Concept development of an underground research tunnel

Concept development of an underground research tunnel for validating the Korean reference HLW disposal system
Sangki Kwon
a,*
,W.J.Cho a ,P.S.Han
b
a P.O.box 105,Validation of Performance of HLW Disposal System,Korea Atomic Energy Research Institute,Deck-Jin Dong,Yusung Ku,
Daejeon 305-600,Republic of Korea
b
P.O.box 105,Radioactive Waste Disposal,Korea Atomic Energy Research Institute,Deck-Jin Dong,Yusung Ku,Daejeon 305-600,Republic of Korea
Received 6October 2004;received in revised form 31January 2005;accepted 5June 2005
Available online 29August 2005
Abstract
In order to dispose of high-level radioactive waste (HLW)safely in geological formations,it is necessary to assess the feasibility,safety,appropriateness,and stability of the disposal concept at an underground research laboratory (URL)constructed in the same geological formation as the host rock.In this study,minimum requirements and the conceptual design for an efficient construction of a small scale URL were derived based on a literature review.To confirm the validity of the conceptual design for construction at KAERI,a geological survey including a seismic refraction survey,electronic resistivity survey,borehole drilling,and in situ and laboratory tests were carried out.The mechanical stability of the URL was investigated with a consideration of the surface topog-raphy,tunnel geometry,tunnel slope,sequential excavation,in situ stress ratio,erosion effect,and rock property variation along the tunnel using the three-dimensional code,FLAC3D.From the study,it was possible to conclude that the small scale URL will be effectively constructed in a granite mass at KAERI and will satisfy the minimum requirements.Ó2005Elsevier Ltd.All rights reserved.
Keywords:URL;HLW disposal;Site characterization;Mechanical stability;FLAC3D
1.Introduction
In Korea,four Canadian deuterium uranium (CAN-DU)reactors and 15pressurized water reactor (PWR)are operating.The current generating capacity is 15,700MWe with a share of 40%of the total production of electricity.The cumulative amount of spent fuel from the nuclear power plants reached 6000MTU in 2003.It is expected that approximately 11,000and 19,000MTU will be accumulated by the years 2010and 2020,respec-tively.For developing a safe disposal concept to perma-nently dispose of the spent fuels generated from the reactors,the Korea Atomic Energy Research Institute
(KAERI)have been carrying out a long-term R&D pro-gram since 1997.According to the preliminary disposal concept,the spent fuels will be encapsulated in corrosion resistant canisters and disposed of in a several hundred meters deep underground repository in crystalline rock (Kang et al.,2000).
In order to dispose of high-level radioactive waste (HLW)safely in geological formations,it is necessary to assess the feasibility,safety,appropriateness,and sta-bility of a disposal concept at an underground research laboratory (URL)in the same geological formation as the host rock.Many countries considering a geological disposal of radioactive waste,therefore,have con-structed underground research laboratories and carried different in situ experiments.Table 1shows the status of the underground research laboratories in the world.Site specific URL refers to the URLs in potential
0886-7798/$-see front matter Ó2005Elsevier Ltd.All rights reserved.doi:10.1016/j.tust.2005.06.008
*
Corresponding author.Tel.:+82428688914;fax:+82428688850.
E-mail address:Kwonsk@kaeri.re.kr (S.Kwon).
/locate/tust
Tunnelling and Underground Space Technology 21(2006)
203–217
Tunnelling and
Underground Space Technology
incorporating Trenchless Technology Research
disposal sites and generic URL refers to the facilities developed elsewhere.
In Korea,a small scale generic URL is planned to accumulate experience and develop the technologies re-lated to HLW disposal.The experience in the small scale URL will be critical for carrying out the large scale site specific URL program successfully in the future.In this study,a concept of a small scale URL was developed and the mechanical stability of the concept was evalu-ated for the case of constructing it at the KAERI site.
2.Development of URL concept
For developing an URL concept,it is necessary to consider the repository system,research items planned to be carried out at the URL,hydrochemical conditions, hydrology,and geological condition of the site,rock sta-bility,and other environmental conditions such as sensi-tive buildings adjacent to the URL site.
