2D and 3D finite element analysis of underground openings in an
inhomogeneous rock mass
K.R. Dhawana, D.N. Singhb,*, I.D. Guptaa
a
b
Central Water and Power Research Station, Khadakwasla, Pune 411 024, India
Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
Abstract
The finite element analysis of the underground openings excavated for Koyna hydroelectric project, Maharashtra, India, has been
conducted. 2D and 3D models have been developed assuming that the rock mass obeys Drucker–Prager failure criterion. The
computed deformations and the stress distribution, around these openings, have been compared with the in situ measurements. The
study reveals that the 2D elasto-plastic analysis underestimates the deformations. On the other hand, the 3D elasto-plastic analysis
yields results, which compare reasonably well with the in situ measurements. The effect of weak zones in the rock mass and creation
of multiple cavities in the nonhomogeneous rock mass has also been considered in the analyses. Such a study is found to be very
helpful for evaluating the stability of underground openings when extensive realistic input data is available for nonhomogeneous
rock mass.
1. Introduction
Several underground hydroelectric projects are under
construction for generation of power by harnessing river
waters. The creation of underground openings results in
significant changes in stresses in the rock mass. In order
to assess the stability of such openings it is necessary
that the stresses and deformations in the rock mass be
accurately analyzed by adopting the realistic rock mass
parameters, in the analysis, rather than using their
approximate or average values [1]. However, limitation
in modeling is expected due to the difficulties associated
with obtaining realistic input data. As such, in the recent
past, numerical simulation is being preferred over the
modeling wherein the rock mass properties are established either with the help of empirical methods, based
on hundreds of case histories, or rational approaches,
based on mainly laboratory or in situ testing [2].
The evaluation of stress distribution, around the
underground openings, is important for designing a
proper support system and must incorporate (diverse)
material properties, presence of discontinuities, nonhomogeniety and state of in situ stresses existing in the
rock mass. In addition to this, nonlinear constitutive
behavior of the rock mass and potentially large strain
deformations must also be considered. In such a
situation, finite element analysis is found to be quite
efficient in handling such complexities [3]. A critical
review of the available literature, on stability analysis of
underground openings, indicates that mostly analysis of
the underground openings are based on the rock mass
parameters which are generally assumed or are representative of the rock mass [4–14]. However, sufficient
information on 3D finite element nonlinear analysis, of
nonsymmetrical openings is not available in the
literature. As such, for an efficient design of underground openings, realistic behavior of materials and an
appropriate model for the analysis must be adopted.
With this in view, relative suitability of 2D and 3D
elasto-plastic analyses has been investigated for a set of
four underground openings that exist at Koyna hydroelectric project, Koyna, Maharashtra, India, by adopting in situ and laboratory rock mass properties. The
computed deformations have been compared with the in
situ deformations, measured by borehole extensometers.
The study reveals that the deformations obtained by 2D
218
Nomenclature
sv
sh
r
Em
in situ stress (vertical)
insitu stress (horizontal)
density of the rock mass
modulus of deformation
analysis are less as compared to the borehole extensometer results, whereas 3D analysis yields a better
matching.
2. Statement of the problem and field investigations
The four nonsymmetrical underground openings, as
shown in Fig. 1, are: (a) the machine hall (50.14 m 20.60 m 145.00 m), (b) the valve house (13.15 m 7.00 m 145.00 m),
(c)
the
collection
gallery
(10.60 m 10.80 m 173.00 m) and (d) the transformer
hall (23.50 m 20.00 m 173.00 m). These openings are
created in amygdaloidal basalt comprising of horizontal
and vertical brecciated rock horizons, at several locations. The volcanic breccia occurring in between the
compact basalt generally exhibits undulating top surface. The rock mass also contains some red tactylyte at
several locations. The average overburden thickness is
about 160.0 m. The size of the model under consideration is 170 m 300 m 360 m, which is 3–4 times the
size of the opening [15]. The field investigations were
conducted to determine in situ stress, modulus of
deformation, cohesion and angle of friction [16]. Flat
jack tests [17] were conducted to determine in situ stress
and modulus of deformation at 12 locations and the
results are presented in Table 1. As depicted in the table,
the rock mass properties for different type of rock mass
existing at different locations were measured, and are
grouped together on the basis of their deformation
modulus and cohesion. The average vertical, sv ; and
horizontal, sh ; in situ stresses are found to be 6.86 and
4.80 MPa, respectively. It should be noted that, the
hydro-fracturing tests conducted at the location yield an
in situ stress ratio of 0.67 [18]. However, in situ stress
ratio of 0.70, determined from the flat jack analysis, is
adopted in the present analysis. Laboratory tests have
also been conducted on NX size rock samples, collected
from different locations in and around the opening area,
to evaluate their mechanical properties such as density,
static modulus of elasticity, unconfined compressive
strength, tensile strength and Poisson’s ratio. Unconfined compressive strength values for basalt and breccia
are noted to vary from 45.2 to 58.2 MPa, and 19.3 to
35.3 MPa, respectively [19]. Hence, a mean value of 53.6
and 29.90 MPa has been chosen for basalt and breccia,
respectively [19]. The tensile strength of these rocks is
n
C
f
Py
Ph
Poisson’s ratio
cohesion of the rock mass
angle of internal friction
induced stress tangential to the boundary of the
opening
induced stress parallel to the axis of the opening
noted to vary from 1.60 to 4.15 MPa [19]. An average
density of 26.5 kN/m3 has been assigned to these rock
masses. For the sake of completeness, the rock mass
properties used in the present analyses are presented in
Table 2.
