Applied Mechanics and Materials Vols 479-480 (2014) pp 1076-1080
© (2014) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMM.479-480.1076
Online: 2013-12-06
Site Response Analysis for a Site with the Dipping Bedrock and
Liquefiable Layers using FLAC 3D
Yuan-Chieh Wu1, a and Meng-Hsiu Hsieh 1, b
1
Institute of Nuclear Energy Research, Atomic Energy Council, Taoyuan 32546, Taiwan
a
ycwu@iner.gov.tw, bmarshall94216@iner.gov.tw
Keywords: Site Response Analysis, Liquefaction, Nuclear power plant
Abstract. To get the precise input motion for seismic analysis of important structures located in
liquefiable soil layers, this study demonstrates site response analysis using FLAC 3D [1]. Based on
the previous earthquake diaster experiences and regulatory requirements for nuclear power plants
(NPP), the seismic wave propagation in the site having dipping bedrock surface was modeled, also the
excess pore water pressure during excitation process was added into the soil elements. The free-field
site response model is used to generate the response spectra at different ground surface locations, and
to predict the influence range of soil liquefaction. The analysis results show that soil liquefaction
could reduce site amplification effect, and might have different degree of impact depending on natural
frequency and soil pressure resistance of structures. The 3D model also can capture the soil
unceratinties and reflect the real topographic effect in one computer run, so the current multiple
one-dimensional equivalent linear analysis process could be improved. Therefore, the FLAC 3D
model can fulfill nuclear regulatory requirement, and provide suitable ground-motion prediction for
liquefiable soil sites and complex bedrock surface sites for the need of seismic evaluations of existing
NPPs after Fukushima Dai-ichi Tragedy.
Introduction
Soil liquefaction during large earthquake is a well-known phenomenon, and causes heavy damage
particularly for life-line structure, for example, 2011 Fukushima earthquake, 2010 Canterbury
earthquake, 2007 Chuetsu offshore earthquake causing the fire of transformer in Kashiwazaki-Kariwa
NPP, etc.. Although engineering methods including pile foundation or soil improvement can mitigate
the damage localy, it is difficult to eliminate this threat due to the cost if total replacement of soil
layers are considered. To design the structures attacked by soil liquefaction, the best way is not only to
consider liquefaction potential using screening methods from empirical datas or labatory tests, also
soil-structure interaction (SSI) analysis should be executed for further safety evaluation. For existing
NPPs located beside the seashore, soil liquefaction could be occurred in soil sediments or backfill
because of high groundwater table or high ground motion level like Kashiwazaki-Kariwa NPP, so site
response analysis before performing soil-structure interaction analysis should consider high
nonlinearity and pore pressure if soil liquefaction occurs.
To establish design earthquake motion for structure/system/component of NPP, NRC set up the
percise process including modeling the properties and uncertainties of structure and soil; besides,
probabilistic seismic hazard analysis and site response analysis reflecting the uncertainty of source,
path and site parameters should be used to determine the design ground motion of a site. After several
decades development and verification by real records, current regulatory guidances such as RG 1.208
[2], NUREG-0800 [3] Sec. 2.5.2, Sec. 3.7.1, and Sec. 3.7.2 provide the reasonable decision-making,
and the accompanying tools like Shake [4] endorsed by the authority make utilities deal easily.
However, the liquefaction impact is not inevitable for the site with high ground-motion level and
susceptible soil backfill even though reactor buildings of NPP usually found on rock layer, so NRC
provides RG 1.198 [5] as the guidance for evaluating the potential for earthquake-induced instability
of soils resulting from liquefaction and strength degradation. Although RG 1.198 only discuss soil
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Applied Mechanics and Materials Vols. 479-480
1077
stability problem, the analytical methods addressed there could be extended to site response, even SSI
including liquefaction.
After Fukushima Daiichi NPP destroyed by Tohoku Earthquake, utilities are performing design
ground-motion re-determination, seismic margin assessment (SMA) or seismic probabilistic risk
assessment (SPRA) referring US NRC Near Term Task Force (NTTF) recommendation [6], and the
SSI play an important role in these tasks. Therefore, the example using FLAC 3D can demonstrate
liquefaction influence range in the site, and predict the ground motion at any point during earthquake
excitation. Furthermore, the ability of new model can lead the future regulatory amendment into
incorporating more geotechnical engineering developments.
Soil Model
Soil Properties. The soil condition of site has been investigated through 4 boreholes, and three
simplified layers, sand (SM2), sand with rubble (SM3) and sand rock, are set to build the underground
structure as Fig. 1. Fig. 1 shows the three dimensional model is 270m width, 270m length, and 20m
depth, and 4 boreholes are located at position 1 to 4. To obtain the soil properties of inner element,
Kriging Method was employed to interpolate soil data so that the interfaces between each layers were
built, and three groundwater table scenario based on seansonal fluctuation were assumed to discuss
their influence.