2.1.Disposal concept
According to the preliminary disposal concept,the repository is supposed to be located in a crystalline rock mass at several hundred meters deep underground.The underground repository and surface facility are to be connected with shafts and/or a ramp(Kang et al.,2000).Fig.1shows the schematic view of the under-ground repository and shafts.The entire facility is con-sidered to be constructed by drill and blasting.The underground facility requires an area of about4km2. Disposal tunnels are a horseshoe shape and the dimen-sions are6m wide7m high and250m long.The recom-mended dimensions of the emplacement tunnel and the borehole are shown in Fig.1.The canisters containing the spent fuel are assumed to be placed in the vertical boreholes drilled along the center line in thefloor.In the reference disposal concept,the migration of radio-nuclides from the HLW will be delayed by natural bar-riers and engineered barriers including the waste form, container,buffer and backfill.
2.2.Research items
The small scale URL at KAERI will be a core infra-structure for the future R&D related to the HLW dis-posal program.Various researches including the excavation damage zone(EDZ)effect,fluidflow through discontinuities,rock mechanics,performance of the engineered barriers,migration of the ion,behav-ior of the colloid,and the validation of the disposal tech-nologies such as the transportation,construction, emplacement of the canister and buffer,backfilling, and the retrieval operations will be carried out at the URL.Table2lists the important research items to be
Table1
Underground research facilities in the world(NEA,2001)
Type URL Country Rock Depth(m)Operation period Generic URL(type1)Asse mine Germany Salt490,800,9501965–1997
Tono Japan Sed.rock200Since1986
Kamaishi Japan Granite2601988–1998
Stripa mine Sweden Granite360–4101976–1992
Grimsel test site Switzerland Granite450Since1983
Mont Terri Switzerland Shale400Since1995
Olkiluoto tunnel Finland Granite60–100Since1993
Climax USA Granite4201978–1983
G-tunnel USA Tuff>3001979–1990
Amelie France Salt1986–1992
Fanay-Augeres France Granite1980–1990
Tournemire France Shale250Since1990
Generic URL(type2)HADES-URF Belgium Clay230Since1980
Whiteshell URL Canada Granite240–420Since1984
Mizunami URL Japan Granite1000Drilling phase
Horonobe URL Japan Sed.rock500Planning
Aspo Sweden Granite200–450Since1990
Busted Butte USA Tuff100Since1998
Site specific URL ONKALO Finland Granite500Drilling phase
Meuse/Haute Marne France Shale450–500Surface work in1999
Gorleben Germany Salt>9001985–1990
Konrad Germany Limestone800Since1980
Morsleben Germany Salt>5251981–1998
Mecsek Mountain Hungary Clay10001995–1999
WIPP USA Salt655Since1982
ESF(YM)USA Tuff300Since1993
204S.Kwon et al./Tunnelling and Underground Space Technology21(2006)203–217
carried out during and after the construction of the small scale URL.2.3.Geochemical condition
It is normally accepted that reducing conditions exist in undisturbed deep underground rock formation.The redox properties of water,which are important for the dissolution of uranium oxide and canister corrosion,are generally determined by the presence of oxygen in a open system.In a closed system,the redox potential is determined by Fe(II)and Fe(III).The geochemical data obtained from the site investigations conducted all over Sweden indicate that the water is reducing at a depth of 100m.Only in one borehole out of 30–40is oxygen measured in the samples from more than a 100m depth (SKB,1993).2.4.Socio-economical situation
When an URL is constructed by expanding an underground mine or road tunnel,it would be possible to reduce the initial cost for excavating an access tun-nel and the installation of some utilities.It is,however,not to be able to utilize the URL as a facility for val-idating the whole disposal processes including site investigation,concept development,design,construc-
tion,maintenance,and closure.It is also not easy to find an adequate site,whose rock type is the same as the candidate host rocks and the rock condition is good enough to carry out various long term in situ experiments.It is preferred to have a site,which is close enough to KAERI for efficient R&D and for uti-lizing it as a facility for enhancing public acceptance to the waste disposal program.The option for construct-ing a small scale URL in the KAERI domain would be an excellent choice,if it satisfies the minimum requirements.
2.5.Minimum requirements
From a literature review,the following minimum requirements were suggested to utilize the URL for the HLW disposal studies:
The research modules,at which major researches will be performed,should be located at the same rock type as the host rock.
The research modules need to be located at a depth of more than 100m.
Good rock conditions in research areas are required for maintaining the underground tunnel for a long time with limited rock supports mainly consisting of rock bolts and wire
mesh.
