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Transcript of FInal Tunnel-2 Report.doc
Design Consultancy services for four-Laning of 'Goa/Karnataka Border - Kundapur Section' of NH-17 from Km 93.700 to Km 283.300 in the State of Karnataka
Tunnels- 2 Design Report
5.0 Numerical Analysis
5.0.1 Introduction of Phase2
An essential part of the design of tunnel is the prediction of the response of rocks / rock masses, in terms of
stresses and displacements, which can be well understood by Numerical Methods.
Phase2 is a 2-dimensional windows based program, very popular for the analysis of underground / surface
excavation in rock mass or soil. The program is used for a wide range of geotechnical engineering projects
including complex tunneling problems in weak rock, stress analysis, tunnel design, slope stability, support
design and groundwater seepage analysis etc. Complex multi staged models can easily be created and ana-
lyzed quickly. The program is user friendly, easy to operate and easy to understand. Some of the basic fea -
tures are:
Elasto-Plastic Analysis,
Constant or Gravity Field Stress,
Staged Model,
Plain Strain or Axisymmetric Analysis,
Support analysis (Rock Bolts, Steel Ribs, Lattice Girders Shotcrete / Concrete Liner etc.),
Multiple materials,
Load splitting,
Slope stability analysis,
Ground water seepage analysis etc.
There are three basic components in Phase2 program - Model, Compute and
Interpret. Model is the pre-processing module used for entering and editing
the model boundaries, support, in-situ stresses, boundary conditions,
material properties and creating the finite element mesh. Model, Compute
and Interpret will each run as standalone programs. They also interact with
each other as illustrated in the schematic diagram on the right side.
Compute and interpret can both be started from within the model.
Compute must be run on a file before results can be analyzed with interpret (red
arrow).
Model can be started from interpret.
5.0.2 Input parameters for Phase2
In phase2, field stress can be constant or gravity stress. The gravity field stress option is used to define a
gravity stress field which varies linearly with depth from a user-specified ground surface elevation. Gravity
field stress is typically used for surface or near surface at shallow depth elevations and the areas where
there is the effect of topography in the stress magnitudes and directions.
Material parameters such as Unconfined Compressive Strength of intact rock (σ ci), Hoek-Brown constant
(mi), Geological strength index (GSI), Young‘s Modulus of intact rock (E i), Poisson‘s ratio (ν), Density of the
rock mass (γ) are the material property inputs in Phase2.
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5.0.3 Interpretation of the results
The principal stresses can be displayed. The major and minor principal stresses and angle with horizontal at
any point can be read and the results can be compared with the gravity stress. The strength factor contours
of the rock mass around the tunnel are also displayed. With elastic analysis if the strength factor is greater
than one everywhere around the tunnel, the result will be the same even if Plastic Analysis is done. Hence
there is no necessity of plastic analysis if the strength factor is less than one. The contours of vertical, hori -
zontal and total displacements can be displayed around the tunnel with values marked. The values can be
compared with the results obtained from analytical/semi-analytical methods and measurements of tunnel
convergence in field.
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5.1.0 Mid Tunnel Section
5.1.0.1 Continuum Modeling
In the Continuum modeling technique rock joints are taken into consideration implicitly, i.e. the rock mass
quality is described by strength and deformability parameters through a failure criterion. Mohr-Coulomb and
Hoek-Brown failure criteria are utilized in the analysis.
5.1.0.2 Finite Element Mesh, Boundary Conditions and Construction Sequence
To eliminate the influence of the applied boundary conditions, the finite element mesh is extended up to the
ground surface and in the lateral direction up to two times the tunnel width. The mesh is of 3272 elements
and 6803 nodes. The gradation factor, ratio of the average length of discretization on excavation boundary
to the length of discretization on the external boundary is 0.2, i.e., the average length of the element on the
external boundary is 20 times the length of the element on the excavation boundary.
Fig 6: Model showing the extent and boundary conditions adopted for the external boundary
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The modeling starts with generation of the initial stress field, followed by a four stage Excavation process.
Fig.7: Model with stages of sequential excavation
Table 11: Mesh and Discretization Parameters
Mesh type Graded
Element type 6 Noded triangles
Gradation factor 0.2
Default number of nodes on all excavations 110
5.1.0.3 Estimation of In-situ Stresses:
Different in-situ horizontal stress conditions are taken into consideration using stress ratio, k=0.5, 1.0, 1.5
and 2.0. The vertical in-situ stress distribution is considered as the result of weight of the overburden, (σ v =
γH).
