculated via Eq. (6).
the field aperture of joints (αF) in each joint set and the circumference
2r
of the shape resulted from the intersection of joints with the tunnel, the θ = Arc tan ⎛ ⎞ ⎜ ⎟
aperture surface area of joints (αJ) in tunnel circumference can be es- ⎝L⎠ (5)
timated for each joint set. Where θ is the critical angle (°); r is the radius of circle (m); L is the
According to different possible angles between the joint strike and length of each zone (m).
the tunnel axis (α), different shapes will be resulted as a consequence of
C = 2a + 2b or C = 2L + 2b (6)
the intersection of joints strike and the tunnel axis (Fig. 2).
Where C is the rectangular circumference (m); a and b are one-half
a. Provided that the joint strike is perpendicular to the tunnel axis of the rectangular major and minor dimensions (m), respectively.
(α = 90), the created shape from their intersection will be circular
and the circumference can be calculated via Eq. (2). By considering the circumference of the resulted shape and the
aperture of joints in the field (aF ), the aperture surface area (aJ ) of each
C = 2πr (2)
joint set can be calculated via Eq. (7).
Where C is the circle circumference (m) and r is the radius of circle (m).
aF (J 1) × C(J 1) ⎞ aF (J 2) × C(J 2) ⎞ aF (Jn) × C(Jn)
b. If the joint strike is oblique to the tunnel axis (0 < α < 90), the aJ 1 = ⎛
⎜ ⎟ , aJ 2 = ⎛ ⎜ ⎟ . .. aJn = ⎛
⎜ ⎟
⎞
⎝ 1000 ⎠ ⎝ 1000 ⎠ ⎝ 1000 ⎠
resulted shape from their intersection will be elliptical. Since the
calculation of elliptical circumference involves using complicated (7)
integral equations, it is recommended to apply Eq. (3) for calcu- Where αJ is the aperture surface area of joints (m2); aF (J ) is the aperture
lating the elliptical circumference in a more simplified way of joints in the field (mm) and CJ is the obtained circumference of shape
(Almkvist and Berndt, 1988). from intersection of joint strike with tunnel axis (m).
In order to calculate the aperture surface area of all joints in a specific
2
⎛
C = π (a + b) ⎜1 +
a−b
3 a+b ( ) ⎞
⎟
zone with length of (L), a new parameter called total aperture surface
area (AJ) is defined. This parameter can be calculated via Eq. (8).
a−b 2
⎜
⎝
10 + 4−3 ( ) a+b
⎟
⎠ (3) AJ 1 = NJ1 × aJ 1, AJ 2 = NJ2 × aJ 2 . .. AJn = NJn × aJn (8)
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M. Rasouli Maleki Tunnelling and Underground Space Technology 71 (2018) 505–517
Fig. 2. Various orientations of joint strike to tunnel axis and the possible shapes created from their intersection.
Fig. 3. Changes of hydraulic head via water seepage into tunnel over time (from a to f).
Where AJ is the total aperture surface area (m2); NJ is the number of explorative boreholes are among the most efficient ways for de-
joints; aJ is the aperture surface area of joints (m2). termining the hydraulic heads and permeability coefficient of the
Lastly, the sum of total aperture surface area (AJ) of several joint tunnel, respectively. But, in the absence of lugeon test results, the
sets can be considered equal to the total aperture surface area of all proposed equation by Barton (2008) can be employed to determine the
joint sets (AJ (total)) around the tunnel according to Eq. (9). permeability coefficient (k) of rock mass. This equation is confirmed by
the Dekchu and Bhasmey hydroelectric projects in Sikkim and in the
AJ (total) = ∑ (AJ 1 + AJ 2 + ...+Ajn ) (9) Himalayas.
Where AJ (total) is the total aperture surface area of all joint sets (m2). 0.002 ⎞ 100 1
k≈⎛ ⎜ ⎛⎟ ⎞⎛
5/3
⎞
⎝ Q ⎠ ⎝ JCS ⎠ ⎝ H ⎠ (10)
3.2. Hydraulic parameters
Where k is the permeability of the rock mass (m s−1), Q is the in situ
rock mass quality (Q = 0.1 to 100) that can be calculated by (RQD/Jn)
Based on conducted studies by numerous researchers (Jacob and
(Jr/Ja) (Jw/SRF), JCS is the joint wall compressive strength (MPa), and
Lohman, 1952; Goodman, 1965; El Tani, 2003; Perrochet (2005a,
H is the depth of a specific point under consideration below the ground
2005b) and Park et al., 2008), it can be perceived that the hydraulic
surface (m).
head (H) and permeability coefficient (k) of rock mass are other ef-
fective factors for estimating the rate of water inflow into the tunnel.
