research article the impact of microearthquakes induced by...

Research ArticleThe Impact of Microearthquakes Induced by Reservoir WaterLevel Rise on Stability of Rock Slope

Dongliang Li12 Xinrong Liu12 Xingwang Li12 and Yongquan Liu12

1School of Civil Engineering Chongqing University Chongqing 400045 China2Key Laboratory of New Technology for Construction of Cities in Mountain Area Chongqing University Ministry of EducationChongqing 400045 China

Correspondence should be addressed to Dongliang Li myheartwillgoon17126com and Xinrong Liu liuxrong126com

Received 10 March 2016 Revised 9 May 2016 Accepted 26 May 2016

Academic Editor Longjun Dong

Copyright copy 2016 Dongliang Li et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In order to study the impact of frequent microearthquakes induced by water level rise on the stability of rock bedded slopes inthe Three Gorges Reservoir (TGR) area Zhaoshuling Landslide (a representative slope) is selected to study Safety factors basedon probability statistics and FLAC3D are used for numerical simulation (under the operating condition that five earthquakes ofIntensity IV are applied to slope in succession after water level rises from 145m to 175m) Then the slopersquos dynamic stabilitycharacteristics and failure mechanism are analyzed The study shows that slope deformation is evidently the result of thrust loadThe deformation starts from the steeply dipping segment in the middle part of slip mass and is controlled by the soft interlayerShear failure tends to occur along the soft interlayer and the horizontal slip displacement increases from the rear to the front ofthe slope The steeply dipping segment shows a general downslide trend Although the gentle slope platform on the rear edge isrelatively stable it is vulnerable to tensile fractures which are precursors of landslide Under the same failure probability as thenumber of microearthquake occurrences increases the safety factor of slope under microearthquake action decreases gradually

1 Introduction

The Three Gorges Project (TGP) is a hydraulic engineeringproject on the Yangtze River that has attracted worldwideattention It involves the construction of a long and narrowchannel reservoir over 600 km long and 1-2 km wide [1ndash3] However this huge artificial water project leads to anumber of pressing issues in addition to great benefits to theeconomic development of China According to relevant data[4ndash6] the length of the unstable segment in the TGR areais 385 km and 1190 slumped masses (with a total volume ofaround 34 billion cubic meters) have been identified alongthe reservoir bank of the TGR In the event of river blockageand water level rise due to failure and instability of thereservoir bank slope catastrophic consequences would becaused For this reason scholars have made relevant researchon the stability of reservoir bank slopes in the TGR area Zuoet al [7] analyzed the relationships between the variationsin the reservoir water level and width of the bank slopersquosstructural plane and the slope stability with the Strength

Reduction Method Luo et al [8] found that the horizontaland vertical displacements of a slope abruptly increased inthe Three Gorges area after reservoir impoundment andrainfall Based on the comparison of the position mineraland structure between incompetent beds and sliding zones oftwo giant deep-seated translational rock landslides Chai et al[9] discussed the correlations between incompetent beds andgiant landslide With Anlesi Landslide as a typical case Jianet al [10] studied the mechanism of gentle dip translationalrock slides in the TGR area Based on spatial data mining andknowledge discovery Wang et al [11] carried out landslidemechanism analysis in the Three Gorges

In addition to the direct influence on the stability ofreservoir bank slopes the variation in the reservoir waterlevel can also cause changes of the stress field and seepagefield in the rock mass thus inducing earthquakes [12ndash15]According to relevant literature andmonitoring data [16ndash22]the frequency of earthquake activities in the reservoir areasoars after impoundment surging up to 15 occurrences perday The earthquake motion with such a high frequency and

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 7583108 13 pageshttpdxdoiorg10115520167583108

2 Shock and Vibration

long term is inevitably a great challenge for the stability of theslope in the TGR area For the stability of rock slopes underthe earthquake action Tang et al [23] analyzed the relationsbetween the rock landslide distribution and five main factors(fault proximity epicenter proximity peak ground accelera-tion slope angle and lithology) Gischig et al [24] presenteda series of 2D distinct-element numerical models which wereaimed at clarifying interactions between earthquakes andlarge rock slope instabilities Guo et al [25] collected 54landslides with travel distances of 347ndash4170m triggered byWenchuan Earthquake in 2008 to discuss the effectiveness ofvarious influential factors on landslide travel distance andhis research results revealed that rock type sliding sourcevolume and slope transition angle were the predominantfactors on landslide travel distance Besides Xu [26] studiedthe stability of steep rock slopes under microearthquakes andJiang [27] analyzed the deformationmechanism and dynamicresponse characteristics of the first typical loess landslidesegment in the TGR area under microearthquakes Howeverlittle research has been conducted on the impact of reservoirwater level fluctuation and frequent microearthquake occur-rences on the dynamic stability of the bedded rock slope

To sum up with Zhaoshuling Landslide (Badong CountyChina) in the TGR area as a representative case numericalsimulation is conducted for the rock bedded slope with asoft interlayer under multiple microearthquakes induced byreservoir water level rise and the dynamic stability and failuremechanism of such slopes are analyzed based on the slopedisplacement deformation and dynamic response to providetheoretical bases for landslide control slope stabilization anddisaster prevention

2 Calculation of Dynamic Safety Factor

21 Time-History Curve of Dynamic Safety Factor The safetyfactor of the slope sliding failure mode under the earthquakeaction can be determined with the limit equilibrium theoryby calculating the earthquake inertia force on the rock massat random time 119905

Assume that (119905) is the resultant force of gravity (119905) andearthquake inertia force (119905) on the rock mass at time 119905 Theresultant force is projected onto the potential sliding directionto obtain the sliding force 119878(119905) as follows

119878 (119905) = (119905) sdot 119894 (1)

where 119894 is the unit vector of the potential sliding direction(119905) is projected onto the normal direction of the slidingsurface to obtain the normal reacting force

According to the Coulomb Friction Laws the slide-resistant force 119877(119905) can be determined as follows

119877 (119905) =10038161003816100381610038161003816 (119905) sdot

10038161003816100381610038161003816sdot tan120593 (119905) + 119860 sdot 119888 (119905) (2)

where is the normal unit vector of the sliding surface 119860 isthe contact area between the sliding mass and the rock massbelow it and 120593(119905) and 119888(119905) are the internal friction angle andcohesion of the sliding surface at time 119905 respectively

Safety factor

Probability

Pf

FR

120583F

120573120590F

density

Figure 1 Distribution of dynamic safety factors

Therefore the dynamic safety factor can be expressed asfollows

119896 (119905) =

[10038161003816100381610038161003816 (119905) sdot

10038161003816100381610038161003816sdot tan120593 (119905) + 119860 sdot 119888 (119905)]10038161003816100381610038161003816 (119905) sdot 119894

10038161003816100381610038161003816

(3)

Based on the formula above a computation program canbe developed using Fish language in Flac3D to obtain thetime-history curve of dynamic safety factor for the slopeunder seismic action thus providing a basis for stabilityanalysis of slopes under frequent microearthquakes

22 Safety Factor Based on Probability Statistics Earthquakeis normally assumed to be a random variable of timeAccordingly the dynamic safety factor of slope under seismicaction can also be seen as a random function of time whichenables the dynamic stability evaluation index of slope to bedetermined based on the reliability theory [28]

Assume that under seismic action when the minimumvalue of the time-history curve for the dynamic safety factoris used as the evaluation index the highest level of safetyis expected (ie the probability of failure is 0) when themaximum value of the time-history curve is used as theevaluation index the slope stabilitymay be overestimated andthe highest level of risk is expected (ie the probability offailure is 1) Based on the assumption above as well as thefundamentals of probability and statistics if the safety factoris taken as the critical index the evaluation index for dynamicstability of the slope can be transformed into the probabilityof the safety factor below 119865

119877due to the earthquake

As shown in Figure 1 the area of the shaded part is theprobability of failure 119875

119891 Based on the principle of probability

analysis the reliability 120573 can be determined as follows

120573 =120583119865minus 119865119877

120590119865

(4)

where 120583119865is the mean of safety factors and 120590

119865is the standard

deviation of safety factors According to the formula above

119865119877= 120583119865minus 120573120590119865 (5)

Shock and Vibration 3

Table 1 Correspondences between 119875119891and 120573

119875119891

120573

05 0025 06701 128005 165001 2330001 31000001 372000001 425

The time-history curve for the dynamic safety factor ofthe slope is discretized and the following formulas can beobtained with the statistical method

120583119865=1

119873

119873

sum

119894=1

119865 (119905119894)

120590119865= radic

1

119873 minus 1

119873

sum

119894=1

(119865 (119905119894) minus 120583119865)2

(6)

where 119873 is the total number of discrete segments of thetime axis and 119865(119905

119894) is the average safety factor in the 119894th

segment When 119865(119905119894) is in normal distribution a one-to-one

correspondence can be established between120573 and probabilityof failure 119875

119891 See Table 1

3 Project Overview

Zhaoshuling Landslide is an area with gentle terrain locatedin eastern New Urban District of Badong County China(Figure 2) Landslides there with an elevation below 400mhave two-stage platforms at their foreparts This gentle slopezone is of great importance for Badongrsquos urban area witha shortage of planned construction land (see Figure 3 forZhaoshuling Landslide and New Badong County)Thereforethe stability of Zhaoshuling Landslide is directly related tothe safety of Riverside Road in the new county Zhaoshulingis located in a transitional zone between Wuxia Gorge andAiling Gorge in the middle section of the Three Gorges andis a relatively wide section in the valley areaThe topographicprofile shows gentle slope platforms alternating with steepslopes In the aspect of terrain the rear part and the riversideat the front edge are steep and the middle part includesthree platforms of gentle slopes with an average gradientof 10∘ sim 15