5.1.0.4 Estimation of rock mass parameters:
Middle section @ km: 107.645, using data of BH No.5 is used for analysis. The effect of variability and
uncertainty sourced from the complex and variable nature of rock mass cannot be considered by
deterministic approaches using single or mean value. Therefore an effort is made to estimate the required
rock mass properties to construct a reliable FEM-model. Mohr Coulomb (MC) & Hoek- Brown (HB) Failure
criterion are used in the analysis.
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Table 12: Uniaxial Compressive Strength (UCS) of intact rock samples of BH5 at km: 107.645
Depth UCS(Mpa) E(Mpa) γ(kN/m3)
58.0-59.0 82 46463 2.95
62.5-63.8 183 28932 3.01
67.0-68.0 70 65872 3.06
71.5-72.5 75 71484 3.02
75.5-76.5 35 88223 2.81
80.5-81.5 130 109647 2.99
Mean 96 68437 2.97
Std. dev. 47.75
UCS values on rock core samples from the borehole are highly distributed. Value of standard deviation of
the data is 47.75% of the mean value. Statistical analysis is therefore required to justify a single value for
use. By using statistical analysis it is possible to determine the percentage of values in the data set that
exceeds a certain value. 90% of UCS values measured are exceeding 35 Mpa and that value will be used as
input parameter in the FEM-model.
Fig. 8: Normal distribution of UCS data
The mean value of 96.0 Mpa may also be used but in that case the rock mass in 50% of cases be less
favorable than the parameter used in the design and would be hard to justify. It will however be used here
for comparison purpose. Fig. 9 shows the correlation between UCS and E.
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Fig.9: Correlation between UCS and E
Fig. 10: Linear correlation between Q and RMR
Residual friction angle, φr = tan-1(Jr/Ja) is worked out to be 56o with field measured values of Jr =1.5 and Ja =
1.So no change is made as regards to the friction angle of rock mass, though the borehole data indicated
friction angle φmean =56o and φ10% = 44o. The stiffness modulus E10% should be around 88.871 Gpa according
to figure 9.
Table 13: The values of cohesion and friction
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C(Mpa) φ(Degrees)
2.25 49.83
1.45 57.02
0.45 61.05
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The following table shows the values considered for Numerical Analysis.
Table 14: Selected Rock Mass Parameters for Numerical Analysis
Confidence Limits 90% 50% Units
Input values of Mohr Coulomb failure Criterion
Cohesion,C 0.350 1.506 Mpa
Friction Angle,φ 44.00 56.00 Degree
Tensile Strength,T 0.300 0.920 Mpa
Modulus of Elasticity,Ei 88.87 68.440 Gpa
Modulus of Deformation,Ed 35.19 30.850 Gpa
Input values of Hoek Brown failure Criterion
Geological Strength Index,GSI 64.00 75.00
Intact Rock Constant,mi 29.00 29.00
Disturbance factor,D 0.00 0.00
Uniaxial compressive strength,UCS 35.00 96.00 Mpa
Modulus of Elasticity,Ei 14.88 40.80 Gpa
Modulus of Deformation,Ed 9.072 33.307 Gpa
Parameter,mb 7.900 11.892
Parameter,s 0.018 0.062
Parameter,a 0.502 0.501
Unit weight,γ 2.870 2.970 kN/cum
Poisson's Ratio,ν 0.130 0.440
5.1.0.5 Stability assessment of tunnels:
Design of effective ground support takes into account the mode of instability so that the support components
can be designed to work efficiently for the anticipated instability mode.
There are three main tunnel instability mechanisms:
Shear Yielding of rock mass is quite common in poor quality rock masses. A plastic zone is formed
around the tunnel and, depending upon the ratio of rock mass strength to in-situ stress, this may
stabilize, or it may continue to expand until the tunnel collapses. The two main mechanisms that
can produce this type of instability are swelling and squeezing conditions. Fig. 11a illustrates, Shear
failure in a plastic zone around tunnels in weak rock
STRUCTURALLY CONTROLLED KINEMATIC INSTABILITY appears in jointed rock masses under
low in-situ stress conditions. Gravity driven wedge instability is typically the dominant instability
mode of the type. The failure involves gravity fall of wedges formed by intersecting geological fea-
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tures. Fig. 11b illustrates Gravity driven wedge instability along pre-existing geological structures in
blocky ground under low in-situ stress conditions
BRITTLE ROCK FAILURE initiates as a result of the propagation of tensile cracks from defects in
highly stressed massive hard rock. These cracks generally propagate along the maximum principal
stress trajectories, resulting in thin splinters or slabs. Depending upon the ratio of intact rock
strength to in-situ stress, spalling may be limited to small plate-sized slabs, or it may develop into a
massive violent failure or rock burst. Fig. 11c illustrates Stress driven brittle failure tends to domi-
nate in massive brittle rock under high in-situ stress conditions
Fig. 11: Potential Modes of Failure
5.1.1 Elastic Analysis
5.1.1.1 Interpretation of the results:
Different output parameters after the simulation through different stages of excavation in elastic mode are
shown in Fig.12 below.
