Seismic Analyses for the Deposition Tunnel in Fractured Rock by 3DEC
Meng-Hsiu Hsieh*, Yuan-Chieh Wu
Institute of Nuclear Energy Research, Atomic Energy Council,
No.1000 Wenhua Rd, Longtan Township, Jiaan Village, 32546 Taoyuan County, Taiwan

Key words; fractured rock, seismic analysis, 3DEC

Abstract
In order to consider the operation safety of spent nuclear fuel final disposal (SNFD), the way of final
disposal is to emplace waste canister in deep underground opening, so the tunnel stability which is the important
issue for operational period must be faced. Taiwan is located in the Circum-Pacific seismic zone; therefore, theimpact of earthquake on the safety of the tunnel should be highly paid attention, and SNFD program in Taiwan
has planned the research path including seismic hazard and tunnel structural capacity perspectives. At thismoment, for the purpose of operation safety confirmation of the SNFD repository design in the offshore island
crystalline rock mass of Taiwan, the seismic stability analysis of deposition tunnel was carried out. Since thefractures in deep granite rock mass might be the key to the instability of the tunnel during the earthquake, the3DEC was used to analyze the stability of tunnel during normal and earthquake period, and analysis cases also
compared intact rock and fractured rock to realize the difference on seismic performance. The results show thatthe safety factor of tunnel during normal period is directly affected by the fractures, while the safety factor isrelatively high in the intact rock, but the impact of the earthquake on the safety factor is relatively small. Fromthe study experience, the tunnel time history analysis by 3DEC has been understood, so the future research plancan be made. And the more fracture related parameters has been planned to input to evaluate the impact ontunnel stability in the future.

1. Introduction
In design of the tunnel section, it not only needs tomeet the basic requirement of space, also consider therock mechanics parameters, stress conditions andother factors to confirm compliance with safety
standards. Earthquake should be the natural disasters
that may cause the tunnel to be unstable during
operation. In order to confirm the stability of thedeposition tunnel during operation, such as the studyof H12 [1] in Japan, the stability of the tunnel during
the earthquake should be evaluated. And Mohr Coulomb failure criteria usually is used to calculate
the safety factor of the tunnel section to represent themargin of stability. Traditionally the numericalanalysis method for the stability of tunnel used
continuum mechanics software. However, thefractures in rock mass probably play important roleon the stability of tunnel section, so the modeling offracture in stability analysis is necessary. In this study,
three-dimensional distant element method software
3DEC was used to consider the intact rock andfracture rock cases, in order to evaluate whether theexistence of fracture has a significant effect on thestability of tunnel section.

2. Analysis methods and considerations
In this study, the discrete fracture network (DFN)
data of the offshore island crystalline rock mass(ITRI, 2015) shown in Table 1 were used, and thestability analyses during normal operation andearthquake period were performed to explore theinfluence of the fractures. The deposition tunnel size
is referred to the Table 1 in SNFD2017 referencecase disposal design and engineering technology andparameter description (2016) [3]. The cross section isshown in Fig 1, and tunnels are located at 500 m
depth. In order to avoid the boundary effect of thenumerical model, the Rock model size is generally
required to be at least 5 times the tunnel size.
Because the tunnel section width is 4.2 m and theheight is 4.8 m, the model size is 21 m x 24 m.
DFN parameters include the randomness offracture sets, so the stability analysis should be
performed for large number of case to find the worst
one. Due to limited time and research target, theanalysis cases did not consider the randomness offractures. For the modeling of fractured rock mass,multiple sets of DFN will be established to cut the6th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, Japanwhole rock model, the element size of the model
should be small enough to avoid the generation oflonger elements. However, it will take large amountof computational resources and time for seismic
analysis, so the element size would take 0.5 m after
assessment. Although, totally five sets of DFN data
are obtained from the geological survey results of theoffshore island crystalline rock mass. Since theseismic analysis will take over 3 months if
considering 5 sets of DFN in one case at the sametime, in order to speed up the research progress, thisstudy only used two sets of DFN which have higher
P32 ratios to discuss the influence before and after theearthquake.
On the other hand, for comparing the difference
between the stability of the intact rock mass and thefractured rock mass in the normal period, five sets ofDFN were used because the computational time canbe controlled in research schedule. The tunnel modelin fractured rock built by 3DEC is shown in Figure 2.
The analysis cases include (1) the stability during
normal period in no fractured rock mass; (2) thestability during earthquake in no fractured rock mass;(3) the stability during normal period for 5 sets ofDFN in rock mass; (4) the stability during earthquakefor 2 sets of DFN in rock mass.
The calculation of the safety factor is based on theMohr-Coulomb failure criterion, which takes intoaccount the stress state to confirm whether the rockmass has entered the plasticity. The comparisons of
the stress conditions among normal period,
earthquake period, fractured rock mass and intact
rock mass will be made, and they can provide theinformation of the impact level to become a basis for
subsequent verification and test plan.
3. Material parameter and boundary condition
From geological investigation data, rock mass canbe partitioned into weathered rock layer R0, which is
70 m thickness from the ground surface, and granite
gneiss body R1. In order to simplify the input
parameters of the model, the parameters aresummarized as Table 2. The fracture related
mechanical parameters have not been investigated, sothe 3DEC built-in parameters as shown in Table 3 areused.
The setting of the in situ stress is referred to thefield data by using Hydraulic Fracturing method in
the depth of 430 m. The measured vertical stress is
σv=11.4 MPa; horizontal maximum principal stress is
σH= 14.43 MPa; and horizontal minimum principal
stress is σh = 9.38 MPa; so the horizontal K0, min is
0.82 and K0, max is 1.27. For tunnel alignment, thetunnel main axial will be parallel to the maximum
horizontal axis; so the tunnel radial stress will belower, and Kx and Ky are set as 0.82 and 1.27
respectively.