∘ Between the gentle slopes are steep slopeswith a gradient exceeding 35∘ which is even larger in someparts Also gully walls on both sides of the gully in thearea are very steep Some parts of the walls have a gradientexceeding 50∘ and are potential unstable parts where slopedeformation occurs The axis of rock folds in Zhaoshulingand its surrounding areas is nearly oriented east and westwhich is the same as the orientation of steep slopes Steepslopes are mainly dip slopes For lithology the bedrock inthe area is mainly argillaceous limestone and marl of TriassicBadong Formation (T

2b) and silty mudstone and siltstone

Yangtze River

Zhaoshuling Landslide

N

Badong County

Figure 2 Location of Zhaoshuling Landslide

It is a typical sliding-prone stratum in the Three Gorgesarea [29] Figure 4 is the simplified topographic map of theZhaoshuling Landslide area

31 Characteristics of Landslide Form Ancient ZhaoshulingLandslide is a bedded rock landslide with its front edge beingclose to the Yangtze River Areas with the elevation of 150sim200mbelong to the gentle slope platformof stage I areaswiththe elevation of 350sim425m belong to the landslide platformof stage II areas with the elevation of 475sim500m belong tothe gentle slope platform at stage III The remaining areas areslopes with a gradient of 25sim50∘ The landslide is terraced inthe east-west orientation like its surrounding terrains

32 Characteristics of Material Structure Zhaoshuling Land-slide is an extra large landslide in T

2b3 and T

2b2 strata and

materials mainly come from the T2b3 stratum The slumped

mass layer in the landslide surface mainly consists of blockfractures cataclastic rock broken stone containing mud andbroken stone The bedrock mainly consists of reddish-purplesilty mudstone of T

2b2 and argillaceous siltstone The rock

mass is in a layer structure with a basically normal sequenceof strataMultiple layers of weak fractured zones can be foundin the exposed T

2b3 stratum in the landslide area The lowest

sliding zone is around the T2b2T2b3 interface Characterized

by a thin rear edge and thick front edge this sliding zone isbasically the same as the topographic relief in terms of shape

33 Characteristics of Geological Structure The Zhaoshulingarea has a special geological structure that the lithologicinterface of T

2b3T2b2 is higher than that of other surround-

ing areas This is the result of local tectonic uplift causedby two conjugated tensional-shear faults which are nearlyoriented south and north In addition to the characteristics ofundulation in the near south-north orientation the interfaceis also characterized by undulation in the east-south orien-tation which is related to tectonism in the near south-northorientation

34 Characteristics of Soil in Sliding Zones The form of slid-ing zones in Zhaoshuling Landslide is undulating under thecontrol of stratum lithology and attitudes The front slidingzone lifts up with an inclination of 8sim11∘ and a length of


Figure 3 Zhaoshuling Landslide and the New Badong County

500

Yangtze River

100

100

150

200

250

300

350

400

400

400

300300

200

200

100

450

500 500

Landslide area

N


Qdel

Qdel

Qdel

Qdel

T2b2

T2b2

T2b2

T2b3

T2b3

T2b3

T2b2 is the second marl of Triassic Badong Formation

T2b3 is the third marl of Triassic Badong Formation

Qdel is accumulation body

0 200 m

Figure 4 Simplified topographicmap of the Zhaoshuling Landslidearea

140sim160m Materials in the sliding zone are mainly grayish-yellow grayish-green and red breccia soil Some parts ofthe sliding zone are mylonitized and relatively compact Itsnatural volume-weight is 229sim246 kNm3 larger than thatof common gravelly soil There are many subsliding zonesand bedded crushed zones in the soft stratum Figure 5 is thesimplified geological section map of Zhaoshuling Landslide

4 Numerical Calculation

41 Establishment of Numerical Model A numerical modelis established based on the typical geological section in the

Yangtze100

200

300

400

500

Vert

ical

hei

ght (

m)

0 400 600 1000200 1200800Horizontal distance (m)

123

456

River

Figure 5 Simplified geological section map of Zhaoshuling Land-slide (plotted based on data of Comprehensive Investigation Insti-tute China Changjiang Water Resources Commission (1995)) (1)Limestone and limestone containing mud (2) mudstone siltstoneand argillaceous siltstone (3) soft stratum (4) landslide deposits (5)red mud broken stone with soil (6) gravelly soil

main sliding direction of the landslide The model is 1200min length and its rear edge has an elevation of 475m Thecontrolling structural plane of the slope is simulated using athin-layer element while other joint fissures are taken intoaccount by reducing the strength and deformation modulusof the rock mass In order to ensure the accuracy of dynamicanalysis the size defined by the mesh should be controlledThe mesh size is limited by the shortest wavelength of theinput seismic wave To ensure the authenticity of wave propa-gation in themedia themaximum sizeΔ119897 of the elementmustbe less than 110sim18 of the minimum wavelength Accordingto the elastic wave propagation theory the propagationvelocities of the longitudinal wave and transverse wave arecalculated with the following formula

119862119901= radic

119864 (1 minus 120583)

120588 (1 + 120583) (1 minus 2120583)

119862119904= radic

119864

2120588 (1 + 120583)

(7)

where 119864 is the elastic modulus 119866 is the shear modulus 120588 isthe density and 120583 is Poissonrsquos ratio of the material


Table 2 Physical and mechanical parameters of numerical model

Rock ] 119870 (msdotdminus1) 119864119889(GPa) 119888 (kPa) 119888sat (kPa) 120593 (∘) 120593sat (

∘) 120588 (kgsdotmminus3) 120588sat (kgsdotmminus3)

Sliding body 03 10 13 190 130 24 22 2000 2200Weak layer 04 3 08 20 12 20 18 2100 2300Silty mudstone 035 05 10 200 120 23 21 2300 2590Argillaceous limestone 02 5 16 260 200 32 30 2550 2690Limestone 018 mdash 32 400 350 35 32 2580 2680] is Poissonrsquos ratio 119870 is permeability coefficient 119864119889 is dynamic elastic modulus 119888 is cohesion 119888sat is saturated cohesion 120593 is internal friction angle 120593sat issaturated internal friction angle 120588 is natural density and 120588sat is saturation density

Horizontal

Vertical

al

0200

400600

8001000

1200X (m)0

100

200

300

400

Z(m

)

Figure 6 Finite element model

Weak layerSilty mudstoneSliding bodyArgillaceous limestoneLimestone

Figure 7 Distribution of rock materials

From formula (7) the propagation velocities of thelongitudinal wave and transverse wave in different rockstrata are obtained With the computation speed and theproposed frequency distribution of seismic waves taken intoconsideration 119891 = 10Hz is used to control mesh accuracyand the maximum mesh size can be determined by thefollowing formula

Δ119897 =1

10sdot119862119904

119891 (8)

The final established numerical model is shown in Fig-ure 6 The distribution of rock is shown in Figure 7

The ideal elastic-plastic model is used Assuming that therock materials follow the Mohr-Coulomb strength criterionthe physical and mechanical parameters selected are shownin Table 2

42 Seismic Wave Input Reservoir-induced earthquakes areusually of low magnitude with concentrated epicenters andshort duration (usually 5ndash10 s) Therefore the time-historycurve of a previously recorded real earthquake accelerationis used in this paper and the record of foreshocks is cutThe waveband in 7 seconds during 26 ssim33 s is selected asthe seismic waveform in this paper (see Figure 8) Then theseismic wave is reduced according to the peak acceleration ofthe corresponding magnitude The acceleration time-history

curve thus obtained is used for numerical calculation in thestudy

The seismic wave shown in Figure 8 cannot be useddirectly for numerical calculation As can be seen from Fig-ure 8(c) the final displacement of the seismic wave is nonzeroafter an earthquake cycle It is not the result of residualdeformation due to failure of objects but the result of theincomplete waveform selected artificially or recording errorsTherefore baseline calibration should be performed on theacceleration time-history curve to eliminate the influence ofacceleration error on velocity and displacement so that thefinal values of velocity and displacement time-history curvesare zero See Figure 9 for the time-history curve of seismicwave after filtering baseline calibration and reduction toIntensity IV (peak acceleration is 022ms2)

As Flac3D software is used for calculation two dynamicboundary conditions are provided that is the free-fieldboundary and viscous boundary In this study the viscousboundary and local damping (damping coefficient is 015)[30] are used for analysis For this boundary conditiontangential and normal dampers are applied on the boundaryto realize the absorption of incident wave energy In otherwords dampers produce tangential and normal force to offsetthe stress caused by reflected waves Accordingly the seismicwave should be input in the form of stress time-history Theexpression for conversion of velocity time-history to stresstime-history is as follows

120590119899= minus2 (120588119862

119901) V119899

120590119904= minus2 (120588119862

119904) V119904

(9)

where 120590119899is normal stress 120590

119904is shear stress 120588 is medium

density 119862119901and 119862

119904are the propagation velocity of P-wave

and S-wave in the medium respectively and V119899and V119904are the

velocity in vertical and horizontal directions respectivelyReservoir-induced earthquakes of the same magnitude

may occur multiple times successively within a shortperiod of time Given this characteristic five earthquakesof Intensity IV (acceleration amplitude is 022ms2) areapplied successively to simulate the frequent occurrence ofmicroearthquakes

43 Numerical Calculation The following operating con-dition is mainly considered during numerical simula-tion the reservoir water level rises to 175m from 145m


minus2000

200

1 2 3 4 5 6 70

Time (sec)

Acce

lera

tion

(cm

sec

2)

(a) Acceleration time-history curve

1 2 3 4 5 6 70

Time (sec)

minus6minus226

Velo

city

(cm

sec

)