5.1.1.2 Principal Stresses:
In Phase2, σ1 corresponds to the in plane major principal stress and σ3 in plane minor principal stress. The
elastic stress redistribution around the excavation suggests that σ1 increases and σ3 decreases in the rock
mass surrounding the tunnel.
5.1.1.3 Major Principal Stress:
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Predominant failure modes of the tunnel for different stress ratio’s (k) are predicted based on the limiting
ratio of tangential stress (σ1) to UCS of intact rock.
Fig. 12: Tunnel instability and brittle failure
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Table 15: Computation of the ratio of Maximum principal stress to uniaxial compressive strength of intact rock
As the stress ratio increases from 0.5 to 2, the failure mode in crown and walls ranges from falling or sliding
of block wedges to localized brittle failure of intact rocks and movement of blocks. The maximum principal
stress being compressive is located in the side wall for k values of 0.5 and 1.0 and in the crown for k values
of 1.5 and 2.0.
5.1.1.4 Strength Factor:
It is defined as the ratio of strength of rock mass to the induced stress. Strength Factor greater than 1.0
indicates that the material strength is greater than the induced stress. A strength factor less than one means
the material will fail, and plastic analysis is necessary.
The tangential stresses in the walls decrease as the stress ratio ‘k’ varied from 0.5 to 2.0 resulting in
improved strength factor values.
The tangential stresses in the roof/crown increase as the stress ratio ‘k’ varied from 0.5 to 2.0 resulting in
decreased strength factor values even though higher horizontal stress provides sufficient constraint and
stability of the roof.
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Fig. 13: Strength factor Contours for MC-90
Fig. 14: Strength factor Contours for MC-50
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Fig. 15: Strength factor Contours for HB-90
Fig. 16: Strength factor Contours for HB-50
Table 16: Extent of zone (meters) of Strength Factor below 1.0
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Strength Factor(Extent of Zone in meter less than 1) k 0.5 1 1.5 2MC-90 Crown 0 0.904 1.066 1.29 Left wall 1.047 0.902 0.904 0.979 Right wall 0.991 0.918 0.822 0.963 Invert 2.174 3.764 5.038 6.071 MC-50 > 1 for all values of k HB-90 Crown 0 0 0.162 0.254 Left wall 0 0 0.145 0.184 Right wall 0 0 0.32 0.389 Invert 1.028 1.451 3.026 3.685 HB-50 > 1 for all values of k
5.1.1.5 Minor Principal Stress induced failure (σ3<0):
The iso-line depicts the region with tensile stresses in the rock exceeding the tensile strength of the rock
mass. Tensile strength is estimated using the Mohr-Coulomb strength relationship, using the formula,
Tensile Strength (σt) = (2c * Cos Φ) / (1+ SinΦ)
Table 17 shows the values of tensile strength adopted in the model using the formula. The maximum
principal stress in tension due to the de-confinement of rock mass in the tunnel floor is lower than the tensile
strength of the rock and hence a flat invert is considered to be adequate.
Table 17: Tensile strength as per Mohr Coulomb failure criteria
c φ σt
MC 90 0.350 44.0 0.30
MC 50 1.506 56.0 0.92
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Fig. 17: Minor principal Stress Contours (<0, Grey Iso-lines) for MC-90
Fig. 18: Minor principal Stress Contours (<0, Grey Iso-lines) for MC-50
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Tensile strength of the rock mass as per Hoek Brown failure criteria is
Tensile Strength (σt) = s * σci / mb
Table 18: Tensile strength as per Hoek Brown failure criteria
s mb σci σt
HB 90 0.0180 8.017 35 0.08
HB 50 0.0621 11.875 96 0.50 Th
e region, in which the tensile strength of rock is exceeded, is significant in HB 90 model and a curved invert
can be considered, based on ground conditions met with.
Fig. 19: Minor principal Stress Contours (<0, Black Iso-lines) for HB-90
Table 19: Extent of tensile stress zone in meters
Extent of Minor principal Stress induced failure (σ3<0) in meter
Invert k MC-90 MC-50 HB-90 HB-50
0.5 1.230 1.268 1.097 1.147
1 1.470 1.551 1.409 1.475
1.5 2.903 2.969 2.889 2.889
2 3.415 3.276 3.481 3.402
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Fig. 20: Minor principal Stress Contours (<0, Black Iso-lines) for HB-50
5.1.1.6 Critical Shear Strain
The maximum shear strain should be smaller than the critical shear strain (γc). If the maximum shear strain
is larger than the critical shear strain, tunnel support must be installed immediately so as to keep the
maximum shear strain less than the critical shear strain.