Table 1 Discrete fracture network parameters
Set No.

trendplunge

κ

P32

123
4
565°
344°
281°
174°
175°

17°
38°
29°
22°
75°

201816
17
19

15%
24%
30%
10%
21%

Note: κ is Fisher distribution parameter; P32 is fracture
intensity (m2/m3).

Table 2 Rock material parameters
Density γ(kg/m3)

CohesionC(MPa)

Frictionangleϕ(°)

Young'smodulusE(GPa)

Poisson
ratio
ν

2,750

27.46

51.05

44.18

0.17

Table 3 Rock fracture material parameters
Joint
normalstiffness(N/m)

Joint shear Dilation
stiffness
angle
(N/m)
Ψ(°)

2.0 x1012 2.0 x1012

20

Joint tensileJointstrengthcohesion
(Pa)
(Pa)

00

Figure 1. The cross section of disposal tunnel anddisposal hole

6th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, Japan

Figure 2. Tunnel model with 5 sets of DFN in rockmass
4. Input of earthquake time history
The response spectrum for tunnel design isgenerated by the seismic hazard analysis [4], and thePGA of spectrum compatible acceleration time
history is 0.288 g. The duration is 40.96 s, and timeinterval is 0.01 s; so, totally there are 4,096 data
points. The earthquake time history was input on therock outcrop surface (at 70 m under the groundsurface, which is the interface between theweathering layer R0 and the granite gneiss body R1).
Using one dimensional site response analysis, thewave will pass down to 500 m under the groundsurface, and the earthquake wave form of 500 m
depth is shown in Figure 3, where the peak groundacceleration is 0.206 g. Because 3DEC dynamic
analysis can only input the velocity or stress time
history, it is necessary to integrate the acceleration
time history to get the velocity time history as shownin Figure 4. This velocity time history was input atthe bottom of the 3DEC model to perform the seismic
analysis.

Figure 3. The input acceleration time history on thebase of deposition tunnel model

Figure 4. The input of velocity time history on thebase of disposal tunnel model
5. Results and discussion(1) Case 1: normal period, rock mass without fracture
After calculating principal stress of each element
by 3DEC to generate the safety factor of eachelement by Mohr-Coulomb failure criterion, theminimum safety factor is 1.6658, which occurs at thebottom of the tunnel edge as shown in Figure 5.
(2) Case 2: earthquake period, rock mass without
fracture
The seismic analysis is carried out and the safety
factor is checked at the time point of the maximum
acceleration of the earthquake. At this point, theminimum safety factor of all elements is 1.6656,
which also occurs at the bottom of the tunnel edge.
The safety factor is only slightly decreased than thatof the normal period. This phenomenon can explainthat in-situ stresses in the deep rock mass are high,and the increasing stresses due to the earthquake haveless impact.
(3) Case 3: normal period, rock mass with 5 sets ofDFN
The minimum safety factor is 1.2283, which also
occurs at the bottom of the tunnel edge, as shown inFig. 7, and the safety factor is significant lower whencompared with case 1 (rock mass without fracture).
However, in the middle of the tunnel floor safety
factor is particularly high. After checking the stressand displacement, it shows there is a relative shift(displacement about 3mm), so that it leads the stressdrop and have a relatively high safety factor.
(4) Case 4: earthquake period, rock mass with two
sets of DFN
The safety factor of the fractured rock mass during
normal period is slightly decreased, and the minimum
safety factor is 1.3840, which also occurs at thebottom of the tunnel edge, as shown in Fig. 8.
However, the safety factor is higher than the case 3
which with five sets of DFN. The result shows thenumber of DFN set is negatively correlated withsafety factor, and more sets of DFN will lower thesafety factor.