Multi-point borehole extensometers were used for
measuring deformations at the arch of the machine and
transformer halls. Location of extensometers in the
machine hall opening is depicted in Fig. 2. It must be
noted that the openings are excavated from top to the
bottom and borehole extensometers were installed
during September 1991 and January 1993. The vertical
borehole extensometers are installed at the center of
machine hall while the inclined extensometers are placed
at a distance of 5 m, from the right-side wall, up to
depths of 25, 10, 5 and 0 m (Fig. 3) and at 25, 55, 65 and
100 m from the starting point of the opening. The
deformations at the surface of the openings are
measured with the help of tape extensometers. Vertical
borehole extensometers are also installed in the transformer hall at depths of 30, 3 and 0 m (Fig. 3) at a
chainage of 60 and 135 m from the starting of the
opening, respectively. The deformations were measured
from the start of excavation (August 1991) of the
machine hall opening till June 1995, using electrical
readout units. A typical plot of the deformations
measured in the arch of the machine hall, with the help
of extensometers installed at chainage 100.0 m, is shown
in Fig. 4. The corrections required in the deformations
due to delay in installation of extensometers and due to
missing data were incorporated using the guidelines
reported in literature [20]. Deformations during
the delay of installation of extensometers, and the
missing data, have been determined with the help
of: (i) Q-method [21], as depicted in the Fig. 5, for
known Q/height of the opening and rock mass quality,
the deformation can be obtained, and (ii) with the help
of the procedure available in literature [15].
3. Details of the FEM analyses
Solvia 90, developed by Solvia Engineering AB,
Sweden, has been used for analyses of underground
openings. This finite element method (FEM) code
consists of Solvia-pre, Solvia, Solvia-temp and Solviapost modules. This code can also be used for birth and
219
160.00
161.74
163.15
155.00
23.6
Valve house
153.50
150.00
Transformer 146.50
45.00
20.60
17.00
hall
26.00
20.00
Gate shaft
Machine
127.00
hall
130.00
Collection gallery
18.70
10.60
116.20
111.00
Fig. 1. Details of the openings at Koyna hydroelectric project.
Table 1
Flat Jack test results for Koyna hydroelectric project
Location
Chainage (m)
Test point
Direction
Em (GPa)
Induced stress (MPa)
Py
Ph
Machine hall drift
25.5
29.0
32.0
42.0
76.3
84.3
102.15
1
2
3
4
5
6
7
Horizontal
Vertical
Horizontal
Horizontal
Horizontal
Horizontal
Horizontal
22.06
16.86
15.49
12.00
22.06
22.06
13.50
15.6
—
6.5
—
4.7
3.6
10.7
—
4.1
—
—
—
—
—
Approach tunnel
1000.0
1017.0
1021.75
1035.0
1045.5
8
9
10
11
12
Horizontal
Horizontal
Vertical
Horizontal
Horizontal
22.50
16.86
22.50
15.49
18.60
8.9
10.1
—
6.7
14.8
—
—
4.1
—
—
Py is the induced stress (tangential to the boundary of the opening, in MPa).
Ph is the induced stress (parallel to the axis of the opening, in MPa).