(b) Velocity time-history curve

1 2 3 4 5 6 70

Time (sec)

minus25minus15minus050515

Disp

lace

men

t(c

m)

(c) Displacement time-history curve

Figure 8 Original seismic wave time-history curve

1 2 3 4 5 6 70

Time (sec)

minus15minus55

15

Acce

lera

tion

(cm

sec

2)

(a) Acceleration time-history curve (Intensity IV)

1 2 3 4 5 6 70

Time (sec)


00204

Velo

city

(cm

sec

)

(b) Velocity time-history curve (Intensity IV)

1 2 3 4 5 6 70

Time (sec)

minus008minus004

0004008

Disp

lace

men

t (cm

)

(c) Displacement time-history curve (Intensity IV)

Figure 9 Original seismic wave time-history curve (Intensity IV)

The calculation mainly involves dead weight seepage anddynamic response analysis

(1) DeadWeight CalculationDuring dead weight calculationgravity acceleration is set first followed by full constraint onthe bottom surface of themodel and constraint on the normaldisplacement around themodelThe stress field under gravityis obtained firstThenephogramof the vertical and horizontalstress fields of the slope under natural state is shown inFigure 10

(2) Seepage CalculationDuring seepage calculation the deeprock mass is thick-layer and compact argillaceous limestoneand as its permeability is weaker than that of the upper rockmass it can be regarded as a relative water-resisting layerof the slope The front part of the slope is in direct contactwith the reservoir water and thus its pore water pressure isset according to the actual water level The rear part of theslope is less affected by water level fluctuation and thus thepore water pressure of the nodes can be set according tothe groundwater depth revealed during drilling explorationWith bilateral seepage of the model the steady seepage fieldsof the slope at water levels of 145m and 175m are obtainedwhich provides a theoretical basis for the subsequent dynamic

analysis See Figure 11 for calculation results of the seepagefields

(3) Dynamic Response Calculation Considering that theinduced earthquake occurs later than the variation in waterlevel all plastic zones displacement and velocity vectors arereset to zero before loading of the earthquake For the lateralboundary whose normal direction is in 119909-axis due to thebuffer effect of dampers the coupling effect between the free-field mesh and the model can be codetermined by (a) thestress generated from the velocity difference between the free-field boundary node and the original model boundary nodeand (b) the nodal force of the free-field boundary node itselfThis boundary condition can be expressed as follows

119865119909= minus120588119862

119901(V119898119909minus V119891119891119909)119860 + 120590

119891119891

119909119909Δ119878119910

119865119910= minus120588119862

119904(V119898119910minus V119891119891119910)119860 + 120590

119891119891

119909119910Δ119878119910

119865119911= minus120588119862

119904(V119898119911minus V119891119891119911)119860 + 120590

119891119891

119909119911Δ119878119910

(10)

where 120588 is the material density 119862119901and 119862

119904are the longitu-

dinal and transverse wave velocity of the lateral boundaryrespectively 119860 is the element area corresponding to 119865

119909 119865119910


minus10558e + 007 to minus10000e + 007minus10000e + 007 to minus90000e + 006minus90000e + 006 to minus80000e + 006minus80000e + 006 to minus70000e + 006minus70000e + 006 to minus60000e + 006minus60000e + 006 to minus50000e + 006minus50000e + 006 to minus40000e + 006minus40000e + 006 to minus30000e + 006minus30000e + 006 to minus20000e + 006minus20000e + 006 to minus10000e + 006minus10000e + 006 to minus21502e + 004

(a) Vertical and horizontal stress field

minus26710e + 006 to minus25000e + 006

minus25000e + 006 to minus20000e + 006

minus20000e + 006 to minus15000e + 006minus15000e + 006 to minus10000e + 006

minus10000e + 006 to minus50000e + 005minus50000e + 005 to 00000e + 00000000e + 000 to 56769e + 003

(b) Horizontal stress field

Figure 10 Initial stress field nephogram of the slope under natural state

00000e + 000 to 10000e + 00510000e + 005 to 20000e + 00520000e + 005 to 30000e + 00530000e + 005 to 40000e + 00540000e + 005 to 50000e + 00550000e + 005 to 60000e + 00560000e + 005 to 70000e + 00570000e + 005 to 80000e + 00580000e + 005 to 83492e + 005

(a) Water level is 145m

00000e + 000 to 10000e + 00510000e + 005 to 20000e + 00520000e + 005 to 30000e + 00530000e + 005 to 40000e + 00540000e + 005 to 50000e + 00550000e + 005 to 60000e + 00560000e + 005 to 70000e + 00570000e + 005 to 80000e + 00580000e + 005 to 90000e + 00590000e + 005 to 10000e + 00610000e + 006 to 11000e + 00611000e + 006 to 11717e + 006

(b) Water level is 175m

Figure 11 Calculation results of the seepage fields

and 119865119911being solved V119898

119909 V119898119910 and V119898

119911are the node velocity of

the model boundary in 119909 119910 and 119911 directions respectivelyV119891119891119909 V119891119891119910 and V119891119891

119911are the node velocity of the free-field

boundary in 119909 119910 and 119911 directions respectively 120590119891119891119909119909 120590119891119891119909119910

and 120590119891119891119909119911

are normal stress in 119909119909 direction shear stress in 119909119910direction and shear stress in 119909119911 direction of the free-fieldmesh node respectively and Δ119878

119910is the influence area of the

free-field mesh node

5 Dynamic Response Analysis

51 Slope Displacement Analysis Figure 12 shows thenephogram of slope displacement in 119883 direction uponwater level rise after each earthquake Figure 13 shows theplastic state of the sliding mass corresponding to Figure 12As can be seen from Figure 12 slope deformation mainlyoccurs in the potential sliding area characterized by slidealong the soft interlayer while in other parts only minordeformation is found Comparison among Figures 12(a)through 12(d) indicates that the displacement contourlines follow a similar distribution pattern relatively largedeformation is observed in the gentle slope platform in thefront part of the potential sliding mass and the horizontaldisplacement maximums appear at the position where thesliding surface is exposed to the free face The displacementof the steeply dipping segment in the middle of the slidingmass however is reduced evidently compared with the frontgentle slope platform This indicates that the slope tendsto be separated by shear failure along the soft interlayerand the uplifted segment in the front supports the steeplydipping segment in the middle prevents it from slidingand limits its sliding space Displacement of the rear gentleslope is relatively small It decreases from the rear part tothe front part indicating the existence of traction from thesteeply dipping segment in the middle and the possibility ofsliding along the soft interlayer Based on the accumulateddisplacement after five earthquake inputs the distributionof deformation follows a certain pattern To be specificthe accumulated horizontal displacement of the front-most

part of the sliding mass reaches 2465mm the accumulatedhorizontal displacement of the front gentle slope is around18mm the accumulated horizontal displacement of themiddle steep segment is 12ndash18mm and the accumulatedhorizontal displacement of the rock mass in the rear edgeis around 8mm According to the horizontal displacementvalues the displacement increases by the largest incrementduring the first earthquake and then by smaller incrementsin subsequent earthquakes indicating a slower rate ofincrease

From the plastic state of the potential slidingmass tensilezones are mainly located at the front shear part and the reargentle slope platform and shear zones at the front upliftedsegment and the upper part of the rear gentle slope platformNo plastic yield is found in the rock stratum of the middlesteeply dipping segment On one hand this indicates thatthe steeply dipping segment shows a general downslide trendunder the action of microearthquakes and the rear gentleslope platform is relatively stable leading to tensile stressin the rear edge of the steeply dipping segment and theyielding ofmany elements there by tension As a result tensilefractures may occur Meanwhile as the front gentile slopeplatform prevents sliding thrust from the upper rock massleads to damage of the upper and lower surfaces of the upliftedsegment by shear On the other hand plastic deformation isfound mainly in the middle and upper part of the rear gentleslope platform while no shear yield is found in the bottomsurface This also indicates that sliding of the middle steeplydipping segment produces traction to the rear gentle slopeplatform which thus presents a downslide trend resulting incontinuous tensile zones in the rear edge of the slope Thatis to say the rear edge is under both tensile force and shearforce

After the first earthquake some elements of the potentialsliding mass are still under shear (shear-119899) after the secondearthquake all elements regain their elasticity and no con-nected plastic zones have ever been developed It indicatesthat under this operating condition the slope remains in astable state regardless of local failure and a certain amount ofpermanent displacement


(a) n = 1 (c) n = 3

30784e minus 004 to 20000e minus 00320000e minus 003 to 40000e minus 00340000e minus 003 to 60000e minus 00360000e minus 003 to 80000e minus 00380000e minus 003 to 10000e minus 00210000e minus 002 to 12000e minus 00212000e minus 002 to 14000e minus 00214000e minus 002 to 16000e minus 00216000e minus 002 to 18000e minus 00218000e minus 002 to 18881e minus 002

80241e minus 004 to 25000e minus 003

50000e minus 003 to 75000e minus 003

12500e minus 002 to 15000e minus 002

25000e minus 003 to 50000e minus 003

75000e minus 003 to 10000e minus 00210000e minus 002 to 12500e minus 002

15000e minus 002 to 17500e minus 00217500e minus 002 to 20000e minus 00220000e minus 002 to 21064e minus 002

13239e minus 003 to 25000e minus 00325000e minus 003 to 50000e minus 00350000e minus 003 to 75000e minus 00375000e minus 003 to 10000e minus 00210000e minus 002 to 12500e minus 00212500e minus 002 to 15000e minus 00215000e minus 002 to 17500e minus 00217500e minus 002 to 20000e minus 00220000e minus 002 to 22497e minus 002