Where ‘ν’ is the poisons ratio of the material and ‘εc’ is the critical strain defined as the ratio of uniaxial
compressive strength to the modulus of elasticity of rock mass.
Table 20: Permissible Shear Strain computation for different models
Permissible Shear Strain (γ) Model σci(Mpa) σcm(Mpa) Em(Mpa) σcm/Em (1+νm) σcm/Em (1+νm)MC 90 35 3.45 35190 9.81E-05 1.13 1.11E-04MC 50 96 15.68 30850 5.08E-04 1.13 5.74E-04HB 90 35 3.45 9072.6 3.80E-04 1.44 5.48E-04HB 50 96 15.68 33307 4.71E-04 1.44 6.78E-04
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Fig.21: Maximum shear strain distribution for MC-90 exceeding permissible values
Fig. 22: Maximum shear strain distribution for HB-90 exceeding permissible values
With increasing stress ratio (k) the need for tunnel support is anticipated in models MC 90 and HB 90. Shear
strain is within limits for model MC 50 and HB 50.
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5.1.1.7 Principal Stress Cone
The location and thickness of the natural roof arch can be determined by the concept of invert principal
stress cone developed in the numerical modeling. The stress trajectories are displayed in Fig. 23.
Fig. 23: Development and application of concept of principal stress cone
Notations used:
k = Stress Ratio
H = Height of rock load in meter
Preqd = Required Maximum support pressure in ‘MPa’ calculated as the product of Unit weight of rock
and the height of rock load in ‘m’.
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Fig. 24: Maximum height of rock load for MC-90
End anchored 25φ rock bolts 4.5 m long at 2 m x 2 m spacing, and shotcrete, 50 mm thickness, M25 grade
yield support pressures of 0.051 Mpa and 0.06 Mpa resply., for all values of ‘k’.
Table 21: Support pressures using bolts and shotcrete to resist the rock load for MC-90
Support Pressure reqd (Mpa) Support Pressure (Mpa)Model k H Preqd End Anchored bolts ShotcreteMC 90 0.5 3.827 0.11 0.025 0.12 1 2.567 0.07 0.025 0.06 1.5 1.871 0.05 0.025 0.06 2 1.535 0.04 0.025 0.06
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Fig. 25: Maximum height of rock load for MC-50
Table 22: Support pressure requirements using bolts and shotcrete to resist the rock load for MC-50
Maximum Support Pressure Calculation
Model k H Preqd End Anchored bolts Shotcrete
MC 50 0.5 3.848 0.11 0.051 0.06
1 1.873 0.06 0.051 0.06
1.5 1.778 0.05 0.051 0.06
2 1.791 0.05 0.051 0.06
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Fig. 26: Maximum height of rock load for HB-90
End anchored 25 φ rock bolts of 4.5 m length at a spacing of 2 m x 2 m and a shotcrete of M30 grade with
thickness of 100mm resulted in a support pressure of 0.051 Mpa and 0.14 Mpa for k=0.5.For all other values
of k, a shotcrete of M25 grade with thickness of 50mm is found adequate with a support pressure of 0.06
Mpa.
Table 23: Support pressure requirements using bolts and shotcrete to resist the rock load f or HB - 9 0
Maximum Support Pressure Calculation
Model k H Preqd End Anchored bolts Shotcrete
HB 90 0.5 5.927 0.17 0.051 0.14
1 2.567 0.07 0.051 0.06
1.5 1.871 0.05 0.051 0.06
2 1.535 0.04 0.051 0.06
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Fig. 27: Maximum height of rock load for HB-50
Table 24: Support pressure requirements using bolts and shotcrete to resist the rock load f or HB-50
Maximum Support Pressure Calculation
Model k H Preqd End Anchored bolts Shotcrete
HB 50 0.5 2.822 0.08 0.051 0.06
1 2.129 0.06 0.051 0.06
1.5 2.106 0.06 0.051 0.06
2 1.132 0.03 0.051 0.06
Equations used for estimating the support pressure of shotcrete and rockbolts
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(Ref: https://www.rocscience.com/documents/pdfs/rocnews/winter2012/Rock-Support-Interaction-Analysis-for-Tunnels-Hoek.pdf)
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5.1.1.8 Deviatoric Stress: The difference in the major and minor principal stress referred as deviatoric stress directly relates to the
maximum shear stress. It controls the degree of distortion, allowing for a material to deform in one direction
more than the other (i.e. in the direction of smaller stress.). In effect, this allows fracturing, rupture and
shearing of the rock to occur. The deviatoric stress should be less than UCS of rock mass (σ cm =σci1.5/60). If
the deviatoric stress is high, plastic analysis is required.