Em is the static modulus of deformation, in GPa.
death options of various elements such as plane stress/
strain and axi-symmetric, 3D solid, beam, shell and pipe
elements, for modeling excavations and repairs, and can
incorporate elastic orthotropic, nonlinear elastic, thermo-elastic, curve description, concrete, Drucker–Prager,
plastic-multilinear, and plastic creep rubber material
models. Results from the analysis, using Solvia, can be
directed via the porthole file to the Solvia-post program
and its database. Post-processing such as selected
display of results in the form of plots and listings,
searching for extreme results and response spectrum and
harmonic response analysis can be carried out using
Solvia-post.
The rock mass in which the openings are excavated is
discretized suitably. The faults and shear zones present
in the rock mass are represented by an equivalent
continuum material [23]. As depicted in Fig. 6, the rock
mass (300 m 360 m) is discretized with the help of 1420
nodes and 467 elements (2D solid plane strain eightnode isoparametric elements) belonging to 23 element
220
groups. Displacements are constrained normal to the
modal surfaces (depicted as C and B), whereas the
bottom corners are pinned (depicted as D). The rock
mass parameters adopted for these element groups are
presented in Table 2. The points at which the field
deformations are monitored are depicted in Fig. 3.
However, stresses in the direction normal to the plane
under consideration have been ignored, as their influence would be negligible [24].
For 3D finite element analysis, the rock mass (of size
170 m 300 m 360 m) has been discretized into 1649
eight-node solid isoparametric elements with 8041
nodes, as shown in Fig. 7. On the boundaries (left,
right, bottom and back) of the rock mass, deformations
are constrained normal to the model surfaces (depicted
as C and B), whereas the bottom corners (depicted as D)
are pinned. To account for the heterogeneity of the rock
mass and its characteristic properties, it is grouped into
23 groups, as depicted in Fig. 8. The rock mass
parameters adopted for these groups are presented in
Table 2. The points at which the field deformations for
3D analysis are monitored are shown in Fig. 3. For
realizing the machine hall opening, elimination of
certain set of elements is considered at different steps,
as depicted in Fig. 9. The following sequence of
excavation has been assumed:
Step 1: No opening in the rock mass (i.e. setting of
initial stress conditions);
Step 2: Excavation from top of the opening progresses
to 23%;
Step 3: Excavation from top of the opening progresses
to 74%;
Step 4: Excavation from top of the opening progresses
to 95%; and
Step 5: Excavation from top of the opening progresses
to 100%.
However, the effect of other small openings in the
rock mass such as openings for bus duct passage,
penstock, tailrace tunnel, etc. is localized and as such
has been ignored [25]. The rock mass properties, as
presented in Table 2, have been used in the present
analyses. It has been assumed that the rock mass obeys
Drucker–Prager yield criterion for Group 4–17, and
elastic behavior for Groups 1–3 and 18–23 [26,27]. This
is mainly due to the fact that the Drucker–Prager failure
Table 2
The rock mass properties used in the present study
Element
group
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Linear elastic analysis
Elasto-plastic analysis
Em (GPa)
n
n
Em (Gpa)
c (MPa)
f (1)
16.86
5.20
16.86
—
—
—
—
—
—
—
—
—
—
—
—
—
—
8.73
18.60
8.73
8.73
18.60
18.60
0.18
0.13
0.18
—
—
—
—
—
—
—
—
—
—
—
—
—
—
0.13
0.18
0.13
0.13
0.18
0.18
—
—
—
0.13
0.18
0.13
0.18
0.18
0.13
0.18
0.13
0.13
0.18
0.13
0.18
0.13
0.18
—
—
—
—
—
—
—
—
—
8.73
22.06
8.73
22.06
22.06
5.2
18.60
8.73
8.73
18.60
8.73
18.60
8.73
18.60
—
—
—
—
—
—
—
—
—
0.3
0.6
0.3
0.6
0.6
0.2
0.5
0.3
0.3
0.6
0.3
0.6
0.5
0.6
—
—
—
—
—
—
—
—
—
36
41
36
41
41
35
40
36
36
41
36
41
40
41
—
—
—
—
—
—
Em is the deformation modulus, c is the cohesion and f is the angle
of friction.
L/S
(MPBX) VERTICAL EXTENSOMETERS
MACHINE HALL DRIFT
CH.-25.0 0M
CH.-55.00M
CH.-65.00M
CH.-100.00M
(MPBX) INCLINED R/S EXTENSOMETERS
R/S
PLAN
Fig. 2. Location of extensometers in the machine hall arch.
