research article effects of upstream water level on...

Research ArticleEffects of Upstream Water Level on Dynamic Response ofEarth Dam

Shong-Loong Chen1 Chun-Fu Lin2 James C Ni1 and Meen-Wah Gui1

1Department of Civil Engineering National Taipei University of Technology Taipei 10608 Taiwan2Institute of Engineering Technology National Taipei University of Technology Taipei 10608 Taiwan

Correspondence should be addressed to Meen-Wah Gui mwguintutedutw

Received 23 October 2014 Revised 18 March 2015 Accepted 18 March 2015

Academic Editor U E Vincent

Copyright copy 2015 Shong-Loong Chen et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The island of Taiwan is located between the boundaries of the Eurasia and the Philippines Plates and thus earthquakes occurredfrequentlyThe excitation of earthquake affects the integrity of earth dams situated in themountainous area of the islandA studywasconducted to evaluate the dynamic response and safety of one of the earthquake damsThe computer program and soil model usedwere calibrated for their appropriate use for the subject dam against a well-instrumented centrifuge model Numerical simulationwas then conducted to examine the influence of upstreamwater storage level on the response of the earth damThenumerical resultsidentified three locations in the dam where attentions are required because these locations were found susceptible to liquefaction

1 Introduction

Earthquakes due to active tectonicmovements are frequent inTaiwan which is located between the boundary of Eurasianand Philippines Sea Plates The plate boundary tectonics aregenerally dominated by the subduction of the Philippines SeaPlate beneath Eurasia along the Ryukyu Trench that runsfrom southwest Japan to Taiwan [1]

A magnitude 73 earthquake on the Richter scale struck asmall town Chi-Chi (pronounced as Ji-Ji) in central Taiwanon September 21 1999 as a result of the violent movement ofthe Chelongpu fault OnOctober 22 of the same year anothermagnitude 64 earthquake on the Richter scale struck thetown of Jiayi in southern Taiwan and one of the accelerom-eters located on the right shoulder of the Renyitan Reservoirdam which was located four kilometers away from the Jiayitown detected a maximum ground acceleration of 992 galCracks were observed at the crest of the dam On March 42010 a magnitude 64 earthquake on the Richter scale withepicenter near the town of Jiaxian jolted southern Taiwanespecially the Gaoxioang county According to the reportsummarized by Water-Watch Nongovernmental Organiza-tion [2] the earthquake resulted in a 3 cm wide 75 cm deepand 15m long crack across the crest of the dam at theHutoupi

Reservoir which was about 25 km away from Jiaxian Theseare just some of the examples showing how frequent seismicactivities occurred in the region and the consequences of theseismic activities on the integrity of earth dam Earth damsmay crumble under seismic loads as the result of soil liq-uefaction The significance of conducting thorough daminvestigation has been emphasized by Zhang [3]

Finite element (FE) analysis has been widely used for theevaluation of the seismic response and safety of earth damClough and Chopra [4] first introduced the application of FEanalysis in the dynamic analysis of earth dam Seed et al[5] and Seed [6] back analyzed the response of the 1971 SanFernando earthquake on the deformation of the Lower andUpper SanFernandodams also using FE analysis Zienkiewiczet al [7] includedmaterial nonlinearity and liquefaction anal-ysis to study the behavior of the dam materials Zienkiewiczand Mroz [8] and Pastor et al [9] proposed the use of thegeneralized plasticity theory in the response analysis of earthdams under seismic activities Khoei et al [10] compared theperformance of Pastor-Zienkiewicz and cap plasticity modelsthrough the dynamic analysis of the failure of lower San Fer-nando dam under the 1971 earthquake and the Mahabad andDoroodzan dams under the 1978 Tabas earthquake Wu et al[11] employed the computer program LIQCA to simulate

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 723904 12 pageshttpdxdoiorg1011552015723904

2 Mathematical Problems in Engineering

the dynamic responses of an earth dam Gui and Chiu[12] simulated the dynamic response of Renyitan earth damusing the Finn model [13] provided in the two-dimensionalfinite difference program FLAC All of these studies yieldedconvincing results