Table 25: Extent of zone greater than UCS of rock mass
Extent of Degree of Distortion in meter
k Crown Walls Invert
MC-90 0.5 0.00 3.287 0.000
σci =35 1.0 2.032 2.797 0.000
σcm =3.45 1.5 4.569 2.531 10.545
2.0 9.445 2.214 full
HB-90 0.5 0.00 3.367 0.000
σci =35 1.0 2.074 2.791 0.00
σcm =3.45 1.5 4.676 2.491 10.667
2.0 9.208 2.287 full
MC-50 0 for all values of k
HB-50 0 for all values of k
Fig. 28: Deviatoric stress distribution (more than UCS of rock mass)
5.1.2 Plastic Analysis:
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5.1.2.1 Yielded Elements:
The depth of the shear (x) and tensile (o) failure zones in the surrounding rock without any support is an
important factor to be considered in the design of required support system.
Fig. 29: Plastic Zones around the tunnel for MC 90
Table 26: Extent of yield zone around tunnels for MC 90 Model.
Extent of zone in m
MC 90
Shear zone
k = 0.5 k = 1 k = 1.5 k = 2
Crown 0.0 1.85 1.84 3.73
Walls 2.0 1.90 1.86 2.85
Invert 2.2 3.45 5.20 5.50
Tension zone
k = 0.5 k = 1 k = 1.5 k = 2
Crown 0.00 0.60 0.78 0.66
Walls 0.80 0.90 0.86 0.87
Invert 1.22 1.34 2.68 2.52
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Fig. 30: Plastic Zones around the tunnel for HB 90
5.1.2.2 Depth of Spalling:
The concentration of compressive stress in sidewalls for k values of 0.5 and 1 is not to the level of intact rock
strength and may not lead to spalling.
Fig. 31: Major Principal stress concentration for k = 0.50 & 1.0
The concentration of compressive stress is shifted to crown and invert for k values of 1.5 and 2. The
potential for spalling may also depend on the joint pattern. The rock bolt length is so chosen to extend
beyond the zone of stress concentration.
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Fig. 32: Major Principal stress concentration for k = 1.5 & 2.0
5.1.2.3 Support System:
Each support component in a support system is intended to perform one of the three functions illustrated in
figure 33.
Reinforce the rock mass to strengthen it and control bulking.
Retain broken rock to prevent key block failure and unraveling.
Hold key blocks and securely tie back the retaining element(s) to stable ground.
While each support element may simultaneously provide more than one of these functions, it is convenient
to consider each function separately:
The goal of reinforcing the rock mass is to strengthen it, thus enabling the rock mass to
support itself. Reinforcing mechanisms generally restrict and control the bulking of the rock mass,
thus ensuring that inter block friction and rock mass cohesion are fully exploited. Typically,
reinforcing behave as stiff support elements or ductile or yielding elements
While retaining the broken rock at the excavation surface is required for safety reasons, it may also
become essential under high stress conditions to avoid the development of progressive failure
process that lead to unraveling of the rock mass. Qualitative observations indicate that full aerial
coverage by retaining elements becomes increasingly important as the stress level increases.
The holding function is needed to tie the retaining elements of the support system back to stable
ground, to prevent gravity-driven falls of ground.
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Fig 33: Three primary functions of support elements
The support system adopted for the Tunnel Section under consideration is shown in Fig. 34.
Fig. 34: Proposed support system
Tension bolts with resin point anchorage are used to apply a compressive force across layered rock strata.
Tension bolts are applied using fast setting resin as the point anchorage in conjunction with slow setting
cement as a corrosion protection for the free stress length. Bolt tension is applied after the fast setting resin
has cured but before the slow setting cement cures.
As seen in Fig. 35, the rock bolts had marginal reduction effect on the roof settlement once a natural roof
arch is formed, and after systematic rock bolting, the roof arch is more stable. A pretension of 10 ton is
applied to the rock bolts to prevent rock dilation of 1.0 m. The application of pre-tensioned bolts is intended
to provide stiffer support by reacting faster to the rock movement.
The existence of high horizontal in-situ stress resulted in higher tunnel crown subsidence, floor uplift and
deformations. This may be explained by rock mass yielding, which is caused by differential principal stress.