221
Fig. 3. Location of MPBX extensometers and cross-section showing anchor length (m) near the center of the openings.
Fig. 4. Maximum deformations by electrical read out unit in the arch near the center of the machine hall at chainage 100 m.
criterion yields a smooth failure surface and can be
adopted quite conveniently for 3D applications [26].
4. Results and discussion
4.1. Deformations
Table 3 presents the computed and corrected field
extensometer results for the 10 points, considered for 2D
analysis at depths of 25, 10, 5 and 0 m for the machine
hall, and at 3 and 0 m depth for the transformer hall (as
depicted in Fig. 3). It can be observed from the table
that the computed results are almost 27–52% lower than
the monitored deformations. Similarly, Table 4 presents
a comparison of the computed and corrected field
extensometer results for 24 points, considered for 3D
analysis, at depths 25 and 0 m for the machine hall, and
30 and 0 m for the transformer hall (Fig. 3). It is noted
that for the machine hall, the computed deformations
222
Fig. 5. Machine hall arch deformations compared with Q-system
database.
Fig. 7. Discretization for the rock mass for 3D finite element analysis
with end fixity conditions.
Fig. 6. Discretization of the rock mass for 2D finite element analysis
with end fixity conditions.
for the nodes on and away from the face of the opening
are lower by 10–21% and higher by 1–23% of the field
extensometer deformations, respectively. For the transformer hall the same trend is noticed and the deformation values are noticed to differ by only 2–10%. In short,
the study reveals that for weak and nonhomogeneous
rock mass, deformations obtained with 3D elasto-plastic
analysis are more as compared to 2D analysis. However,
for the strong and homogeneous rock mass, deformations are found to be lesser for 3D elastic analysis as
compared to 2D analysis. This can be attributed to the
fact that weak zones have pronounced effect on
deformations when 3D analysis is carried out.
Fig. 8. Discretization of rock mass for 2D and 3D analyses showing
different rock mass groups.
223
Fig. 9. Excavation sequence for the machine hall opening.
Table 3
Computed and monitored deformations of the openings (2D analysis)
Opening
Machine
hall
Transformer
hall
a
Location of
the node
Depth of
the nodea (m)
Deformation (mm)
Computed
Monitored
Center
25.0
10.8
18.8
Right
10.0
5.0
0.0
25.0
10.0
5.0
0.0
11.1
12.7
14.3
14.0
14.1
14.0
14.6
21.3
26.2
26.5
19.2
22.5
25.3
27.4
3.0
21.0
29.7
0.0
21.5
32.3
Center
From the face of the opening.
4.2. Stresses
The maximum and minimum principal stresses
computed for 2D and 3D analyses are presented in
Table 5, for in situ stress ratio of 0.7 and for various
excavation steps. From the table it can be noticed that
for 2D and 3D analyses, when compared with the initial
stress conditions (Step 1), the maximum major principal
stress is found to increase by approximately 27%, 18%,
31% and 8%, and 1%, 34%, 40% and 25%, respectively, as the excavation progresses. It can be noticed
that for the 2D analysis, the maximum major principal
stress increases significantly for Step 2. This may be
attributed to the excavation of top portion of the
machine and transformer halls, and valve house (which
have sharp corners and as such exhibit unfavorable
effect on the stress). However, Step 3 corresponds to
excavation in the vertical direction, in a rectangular
shape, which helps in reduction of stresses. For Step 4, a
substantial increase in the stresses may be attributed
mainly to the effect of creation of the collection gallery,
in the vicinity of the machine hall. It can also be noticed
from the data presented in the table that for Steps 2–5 of
excavation, a small amount of tensile stress develops.
The depiction of major principal stresses around the
cavities, at Step 5 of the excavation, is shown in Figs. 10
and 11, for 2D and 3D analyses, respectively. It can be
noted that wherever weak zones exist, say at the top
portion of the openings, stresses are found to be
nominal. However, an increase in stress is noted in the
surrounding of the weak zones. Tensile stresses, depicted
as negative stresses, develop at the sharp corners and in
the vicinity of the weak zones. In the surrounding area
of the openings, maximum stresses are noticed to
develop at the bottom of the valve house. At the top
of the openings, low stresses are found which are well
distributed due to the arching effect. However, stresses
at the external boundaries of the rock mass, in the left
and the right sides of the openings, are found to be less
than the in situ stress (which is equal to 6.86 MPa). Also,
an irregular pattern of the stress distribution at the
bottom of the openings has been observed which may be
attributed to various parameters such as the self-weight,
in situ stress ratio, and variability in the deformation
modulus.