(e) n = 5



(b) n = 2

(d) n = 4

Figure 12 Nephogram of slope displacement in119883 direction

(a) n = 1 (c) n = 3

NoneShear-n shear-pShear-p

Tension-pShear-p tension-p

NoneShear-p


NoneShear-p


(e) n = 5

None

Shear-p

Tension-p

Shear-p tension-p

None

Shear-p

Tension-p

Shear-p tension-p

(b) n = 2

(d) n = 4

Figure 13 Plastic state of the sliding mass

Under this operating condition the water level rises sorapidly that the water pressure variation is not completelytransferred into the slope and the variation in pore waterpressure is detected mainly on the surface part in contactwith water The huge additional water pressure functions likea presser foot to some extent The seepage unbalance vectorthus caused points to the interior of the slope and has littleimpact on slope stability

52 Analysis ofMain Sliding Zone Figure 14 shows the plasticstate distribution of elements in the main sliding zone afterfive earthquakes Shear failure has been found in most ofthe elements but the sliding zone at the bottom surfaceof the rear gentle slope platform is never destroyed whichindicates that this part is of great slide-resistant capacityThus there is relatively small possibility of sliding failure inpositions above it In case of overall failure of the slope themiddle steeply dipping segment first slides and deforms andthen gradually overcomes the resistance of the front upliftedsegment resulting in overall instability As the steeply dippingsegment slides down tensile stress occurs in its rear edge andlarge tensile fractures appearThe rockmass at the rear part isthen subject to traction and may as a result slide down Afterfive earthquakes elements in the main sliding zone regaintheir elasticity in the end indicating that the slope is stillstable under this operating condition

None

Shear-p

Figure 14 Plastic state of the main sliding zone after five earth-quakes

The comparison above shows that deformation of theslope is controlled by the soft interlayer and is mainlymanifested as bedding slide of the slope along the softinterlayer Throughout the calculation process no obvioussign of overall failure is found in the slope due to the followingfactors (1) the main sliding zone has been adjusted aftermultiple earthquakes and thus has certain stability (2) themain sliding zone is buried deep between the soft rock andblock-layered rock with no surface directly connected to thefree face and the uplifted segment in the front part plays arole of sliding prevention and (3) microearthquakes affectslope stability mainly through long-term coupling with otherfactors

53 Analysis of Slope Dynamic Response Amplitudes Fromthe analysis above it is evident that the slope deformation


(a) n = 1 (c) n = 3

70359e + 000 to 10000e + 001

10000e + 001 to 20000e + 001

20000e + 001 to 30000e + 001

30000e + 001 to 40000e + 001

40000e + 001 to 50000e + 001

50000e + 001 to 60000e + 001

60000e + 001 to 65000e + 001

74313e + 000 to 10000e + 00110000e + 001 to 20000e + 00120000e + 001 to 30000e + 00130000e + 001 to 40000e + 00140000e + 001 to 50000e + 00150000e + 001 to 60000e + 00160000e + 001 to 70000e + 00170000e + 001 to 72200e + 001


(e) n = 5



(b) n = 2

(d) n = 4

Figure 15 Acceleration amplitude nephogram of the slope

(a) n = 1 (c) n = 3

38732e minus 001 to 40000e minus 00140000e minus 001 to 50000e minus 00150000e minus 001 to 60000e minus 00160000e minus 001 to 70000e minus 00170000e minus 001 to 80000e minus 00180000e minus 001 to 90000e minus 00190000e minus 001 to 10000e + 00010000e + 000 to 11000e + 00011000e + 000 to 12000e + 00012000e + 000 to 13000e + 00013000e + 000 to 13675e + 000

41377e minus 001 to 50000e minus 00150000e minus 001 to 60000e minus 00160000e minus 001 to 70000e minus 00170000e minus 001 to 80000e minus 00180000e minus 001 to 90000e minus 00190000e minus 001 to 10000e + 00010000e + 000 to 11000e + 00011000e + 000 to 12000e + 00012000e + 000 to 13000e + 00013000e + 000 to 14000e + 00014000e + 000 to 14129e + 000

41377e minus 001 to 50000e minus 00150000e minus 001 to 60000e minus 00160000e minus 001 to 70000e minus 00170000e minus 001 to 80000e minus 00180000e minus 001 to 90000e minus 00190000e minus 001 to 10000e + 00010000e + 000 to 11000e + 00011000e + 000 to 12000e + 00012000e + 000 to 13000e + 00013000e + 000 to 14000e + 000

(e) n = 5



(b) n = 2

(d) n = 4

Figure 16 Velocity amplitude nephogram of the slope

mainly occurs during the first seismic wave input and isgreatly affected by the priming effect After entering the stableresponse phase the displacement time-history curve repeatsitself to a certain extent Flac3Drsquos built-in programming lan-guage FISH language is used to record the acceleration andvelocity amplitude of each node of the slopeThe nephogramof amplitudes gives a general overview of dynamic responsecharacteristics of the slope

Figure 15 presents the acceleration amplitude nephogramof the slope after five earthquake inputs It can be found thatthe acceleration amplitudes are generally larger in the mainsliding zone This is because the bedding of this zone is asubstance differentiation plane where the media have rela-tively low elastic moduli When the seismic wave propagatesto this bedding strong reflection occurs followed by strongdynamic response that easily causes its further degradationAfter the second earthquake the acceleration amplitude ofthe slope becomes flat and the slope enters the stable responsephase From the distribution of acceleration amplitudes inthe main sliding zone the steeply dipping segment and thearea below it have significantly larger acceleration amplitudesthan the upper part indicating that the upper rock mass isrelatively stable and the lower rock mass has a downslidetrend

Figure 16 shows the nephogram of velocity amplitudesafter five earthquake inputs It can be found that velocityamplitudes are also larger in the main sliding zone especially

at the shear opening in the front edge where the maximumvelocity amplitude appears indicating that the slope tendsto have shear failure along the main sliding zone After thesecond earthquake the distribution of velocity amplitudesbecomes stable with the larger values found near the mainsliding zone and the free face The distribution of velocityamplitudes in the main sliding zone is consistent with thatof the acceleration amplitudes All these indicate that themiddle and lower soft interlayer have stronger dynamicresponse than the upper part and thus are more likely toexperience degradation under long-term microearthquakeaction

Under frequent earthquakes of Intensity IV inducedby reservoir water level rise the dynamic response of theslope has the following characteristics (1) the soft interlayerabsorbs and reflects much of the seismic wave The reflectedseismic wave is then superimposed with the incident wavecausing the development of an obvious amplification effectin the soft interlayer as a result the response amplitudes ofthe nodes in the soft interlayer are generally larger easilyleading to further degradation of the soft interlayer (2) failuremode of the slope is closely related to its dynamic responsecharacteristics the dynamic response value changes greatly inpossible failure positions (3) under the operating conditionof five earthquakes the slope enters the stable response phaseafter a short adaptation period which demonstrates thatmicroearthquakes have limited influences on the slope



(a) Final nephogram of shear strain increments


(b) Final nephogram of shear strain rates

Figure 17 Nephogram of shear strain increments and shear strain rates of the slope after five earthquakes

Table 3 Safety factors under different numbers of earthquakes andfailure probabilities

119875119891

119899

119899 = 1 119899 = 2 119899 = 3 119899 = 4 119899 = 5

005 1085 1073 1062 1053 1045001 1074 1061 1051 1042 10340001 1060 1049 1038 1029 102100001 1050 1038 1028 1019 1011000001 1041 10293 1019 1011 1003119899 is the number of intensity IV microearthquake inputs

Figure 17 shows the nephogramof shear strain incrementsand shear strain rates It can be found that shear strain incre-ments are concentrated in themiddle of the soft interlayer andare small in values the maximum appears at the front shearopening and no connected plastic zones are developed Shearstrain rates are higher in the steeply dipping segment thanin other segments but the overall level remains low and theslope is in a stable state proving that the impact of frequentmicroearthquakes on the slope is finitely convergent

In conclusion after five earthquakes of Intensity IV uponreservoir water level rise the slope deformation shows aconvergent trend without obvious connection in the plasticzone Its dynamic response becomes stable after a shortadaptation period indicating that microearthquakes havecertain influences on slope stability

54 Dynamic Safety Factor The dynamic safety factor time-history curve of the slope after each earthquake can beobtained according to Section 21 The section between theminimum safety factor and the maximum safety factor isdiscretized into a set of smaller equal intervals (Δ119889 = 001)and instantaneous safety factors of the slope at each momentare counted to obtain the number of safety factors in eachdiscrete interval and thus the distribution probability in eachdiscrete interval

As can be found from Figure 18 safety factors of theslope are in an approximately normal distribution Basedon the basic method of mathematical statistics the sta-tistical parameter average 120583

119865and standard deviation 120590

119865

of the probability distribution of safety factors after eachmicroearthquake input can be determined Based on formula(5) and the acceptable failure probability the safety factor canbe determined See Table 3

Figure 19 shows that under the same probability offailure as the number of earthquakes increases the safety

factor of the slope under microearthquakes of Intensity IVgradually decreases

6 Conclusions

In this study numerical simulation is conducted for frequentmicroearthquakes (Intensity IV) induced by reservoir waterlevel rise at the rock bedded slope with a soft interlayer inthe TGR area and calculation results are analyzed based onthe displacement deformation and dynamic response of theslope The following conclusions are obtained

(1) Although continuousmicroearthquake action has ledto local failure and a certain amount of permanentdisplacement of the slope the slope is eventuallyin a stable state Under microearthquake action thesteeply dipping segment shows a general downslidetrend while the gentle slope platform at the rear edgeis relatively stable As a result tensile stress developsat the rear edge of steeply dipping segment leading toyielding of the rock mass in this position which mayfurther lead to the development of tensile fracturesan early sign of landslide