These characteristics of rock mass are highly affected by groundwater 3.3. Tunnel properties
level, characteristics of joint and fracture systems, crushed intensity of
rock mass etc. Another effective parameter for estimating the quantity of water in-
Piezometering and carrying out pumping test (lugeon test) in flow is the radius of underground structure. The effect of this parameter
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M. Rasouli Maleki Tunnelling and Underground Space Technology 71 (2018) 505–517
Fig. 4. Excavation of tunnel with fixed (a) and cone (b) hydraulic head.
Fig. 5. The effective discharge length (Le) with regards to the tunnel face advance.
has been considered directly in the geological parameters to estimate the Q = AV = Aki (11)
resulted shape from intersection of joint sets with tunnel section. 3 −1
Where Q is the groundwater inflow (m s ); V is the discharge
velocity (m s−1); A is the surface area (m2); k is the hydraulic con-
4. Calculation of groundwater inflow rate (Q) ductivity (m s−1); i is hydraulic gradient (without unit).
In the Groundwater Seepage Rate (GSR) model, the flow of 4.1. The maximum volume of water inflow into tunnel in the each zone
groundwater is presumed to be governed by Darcy’s law (1856), which (QMax)
states that the velocity of the flow is directly proportional to the per-
meability coefficient and hydraulic gradient. By defining Q as the total Based on GSR model, for estimating the maximum volume of water
volume of flow per unit time through a cross-sectional area A, Darcy’s inflow, the area of cross section from which water flows into the tunnel
law would be as follows in Eq. (11): is considered equal to the total aperture surface area (AJ (total)) in the
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M. Rasouli Maleki Tunnelling and Underground Space Technology 71 (2018) 505–517
Fig. 6. Correlation between the steady state inflow and equivalent permeability (Heuer, 2005).
excavation length of tunnel. Therefore, the maximum amount of water attention towards fluctuation of water level while excavating tunnels.
inflow into the tunnel, in a condition that the whole tunnel path is In other words, the hydraulic head is not fixed and varies as water is
excavated under a fixed hydraulic head, is considered equal to the drained during tunnel excavation process (Fig. 3).
amount of water flown into the tunnel through all joints of tunnel path . Therefore, it should be noted that the amount of water inflow ob-
It can be defined as Eq. (12). tained from Eq. (12) cannot be actual unless the whole tunnel path is
excavated under a fixed hydraulic head (Fig. 4 – groundwater surface (a
QMax = AT nkH or QMax = AJ (total) kH (12)
and Le-a)) . However, this condition is not plausible. It is due to the fact
Where QMax is the maximum value of water inflow into tunnel in that in the first stages of excavation, the depression cone is formed
each zone (m3 s−1 in L zone); AT is the surface area of tunnel (m2); n is around the tunnel and brings about variability in the hydraulic head
the fracture ratio (without unit); AJ (total) is the total aperture surface and the effective discharge length (Le) (Fig. 4 –groundwater surface (b
area of all joint sets (m2); k is the hydraulic conductivity (m s−1) and H and Le-b)). As a result, it can be inferred that the results obtained from
is the distance from the groundwater level in the tunnel (m). Eq. (14) indicate the maximum capability of the surrounding rock mass
to discharge water into the tunnel. Accordingly, the main advantage of
4.2. The volume of water inflow into unit length of tunnel (Qu) Eq. (14) is to estimate the maximum amount of water inflow into the
tunnel.
The amount of water inflow into unit length of a tunnel can be
obtained by dividing the maximum volume of water inflow (QMax) by
the tunnel length in each zone (L). (Eq. (13)). 4.3.2. The effective discharge length (Le)
All in all, the quantity of water inflow into tunnels is highly affected
QMax H
Qu = or Qu = AJ (total) K by different factors. One of the effective factors is the part of tunnel
L L (13)
length which is situated below the groundwater table, which depends
Where Qu is the groundwater inflow for unit length of tunnel (m3 on the ratio of excavation speed to drainage rate into the tunnel.
s−1) and L is the tunnel length (m). In GSR method for determining the logical volume of water inflow
into tunnel the effective discharge length (Le) is defined. It is worth
4.3. Actual groundwater inflow into tunnel (QActual) mentioning that effective discharge length (Le) is highly dependent
upon the excavation speed and permeability coefficient (k) of the sur-
In addition to the geological and hydraulic parameters (ground- rounding rock mass that can be a constant value in isotropic environ-
water head and permeability) of rock mass in the tunnel path, effective ments. As the excavation operation progresses, the specific effective
discharge length is also among the main factors affecting the calcula- discharge length (Le) also advances forward (See Fig. 5). It means that
tion process of the proposed GSR model. in the high excavation rate the and low permeability coefficient (k) of
rock mass the effective discharge length (Le) will have a higher value.