Fig.1.Conceptual underground repository for the HLW disposal in Korea.
S.Kwon et al./Tunnelling and Underground Space Technology 21(2006)203–217205
It should be possible to perform researches related to rock mechanics and groundwaterflow through the rock mass.
Geological and geochemical conditions for carrying various R&D for the validation of the disposal con-cept,safety analysis,and THM test can be provided. Economic construction is available.
2.6.Basic URL concept
In order to select the best location for the URL at KAERI,a previous geological survey done by Kim et al.(1996)in the circled area,Area A in Fig.2,was reviewed.According to the survey,the weathered zone thickness is several tens of meters.Because of the thick weathered zone and the more or lessflat topography in the area,a long access tunnel is required to reach the minimum depth of100m.In order to reach the min-imum depth more efficiently with a shorter access tun-nel,Area B with a mountain was selected.By placing the research modules below the208m high mountain, the required depth can be easily achieved with a much shorter access tunnel.With a consideration of the local topography and the borderline of the KAERI domain, the tunnel direction of N56°W was chosen.Tunnel size of6m·6m was recommended to allow for the utiliza-tion of a jumbo drill and other equipments typically used for tunnel construction.
The access tunnel is considered to have a downward slope to place the research modules as deep as possible with a limited length of the access tunnel.It is also neces-sary to consider the transportation during the construc-tion and operation for selecting the tunnel slope.With consideration of the workability and efficiency of achiev-ing the required depth,aÀ10%access tunnel was sug-gested.However,thefinal tunnel geometry,direction, and slope should be determined with the consideration of other factors including the geological,environmental, hydraulic conditions,and mechanical stability.
2.7.Environmental condition
If the small scale URL is constructed at KAERI,it is necessary to assure that the blasting impact will not dis-turb the operation of the research reactor,Hanaro, which is located at about650m from the URL site, and the nearest building at about212m from the site. In order to check the blasting effect,the following general equation for calculating the blasting vibration was used:
Table2
Research items to be carried out at the URT
R&D items
Rock mechanics
–Rock mass classification
–Rock stress and deformation measurement and analysis
–Properties and mechanical effects of rock discontinuity and fracture zone
–Effects of stress change on the hydraulic properties of rock discontinuity
–Blasting techniques and blasting effect on adjacent tunnels
–EDZ development and its properties
–Evaluation of tunnel stability and rock support design
–Thermal property of rock(heater test)
–Infleuence of earthquake on underground facility
Geology
–prediction of rock boundaries
–Distribution rock discontinuity and fracture zone
–Groundwater network andflow characteristics in rock discontinuity
–Flow test through fracture system
–Prediction technique offlow rate into tunnel
Engineered barrier system
–Thermal-hydro-mechanical(THM)behavior of EBS
–Gas migration in engineered barrier system
–Contaminant diffusion and chemical buffering of buffer
–Colloid generation and migration at the interface between buffer and rock
Fluid migration
–Contaminant migration in rock mass
–Gas migration in shear zone
–Contaminant diffusion in rock matrix
–Colloid migration and retardation in geosphere
System design
–Demonstration of emplacement technology
–Tunnel sealing technology
–Verification of deposition hole drilling
–Concrete plug design and its application
–Verification of retrieval operation
–Verification of transportation
method Fig.2.Survey areas in1996and2003.
206S.Kwon et al./Tunnelling and Underground Space Technology21(2006)203–217
V¼k
D
W b
n
;ð1Þ
where V is the ground velocity(cm/s),D is the distance from the blasting source(m),W is the amount of explosive per delay(kg/delay),and k,n,b are the ground constants.In this study,k=160,n=À1.6, b=0.5,which were suggested by the US Bureau of Mines and typically used in Korea,were used.When D is15kg/delay,ground velocities at the nearest build-ing and the reactor are calculated as0.27and 0.047cm/s,respectively.According to the design crite-ria for blasting in Korea,0.3cm/s is the limited ground velocity allowed for the most sensitive structures such as cultural assets and precision machines.Therefore, a blasting at the site with less than15kg/delay would not cause any serous problem to the nearby buildings and the research reactor.