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Fig. 35: Total displacement of crown
Fig. 36: Total displacement of side wall
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Table 27: Number of yielded elements in Elastic Perfectly plastic analysis
(Static Analysis/) Yielded elements
k No sup RB SC RB & SC
0.5 259 254 261 249
1.0 295 301 299 290
1.5 320 324 323 320
2.0 351 347 342 337
Redistribution of stresses is concentrated in the rock mass at a distance of 3.0 m from the tunnel boundary
which delineates the Plastic and Elastic zones. Pattern bolting and SFRS result in a near triaxial stress
condition.
Fig. 37: Principal stress Distribution near side wall from tunnel boundary for k=0.5
Fig. 38: Principal stress Distribution near side wall from tunnel boundary for k=1
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Fig. 39: Principal stress Distribution near side wall from tunnel boundary for k=1.5
Fig. 40: Principal stress Distribution near side wall from tunnel boundary for k=2
Examination of the distribution of radial and tangential stresses indicates the function of the radial
reinforcement. It reduces the radial displacement (ur) and generates a higher magnitude of σr in the fractured
zone, resulting in a higher gradient in the σt distribution. The effect is to shift the plastic–elastic transition
closer to the excavation boundary. Thus, both closure of the excavation and the depth of the zone of yielded
rock are reduced.
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5.1.3 Seismic Design
5.1.3.1 Pseudo-Static Analysis:
For most underground structures, the inertia of the surrounding rock is large, relative to the inertia of the
structure and therefore the seismic response of the tunnel is dominated by the response of the surrounding
rock mass. In phase2, seismic loading is based on pseudo-static approach, where the seismic force is
calculated as the product of the specified seismic coefficient, a dimensionless vector, and the amplitude of
the body force, which is the self weight of the finite element.
5.1.3.2 Seismic Coefficient Method:
The inertial forces due to earthquake are obtained by multiplying the rock load with the design coefficient
(0.08) which is expressed by the following equation (IS: 1893- 1984:Cl.3.4.2.3 (a))
Where
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Selected Values in Blocks from Tables 2, 3 & 4 of IS: 1893:1984
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Fig. 41: Mesh Generation for Seismic Analysis
Fig. 42: Stages of sequential excavation, support application and application of seismic loadA large zone of tensile failure is seen in the upper left hand corner in all models, which can be attributed to
the effect of boundary conditions, when horizontal seismic loading is applied from left to right. .At the
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external boundary, the material when pulled away by applied seismic force, creates a large tensile stress
due to the applied boundary conditions and their effect can be minimized by increasing the extent of the
external boundary, or by placing the an elastic material away from the tunnel.
Fig. 43: Tensile zone in Upper left corner due to earthquake loading
Table 28: Number of yielded elements in Elastic Perfectly plastic seismic analysis
Seismic
k No sup RB SC RB & SC
0.5 466 452 458 443
1.0 410 398 401 388
1.5 393 379 380 375
2.0 415 403 399 395
5.1.3.3 Interaction Diagrams of shotcrete and final lining:
Interaction diagrams are therefore useful to estimate if the tunnel lining is able to tolerate applied loading
from the rock mass. Results of analysis for static and seismic loading are presented in fig.44 to 51. Lining is
never loaded by the stress which is initially prevailed in the ground. Initial stress is reduced by deformation of
the ground that occurs during excavation. The Stress relaxation of the rock mass when considered
eliminates the data points outside the envelope.
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Fig. 44: Interaction diagrams of of shotcrete for k=0.5 (Static case)
Fig. 45: Interaction diagrams of shotcrete for k=1.0 (Static case)
Fig. 46: Interaction diagrams of of shotcrete for k=1.5 (Static case)
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Fig. 47: Interaction diagrams of shotcrete for k=2.0 (Static case)
Fig. 48: Interaction diagrams of final lining for k=0.5 (Seismic case) with M25 Grade concrete
Fig. 49: Interaction diagrams of final lining for k=1.0 (Seismic case) with M25 Grade concrete
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Fig. 50: Interaction diagrams of final lining for k=1.5 (Seismic case) with M30 Grade concrete
Fig. 51: Interaction diagrams of final lining for k=2.0 (Seismic case) with M30 Grade concrete
5.1.3 Conclusions:
5.1.3.1 Numerical Analysis of twin tube tunnels using Phase2 with poor rock mass properties is carried out.
In-situ stress ratio, k (σH / σv) varies along the length of tunnel due to variation in the direction/mag-
nitude of σH and σv with geology and topography. k= 0.5, 1.0, 1.5 and 2.0 are considered for critical
condition. In-situ vertical stress is due to gravity. Mohr- coulomb and Hoek Brown failure criteria are
utilized. Excavation of tunnels is by heading and bench method.