4.3.1. Fixed and variable hydraulic heads Therefore, it should be noted that the calculated quantity of water
One of the most important challenges presented by different re- based on the Le is the maximum expected inflow of water into the
searchers in the water inflow calculation process is the lack of sufficient tunnel.
510
Table 2a
Basic input parameters for calculation of groundwater inflow into Zagros tunnel in accordance with GSR method.
Name Tunnel length Length of zone Overburden, H Rock mass quality, Q Joint wall compressive Joint Sets Azimuths or Spacing, SJ Aperture, αF Number of joints
(m) (m) (m) strength, JCS (MPa) Direction to (min–max (min–max in zone, NJ
North (°) (mean)), (m) (mean)), (mm)
511
P6 7235–7350 115 165–205(1 8 5) 0.1–0.05(0.075) 25–100(62.5) J1 310 0.5–0.6(0.55) 0.5–0.6(0.55) 207
(ML-SH5) J2 14 0.42–0.52(0.47) 0.5–0.6(0.55) 140
J3 305 0.06–0.08(0.07) 1.24–1.26(1.2- 1594
5)
Bedding 210 0.25–0.35(0.3) 1.45–1.55(1.5) 125
G5 9415–9910 495 210–230(2 2 0) 0.1–0.5(0.3) 25–50(37.5) J1 50 0.2–0.3(0.25) 0.65–0.75(0.7) 35
(SH-LS4) J2 240 0.08–0.18(0.13) 0.65–0.75(0.7) 732
J3 205 0.39–0.41(0.4) 1.99–2.01(2) 505
Bedding 50 0.3–0.4(0.35) 0.65–0.75(0.7) 25
Zone 1- GEOLOGICAL PARAMETERS 2- HYDRAULIC PARAMETERS 3- TUNNEL PROPERTISE Groundwater inflow into tunnel, Qt (L s-1)
Name Aperture area Total Fracture ratio, n Hydraulic head, Hydraulic Radius, r (m) Axis Orientation - For each joint sets For unit length For total zone
surface of one aperture area (%) H (m) conductivity, Trend (°)
joint, AJ (mm2) surface of one k (m s-1)
joint, AJ(total)
(m2)
4.3.3. The actual and expected water inflow into tunnel (QActual)
In the GSR model, actual water inflow into tunnel (QActual) can be
For total zone
calculated via multiplying the amount of water inflow for the unit
length of the tunnel (Qu) by the effective discharge length (Le) ac-
50.6
37.4
86.7
cording to Eq. (14).
H
Q Actual = Le QU = Le ⎛AJ (total) k ⎞
⎝ L⎠ (14)
Groundwater inflow into tunnel, Qt (L s-1)
0.325
0.175
of all joint set (m2) and Le is the effective discharge length under
groundwater table (m).
The obtained equations for estimating the water inflow into tunnel
For each joint sets
SH-ML: Shale, Marly Limestone (Pd formation), SH-LS: Shale, Shaly Limestone, Sandstone (Gu formation), LI: Limestone (LI formation), ML-SH: Marly Limestone, Shale (Pd formation).
a ×C × sin (α )J1
⎛ F (J 1) (J 1) +⎞
1000SJ 1
⎜a ⎟
2.848
1.439
0.001
0.080
0.046
0.079
0.020
0.000
0.014
0.012
0.258
0.041
0.023
0.061
0.074
0.017
F (J 2) × C(J 2) × sin (αJ 2)
+⎟
Q Actual =⎜ 1000SJ 2 kHLe
⎜ ...+ ⎟
⎜ aF (Jn) × C(Jn) × sin (αJn) ⎟
⎜ ⎟
Axis Orientation -
⎝ 1000SJn ⎠
(15)
Trend (°)
Where QActual is the actual groundwater inflow into tunnel in the ef-
3- TUNNEL PROPERTISE
fective discharge length (m3 s−1 m); aF (J ) is the aperture of joints in the
field (mm); aJ the is the aperture surface area of joints (m2); CJ is the
obtained circumference of shape from intersection of joint strike with
Radius, r (m)
tunnel axis (m); SJ is the spacing of joints (m); k is the hydraulic con-
ductivity (m s−1); L is the tunnel length (m) and H is the distance from
the groundwater level in the tunnel (m) and J1, J2… Jn are the joint
sets.