3.Geological condition
In order to determine the geological condition of the site,surface survey,seismic survey,electric resistivity survey,borehole drilling,borehole observation using Televiewer,and laboratory tests were carried out in 2003.3.1.Surface survey
In order to investigate the geological and topological characteristics of the site,a surface survey was carried out.However,it was not possible tofind outcrops ade-quate enough for a measuring joint orientation and dip, because of the thick weathered zone in the area.Accord-ing to the lineament analysis from the aerial photograph around the KAERI site,the primary direction of the lin-eaments is N30°W and N50°E is the secondary.Fig.3 shows the geology around the potential URL site at KAERI.
3.2.Seismic refraction survey
In order to estimate the location and size of the linea-ments and tofind the thickness of the overburden,a seis-mic refraction survey was carried out.As the seismic source,SISSY was used to reduce the vibration and noise.The survey lines for the geophysical survey were decided with a consideration of the potential tunnel length and tunnel direction,N56°W.Fig.4shows the survey lines for the seismic as well as the electronic resistivity surveys.In the case of the seismic survey, three lines(S-1–S-3)were along the tunnel direction with a100m interval and four lines(S-4–S-7)
were Fig.3.Geology around the potential URT site in KAERI.
S.Kwon et al./Tunnelling and Underground Space Technology21(2006)203–217207
perpendicular to the tunnel with about a50m interval. For each line,5–7shots were recorded using the geo-phones installed at a5m interval.The total length of the seismic survey lines was1.6km.
Fig.5shows the seismic survey result along the line, S-2,which lies along the expected tunnel direction.It is possible tofigure out that the weathered soil with a lower velocity covers the area with different thick-nesses from5to15m.The extremely low velocity zones located at around30,250,and360m,are likely to be due to the lineaments,F-4,F-5,and F-3, respectively.3.3.Electric resistivity survey
In the electric resistivity surveys,a pole–dipole array was used.In the resistivity survey,a series of electrodes were nailed into the ground about15cm deep along the survey lines up to800m.For each survey,40electrodes installed at a10m interval and a remote electrode was utilized to inject a current and to measure the resulting voltage.
Fig.6shows the survey results along survey lines,R-2 and R-5,and the resistivity contours around the tunnels with different slopes.It is possible to observe that
the
Fig.4.Survey lines and estimated tunnel
location.
Fig.5.Survey result along the S-2line.
208S.Kwon et al./Tunnelling and Underground Space Technology21(2006)203–217
research modules with any tunnel slope ranges from0to À10%and that it will be located in a good rock mass, whose resistivity is over2000X m.
The depth of the research modules is dependent on the access tunnel length and slope.With a230m long access tunnel,the research module depth varies from 92to116m with different tunnel slopes from0%to À10%.In order to satisfy the minimum requirements for the depth of the research modules,the access tunnel should have more than a5%tunnel slope.In the concep-tual design,a10%slope was selected tofirmly achieve the minimum requirements.By plotting the resistivity along survey line R-5,it is possible to observe that the research modules are to be located in a good rock con-dition with some distance from the lineaments as shown in Fig.6(c).
3.4.Borehole drilling
A160m long vertical borehole and a252m long de-clined borehole were drilled for investigating the geolog-ical characteristics,base rock condition,weathered zone thickness,and for the in situ tests.The location of the vertical borehole is close to the expected tunnel entrance and thus it can provide data for the design of the tunnel entrance.In the case of the declined borehole,the slope was the same as the expected tunnel slope,which is À10%.A diamond core bit and a double core barrel were used for the borehole drillings.For protecting the upper weak zone,casings were installed in the vertical and declined borehole up to4and30m,respectively.
Vertical borehole.Underneath the2m thick weath-ered soil,2.2m thick weathered rock is laid.Weak rock and normal rock showed up at aÀ10.3andÀ19.8m le-vel,respectively.Hard rock is underneath the normal rock.Biotite granite and schistose granite are the major rock types and andesite dikes are encountered in some locations.Fig.7shows the RQD variation with depth along the vertical borehole.A better rock condition is expected with increase of depth.The variation of the RQD with an increase of depth couldfit well with the following equation:
RQD¼109.8À
219.74
Z0.5
.ð2ÞDeclined borehole.Along the declined borehole,weath-ered soil showed at4m from the entrance.Below the weathered soil layer,a10m thick weathered rock layer and14m thick weak rock layer are located.After that hard rock continues up to250m.At thefive
locations Fig.6.Resistivity contours around the tunnels with different survey lines and different slopes.(a)Resistivity with different dips.(b)Resistivity along R-2survey line.(c)Resistivity along R-5survey line.