(a) Soil Profile
(b) Three dimensional model with dipping layers
Fig. 1: The simplified soil layers and three dimensional free-field soil model
Liquefaction Model. To test the uncertainty of available material model, three models including
(A) elastic model, (B) elasto-plastic model, and (C) elasto-plastic model with Finn increment model
were used for three layers as shown in Tables 1. Model A is tranditional equivalent linear apporach to
generate site response, it is used to check the result with Shake. Model B considers Mohr-Coulomb
failure criteria and is given the cohesion and friction angle by SPT-N value using empirical equation;
Model C uses Finn increment model to simulate excess pore pressure, and uses Byrne(1991) [7] pore
pressure model in liquefaction simulation.
Table 1: Material models for the different layers
Model A: Elastic Model with 2% viscous damping
Layer
SM2
SM3
Rock
rt(t/m3)
2.05
2.10
2.20
Gmax(MPa) Bulk Modulus (MPa) Porosity Material Model
251
544
0.35
Elastic
425
709
0.33
Elastic
2200
3195
0.21
Elastic
Model B: Elasto-Plastic Model, Mohr-Column Criteria, and 2% viscous damping
Layer
SM2
SM3
Rock
rt(t/m3)
2.05
2.10
2.20
Gmax(MPa)
251
425
2200
B(MPa)
544
709
3195
Porosity
0.35
0.33
0.21
c(kN/m2)
0
0
None
Friction Angel (
33
36
None
∘)
Material Model
Mohr-Coulomb
Mohr-Coulomb
Elastic
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Applied Science and Precision Engineering Innovation
Model C: Elasto-Plastic, Mohr-Column Criteria, 2% viscous damping, and Finn increment model
Layer
SM2
SM3
Rock
rt(t/m3)
2.05
2.10
2.20
Gmax(MPa)
251
425
2200
B(MPa)
544
709
3195
Porosity
0.35
0.33
0.21
c(kN/m2) Friction Angel (
0
33
0
36
None
None
∘)
N60
20
30
None
Material Model
Finn increment
Finn increment
Elastic
Seismic Input Motion
The input motion at model base which is defined as the design basis event of the NPP is shown in
Fig. 2, and Fourier transform result indicates the fundamental frequency is about 2 Hz and frequency
content of this waveform is majorly below 10 Hz.
0.5
0.5
FFT from modified NC2 designed acceleration
Modified Designed Acceleration, PGA = 0.36g
0.45
0.4
0.4
Fourier amplitude (m/sec)
0.3
Acceleration (g)
0.2
0.1
0
-0.1
-0.2
0.3
0.25
0.2
0.15
0.1
-0.3
0.05
-0.4
-0.5
0
0.35
0
5
10
15
20
0
2
4
6
Time (s)
8
10
12
Frequency (Hz)
14
16
18
20
(a) Acceleration time history
(b) Fourier Transform
Fig. 2: Waveform and Fourier transform of input motion at model base
Results and Discussion
Site Amplification Analysis. To verify three dimensional model for predicting ground motion as
one-dimensional equivalent linear method, fundamental frequency anlaysis of Model A is performed
as shown in Fig. 3. The modal frequencies of transfer function show the difference among different
surface position, and can be related to various soil column depth because of dipping rock surface.
Hence, the model can predict ground motion considering soil uncertainty and dipping beadrock per
RG 1.208. Fig. 4 shows the influence of material model on amplification ratio, and Model C induces
less site amplification than Model B and Model A due to liquefaction model used. Fig. 4 also shows
deeper water table having less amplification about at 0.5 sec (2 Hz) in Model C; therefore, more
excess pore pressure not only can prevent more seismic wave from arriving at ground surface, but can
eliminate the earthquake energy of main frequency content. The comaprison of ground motion at
different elevation between rock (position 1) and sand (position 3) is aslo shown in Fig.5, and the
seismic wave cannot be transmitted to 5 m depth and ground surface.