When an earth dam is subjected to a seismic load pore-water pressure responded faster than the deformation at thetop of damThus for safety management of earth dam pore-water pressure response is an important indicator This studyaims at investigating the influence of the upstream waterstorage level on the pore-water pressure response in the bodyof an earth dam subjected to synthetic earthquake excitationExperimental results from a dynamic centrifuge test were firstused to calibrate the appropriate use of the chosen constitu-tive law for the following numerical simulation Subsequentlyeffective stress analysis was conducted to evaluate the safetyof the study earth dam under the synthetic seismic loading

2 Governing Equations

Total stress analysis yields only the deformation of soil fromthe given stress-strain relationship but provides no informa-tion on the changes in excess pore-water pressure (EPWP)when the soil is subjected to excitation Thus the use ofthe total stress analysis for liquefaction study is insufficientBiot [15] incorporated Darcyrsquos law for the representation ofthe fluids flow in the soil to the linear elastic solid mechanicsframework and thus formulated the so-called two-phasemix-ing theory to deal with the pore-water pressure issues that thetotal stress analysis failed to handle The equations of motionfor elastic porous media saturated with a pore fluid consistof two variablesrsquo fields (i) pore pressure 119901 and (ii) skeletondisplacements 119906 A simplified numerical framework knownas the 119906-119901 formulation was formulated by assuming Darcyrsquosflow rule (laminar flow) and neglecting the fluid inertia [716ndash18] By denoting was the flow rate of the fluid we thushave the overall balance or momentum equilibrium equationof soil-liquid mixture as [19]

[M 00 0]

u

+ [0 0

QT S]

u

+ [

K minusQ0 H]

u119901 =

f119906

f119901

(1)

whereM andK are the total mass and total stiffness matrixesQ is the discrete gradient operator coupling the soil andfluid phase H is the permeability matrix and S is the com-pressibility matrix Vectors f119906 and f119901 represent the effect ofbody forces along with prescribed boundary conditions forthe solid-fluid mixture and fluid phases

The model used to simulate the dynamics behavior of thesoil is the Pastor-Zienkiewiczmark III (P-Z III) model whichhas been recognized as the model most suitable for modelingmaterials susceptible to liquefaction [19] The model wasproposed in 1985 by Pastor et al for saturated sands subjectedto dynamic excitation and liquefaction was imminent Themain advantage of the theory is that neither the yield surfacenor the plastic potential surface needs to be explicitly definedsee for example Merodo et al [20] and Khoei et al [10]

Detailed description of the theory and constitutive relationfor P-Z III can be found in for example Merodo et al [20]Khoei et al [10] Borowiec [19] Zienkiewicz and Mroz [8]they are thus not repeated here

3 Calibration of Soil Model and FE Program

To calibrate the appropriateness of the soil model chosen forthis study it is necessary to calibrate the result obtained fromthe finite element analysis with that of a well-instrumentedexperimental test

31 Centrifuge Model A dynamic centrifuge test performedat the University of Colorado at Boulder was selected forthis purpose [11 14 21] The centrifuge model test selectedfor this study was one of the three tests performed in theUniversity of Colorado to obtain data for safety assessment ofa dam in Taiwan that was rocked by a strong earthquake on21 September 1999 The soil used in the construction of themodel dam was taken within the reservoir of the dam so thata better representation of the behavior of the prototype damcould be simulated in the centrifuge The centrifuge hasa maximum capacity of 400 g-ton and equipped with anelectrohydraulic shaking tableThus the shockwavewas gen-erated by this in-flight electrohydraulic shaker table whichis a displacement-controlled system [21]

For all the three centrifugemodels tested at theUniversityof Colorado the slope at the upstream and downstream sideswas 1 3 and 1 35 respectively Model I of the earth dam wasbuilt entirely using the prototype core material which is thelow-plasticity clay (CL) and it was founded directly on theimpervious and rigid base of the aluminum model container[21] Model II was analogous toModel I but with a 33m thicklow-plasticity silt (ML) foundation Model III was built tomimic the actual section of the prototype dam as shown inFigure 1 The materials used to construct the model damincluded low-plasticity clay (CL) for the core low-plasticitysilt (ML) for the upstream and downstream slopes and silty-sand (SM) for the 33m thick foundation All the models werescaled down 150 times from the actual dam the models werethen subjected to 150 g of gravitational acceleration to repli-cate the field stress state as in the actual dam [21] Model IIIis the subject of this study