4.3. Criticality of stresses
From Table 5, it can be observed that both
compressive and tensile stresses occur in the rock mass
due to the excavation of the openings and if the
maximum stresses exceed the strength of the weak rock
mass, then suitable strengthening measures must be
adopted.
The maximum compressive stress of 28.33 MPa
corresponds to Step 4 in 3D analysis. The rock mass
strength determined for breccia, corresponding to an in
situ minor principal stress, s3 ; of 4.90 MPa, has been
obtained from the data presented in Fig. 12 [22] and the
same is found to be equal to 22.37 MPa. The rock mass
comprises of horizontal and vertical brecciated rock
horizons at several locations in the main amygdaloidal
224
Table 4
Computed and monitored deformations of the openings (3D elasto-plastic analysis)
Opening
Chainage (m)
Location of the node
Machine hall
Center
25.0
Right
Center
55.0
Right
Center
65.0
Right
Center
100.0
Right
Transformer hall
a
65.0
Center
75.0
Center
100.0
Center
135.0
Center
Deformation (mm)
Computed
Monitored
0.0
25.0
0.0
25.0
0.0
25.0
0.0
25.0
0.0
25.0
0.0
25.0
0.0
25.0
0.0
25.0
22.8
19.3
22.7
19.5
22.3
19.3
21.5
19.0
22.9
19.6
22.7
19.8
22.8
18.8
22.6
18.5
26.5
18.8
27.4
19.2
28.2
17.0
26.2
15.8
20.9
16.8
22.4
18.0
25.2
15.3
26.2
18.0
0.0
30.0
0.0
30.0
0.0
30.0
0.0
30.0
30.1
27.7
31.3
28.4
29.3
28.4
29.1
25.5
28.9
25.3
—
—
—
—
29.8
23.3
From the face of the opening.
Table 5
Maximum and minimum major principal stresses due to the self-weight
of the rock mass by elasto-plastic analysis (in situ stress ratio=0.70)
Excavation step
Major principal stresses (MPa)
2D analysis
1
2
3
4
5
Depth of the nodea (m)
3D analysis
Maximum
Minimum
Maximum
Minimum
15.23
20.94
18.49
22.02
16.46
0.15
2.04
1.23
2.20
1.53
16.95
17.10
25.55
28.33
22.58
0.37
0.72
1.02
0.88
1.30
basalt rock. The estimated rock mass strength when
compared with the calculated maximum compressive
stresses, factor of safety is found to be o1 for the weak
rock mass. This indicates initiation of the failure at
points where maximum stresses are generated and as
such the rock mass requires external support. Hence,
tensioned grouted rock bolts are used to provide the
external supports.
5. Analysis with the grouted rock bolts
If the rock bolts are installed very close to the
excavation face of the opening, or during each stage of a
multi-stage excavation sequence, the deformation of the
rock mass before installation of the bolts will be minimal
and as such pre-tensioning of the rock bolts is not
required [28]. The FEM analysis has been conducted to
analyze the rock mass reinforcement and to achieve this
the rock bolts are modeled as two-node truss elements.
For estimating the length, L; of the rock bolts in the
central section of the opening, Eq. (1) proposed by the
Norwegian Institute of Rock Blasting Technique has
been used [29]:
L ¼ 1:40 þ 0:184a;
ð1Þ
where a is the span of the opening.
Based on this equation, the minimum bolt length is
taken as the greater of the height of the loosened zone or
one-fifth of the height of the opening. The rock bolts of
10 m length and 25 mm diameter have been provided at
every 12.50 m, along the length of the Machine hall and
the Transformer hall openings, and at 10 m spacing
along the width of the opening, as the primary
reinforcement, for the overall stability. In addition to
this, to avoid fall of loose rock pieces and to inhibit
further loosening of rock mass, secondary reinforcement
and spot bolting of 2–3 m length has been provided in
the walls and roof of the machine and transformer halls,
with 2.5 cm thick shotcrete with the wire mesh.
However, the same have been ignored in the analysis
due to their insignificant contribution to reduction of
225
Fig. 10. Contours of major principal stresses computed with the help of 2D finite element analysis corresponding to Step 5 of excavation.