(2) The horizontal slip displacement of the slopeincreases from the rear to the front Due to frequentmicroearthquakes shear failure tends to developalong the soft interlayer However the upliftedsegment in the front supports the steeply dippingsegment in the middle prevents it from sliding andlimits its sliding space For slopes affected by frequentmicroearthquakes appropriate antislide measurescan effectively limit slope displacement

(3) Under the action of frequent microearthquakesimpact of the priming effect on slope deformation isthe greatest and microearthquakesrsquo impact on slopedeformation is finitely convergent

(4) Under microearthquake action slope deformation ispassive deformation caused by thrust load It startsfrom the steeply dipping segment in the middle andis controlled by the soft interlayer as can be seenfrom translational sliding of the slope along the softinterlayer The soft interlayer absorbs much moreseismic wave energy than the upper rock mass whichenables it to serve as a filter

(5) Under the same probability of failure as the numberof microearthquake inputs increases the safety factorof the slope gradually decreases


106 107 108 109 11 111 112 113 114 115 116Safety factor

0

002

004

006

008

01

012

014Fr

eque

ncy

(a) 119899 = 1

104 105 106 107 108 109 11 111 112 113 114 115Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(b) 119899 = 2

103 104 105 106 107 108 109 11 111 112 113 114Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(c) 119899 = 3

103 104 105 106 107 108 109 11 111 112 113Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(d) 119899 = 4

102 103 104 105 106 107 108 109 11 111 112Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(e) 119899 = 5

Figure 18 Distribution of safety factors

Although the slope deformation under microearthquakeaction tends to be convergent reservoir-induced earthquakeis usually in close association with the operation cycle ofthe reservoir and is characterized by continuous occurrenceThe cumulative deformation effect thus caused should receivehigh attention In particular earthquake monitoring andprediction shall be properly carried out according to the

dynamic response and deformation mechanism of the slopeunder seismic action

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper


0991

101102103104105106107108109

Safe

ty fa

ctor

1 2 3 4 5 60The number of earthquake inputs

Pf = 005

Pf = 001

Pf = 0001

Pf = 00001

Pf = 000001

Figure 19 Curves of the number of earthquake inputs and safetyfactors under different failure probabilities

Acknowledgments

Financial support for this paper was provided by 2015Chongqing University Postgraduatesrsquo Innovation Project(CYB15038) and the National Natural Science Foundationof China (41372356) The authors thank the anonymousreferees for their careful reading of this paper and valuablesuggestions

References

[1] D Deyerling JWangW Hu et al ldquoPAH distribution andmassfluxes in theThree Gorges Reservoir after impoundment of theThree Gorges Damrdquo Science of the Total Environment vol 491-492 pp 123ndash130 2014

[2] C D Li H M Tang Y F Ge X Hu and L Wang ldquoApplica-tion of back-propagation neural network on bank destructionforecasting for accumulative landslides in the three GorgesReservoir Region Chinardquo Stochastic Environmental Researchand Risk Assessment vol 28 no 6 pp 1465ndash1477 2014

[3] S P Yu J S Yang and G M Liu ldquoImpact assessment of ThreeGorges Damrsquos impoundment on river dynamics in the northbranch of Yangtze River estuary Chinardquo Environmental EarthSciences vol 72 no 2 pp 499ndash509 2014

[4] L X Wu F Ren and R Q Niu ldquoLandslide susceptibilityassessment using object mapping units decision tree andsupport vector machine models in the Three Gorges of ChinardquoEnvironmental Earth Sciences vol 71 no 11 pp 4725ndash47382014

[5] M X Liu W Z Du and H L Zhang ldquoChanges of preferentialflow path on different altitudinal zones in the Three GorgesReservoir Area Chinardquo Canadian Journal of Soil Science vol94 no 2 pp 177ndash188 2014

[6] N J Austin J-P Muller L Gong and J Zhang ldquoA regionalinvestigation of urban land-use change for potential landslidehazard assessment in theThree Gorges Reservoir Area PeoplersquosRepublic of China Zigui to Wanzhourdquo International Journal ofRemote Sensing vol 34 no 8 pp 2983ndash3011 2013

[7] L D Zuo S L Zhou and F Q Wu ldquoResearch on the stabilityof a rock slop in the Three Gorges Reservoir influenced byreservoir flowrdquo Chinese Journal of Underground Space andEngineering vol 6 no 2 pp 429ndash435 2010

[8] X Q Luo H Sun L G Tham and S M Junaideen ldquoLand-slide model test system and its application on the study ofshiliushubao landslide in three gorges reservoir areardquo Soils andFoundations vol 50 no 2 pp 309ndash317 2010

[9] B Chai K Yin J Du and L Xiao ldquoCorrelation betweenincompetent beds and slope deformation at Badong town in theThree Gorges reservoir Chinardquo Environmental Earth Sciencesvol 69 no 1 pp 209ndash223 2013

[10] W Jian Z Wang and K Yin ldquoMechanism of the Anlesilandslide in the Three Gorges Reservoir Chinardquo EngineeringGeology vol 108 no 1-2 pp 86ndash95 2009

[11] X Wang R Niu and Y Wang ldquoLandslide mechanism analysisin the Three Gorges based on cloud model and formal conceptanalysisrdquo Quarterly Journal of Engineering Geology and Hydro-geology vol 44 no 2 pp 249ndash258 2011

[12] H Keqiang Y Guangming and L Xiangran ldquoThe regionaldistribution regularity of landslides and their effects on theenvironments in the Three Gorges Reservoir Region ChinardquoEnvironmental Geology vol 57 no 8 pp 1925ndash1931 2009

[13] X B Li L J Dong G Y Zhao et al ldquoStability analysis andcomprehensive treatmentmethods of landslides under complexmining environment-a case study of Dahu landslide fromLinbao Henan in Chinardquo Safety Science vol 50 no 4 pp 695ndash704 2012

[14] M Basharat A Ali I A K Jadoon and J Rohn ldquoUsing PCAin evaluating event-controlling attributes of landsliding in the2005 Kashmir earthquake region NW Himalayas PakistanrdquoNatural Hazards vol 81 pp 1999ndash2017 2016

[15] S W Qi H X Lan and J Y Dong ldquoAn analytical solution toslip buckling slope failure triggered by earthquakerdquo EngineeringGeology vol 194 pp 4ndash11 2015

[16] L J Dong and X B Li ldquoComprehensive models for evaluatingrockmass stability based on statistical comparisons of multipleclassifiersrdquo Mathematical Problems in Engineering vol 2013Article ID 395096 9 pages 2013

[17] J Du K Yin and S Lacasse ldquoDisplacement prediction incolluvial landslidesThreeGorges Reservoir Chinardquo Landslidesvol 10 no 2 pp 203ndash218 2013

[18] X-R Liu D-L Li J-B Wang and Z Wang ldquoSurroundingrock pressure of shallow-buried bilateral bias tunnels underearthquakerdquo Geomechanics and Engineering vol 9 no 4 pp427ndash445 2015

[19] C Occhiena M Pirulli and C Scavia ldquoA microseismic-based procedure for the detection of rock slope instabilitiesrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 69 pp 67ndash79 2014

[20] Z Liang N W Xu K Ma S B Tang and C Tang ldquoMicroseis-micmonitoring and numerical simulation of rock slope failurerdquoInternational Journal of Distributed Sensor Networks vol 2013Article ID 845191 10 pages 2013

[21] M Chang C Tang C Xia and Q Fang ldquoSpatial distributionanalysis of landslides triggered by the 2013-04-20 Lushanearthquake Chinardquo Earthquake Engineering and EngineeringVibration vol 15 no 1 pp 163ndash171 2016

[22] T-S Hou X-G Wang and S Pamukcu ldquoGeological charac-teristics and stability evaluation of wanjia middle school slopein wenchuan earthquake areardquo Geotechnical and GeologicalEngineering vol 34 no 1 pp 237ndash249 2016


[23] C Tang G Ma M Chang et al ldquoLandslides triggered by the20 April 2013 Lushan earthquake Sichuan Province ChinardquoEngineering Geology vol 187 pp 45ndash55 2015

[24] V S Gischig E Eberhardt J R Moore and O Hungr ldquoOnthe seismic response of deep-seated rock slope instabilitiesmdashinsights from numerical modelingrdquo Engineering Geology vol193 pp 1ndash18 2015

[25] D P Guo M Hamada C He Y F Wang and Y L ZouldquoAn empirical model for landslide travel distance prediction inWenchuan earthquake areardquo Landslides vol 11 no 2 pp 281ndash291 2014

[26] NWXu Study onmicroseismicmonitoring and stability analysisof high steep rock slope [PhD thesis] Dalian University ofTechnology Dalian China 2011

[27] JW JiangResearch on the deformationmechanism and dynamicresponse of typical landslides in Three Gorges Reservoir in caseof frequent microseisms [PhD thesis] China University ofGeosciences Wuhan China 2012

[28] H S Liu Study on analysis method of rock slope seismicstability [PhD thesis] Institute of Engineering MechanicsChina Earthquake Administration Harbin China 2006

[29] X-W Hu H-M Tang and Y-R Liu ldquoPhysical model studieson stability of Zhaoshuling landslide in area of Three GorgesReservoirrdquo Journal of Rock Mechanics and Engineering vol 24no 12 pp 2089ndash2095 2005

[30] Y R Zheng H L Ye and R Q Huang ldquoAnalysis and discussionof failure mechanism and fracture surface of slope under earth-quakerdquo Chinese Journal of Rock Mechanics and Engineering vol28 no 8 pp 1714ndash1723 2009