To provide a better representation and understanding ofthe responses of the dam during excitation a number ofaccelerometers pore-water pressure transducers and linearvariable differential transformers were installed in the bodyof the model dam as shown in Figure 1 Specifically eightaccelerometers and six pore-water pressure transducers wereinstalled to measure the time-history responses of horizontaland vertical accelerations and the EPWP respectively duringthe seismic excitation of the dam In addition four linear vari-able differential transformers (LVDTs) were installed at thedam crest and the shoulder of the downstream slope to mon-itor both the horizontal and vertical displacements of theselocations during excitation

Mathematical Problems in Engineering 3

Table 1 Parameters used for the Pastor-Zienkiewicz model

Soil type 119872119892

119872119891

119870ev0119888 (MPa) 119870es0119888 (MPa) 1198670

1198671198800

(MPa) 120574 119867DM 1199011015840 (kPa)

CL 150 13 95 210 200 125 4 8 1962ML 154 13 30 318 280 300 8 4 1962SM 154 14 30 155 150 400 4 10 1962

AccelerometerPore-water pressure transducerLVDT

3

1 35

PPT2PPT5

PPT4PPT3PPT6

PPT1 ACC5ACC6

ACC7ACC8

ACC2

ACC3ACC4

ACC18250m 9550m

26

m3315

m

Upstream

5615m

LVDT4LVDT3

LVDT2 LVDT1

9m

SM

ML MLCL

65m 175m175m 78m

Downstream2

1

1

Figure 1 Cross-section of model dam and its instrumentation layout (prototype dimensions)

32 Soil Parameters The finite element program used forthe following dynamic numerical analysis is called DIANA-SWANDYNE II The Pastor-Zienkiewicz (P-Z) model wasalready built-in as its constitutive model The parametersof the P-Z constitutive model were determined through aseries of one-dimensional consolidation test drained andundrained monotonic triaxial consolidated test (see eg[22]) and undrained cyclic triaxial test and triaxial perme-ability test The parameters of the constitutive model for thethree types of the soil used in the simulation of the modeldam are summarized in Table 1 in which119872

119892is the slope of

the critical state line119872119891 119870ev0119888 119870es0119888 1198670 1198671198800 120574 and 119867DM

are constitutive parameters of P-Z model [9 16 23] while 1199011015840is the mean effective confining stress

33 Experimental and Numerical Results The time-historyaccelerations and time-history pore-water pressure obtainedfrom both the centrifuge test and the numerical analysis arecompared and discussed in this section The time-history ofaccelerometer ACC1 installed at the base of the centrifugemodel was used as the input of the earthquake acceleration inthe numerical analysis

331 Acceleration Comparison The full 35 seconds of time-history horizontal accelerations recorded in the centrifugeand the numerical analysis are compared in Figure 2 whiletheir corresponding maximum amplitudes are summarized

in Table 2The input shock wave was essentially the 1999 Chi-Chi earthquake ground motion but with all the frequencieshigher than 400Hz filtered out because of the capacity of theshaking table used in the University of Colorado [21] Themaximum amplitude recorded at the base of the centrifugemodel (ACC1) was 0099 g and as the shock wave wastransmitted to the crest of dam the maximum amplitude atthe crest (ACC2) became 0125 g Thus the maximum ampli-tude of the acceleration was amplified by about 125 as theshock wave was transmitted from the base to the top of thedamThenumerical result overestimated the centrifuge resultby about 25 with an amplification of about 150 This sortof topographic amplification is to be anticipated especially atthe crest of a sloping ground see for example Bouckovalasand Papadimitriou 2005 [24] and Brennan andMadabhushi2009 [25] The deviation between the two ACC4 (verticalaccelerometer) profiles could be that it was placed near thedamcrest of the damand as such itmight not be firmly hold inposition which resulted in its failure to capture the realexcitation as compared to that of the numerical result