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5.1.3.2 ELASTIC Analysis:
A strength factor less than one in MC 90 and HB 90 models indicated that the material will fail and
plastic analysis is necessary.
As the stress ratio increases from 0.5 to 2.0, the failure mode in crown and walls range from falling
or sliding of block wedges to localized brittle failure of intact rocks and movement of blocks.
The tangential stresses in the walls decrease as the stress ratio k varied from 0.5 to 2.0 resulting in
improved strength factor values. In roof/crown it increase as k varied from0.5 to 2.0 resulting in de-
creased strength factor values, even though higher horizontal stress provides sufficient constraint
and stability of the roof.
The region in which the tensile strength of rock is exceeded is significant in HB 90 model and can
be attributed to the use of a lower modulus of deformation value which stressed the use of a curved
invert.
With increasing stress ratio (k) the need for immediate tunnel support is anticipated for stability in
models MC 90 and HB 90
For MC 90 and HB 90 models, the max. height of rock load above crown determined by the concept
of invert principal stress cone, is 3.848m for k=0.5. As k increases the rock load decreases. But MC
50 model indicates the height of rock load is 5.927m for k=0.5. End anchored 25dia rock bolts 4.5m
long at 2m x 2m spacing, and shotcrete, 50mm, M25 grade is adequate for the rock load except for
HB 90 model with k=0.5. Since this approach is based on empirical formulas,
The deviatoric stress (σ1-σ3) which directly relates to shear stress, controlling the degree of distor-
tion and fracturing, rupture and shearing of tunnel section, is more than UCS of rock mass, for MC
90 and HB 90 models for k=0.5-2.0, indicating Plastic analysis is necessary.
5.1.3.3 PLASTIC Analysis:
The depth of the shear and tensile failure zones in the rock mass without any support is an impor-
tant factor in the design of required support system.
The extent of yielded zone in crown is 3.73m, walls 2.85 and invert 5.5m for k=2 and reduces with k
for MC 90 model. But plastic zone is limited to invert in HB-90model.
25dia rock bolts, resin end anchored + slow setting cement capsules, 4.5m long, shotcrete 50mm
thick and 200mm thick SFRS final lining is considered.
Redistribution of stresses is concentrated in the rock mass at a distance of 3m from the tunnel
boundary which delineate the plastic and elastic zones.
5.1.3.4 Seismic Design:
The tunnels are located in Zone III of seismic map of India. Tunnel section with Liner 1 of 50mm shotcrete
and Liner 2 of 200mm SFRS lining is analysed with Phase2 for its adequacy with and without seismic. Inter-
action diagrams are generated. Thrust, Shear and Moments in tunnel section during different stages of con-
struction are plotted on the interaction diagrams. Though some of the values are outside the diagram, stress
relaxation of the rock mass when considered eliminates the data points outside the envelope.
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5.2 Portal Section
5.2.1 Estimation of rock mass parameters:
Portal section @ km: 107.845 and Borehole No.6 is used for the calculations. Mohr Coulomb Failure
criterion is used in the analysis. It is assumed similar rock conditions prevail at new north portal section after
shifting by 30 m.
Table 29 : Test results on intact rock samples of BH 6 at km: 107.845
Depth UCS(Mpa) E(Mpa) γ(kN/m3)
17.0-18.0 102.70 42062 2.67
21.5-22.5 94.200 34673 2.66
26.0-27.0 115.30 45709 2.64
30.5-31.5 76.10 36119 2.68
35.0-36.0 116.50 38438 2.66
39.5-41.0 125.40 79032 2.74
Mean 105.00 46005.5 2.67
St dev 16.400
Value of standard deviation of the UCS data is 16.40 % of the mean value. 90% of UCS values measured
are exceeding 84.0 MPa and the value will be used as input parameter in the FEM-model. Fig. 52 shows the
correlation between UCS and E.
Fig. 52: Linear Correlation between UCS vs E
Measurements of cohesive strength in the same borehole indicates Cmean=4.14 MPa and C10%=2.5 MPa.
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Fig. 53: Linear correlation between Q and RMR
Friction angle in the borehole indicates φmean=70o and φ10%=68o.is Residual friction angle, φr = tan-1(Jr/Ja)
is worked out to be 36o with Jr =1.5 and Ja = 2.0. So friction angle of rock mass equal to residual friction is
considered in the analysis. The stiffness modulus E10% is 33.0 GPa according correlation in Fig. 52.