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



long term is inevitably a great challenge for the stability of theslope in the TGR area For the stability of rock slopes underthe earthquake action Tang et al [23] analyzed the relationsbetween the rock landslide distribution and five main factors(fault proximity epicenter proximity peak ground accelera-tion slope angle and lithology) Gischig et al [24] presenteda series of 2D distinct-element numerical models which wereaimed at clarifying interactions between earthquakes andlarge rock slope instabilities Guo et al [25] collected 54landslides with travel distances of 347ndash4170m triggered byWenchuan Earthquake in 2008 to discuss the effectiveness ofvarious influential factors on landslide travel distance andhis research results revealed that rock type sliding sourcevolume and slope transition angle were the predominantfactors on landslide travel distance Besides Xu [26] studiedthe stability of steep rock slopes under microearthquakes andJiang [27] analyzed the deformationmechanism and dynamicresponse characteristics of the first typical loess landslidesegment in the TGR area under microearthquakes Howeverlittle research has been conducted on the impact of reservoirwater level fluctuation and frequent microearthquake occur-rences on the dynamic stability of the bedded rock slope

To sum up with Zhaoshuling Landslide (Badong CountyChina) in the TGR area as a representative case numericalsimulation is conducted for the rock bedded slope with asoft interlayer under multiple microearthquakes induced byreservoir water level rise and the dynamic stability and failuremechanism of such slopes are analyzed based on the slopedisplacement deformation and dynamic response to providetheoretical bases for landslide control slope stabilization anddisaster prevention

2 Calculation of Dynamic Safety Factor

21 Time-History Curve of Dynamic Safety Factor The safetyfactor of the slope sliding failure mode under the earthquakeaction can be determined with the limit equilibrium theoryby calculating the earthquake inertia force on the rock massat random time 119905

Assume that (119905) is the resultant force of gravity (119905) andearthquake inertia force (119905) on the rock mass at time 119905 Theresultant force is projected onto the potential sliding directionto obtain the sliding force 119878(119905) as follows

119878 (119905) = (119905) sdot 119894 (1)

where 119894 is the unit vector of the potential sliding direction(119905) is projected onto the normal direction of the slidingsurface to obtain the normal reacting force

According to the Coulomb Friction Laws the slide-resistant force 119877(119905) can be determined as follows

119877 (119905) =10038161003816100381610038161003816 (119905) sdot

10038161003816100381610038161003816sdot tan120593 (119905) + 119860 sdot 119888 (119905) (2)

where is the normal unit vector of the sliding surface 119860 isthe contact area between the sliding mass and the rock massbelow it and 120593(119905) and 119888(119905) are the internal friction angle andcohesion of the sliding surface at time 119905 respectively

Safety factor

Probability

Pf

FR

120583F

120573120590F

density

Figure 1 Distribution of dynamic safety factors

Therefore the dynamic safety factor can be expressed asfollows

119896 (119905) =

[10038161003816100381610038161003816 (119905) sdot

10038161003816100381610038161003816sdot tan120593 (119905) + 119860 sdot 119888 (119905)]10038161003816100381610038161003816 (119905) sdot 119894

10038161003816100381610038161003816

(3)

Based on the formula above a computation program canbe developed using Fish language in Flac3D to obtain thetime-history curve of dynamic safety factor for the slopeunder seismic action thus providing a basis for stabilityanalysis of slopes under frequent microearthquakes

22 Safety Factor Based on Probability Statistics Earthquakeis normally assumed to be a random variable of timeAccordingly the dynamic safety factor of slope under seismicaction can also be seen as a random function of time whichenables the dynamic stability evaluation index of slope to bedetermined based on the reliability theory [28]

Assume that under seismic action when the minimumvalue of the time-history curve for the dynamic safety factoris used as the evaluation index the highest level of safetyis expected (ie the probability of failure is 0) when themaximum value of the time-history curve is used as theevaluation index the slope stabilitymay be overestimated andthe highest level of risk is expected (ie the probability offailure is 1) Based on the assumption above as well as thefundamentals of probability and statistics if the safety factoris taken as the critical index the evaluation index for dynamicstability of the slope can be transformed into the probabilityof the safety factor below 119865

119877due to the earthquake

As shown in Figure 1 the area of the shaded part is theprobability of failure 119875

119891 Based on the principle of probability

analysis the reliability 120573 can be determined as follows

120573 =120583119865minus 119865119877

120590119865

(4)

where 120583119865is the mean of safety factors and 120590

119865is the standard

deviation of safety factors According to the formula above

119865119877= 120583119865minus 120573120590119865 (5)



119875119891

120573

05 0025 06701 128005 165001 2330001 31000001 372000001 425


120583119865=1

119873

119873

sum

119894=1

119865 (119905119894)

120590119865= radic

1

119873 minus 1

119873

sum

119894=1

(119865 (119905119894) minus 120583119865)2

(6)





119891 See Table 1

3 Project Overview




Yangtze River


N

Badong County





2b3 and T

2b2 strata and














500

Yangtze River

100

100

150

200

250

300

350

400

400

400

300300

200

200

100

450

500 500

Landslide area

N


Qdel

Qdel

Qdel

Qdel

T2b2

T2b2

T2b2

T2b3

T2b3

T2b3




0 200 m





Yangtze100

200

300

400

500

Vert

ical

hei

ght (

m)


123

456

River



119862119901= radic

119864 (1 minus 120583)

120588 (1 + 120583) (1 minus 2120583)

119862119904= radic

119864

2120588 (1 + 120583)

(7)







Horizontal

Vertical

al

0200

400600

8001000

1200X (m)0

100

200

300

400

Z(m

)





Δ119897 =1

10sdot119862119904

119891 (8)







120590119899= minus2 (120588119862

119901) V119899

120590119904= minus2 (120588119862

119904) V119904

(9)



density 119862119901and 119862







minus2000

200

1 2 3 4 5 6 70

Time (sec)

Acce

lera

tion

(cm

sec

2)


1 2 3 4 5 6 70

Time (sec)

minus6minus226

Velo

city

(cm

sec

)


1 2 3 4 5 6 70

Time (sec)


Disp

lace

men

t(c

m)



1 2 3 4 5 6 70

Time (sec)

minus15minus55

15

Acce

lera

tion

(cm

sec

2)


1 2 3 4 5 6 70

Time (sec)


00204

Velo

city

(cm

sec

)


1 2 3 4 5 6 70

Time (sec)

minus008minus004

0004008

Disp

lace

men

t (cm

)








119865119909= minus120588119862

119901(V119898119909minus V119891119891119909)119860 + 120590

119891119891

119909119909Δ119878119910

119865119910= minus120588119862

119904(V119898119910minus V119891119891119910)119860 + 120590

119891119891

119909119910Δ119878119910

119865119911= minus120588119862

119904(V119898119911minus V119891119891119911)119860 + 120590

119891119891

119909119911Δ119878119910

(10)




119909 119865119910




minus26710e + 006 to minus25000e + 006

minus25000e + 006 to minus20000e + 006











119909 V119898119910 and V119898





and 120590119891119891119909119911










(a) n = 1 (c) n = 3


80241e minus 004 to 25000e minus 003

50000e minus 003 to 75000e minus 003

12500e minus 002 to 15000e minus 002

25000e minus 003 to 50000e minus 003




(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3



NoneShear-p


NoneShear-p


(e) n = 5

None

Shear-p

Tension-p

Shear-p tension-p

None

Shear-p

Tension-p

Shear-p tension-p

(b) n = 2

(d) n = 4




None

Shear-p





(a) n = 1 (c) n = 3

70359e + 000 to 10000e + 001

10000e + 001 to 20000e + 001

20000e + 001 to 30000e + 001

30000e + 001 to 40000e + 001

40000e + 001 to 50000e + 001

50000e + 001 to 60000e + 001

60000e + 001 to 65000e + 001



(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3




(e) n = 5



(b) n = 2

(d) n = 4














119875119891

119899

119899 = 1 119899 = 2 119899 = 3 119899 = 4 119899 = 5







119865




6 Conclusions








106 107 108 109 11 111 112 113 114 115 116Safety factor

0

002

004

006

008

01

012

014Fr

eque

ncy

(a) 119899 = 1

104 105 106 107 108 109 11 111 112 113 114 115Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(b) 119899 = 2

103 104 105 106 107 108 109 11 111 112 113 114Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(c) 119899 = 3

103 104 105 106 107 108 109 11 111 112 113Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(d) 119899 = 4

102 103 104 105 106 107 108 109 11 111 112Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(e) 119899 = 5




Competing Interests



0991

101102103104105106107108109

Safe

ty fa

ctor


Pf = 005

Pf = 001

Pf = 0001

Pf = 00001

Pf = 000001


Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119875119891

120573

05 0025 06701 128005 165001 2330001 31000001 372000001 425


120583119865=1

119873

119873

sum

119894=1

119865 (119905119894)

120590119865= radic

1

119873 minus 1

119873

sum

119894=1

(119865 (119905119894) minus 120583119865)2

(6)





119891 See Table 1

3 Project Overview




Yangtze River


N

Badong County





2b3 and T

2b2 strata and














500

Yangtze River

100

100

150

200

250

300

350

400

400

400

300300

200

200

100

450

500 500

Landslide area

N


Qdel

Qdel

Qdel

Qdel

T2b2

T2b2

T2b2

T2b3

T2b3

T2b3




0 200 m





Yangtze100

200

300

400

500

Vert

ical

hei

ght (

m)


123

456

River



119862119901= radic

119864 (1 minus 120583)

120588 (1 + 120583) (1 minus 2120583)

119862119904= radic

119864

2120588 (1 + 120583)

(7)







Horizontal

Vertical

al

0200

400600

8001000

1200X (m)0

100

200

300

400

Z(m

)





Δ119897 =1

10sdot119862119904

119891 (8)