332 Pore-Water Pressure Comparison Pore-water pressuretransducer PPT6 was installed at the upstream toe of themodel dam to monitor whether the upstream water storagelevel was kept at the predetermined level during the in-flighttest Fivemore pore-water pressure transducerswere installedin the body and the foundation of the dam as shown inFigure 1 for monitoring the pore-water pressure response ofthe dam during in-flight earthquake excitation


Table 2 Dominant frequency and maximum amplitude obtained from centrifuge and FE analysis

Parameter ACC1 (g) ACC2 (g) ACC3 (g) ACC4 (g) ACC5 (g) ACC6 (g) ACC7 (g) ACC8 (g)

Maximum Amplitude g Centrifuge 0099 0125 0070 0005 0109 0086 0076 0109FE 0099 0156 0131 0049 0118 0111 0101 0091

Dominant Centrifuge 07 07 25sim33 18sim20 07 07 07 07Frequency Hz FE 07 07 07 22sim25 07 07 07 07lowastPS ACC1 is input motion ACC4 is vertical acceleration and the rest are horizontal acceleration

Figure 3 shows the time-history of EPWP recorded dur-ing the centrifuge test The excitation of the EPWP was rela-tively small in the upstream silt shell (PPT1) clay core (PPT3)and downstream silt shell (PPT4) of the dam The centrifugedata shows that most of the excitation was registered in theSM foundation layer of the model dam However as PPT5and PPT2were installed not very far apart the discrepancy inthe recorded EPWP of both transducers indicated that PPT5could be malfunction at time of testing The time-historyof EPWP produced by the numerical analysis is shown inFigure 3 The numerical result shows that some 10sim20 kPa ofEPWP were observed in the SM foundation CL core anddownstream ML shell Both the centrifuge and numericalresults confirmed that at the location of PPT1 in the upstreamML shell the EPWPwas able to dissipate quickly such that noEPWP was recorded in this location The centrifuge modelregistered some 20 kPa of EPWP at the end of the excitationwhile the numerical analysis underestimated the value byabout 25

The contour of the initial hydrostatic PWP and the EPWPat 119905 = 5 10 15 25 and 35 seconds of excitation are plottedin Figures 4(a)ndash4(f) Figures 4(b)ndash4(f) revealed that negativeEPWP was generated between 119905 = 5 and 35 seconds nearthe intersection of the clay core downstream ML shell andthe SM foundation of the dam and extended below the claycore that is along the interface between the clay core and theSM foundation layer whereas positive EPWP was generatedalong the interface between the downstream ML shell andthe SM foundation layer The region of the positive EPWPwas expanding with elapsed time and moving towards thedownstream toe as indicated in Figure 4(f) As shown inFigure 3 PPT4 revealed that the EPWP was slightly on thenegative side throughout the earthquake excitation in thecentrifuge but the numerical result shows otherwise with anEPWP of about 18 kPa towards the end of the simulationOne could argue that PPT4 could well be shifted during thecentrifuge test from its original location to a location slightlyabove the water table in the dam

4 Dynamic Finite Element Analysis

41 Model Setup The 1535m long Renyitan dam is an off-stream dam with a height of 203m and a 9m wide crestthe dam has a water-storage area of about 366 km2 witha total water-storage capacity of about 2911 million cubicmeters of which the effective water-storage capacity is 2731million cubic meters [12] The construction of the dam atthe upstream of the Bazhang River took seven years and was

completed in 1987 A typical cross-section of the dam is shownin Figure 6 The core of the dam was built with low plasticityclay (CL) the outer shell was built with silty-sand (SM) thetransition shells sandwiched between the outer shell and thecore were built with low plasticity silt (ML) and the filterlayer at the downstream side of the core was built with silty-sand (SM) The soil stratum of the foundation of the dammay be broadly divided into silty-sand (SM) low-plasticitysilt (ML) and silty-sand (SM) layers

The cross-section selected for the dynamic numericalanalysis is shown in Figure 5 Figure 6 shows the layout of thepore-water pressure monitoring points in the study dam Intotal 28 pore-water pressure points were assigned to monitorthe changes of the pore-water pressure at these locationswhen the dam was numerically subjected to earthquakeexcitation Figure 6 also shows variouswater levels thatwouldbe used to study the influence of the upstream water storagelevel on the stability of the dam