6.60E−06
6.60E−06
9.24E−06
Hydraulic
k (m s-1)
2- HYDRAULIC PARAMETERS
145
140
165
1.67%
0.54%
headthe ratio of flow rate to hydraulic head q/Hs (Fig. 6), relationship
(%)
(m2)
60.2
30.4
15.7
18.8
10.9
18.5
32.1
19.7
24.2
4.7
1.8
1.8
1.5
5.1
7.6
5.4
In this section, GSR method results have been compared with the
inflow rate obtained by the empirical method (Heuer, 1995) and actual
joint, AJ (mm2)
surface of one
Aperture area
condition in the Zagros tunnel. This tunnel is located in the western part
of Iran and is under construction to convey water from Sirvan river
112237
156879
219632
219632
63149
74653
63313
24154
63558
10857
20130
40542
26858
47894
8642
50 km that has been divided into two lots of (I) and (Π) with length of
Table 2a (continued)
(ML-SH5)
(SH-LS4)
(TBM). From the geological aspect, the region which is being excavated
Name
G5
P5
P6
512
Table 2b
The remaining contents of Table 2a.
Name Tunnel length Length of zone Overburden, H Rock mass quality, Q Joint wall compressive Joint Sets Azimuths or Spacing, SJ Aperture, αF Number of joints
(m) (m) (m) strength, JCS (MPa) Direction to (min–max (min–max in zone, NJ
North (°) (mean)), (m) (mean)), (mm)
513
Zone 1- GEOLOGICAL PARAMETERS 2- HYDRAULIC PARAMETERS 3- TUNNEL PROPERTISE Groundwater inflow into tunnel, Qt (L s-1)
Name Aperture area Total aperture area Fracture ratio, n (%) Hydraulic head, Hydraulic Radius, r (m) Axis Orientation - For each joint sets For unit length of For total zone
surface of one surface of one joint, H (m) conductivity, k (m Trend (°) tunnel
joint, AJ (mm2) AJ(total) (m2) s-1)
SH-LS: Shale, Shaly Limestone, Sandstone (Gu formation), LI: Limestone (LI formation).
M. Rasouli Maleki Tunnelling and Underground Space Technology 71 (2018) 505–517
for Le ∼ 50 m (L/s)
157.5–232.5(1 9 5)
In this research, investigations were conducted in four steps: In the
295–440(367.5)
10.5–14.5(12.5)
first step, 13 zones were selected randomly among excavated zones of
260–350(3 0 5)
215–355(2 8 5)
165–255(2 1 0)
37.5–42.5(40)
3.5–9.5(6.5)
5.5–10.5(8)
the Zagros tunnel. In the second step, geological and hydraulic para-
1–2(1.5)
1–2(1.5)
meters in the GSR method were determined based on joint mapping
from rock outcrops in the field and water pressure tests (lugeon test) in
the boreholes, respectively. The magnitude of water inflow was calcu-
lated based on GSR and Heuer methods for unit length and 50 m length
Observed (Actual)
during excavation of every 50 m length in each zone of the tunnel path.
0.02–0.04(0.03)
0.02–0.04(0.03)
0.07–0.19(0.13)
0.11–0.21(0.16)
0.21–0.29(0.25)
0.75–0.85(0.8)
3.15–4.65(3.9)
Subsequently, the average measured values considered as actual volume
5.9–8.8(7.35)
4.3–7.1(5.7)
3.3–5.1(4.2)
5.2–7(6.1)
inflow into the zone (In the P1 zone with 735 m length, for example, the
first zone was divided into 15 parts (L = 50 m) and then the amount of
water inflow was measured and recorded for each part and the average of
these parts were finally determined as actual inflow volume into the P1
zone). Fig. 7 shows the water inflow volume measured for each of the zones.
119.58
137.50
217.50
229.58
240.63
33.92
with each other. But for some cases, differences were observed
0.98
2.57
3.38
3.27
5.50
which are due to the effect of geological parameters in the GSR
Empirical method (Heuer, 1995)
B. In the limestone units (Ki2, Ki7, Ki10 and Ki12), the magnitude of
length of tunnel (L/s/m)
water inflow volume calculated using GSR method is higher than the
empirical method. it can be argued that in rock masses with elastic
behavior (such as limestone), more actual results can be obtained by
taking the role of joint and fracture systems into consideration. This
fact is verified according to a drawn comparison between the water
0.02
0.05
2.39
0.07
0.07
0.11
0.68
2.75
4.35
4.59
4.81
inflow values calculated by the GSR method and actual observed
ones for Ki units (Fig. 8).
tunnel for Le ∼ 50 m (L/s)
Groundwater inflow into
Groundwater inflow rate for the unit length of Zagros tunnel based
Groundwater inflow Calculated into the Zagros tunnel by dint of GSR and empirical methods.