120590119899= minus2 (120588119862

119901) V119899

120590119904= minus2 (120588119862

119904) V119904

(9)



density 119862119901and 119862







minus2000

200

1 2 3 4 5 6 70

Time (sec)

Acce

lera

tion

(cm

sec

2)


1 2 3 4 5 6 70

Time (sec)

minus6minus226

Velo

city

(cm

sec

)


1 2 3 4 5 6 70

Time (sec)


Disp

lace

men

t(c

m)



1 2 3 4 5 6 70

Time (sec)

minus15minus55

15

Acce

lera

tion

(cm

sec

2)


1 2 3 4 5 6 70

Time (sec)


00204

Velo

city

(cm

sec

)


1 2 3 4 5 6 70

Time (sec)

minus008minus004

0004008

Disp

lace

men

t (cm

)








119865119909= minus120588119862

119901(V119898119909minus V119891119891119909)119860 + 120590

119891119891

119909119909Δ119878119910

119865119910= minus120588119862

119904(V119898119910minus V119891119891119910)119860 + 120590

119891119891

119909119910Δ119878119910

119865119911= minus120588119862

119904(V119898119911minus V119891119891119911)119860 + 120590

119891119891

119909119911Δ119878119910

(10)




119909 119865119910




minus26710e + 006 to minus25000e + 006

minus25000e + 006 to minus20000e + 006











119909 V119898119910 and V119898





and 120590119891119891119909119911










(a) n = 1 (c) n = 3


80241e minus 004 to 25000e minus 003

50000e minus 003 to 75000e minus 003

12500e minus 002 to 15000e minus 002

25000e minus 003 to 50000e minus 003




(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3



NoneShear-p


NoneShear-p


(e) n = 5

None

Shear-p

Tension-p

Shear-p tension-p

None

Shear-p

Tension-p

Shear-p tension-p

(b) n = 2

(d) n = 4




None

Shear-p





(a) n = 1 (c) n = 3

70359e + 000 to 10000e + 001

10000e + 001 to 20000e + 001

20000e + 001 to 30000e + 001

30000e + 001 to 40000e + 001

40000e + 001 to 50000e + 001

50000e + 001 to 60000e + 001

60000e + 001 to 65000e + 001



(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3




(e) n = 5



(b) n = 2

(d) n = 4














119875119891

119899

119899 = 1 119899 = 2 119899 = 3 119899 = 4 119899 = 5







119865




6 Conclusions








106 107 108 109 11 111 112 113 114 115 116Safety factor

0

002

004

006

008

01

012

014Fr

eque

ncy

(a) 119899 = 1

104 105 106 107 108 109 11 111 112 113 114 115Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(b) 119899 = 2

103 104 105 106 107 108 109 11 111 112 113 114Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(c) 119899 = 3

103 104 105 106 107 108 109 11 111 112 113Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(d) 119899 = 4

102 103 104 105 106 107 108 109 11 111 112Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(e) 119899 = 5




Competing Interests



0991

101102103104105106107108109

Safe

ty fa

ctor


Pf = 005

Pf = 001

Pf = 0001

Pf = 00001

Pf = 000001


Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











500

Yangtze River

100

100

150

200

250

300

350

400

400

400

300300

200

200

100

450

500 500

Landslide area

N


Qdel

Qdel

Qdel

Qdel

T2b2

T2b2

T2b2

T2b3

T2b3

T2b3




0 200 m





Yangtze100

200

300

400

500

Vert

ical

hei

ght (

m)


123

456

River



119862119901= radic

119864 (1 minus 120583)

120588 (1 + 120583) (1 minus 2120583)

119862119904= radic

119864

2120588 (1 + 120583)

(7)







Horizontal

Vertical

al

0200

400600

8001000

1200X (m)0

100

200

300

400

Z(m

)





Δ119897 =1

10sdot119862119904

119891 (8)







120590119899= minus2 (120588119862

119901) V119899

120590119904= minus2 (120588119862

119904) V119904

(9)



density 119862119901and 119862







minus2000

200

1 2 3 4 5 6 70

Time (sec)

Acce

lera

tion

(cm

sec

2)


1 2 3 4 5 6 70

Time (sec)

minus6minus226

Velo

city

(cm

sec

)


1 2 3 4 5 6 70

Time (sec)


Disp

lace

men

t(c

m)



1 2 3 4 5 6 70

Time (sec)

minus15minus55

15

Acce

lera

tion

(cm

sec

2)


1 2 3 4 5 6 70

Time (sec)


00204

Velo

city

(cm

sec

)


1 2 3 4 5 6 70

Time (sec)

minus008minus004

0004008

Disp

lace

men

t (cm

)








119865119909= minus120588119862

119901(V119898119909minus V119891119891119909)119860 + 120590

119891119891

119909119909Δ119878119910

119865119910= minus120588119862

119904(V119898119910minus V119891119891119910)119860 + 120590

119891119891

119909119910Δ119878119910

119865119911= minus120588119862

119904(V119898119911minus V119891119891119911)119860 + 120590

119891119891

119909119911Δ119878119910

(10)




119909 119865119910




minus26710e + 006 to minus25000e + 006

minus25000e + 006 to minus20000e + 006











119909 V119898119910 and V119898





and 120590119891119891119909119911










(a) n = 1 (c) n = 3


80241e minus 004 to 25000e minus 003

50000e minus 003 to 75000e minus 003

12500e minus 002 to 15000e minus 002

25000e minus 003 to 50000e minus 003




(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3



NoneShear-p


NoneShear-p


(e) n = 5

None

Shear-p

Tension-p

Shear-p tension-p

None

Shear-p

Tension-p

Shear-p tension-p

(b) n = 2

(d) n = 4




None

Shear-p





(a) n = 1 (c) n = 3

70359e + 000 to 10000e + 001

10000e + 001 to 20000e + 001

20000e + 001 to 30000e + 001

30000e + 001 to 40000e + 001

40000e + 001 to 50000e + 001

50000e + 001 to 60000e + 001

60000e + 001 to 65000e + 001



(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3




(e) n = 5



(b) n = 2

(d) n = 4














119875119891

119899

119899 = 1 119899 = 2 119899 = 3 119899 = 4 119899 = 5







119865




6 Conclusions








106 107 108 109 11 111 112 113 114 115 116Safety factor

0

002

004

006

008

01

012

014Fr

eque

ncy

(a) 119899 = 1

104 105 106 107 108 109 11 111 112 113 114 115Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(b) 119899 = 2

103 104 105 106 107 108 109 11 111 112 113 114Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(c) 119899 = 3

103 104 105 106 107 108 109 11 111 112 113Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(d) 119899 = 4

102 103 104 105 106 107 108 109 11 111 112Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(e) 119899 = 5




Competing Interests



0991

101102103104105106107108109

Safe

ty fa

ctor


Pf = 005

Pf = 001

Pf = 0001

Pf = 00001

Pf = 000001


Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Horizontal

Vertical

al

0200

400600

8001000

1200X (m)0

100

200

300

400

Z(m

)





Δ119897 =1

10sdot119862119904

119891 (8)







120590119899= minus2 (120588119862

119901) V119899

120590119904= minus2 (120588119862

119904) V119904

(9)



density 119862119901and 119862







minus2000

200

1 2 3 4 5 6 70

Time (sec)

Acce

lera

tion

(cm

sec

2)


1 2 3 4 5 6 70

Time (sec)

minus6minus226

Velo

city

(cm

sec

)


1 2 3 4 5 6 70

Time (sec)


Disp

lace

men

t(c

m)



1 2 3 4 5 6 70

Time (sec)

minus15minus55

15

Acce

lera

tion

(cm

sec

2)


1 2 3 4 5 6 70

Time (sec)


00204

Velo

city

(cm

sec

)


1 2 3 4 5 6 70

Time (sec)

minus008minus004

0004008

Disp

lace

men

t (cm

)








119865119909= minus120588119862

119901(V119898119909minus V119891119891119909)119860 + 120590

119891119891

119909119909Δ119878119910

119865119910= minus120588119862

119904(V119898119910minus V119891119891119910)119860 + 120590

119891119891

119909119910Δ119878119910

119865119911= minus120588119862

119904(V119898119911minus V119891119891119911)119860 + 120590

119891119891

119909119911Δ119878119910

(10)




119909 119865119910




minus26710e + 006 to minus25000e + 006

minus25000e + 006 to minus20000e + 006











119909 V119898119910 and V119898





and 120590119891119891119909119911










(a) n = 1 (c) n = 3


80241e minus 004 to 25000e minus 003

50000e minus 003 to 75000e minus 003

12500e minus 002 to 15000e minus 002

25000e minus 003 to 50000e minus 003




(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3



NoneShear-p


NoneShear-p


(e) n = 5

None

Shear-p

Tension-p

Shear-p tension-p

None

Shear-p

Tension-p

Shear-p tension-p

(b) n = 2

(d) n = 4




None

Shear-p





(a) n = 1 (c) n = 3

70359e + 000 to 10000e + 001

10000e + 001 to 20000e + 001

20000e + 001 to 30000e + 001

30000e + 001 to 40000e + 001

40000e + 001 to 50000e + 001

50000e + 001 to 60000e + 001

60000e + 001 to 65000e + 001



(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3




(e) n = 5



(b) n = 2

(d) n = 4














119875119891

119899

119899 = 1 119899 = 2 119899 = 3 119899 = 4 119899 = 5







119865




6 Conclusions








106 107 108 109 11 111 112 113 114 115 116Safety factor

0

002

004

006

008

01

012

014Fr

eque

ncy

(a) 119899 = 1

104 105 106 107 108 109 11 111 112 113 114 115Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(b) 119899 = 2

103 104 105 106 107 108 109 11 111 112 113 114Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(c) 119899 = 3