Fig. 11. Contours of major principal stresses computed with the help of 3D finite element analysis corresponding to Step 5 of excavation.
stresses. For steel bolts, Em is adopted as 211 GPa and a
yielding stress of 7 MPa.
Due to the application of rock bolts, the reduction in
nodal deformations and stresses is observed, as depicted
in Tables 6 and 7, respectively. From these tables, it can
be noted that there is a reduction of 5.63–12.76% in the
deformation, for 3D elasto-plastic analysis. It can also
be observed that the major principal stresses have
reduced from 25.55 to 18.19 MPa, 28.23 to 18.55 MPa
and 22.58 to 17.07 MPa, corresponding to Steps 3, 4
and 5 of excavation, respectively. It is interesting to
note that the maximum value of major principal
stress after providing rock bolts reduces to 18.55 MPa,
which is approximately 20% less than the strength of
breccia.
6. Conclusions
Based on the results and discussion presented in this
paper, the following conclusions can be drawn:
1. 3D elasto-plastic FEM analysis exhibits the best
agreement with the field deformation observations
for the nonhomogeneous rock mass with weak zones.
However, 2D elasto-plastic analysis yields conservative results.
2. The effect of nonhomogeniety of the rock mass is
better understood by 3D analysis, as the effect of
weak zones are suitably taken into account in 3D
analysis, as compared to the 2D analysis.
226
3. The major principal stresses obtained from 3D elastoplastic analysis compare very well (in terms of
stability) with the strength of the rock mass.
Mojor principal stress (MPa)
40
4. Reduction of stresses and deformations around the
openings is observed due to the application of the
primary reinforcement.
5. In multi-stage excavation, stresses at the end of a
partial stage are noticed to be higher than those
occurring at the end of the complete excavation.
Acknowledgements
30
Relationship
by Hoek and Brown
criterion
20
The first author would like to express his sincere
gratitude to Director, CW&PRS, Pune for granting
permission to pursue the doctoral research at IIT
Table 7
Maximum and minimum major principal stresses due to the self-weight
of the rock mass by 3D elasto-plastic analysis (in situ stress
ratio=0.70)
Excavation step Major principal stresses (MPa)
10
0
0
2
4
6
8
10
Minor principal stress (MPa)
1
2
3
4
5
Without reinforcement
With reinforcement
Maximum
Minimum
Maximum Minimum
16.95
17.10
25.55
28.23
22.58
0.37
0.72
1.02
0.88
1.30
16.95
17.10
18.19
18.55
17.07
0.37
0.53
0.86
0.94
0.97
Fig. 12. Plot of rock mass strength curve for the breccia rock mass.
Table 6
Effect of reinforcement on the nodal deformation of the openings (3D elasto-plastic analysis)
Opening
Chainage (m)
Machine hall
Location of the node
Center
25.0
Right
Center
55.0
Right
Center
65.0
Right
Center
100.0
Right
Transformer hall
a
65.0
Center
75.0
Center
100.0
Center
135.0
Center
From the face of the opening.
Depth of the nodea (m)
Deformation (mm)
Without reinforcement
With reinforcement
Monitored
0.0
25.0
0.0
25.0
0.0
25.0
0.0
25.0
0.0
25.0
0.0
25.0
0.0
25.0
0.0
25.0
22.8
19.3
22.7
19.5
22.3
19.3
21.5
19.0
22.9
19.6
22.7
19.8
22.8
18.8
22.6
18.5
20.8
17.8
20.6
18.0
20.4
18.1
19.4
17.6
20.9
18.2
20.6
18.5
20.4
16.4
20.3
16.2
26.5
18.8
27.4
19.2
28.2
17.0
26.2
15.8
20.9
16.8
22.4
18.0
25.2
15.3
26.2
18.0
0.0
30.0
0.0
30.0
0.0
30.0
0.0
30.0
30.1
27.7
31.3
28.4
29.3
28.4
29.1
25.5
27.2
25.9
28.1
26.5
26.8
26.8
26.4
23.9
28.9
25.3
—
—
—
—
29.8
23.3
227
Bombay. Thanks are also due to Koyna Hydro Electric
Project Design Authorities for providing funds for
carrying out the in situ investigations and for supplying
borehole deformation data. Suggestions received from
Sh. Rizwan Ali, Research officer, CWPRS during the
course of this study are gratefully acknowledged.
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