42 Synthetic Earthquake Simulation The acceleration timehistory to be used in numerical analysis may be selected fromthe (i) past acceleration time history captured in real earth-quakes (ii) simulated synthetic ground acceleration fromtheoretical seismological models of seismic fault ruptureand (iii) simulated spectrum matched artificial accelerationusing stochastic or random vibration theory [26] This studyadopted the simulated spectrum-matched artificial acceler-ation because it is generally recognized that it is able toproduce results that present relatively lower dispersionwhichis important for nonlinear analysis [27] In this case thedesign ground acceleration was obtained through the modi-fication of the ground acceleration captured from the magni-tude 73 earthquake on the Richter scale that rocked the islandof Taiwan on September 21 1999

A trapezoidal spectrum was selected for deriving thesynthetic earthquake The trapezoid envelope rises to itshighest point and then stays at the plateau before falling backdown to zero The trapezoid envelope thus represents thecomponents of the rise time119879

119903 the strong groundmovement

duration119879119904 and the total groundmovement duration119879

119889The

rise time 119879119903signifies the time difference between the arrivals

of P-wave and S-wave the time119879119903for Taiwan is approximately

3 seconds according to Yeh and Tsai [28] The duration of thestrong ground movement 119879

119904is an important parameter for

the energy spectrum density function from the major earth-quake records in Taiwan the average 119879

119904in Taiwan is about

507 seconds with a standard deviation of 360 seconds [29]The longest 119879

119904was assumed to be the sum of both that is


ACC1

ACC2

ACC3

ACC4

ACC5

ACC6

ACC7

ACC8

CentrifugeNumerical

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

0

02

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

0

0

02

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

Figure 2 Comparison of time-history acceleration of Model III

867 seconds Based on the total duration relationship forvarious earthquake scales and ground vibrations greater than005 g [30] the total ground movement duration 119879

119889cor-

responding to the scale 72 is 35 seconds In addition the

0 5 10 15 20 25 30 35

02040 PPT1

PPT2

PPT3

PPT4

PPT5

EPW

P (k

Pa)

Time (s)

0 5 10 15 20 25 30 35

02040

EPW

P (k

Pa)

Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

CentrifugeNumerical

Figure 3 Comparison of time-history of EPWP of Model III

maximum ground acceleration of 1 g and a magnitude of 72determined from the past two largest earthquakes in 1941 and1999 recorded nearby the study area were also requiredinformation

With the above information as input parameters andusing the principle of natural random excitation the syn-thetic earthquake program SIMQKE-II [31] was then used togenerate the synthetic earthquake that met the criteria of thedesign response spectrum of the Renyitan Reservoir Thetime-history acceleration of the synthetic earthquake gener-ated by SIMQKE-II is shown in Figure 7

5 Results and Discussion

51 EPWP Twelve (PPT1ndashPPT12) of the 28 pore-waterpressure monitoring points were placed in the body of theearth dam and the rest (PPT13ndashPPT28) were installed in thefoundation layers PPT1 PPT6 and PPT10were located in theouter shell of the dam at the upstream side which is made ofsilty-sand (SM) PPT2 PPT7 andPPT11were in the transitionshell at the upstream side which is made of low plasticity silt


Hydrostatic PWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(a)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(b)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(c)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(d)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(e)

EPWP (kPa)05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(f)

Figure 4 Distribution of (a) hydrostatic PWP and EPWP at (b) 119905 = 5 sec (c) 119905 = 10 sec (d) 119905 = 15 sec (e) 119905 = 25 sec and (f) 119905 = 35 sec

11

11

124 12 23 34

6

6

5

(1) Core CL (2) Shell ML(3) Sand fill SM

(4) Filter SM(5) Foundation ML(6) Foundation SM

Upstream

Downstream2

125

12 12

131

493m

32m

9m

32m1206m

32m

86

m203

m97

m137

m

Figure 5 Cross-section of the Renyitan earth dam (after [14])