103 104 105 106 107 108 109 11 111 112 113Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(d) 119899 = 4

102 103 104 105 106 107 108 109 11 111 112Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(e) 119899 = 5




Competing Interests



0991

101102103104105106107108109

Safe

ty fa

ctor


Pf = 005

Pf = 001

Pf = 0001

Pf = 00001

Pf = 000001


Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus2000

200

1 2 3 4 5 6 70

Time (sec)

Acce

lera

tion

(cm

sec

2)


1 2 3 4 5 6 70

Time (sec)

minus6minus226

Velo

city

(cm

sec

)


1 2 3 4 5 6 70

Time (sec)


Disp

lace

men

t(c

m)



1 2 3 4 5 6 70

Time (sec)

minus15minus55

15

Acce

lera

tion

(cm

sec

2)


1 2 3 4 5 6 70

Time (sec)


00204

Velo

city

(cm

sec

)


1 2 3 4 5 6 70

Time (sec)

minus008minus004

0004008

Disp

lace

men

t (cm

)








119865119909= minus120588119862

119901(V119898119909minus V119891119891119909)119860 + 120590

119891119891

119909119909Δ119878119910

119865119910= minus120588119862

119904(V119898119910minus V119891119891119910)119860 + 120590

119891119891

119909119910Δ119878119910

119865119911= minus120588119862

119904(V119898119911minus V119891119891119911)119860 + 120590

119891119891

119909119911Δ119878119910

(10)




119909 119865119910




minus26710e + 006 to minus25000e + 006

minus25000e + 006 to minus20000e + 006











119909 V119898119910 and V119898





and 120590119891119891119909119911










(a) n = 1 (c) n = 3


80241e minus 004 to 25000e minus 003

50000e minus 003 to 75000e minus 003

12500e minus 002 to 15000e minus 002

25000e minus 003 to 50000e minus 003




(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3



NoneShear-p


NoneShear-p


(e) n = 5

None

Shear-p

Tension-p

Shear-p tension-p

None

Shear-p

Tension-p

Shear-p tension-p

(b) n = 2

(d) n = 4




None

Shear-p





(a) n = 1 (c) n = 3

70359e + 000 to 10000e + 001

10000e + 001 to 20000e + 001

20000e + 001 to 30000e + 001

30000e + 001 to 40000e + 001

40000e + 001 to 50000e + 001

50000e + 001 to 60000e + 001

60000e + 001 to 65000e + 001



(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3




(e) n = 5



(b) n = 2

(d) n = 4














119875119891

119899

119899 = 1 119899 = 2 119899 = 3 119899 = 4 119899 = 5







119865




6 Conclusions








106 107 108 109 11 111 112 113 114 115 116Safety factor

0

002

004

006

008

01

012

014Fr

eque

ncy

(a) 119899 = 1

104 105 106 107 108 109 11 111 112 113 114 115Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(b) 119899 = 2

103 104 105 106 107 108 109 11 111 112 113 114Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(c) 119899 = 3

103 104 105 106 107 108 109 11 111 112 113Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(d) 119899 = 4

102 103 104 105 106 107 108 109 11 111 112Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(e) 119899 = 5




Competing Interests



0991

101102103104105106107108109

Safe

ty fa

ctor


Pf = 005

Pf = 001

Pf = 0001

Pf = 00001

Pf = 000001


Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












minus26710e + 006 to minus25000e + 006

minus25000e + 006 to minus20000e + 006











119909 V119898119910 and V119898





and 120590119891119891119909119911










(a) n = 1 (c) n = 3


80241e minus 004 to 25000e minus 003

50000e minus 003 to 75000e minus 003

12500e minus 002 to 15000e minus 002

25000e minus 003 to 50000e minus 003




(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3



NoneShear-p


NoneShear-p


(e) n = 5

None

Shear-p

Tension-p

Shear-p tension-p

None

Shear-p

Tension-p

Shear-p tension-p

(b) n = 2

(d) n = 4




None

Shear-p





(a) n = 1 (c) n = 3

70359e + 000 to 10000e + 001

10000e + 001 to 20000e + 001

20000e + 001 to 30000e + 001

30000e + 001 to 40000e + 001

40000e + 001 to 50000e + 001

50000e + 001 to 60000e + 001

60000e + 001 to 65000e + 001



(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3




(e) n = 5



(b) n = 2

(d) n = 4














119875119891

119899

119899 = 1 119899 = 2 119899 = 3 119899 = 4 119899 = 5







119865




6 Conclusions








106 107 108 109 11 111 112 113 114 115 116Safety factor

0

002

004

006

008

01

012

014Fr

eque

ncy

(a) 119899 = 1

104 105 106 107 108 109 11 111 112 113 114 115Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(b) 119899 = 2

103 104 105 106 107 108 109 11 111 112 113 114Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(c) 119899 = 3

103 104 105 106 107 108 109 11 111 112 113Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(d) 119899 = 4

102 103 104 105 106 107 108 109 11 111 112Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(e) 119899 = 5




Competing Interests



0991

101102103104105106107108109

Safe

ty fa

ctor


Pf = 005

Pf = 001

Pf = 0001

Pf = 00001

Pf = 000001


Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) n = 1 (c) n = 3


80241e minus 004 to 25000e minus 003

50000e minus 003 to 75000e minus 003

12500e minus 002 to 15000e minus 002

25000e minus 003 to 50000e minus 003




(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3



NoneShear-p


NoneShear-p


(e) n = 5

None

Shear-p

Tension-p

Shear-p tension-p

None

Shear-p

Tension-p

Shear-p tension-p

(b) n = 2

(d) n = 4




None

Shear-p





(a) n = 1 (c) n = 3

70359e + 000 to 10000e + 001

10000e + 001 to 20000e + 001

20000e + 001 to 30000e + 001

30000e + 001 to 40000e + 001

40000e + 001 to 50000e + 001

50000e + 001 to 60000e + 001

60000e + 001 to 65000e + 001



(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3




(e) n = 5



(b) n = 2

(d) n = 4














119875119891

119899

119899 = 1 119899 = 2 119899 = 3 119899 = 4 119899 = 5







119865




6 Conclusions








106 107 108 109 11 111 112 113 114 115 116Safety factor

0

002

004

006

008

01

012

014Fr

eque

ncy

(a) 119899 = 1

104 105 106 107 108 109 11 111 112 113 114 115Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(b) 119899 = 2

103 104 105 106 107 108 109 11 111 112 113 114Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(c) 119899 = 3

103 104 105 106 107 108 109 11 111 112 113Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(d) 119899 = 4

102 103 104 105 106 107 108 109 11 111 112Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(e) 119899 = 5




Competing Interests



0991

101102103104105106107108109

Safe

ty fa

ctor


Pf = 005

Pf = 001

Pf = 0001

Pf = 00001

Pf = 000001


Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) n = 1 (c) n = 3

70359e + 000 to 10000e + 001

10000e + 001 to 20000e + 001

20000e + 001 to 30000e + 001

30000e + 001 to 40000e + 001

40000e + 001 to 50000e + 001

50000e + 001 to 60000e + 001

60000e + 001 to 65000e + 001



(e) n = 5



(b) n = 2

(d) n = 4


(a) n = 1 (c) n = 3




(e) n = 5



(b) n = 2

(d) n = 4














119875119891

119899

119899 = 1 119899 = 2 119899 = 3 119899 = 4 119899 = 5







119865




6 Conclusions








106 107 108 109 11 111 112 113 114 115 116Safety factor

0

002

004

006

008

01

012

014Fr

eque

ncy

(a) 119899 = 1

104 105 106 107 108 109 11 111 112 113 114 115Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(b) 119899 = 2

103 104 105 106 107 108 109 11 111 112 113 114Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(c) 119899 = 3

103 104 105 106 107 108 109 11 111 112 113Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(d) 119899 = 4

102 103 104 105 106 107 108 109 11 111 112Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(e) 119899 = 5




Competing Interests



0991

101102103104105106107108109

Safe

ty fa

ctor


Pf = 005

Pf = 001

Pf = 0001

Pf = 00001

Pf = 000001


Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















119875119891

119899

119899 = 1 119899 = 2 119899 = 3 119899 = 4 119899 = 5







119865




6 Conclusions








106 107 108 109 11 111 112 113 114 115 116Safety factor

0

002

004

006

008

01

012

014Fr

eque

ncy

(a) 119899 = 1

104 105 106 107 108 109 11 111 112 113 114 115Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(b) 119899 = 2

103 104 105 106 107 108 109 11 111 112 113 114Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(c) 119899 = 3

103 104 105 106 107 108 109 11 111 112 113Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(d) 119899 = 4

102 103 104 105 106 107 108 109 11 111 112Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(e) 119899 = 5




Competing Interests



0991

101102103104105106107108109

Safe

ty fa

ctor


Pf = 005

Pf = 001

Pf = 0001

Pf = 00001

Pf = 000001


Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










106 107 108 109 11 111 112 113 114 115 116Safety factor

0

002

004

006

008

01

012

014Fr

eque

ncy

(a) 119899 = 1

104 105 106 107 108 109 11 111 112 113 114 115Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(b) 119899 = 2

103 104 105 106 107 108 109 11 111 112 113 114Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(c) 119899 = 3

103 104 105 106 107 108 109 11 111 112 113Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(d) 119899 = 4

102 103 104 105 106 107 108 109 11 111 112Safety factor

0

002

004

006

008

01

012

014

016

Freq

uenc

y

(e) 119899 = 5




Competing Interests



0991

101102103104105106107108109

Safe

ty fa

ctor


Pf = 005

Pf = 001

Pf = 0001

Pf = 00001

Pf = 000001


Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0991

101102103104105106107108109

Safe

ty fa

ctor


Pf = 005

Pf = 001

Pf = 0001

Pf = 00001

Pf = 000001


Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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