162.0
360.2
459.5
249.3
the Ki2 (LI2), Ki7 (LI2), Ki10 (LI2), Ki12 (LI2) and Ki21 (LI2) units
11.2
16.3
46.5
2.1
2.7
8.8
prove that the amount of water inflow into the tunnel is at a critically
high level and can be dangerous for the personnel and also hinder the
Groundwater inflow for unit
excavation process.
length of tunnel (L/s/m)
Fig.9 presents the results of actual observed water inflow rate and
those calculated using GSR and empirical methods. The drawn com-
parison between these three methods demonstrates the capability of the
proposed GSR method for estimating the groundwater inflow rate into
Groundwater Seepage Rate (GSR)
the tunnel. Indeed, the values obtained via GSR method are close to
0.04
0.05
6.94
0.22
0.33
0.18
0.93
3.24
7.20
9.19
4.99
actual conditions.
Similar to other methods, the GSR model also has some limitations
tunnel (L/s)
2640.2
4538.6
5468.4
5000.2
50.6
37.4
86.7
tioned as follows:
P1 (SH-ML1)
P5 (ML-SH5)
P6 (ML-SH5)
G5 (SH-LS4)
G8 (SH-LS4)
Ki7 (LI2)
G1 (SH-
Zone
b) The inability to carry out joint studies on the intense crushed and
faulted regions.
514
M. Rasouli Maleki Tunnelling and Underground Space Technology 71 (2018) 505–517
Fig. 7. The water inflow volume measured for every 50m length of zones.
Fig. 8. The groundwater inflow rate for unit length of the Zagros tunnel (Qu) using GSR method in comparison to the values obtained by empirical methods in different geological zones.
c) The inability to predict the volume of groundwater inflow into the 7. Conclusion
tunnels containing large and buried fractures.
d) The difficulties for accurate determination of the effective discharge Groundwater Seepage Rate (GSR) is a new method introduced to
length (Le) in the tunnel path which requires doing statistical ana- estimate the amount of groundwater flow into tunnels excavated in
lyses and creating logical relationship on the obtained data from rock. The main inputs in this method are geological and hydraulic
different tunnels around the world. This can be fulfilled in the parameters of the tunnel path. The GSR method is generally based on
coming years. the effect of rock mass joints and fractures in conducting the
515
M. Rasouli Maleki Tunnelling and Underground Space Technology 71 (2018) 505–517
Fig. 9. The observed water inflow rate into Zagros tunnel in comparison with the obtained results using GSR and empirical methods for excavated units.
groundwater flow into tunnels. Attempts were made to correlate geo- 614–695 (In Spanish).
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Ernst & Sohn, Berlin.
ingly. Heuer, R. E., 1995. Estimating Rock Tunnel Water Inflow. RETC Proceedings, p. 41–60
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Author's Note and Reminders Heuer, R.E., 2005. Estimating rock tunnel water inflow, Rapid Excavation and Tunneling
Conference, pp. 394–407 (Chapter 30).
Hwang, J.-H., Lu, C.-C., 2007. A semi-analytical method for analyzing the tunnel water
In the end, I would like to thank the enthusiastic researchers in the inflow. Tunn. Undergr. Space Technol. 22, 39–46.
field of groundwater in underground spaces and the related topics. It Jacob, C.E., Lohman, S.W., 1952. Nonsteady flow to a well of constant drawdown in an
extensive aquifer. Trans. Am. Geophys. Union 33 (4), 559–569.
should be noted that GSR model is a recently adopted method for es- Jang, H.I., Chang, K.M., Lee, C.I., 1996. Groundwater flow analysis of discontinuous rock
timating the groundwater inflow in tunnels which is introduced for the mass with probabilistic approach. In: Proc. Korea-Japan Joint Symp. Rock Eng.,
first time in this paper. Therefore, it can be improved by similar in- Seoul, Korea, pp. 519–523.
Karlsrud, K., 2001. Water control when tunneling under urban areas in the Olso region.
vestigations by interested researchers throughout the world in the
NFF Publication 12 (4), 27–33.
coming years. Knutsson, G., Olofsson, B., Cesano, D., 1996. Prognosis of groundwater inflows and
drawdown due to the construction of rock tunnels in heterogeneous media. Res. Proj.
Rep. Kungl Tekniska, Stokholm.
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