0.1
Position 1
Position 2
Position 3
Position 4
Position 5
Position 6
Position 7
Position 8
Position 9
0.09
0.08
Amplitude (kines)
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0
5
10
15
20
25
30
35
40
45
50
Frequency (Hz)
Fig. 3: Comparison of tranfer function for different surface locations
Applied Mechanics and Materials Vols. 479-480
(a) Position 1
(b) Position 2
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(c) Position 3
Fig. 4: Comparison of the site amplification ratio among material models
(B)
(B)
1
1
Depth = 0 m
Depth = 0 m
0
-1
0
0
5
10
15
-1
20
1
0
5
10
15
20
1
Depth = 5 m
Depth = 5 m
Acceleration (g)
-1
0
0
5
10
15
20
1
Depth = 10 m
0
-1
0
5
10
15
20
1
Acceleration (g)
0
-1
0
5
10
15
20
1
Depth = 10 m
0
-1
0
5
10
15
20
1
Depth = 15 m
0
-1
Depth = 15 m
0
0
5
10
15
-1
20
1
0
5
10
15
20
1
Depth = 20 m
0
-1
Depth = 20 m
0
0
5
10
15
20
Time (s)
-1
0
5
10
15
20
Time (s)
(a) position 1
(b) position 3
Fig. 5: Comparison of the influence of pore pressure on ground motion
Liquefaction Analysis. The distribution of the excess pore pressure ratio (Ru) at depth 5 m in
water table scenario at 6 m case generated by the site response analysis from liquefaction model is
presented in Fig. 6. Liquefaction occurs when Ru reach 1 because Ru is defined as the ratio of excess
pore pressure to effective vertical tress. From Fig.2, minimum acceleration occurs at 8.5 sec,
maximum occurs at 11 sec, and strong motion ends about at 15sec. Fig 6 shows the liquefaction is
going to occur at 9 sec because Ru approaches 1, and the liquefaction area expands till 11sec then
shrinks. The model also shows location of pore water pressure induced firstly could be at the
boundary Rock and SM2, and liquefaction occur at most area of SM2.
250
Y Coordinate (m)
200
150
100
50
50
100
150
X Coordinate (m)
200
250
(a) Plan and section view of model at depth 8.5m
(b) Excess pore water pressure contour
Fig. 6: Influence area of the excess pore water pressure generated by liquefaction
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Applied Science and Precision Engineering Innovation
Conclusions
The results of transfer function show three dimensional model using FLAC can perform site response
analysis for different site locations at one run, so at least 60 Shake runs per RG 1.208 considering soil
uncertainties of borehole data can be replaced. To predict the ground motion of liquefiable site, the
suitable material model tested demonstrates the ability, and the range of liquefaction influence can be
provided for determining the decision of soil improvement. The simulated liquefaction scenarios
show dipping bedrock surface would be the excess pore pressure path at the initial state because
bedrock can transmit more seismic wave energy than soil undergoing buildup of pore pressure, and
the pore water pressure along interface between soil and rock possibly could cause unstability of soil.
Therefore, the past lateral spreading failure cases induced by liquefaction could be explained by this
simulation, and issue of RG 1.198 could be solved.
Acknowledgement
This support of the National Science Council (NSC) under the Grants NSC102-3113-P-042A-009
is gratefully acknowledged.
References
[1] Itasca Consulting Group, Inc., Fast Lagrangian Analysis of Continua in 3 Dimensions User's
Manual, Minneapolis, Minnesota, U.S.A., 2009.
[2] Regulatory Guide 1.208, A Performance-Based Approach to Define the Safe Shutdown
Earthquake Ground Motion, U.S. Nuclear Regulatory Commission, Office of Nuclear Reactor
Regulation, 2007.
[3] NUREG-0800, Standard Review Plan for the Review of Safety Analysis Reports for Nuclear
Power Plants, U.S. Nuclear Regulatory Commission, Washington, DC
[4] Schnabel, P. B., Lysmer, J., and Seed, H. B., SHAKE: A computer program for earthquake
response analysis of horizontally-layered sites, Report No. EERC-72/12. Earthquake
Engineering Research Center, University of California at Berkeley, 1972.
[5] Regulatory Guide 1.198, Procedure and Criteria for Assessing Seismic Soil Liquefaction at
Nuclear Power Plants Sites, U.S. Nuclear Regulatory Commission, Office of Nuclear Reactor
Regulation, 2003..
[6] NRC Letter, Request for Information Pursuant to Title 10 of the Code of Federal Regulations
50.54(f) Regarding Recommendations 2.1,2.3, and 9.3, of the Near-Term Task Force Review of
Insights from the Fukushima Dai-Ichi Accident ; dated March 12,2012.
[7] Byrne, P. M., A model for predicting liquefaction induced displacement, Proceedings of the
Second International Conference on Recent Advances in Geotechnical Earthquake Engineering
and Soil Dynamics, St. Louis, Missouri, Vol. 2, 1027–1035, 199.
Applied Science and Precision Engineering Innovation
10.4028/www.scientific.net/AMM.479-480
Site Response Analysis for a Site with the Dipping Bedrock and Liquefiable Layers Using FLAC 3D
10.4028/www.scientific.net/AMM.479-480.1076