6th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, Japan

For earthquake period, the minimum safety factorof the tunnel is 1.4142, which occurs at the bottom of
the tunnel edge as shown in Fig. 9, but it is slightly
increased when compared to the safety factor for rockmass with 2 sets of DFN in normal period. Thisphenomenon shows that, for considering thediscontinuous property of the fracture, the fractures
will induce relative displacements during earthquake;they would cause the stress release of the rock mass,
so the safety factor of the stress calculation is reduced.
This result is different from Case 2 which the rockmass is without fracture, and it also shows thecomparison between continuous and discontinuous
mechanics treatment on stress analysis..
Although the safety factor changes in this caseduring the earthquake, but only slightly different, it
can see the seismic wave impact of the deep rockmass is low.

Figure 5. Safety factor for rock mass without
fracture when normal period

Figure 7. Safety factor for rock mass with 5 sets of
DFN when normal period

Figure 8. Safety factor for rock mass with 2 sets of of
DFN when normal period

Figure 9. Safety factor for rock mass with 2 sets of
DFN when earthquake period
Figure 6. Safety factor for rock mass without fracture
when earthquake period
6. Conclusion
Conclusions of the analyses are as follows :(1) The analysis results show that the safety of tunnel
during normal period in deep rock mass is highly
correlated with the number of fractures. However,even five sets of fractures are considered, theminimum safety factor is still 1.2283. So if the6th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, Japanfractured cannot create the weak plane to form
instable wedge or rock spalling, the influence
would be minor.
(2) For current test site of offshore island crystalline
rock mass in Taiwan SNFD program, whether inintact rock or fractured rock, the earthquake
influence is slightly low, and the tunnel is still in asafe state, because the stress induced by 0.2g
PGA earthquake seems low compared to that ofin-situ stress.
And there are some suggestions as follows:(1) From analysis results, the displacement causedby fracture movement will release the stress andincrease safety factor; however, large
displacement may result in instability. Therefore,
the analysis should not only focus on the safety
factor calculated from stress results, but also
should check displacement results.
(2) Because seismic analysis requires a lot ofcomputing resources and computing time, it isdifficult to meet the randomness of DFN.
Therefore, it is suggested that the deterministic
fracture information or critical fracture should beassessed by investigation group. On the other
hand, the process by using static nonlinear
analysis, equivalent-static load, or frequency
domain method from structural engineeringexperience could be introduced and developed tohelp determine safety factor quickly.
7. Reference[1] JNC, H12: Project to establish the scientific andtechnical basis for HLW disposal in Japan,
Supporting report 2, Japan Nuclear Cycle
Development Institute, JNC-TN1410-2000-003,2000.
[2] ITRI，The Spend Nuclear Fuel Final Disposal
Program Potential Host Rock Characterizationand Evaluation Stage Potential Host RockCharacteristics
Investigation(Project2015–2018) The Taiwan Reference Case of the
SNFD2017 Report Table ‐ 2: Geological
Conceptual Models and Characteristic Data，
Taiwan Power Company，2015.
[3] Institute of Nuclear Energy Research, Atomic
Energy Council ， SNFD2017 reference casedisposal design and engineering technology andparameter description ，Taiwan PowerCompany, 2016.
[4] Yuan-Chieh Wu、Cheng-Yu Pan、Meng-Hsiu
Hsieh，The Spent Nuclear Fuel Final Disposal
Program Potential Host Rock Characterizationand Evaluation Stage Technology Developmentof Performance and Safety Assessment(Project2015-2018) Seismic Hazard Analysis for thecrystalline rock regions of the western offshoreislands，Institute of Nuclear Energy Research,
Atomic Energy Council，2016.

6th East Asia Forum on Radwaste Management Conference
November 27-29, 2017, Osaka, Japan