Upstream

Downstream

PPT1

PPT6PPT10

PPT2PPT7

PPT3PPT8PPT11

PPT14PPT12

PPT15

PPT4 PPT9 PPT5

PPT16 PPT17PPT19

PPT20 PPT21

PPT22 PPT23 PPT24 PPT25PPT27

PPT13

PPT26

PPT18

PPT28

152m173m

102m127m

76m

Figure 6 Layout of numerical PWP monitoring points

minus1

minus05

0

05

1

0 5 10 15 20 25 30 35

Time (s)

Acce

lera

tion

(g)

0

05

1

15

2

25

3

35

4

0 05 1 15 2 25 3

Frequency (1s)

Acce

lera

tion

spec

trum

(g)

Figure 7 Earthquake acceleration and acceleration spectrum used in the FE analysis

(ML) PPT3 PPT8 and PPT12 were in the low plasticity clay(CL) core of dam PPT4 and PPT5 were in the transition shelland outer shell respectively of the downstream side PPT9was placed in the filter layer at the downstream side PPT13through PPT28 was in the foundation layers

A filter layer was present on the right side of the coreat the downstream side because of the need to reduce thephreatic surface running across the dam The seepage andstress analyses provided the initial hydrostatic pore-waterpressures and the initial vertical stresses of the dam for thedynamic analysisThe subsequent dynamic analysis providedthe EPWP generated in the dam as a result of the syntheticearthquake excitation Table 3 shows the initial stresses andEPWP measured at the pore-water pressure monitoringpoints when the upstream water storage level was at 173m

The dynamic numerical results are evaluated in terms ofthe normalized EPWP defined as the ratio of the EPWP to theinitial vertical effective stress It is shown in Table 3 that theEPWP ratio was close to zero at PPT4 PPT5 and PPT9 at thedownstream side of the damThe EPWP excited was negativeat PPT1 PPT7 andPPT11 at the upstream side resulting in thenegative EPWP ratios Most of these ratios ranged from 10 to80 The EPWP excited at PPT3 located in the core reached

as high as 215 kPa with a normalized EPWP ratio of nearly90 However the EPWP ratio at PPT18 was greater than100 indicating that the EPWP was greater than the initialvertical effective stress in the shallow part of foundation at thedownstream side thus leading to instability in soil mass

52 Influence of Upstream Water Storage Level To examinethe effect of upstreamwater storage level on the stability of thedam at the end of the synthetic earthquake excitation fivehypothetical upstream water storage levels at 76m 102m127m 152m and 173m were assumed to take place at the203m high Renyitan earth dam The distribution of theEPWPs generated in the dam for water storage level of 037050 and 075 of the dam height is shown in Figure 8 whileTable 4 shows the critical (maximum) EPWP generated andits coordinates in the dam

Figure 8(a) shows the distribution of the EPWP whenthe water storage level was at 37 of the dam height Thecritical EPWP of 274 kPa occurred near the bottom part ofthe upstream transition shell albeit the affected area was veryvery small In general the whole dam suffered an EPWP ofnot more than 25 kPa In the middle layer of the downstreamfoundation soil mostly directly beneath the downstream


Table 3 Initial stresses and EPWPs obtained from FE analysis

Water pressure gauge PPT1 PPT2 PPT3 PPT4 PPT5 PPT6 PPT7 PPT8 PPT9Initial vertical effective stress (kPa) 130 917 2427 2718 824 111 1303 3019 2632Initial pore-water pressure (kPa) 286 651 148 minus316 minus197 900 700 644 minus85EPWP (kPa) minus73 287 2150 minus09 minus01 18 minus102 1679 minus00EPWP ratio () minus562 313 886 minus03 minus01 161 minus78 556 00Water pressure gauge PPT10 PPT11 PPT12 PPT18 PPT19 PPT21 PPT23 PPT24 PPT25Initial vertical effective stress (kPa) 209 1925 3308 193 3987 2861 4451 4371 2582Initial pore-water pressure (kPa) 1276 797 295 272 1268 1255 2847 2541 2478EPWP (kPa) 125 minus48 376 218 1538 1671 644 2022 1955EPWP ratio () 596 minus25 114 1132 386 584 145 463 757

zH = 037

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(a)

zH = 05

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(b)

zH = 07560

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(c)