S.Kwon et al./Tunnelling and Underground Space Technology21(2006)203–217209
28,47,118,124,and235m from the entrance,1–3m wide andesite veins were encountered.Observable peg-matite veins were also found at10locations.At two locations,70and75m from the entrance,0.8and2m wide faults were identified.During the drilling work,a significant amount of waterflooding into the hole was observed at50,80,and180m.The waterflooding at 50and80m might be due to the fracture zone around the steep faults located at70and75m.The other one at180m seems to be the major water-conducting zone. Pre-grouting at the water conducting zones would be necessary for an efficient construction and maintenance of the tunnel.
The variation of the rock condition along the de-clined borehole could be described with a variation of the RMR as shown in Fig.8.The poor rock condition up to82m becomes better at the82–125m range.After the poor rock shown shortly at around125m,good and hard rock is likely to be met until177m.There is an-other fracture zone at the range of177–192m.After that the rock conditions become better.The ranges with the RMR higher than41%are85%of the whole range. About24%of the whole range shows the RMR at over 81.According to the rock mass rating based on the RMR(Bieniawski,1989),a RMR of61–80is described as‘‘Good Rock’’and a RMR of over81as‘‘Very good
Fig.8.Variation of the RMR along the declined borehole.
210S.Kwon et al./Tunnelling and Underground Space Technology21(2006)203–217
rock’’.The average RMR of the rock zone is calculated as 64.The low RMR values around 75and 180m are likely to be related to the fracture zones.
Based on the RMR variation,the declined hole could be divided into six ranges.Different parameters repre-senting the rock conditions for the six ranges were calcu-lated and are listed in Table 3.Joint spacing in the rock zones varies from 2.8to 80cm.The RQD varies from 35to 79and its average is 71.In the case of Q ,the average value is about 40.The maximum unsupported span can be calculated as follows (Bieniawski,1989):Span ðm Þ¼2ESR Q 0.4;ð3Þwhere the ESR is the excavation support ratio and deter-mined with a consideration of the degree of the safety demand.When the ESR is 1,which is applied to the excavations for power stations,major highways,or rail-road tunnels,the unsupported span in the range of 192–252m,where the research modules will be located,is calculated as 8m.
The relationship between the RMR and the resistivity along the boreholes is plotted in Fig.9.Even though there is a wide variation of the RMR and resistivity,it is possible to observe that the RMR increases with and increase of the resistivity.The relationship between the RMR and the resistivity along the declined (KP-1)
and vertical (KP-2)boreholes could be fitted using the line equation and the logarithmic equation as shown in Fig.9.With the logarithmic fitting curve,the RMR values around the 10%declined access tunnel and the re-search modules were calculated and plotted as shown in Fig.10.The RMR is found to be over 60in most regions and the research modules are expected to be located in a good rock with the RMR about 70.
Fig.11shows the rose diagram of the joints detected from the Televiewer in the declined borehole.When the tunnel direction is N56°W,it would cross the major joint set almost perpendicularly and thus a tunnel stability would be achieved more easily.From the borehole investigation using the Televiewer,the geological condi-tions to be encountered during the excavation of the ac-cess tunnel with a 10%slope could be predicted as shown in Fig.12.4.Rock stability
The mechanical stability of the small scale URL was investigated using the three-dimensional continuum code,FLAC3D,which is an explicit finite difference
Table 3
Joint spacing,RMR,and Q in the ranges along the declined hole,KP-1Range (m)Interval (m)Avg.joint spacing (cm)Avg.
RQD (%)Avg.RMR Avg.Q 30–8252.9 5.244.045.9 5.782–12542.62476.362.841.9125–177518094.380.793.3177–19215.2 2.834.748.7 5.1192–25260.1
1579.468.532.9Average
28
70.6
64
39.8
Fig.10.RMR values on the plane with À10%.
S.Kwon et al./Tunnelling and Underground Space Technology 21(2006)203–217211
program and developed by the Itasca Consulting Group Inc.(Itasca,1996).In order to investigate the influence of the tunnel slope,a tunnel slope of À10%was considered.The tunnel in the model is 6m wide and 6m high with a horseshoe shape.Since the access tunnel is located at a shallow depth near the entrance,the surface topography might influence the tunnel stability.The actual surface topography could be implemented in the model by using a Fortran program developed for generating the FLAC3D input file from the three-dimensional topogra-phy data.The access tunnel,which is about 200m in hard rock,was assumed to be excavated sequentially with a 10m advance at each excavation step.4.1.Rock properties
The deformation modulus for a site can be calculated using the following equations suggested by Hoek et al.(2002).