Table 30: Test results of cohesion and friction of rock mass
C(Mpa) φ(degrees)
3.80 71.36
2.76 68.91
5.85 67.61
After doing the Probabilistic Analysis, the following Rock Properties are considered for Numerical Modeling.
Table 31: Selected Rock Mass Properties for Numerical Analysis
Soil (Assumed)
Cohesive Strength,C 0.11 Mpa
Friction Angle,φ 16.00 Degree
Tensile Strength, T 0.00 Mpa
Modulus of Deformation, Ed 0.045 Gpa
Highly weathered Rock (Assumed)
Cohesive Strength, C 0.11 Mpa
Friction Angle, φ 35.00 Degree
Tensile Strength, T 0.00 Mpa
Modulus of Deformation, Ed 1.00 Gpa
Rock
Confidence Limit 90% units
Input values of Mohr Coulomb failure Criterion
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Cohesive Strength, C 2.50 Mpa
Friction Angle, φ 36.0 Degree
Tensile Strength, T 0.00 Mpa
Modulus of Elasticity, Ei 32.94 Gpa
Modulus of Deformation, Ed 1.32 Gpa
5.2.2 In-situ Rock Stress
Close to the ground surface k value is small due to weathering and hence k values of 0.35 and 0.50 are
considered for the analysis of portal section. Analysis with k=0.35 is reported since k=0.5 is not found critical.
Fig. 54: Model showing the extent and boundary conditions adopted for the external boundary
5.2.3 Elastic Perfectly Plastic Analysis
The direction of total displacement is semi horizontal parallel to the hill slope, as in near valley side model.
The deformation behavior in both tube tunnels indicates that the right wall and crown are in de-stressed
mode due to the excavation and there is stress concentration on the left wall. The intensity of distressed rock
in the tube tunnel roofs decrease as the tunnel advances into the hill.
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Fig. 55: Displacement vectors and deformed excavation shapes at portal
The maximum principal stress in tension due to the de-confinement of rock mass in the tunnel floor is lower
than the tensile strength of the rock and hence a flat invert is considered to be adequate.
Fig. 56: Extent of Plastic Zone in tension(unsupported with Static)
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Fig. 57: Extent of Plastic Zone in tension(Unsupported with Earthquake)
5.2.4 Design of Initial Support System
A top heading excavation with steel sets fully embedded in shotcrete to form a very strong structural shell on
enlarged footings (“elephant’s feet”) have been used. In addition to steel ribs, fully grouted rock bolt anchors
4.00 m long are installed at elephant foot location. The normal force in the footing of the lining, 0.4m wide, is
1.204 MN/m, resulting in stress of 3.10 Mpa, which is well below the sustainable stress of the rock mass.
Spilling is proposed to reduce the vertical stress ahead of the tunnel face to increase the stability.
Fig. 58: Extent of Plastic Zone in tension (supported with static)
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Fig. 59: Extent of Plastic Zone in tension (supported with Earthquake)
The extent of plastic zones with support system is insignificantly small in without and with earthquake. The
interaction diagrams with primary support system of steel ribs and shotcrete are given below.
Fig. 60: Interaction diagrams of Steel rib embedded in shotcrete for k=0.35
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Fig. 61: Interaction diagrams of 50 mm Shotcrete for k=0.35
The moment-axial thrust capacity curves plotted in Figure 60 & 61 are calculated for a factor of safety of 1.0.
5.2.5 Design of Final lining
The final unreinforced final concrete lining is designed with a factor of safety of 2, in the portal section.
Fig. 62: Interaction diagrams of final lining 250 mm thick M 25 grade PCC for k=0.35
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The moment-axial thrust capacity diagram for a 250 mm thick lining of M25 grade, unreinforced concrete, is
plotted in Fig. 62. In the same figure, the induced moment-axial thrust combinations are also plotted. The
points all fall within the capacity envelope. Hence an unreinforced final concrete lining 250mm thick is
adequate in the portal.
5.2.6 Conclusions:
Mohr coulomb failure criteria is used in the analysis. Properties of rock mass of BH 6 are consid-
ered with k = 0.35, since tunnel is at shallow depth below ground level.
Elastic Perfectly plastic analysis indicates direction of total displacement is parallel to the hill slope
and thereby stresses concentration is on hill side walls of both the tubes. Seismic condition is in-
cluded.
Interaction diagrams are generated for shotcerete, steel rib, and final concrete lining. Thrust, shear
and moments in tunnel section are within the interaction diagrams.
Excavation is by heading and bench with spiling umbrella. Initial support system is steel sets
W200x35.9, fully embedded in shotcrete. Steel ribs rest at bench on elephant foot footing. The final
lining is 250mm thick plain cement concrete M 25 grade.
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