E m ¼
1À
D 2
ffiffiffiffiffiffiffiffi
r c 100
r Â10GSI À10
40½ for r c 6100MPa ;
ð4Þ
E m ¼
1ÀD
2
Â10GSI À1040½
for r c >100MPa ;ð5Þ
where r c is the uniaxial compressive strength of intact rock (MPa);GSI is the geological strength index (Hoek et al.,1998);D is the degree of disturbance due to blast damage and stress relaxation.
In the URL site,blasting will be done carefully so as not to disturb the rock mass as well as the neigh-boring buildings at KAERI and thus D can be 0.The following equation,derived from the laboratory test using the rock cores from the declined borehole,was used to calculate r c at different regions (Kwon et al.,2004):r c ¼135À
779.6
L .;ð6Þ
where L (m)is the distance from the borehole entrance.Table 4lists the calculated rock properties for the six ranges divided by the RMR in Fig.8.The dips of the ranges were determined from the major geological fea-tures shown in Fig.10.Since the tunnel depth is shallow and it is not expected to have a serious plastic zone,an elastic model was
used.
Fig.11.Rose diagram of the joints detected from the Televiewer in KP-1hole.
Table 4
Properties of the rock mass in the six ranges Range (m)Interval (m)Dip
UCS (MPa)Em (GPa)Bulk modulus (GPa)Shear modulus (GPa)30–8252.98830.8 3.2 2.13 1.2882–12542.668–8858.412.18.07 4.84125–1775168–9071.637.925.315.16177–19215.29077.6 6.21 4.14 2.48192–252
60.1
90
82.7
20.4
13.6
8.16
212S.Kwon et al./Tunnelling and Underground Space Technology 21(2006)203–217
4.2.Initial and boundary conditions
For the stability analysis of the underground tunnel,a model mesh with a consideration of the actual topog-raphy around the small scale URL site was made (Fig.13).Because the stress and displacement variation after an excavation would be higher around the tunnel,relatively small meshes were allocated around the tun-nel.In order to develop the in situ stress condition in the model,it was assumed that the current topography was made by step by step erosion.Fig.14shows the five erosion steps from the flat surface to the current topog-raphy.Before erosion process is started,horizontal stresses were distributed with a initial stress ratio,K ini .To check the influence of initial stress ratio,three differ-ent stress ratios were used:(a)overburden load,(b)K ini =1,and (c)K ini =2.Between the erosion steps,iter-ations were made until mechanical equilibrium.
The total number of zones in the model before erosion is 27,250.The model width and length are 100and 250m,respectively.After erosion,the model height varies from 80to 160m depending on the surface topography.In the modeling,a 200m access tunnel was considered and then the dead end of the tunnel was located at about 116m be-low the surface.In the case of the mechanical stability analysis of a tunnel,a model size of about three to four times the tunnel size is normally acceptable.In this case,however,a much larger model size was used to consider the variation of the surface topography.4.3.Modeling results
In order to validate the assumptions for the initial and boundary conditions,the stress distribution before the excavation of tunnel was compared with the actual in situ stress measurements by hydraulic fracturing.After finishing the erosion process,the ratios between the horizontal and the vertical stresses at the model meshes was calculated using the following equation:
K avg ¼
r H þr h
r Z
;ð7Þ
where r H and r h are the maximum and minimum hori-zontal stresses and r Z is the vertical stress.Since there is no function to plot the stress ratio in FLAC3D,the stress ratios of modeling results were calculated using a Fortran code and then imported to FLAC3D.Fig.15shows the distribution of stress ratio after ero-sion,when the initial stress ratio K ini =1.02.It is possi-ble to observe that the stress ratio decreases with depth.In some areas,the stress ratio is up to 10depending on the rock properties and topography.At the location of the vertical borehole,KP-2,marked in Fig.15,the var-iation of the stress ratio with depth was plotted with the actual measurement in Fig.16.When the initial stress
is
Fig.13.Model mesh from real
topography.
Fig.14.Steps for simulating the erosion effect.。