Figure 8 Distribution of EPWP for various upstream water storage levels

Table 4 Locations of maximum EPWP in the dam

Water level ratio (119911119867) 037 050 062 075 085

Max EPWP (kPa) 2743 2894 3127 3404 3549119883-coordinate (m) 824 1014 1014 1014 1014119884-coordinate (m) 347 337 337 337 337Location in dam Upstream shell Core Core Core Core

transition shell it was shown that a small zone was boundedby the 200 kPa EPWP

Figure 8(b) shows the distribution of the EPWPwhen thewater storage level was at 50 of the dam height This timethe critical EPWP of 290 kPa occurred near the bottom of thecore in addition the bottom part of the upstream transitionshell also suffered from large EPWP that is greater than200 kPa Except for a small portion of the top left corner ofthe dam that has suction (negative pore-water pressure)generated during the excitation inmost parts of the dam theirEPWP was less than 25 kPa As for the foundation layer thearea bounded by the 200 kPa EPWP has expanded to a largerarea compared to the case shown in Figure 8(a)

The distribution of the EPWP when the water storagelevel was at 75 of the dam height is shown in Figure 8(c)


The critical EPWP also occurred near the bottom of the coreof the dam and it was also shown that an even larger portionof the top of the dam compared to Figure 8(b) has suctiongenerated at the end of excitation As for the foundation layerthe area bounded by the 200 kPa EPWP has expanded to aneven larger area compared to the cases shown in Figures 8(a)and 8(b)

In general it was seen that the area bounded by the200 kPa EPWP in the foundation layer expanded with theincreased of the upstream water storage level The criticalEPWP tended to occur near the bottom of the upstream tran-sition shell and the core of the dam this is because the filterlayer placed on the right shoulder of the core and the bottomof the downstream transition shell was able to dissipatealmost all the EPWPs generated at the end of the excitation

The generation of excess pore-water pressure (EPWP)varied across the earth dam as the water storage levelincreasedThe final EPWPs normalized by their correspond-ing initial effective vertical stress across the dam at theend of the earthquake excitation are presented in Figure 9Figure 9(a) shows the normalized EPWP against the normal-ized water storage level for PPT1 PPT6 and PPT10 located inthe upstream outer shell PPT10 which was located near tothe foundation layer showed a linear increase between theEPWPand the increment of thewater storage level For PPT6the normalized EPWP showed no significant variation withthe increase of the water storage levelThe normalized EPWPfor PPT1 showed a negative relationship with the incrementof the water storage level thus the EPWP near the top-thirdof the upstream outer shell was becoming more and morenegative (suction) until the water level reached 75 of damheight where a reversal of trend is seen In general themaximum EPWP ratio in the upstream outer shell was 06and hence no liquefaction is possible in this region

Figure 9(b) shows the ratios of the EPWP and waterstorage level recorded by PPT2 PPT7 and PPT11 in theupstream transition shell PPT2 which is located near themidheight of the dam showed a similar trend as PPT1 inFigure 9(a) albeit this time the decrement was not as signifi-cant as in PPT1 Thus suction existed in the dam if the waterstorage level was less than 75 dam height

The profiles of the EPWP ratio registered by PPT3 PPT8and PPT12 in the dam core are shown in Figure 9(c) PPT3which was located near the midheight of the CL core showeda positive relationshipwith the increment of the water storageratio The EPWP reached some 90 of the initial effectivestress when the water level ratio was at 085Thus the stabilityof the core requires attention at this instance The EPWPratio of PPT8 only increased slightly from 50 to 55 forwater storage ratio that ranged between 037 and 085 TheEPWP ratio of PPT12 which was located near theinterface between the core and the foundation layer remainedreasonably constant at 02 until the water storage levelreached 75 of the dam height where the EPWP ratio beganto drop

Figure 9(d) shows that no EPWP was generated in thetransition shell outer shell and the filter layer at the down-stream side of the dam regardless of the level of the upstreamstorage waterThis was because these PPTs were placed in thevicinity of the highly permeable filtering layer

The EPWP ratio profile registered by the PPTs in theupper layer of SM foundation is shown in Figure 9(e) Asshown in Figure 6 PPT13 PPT14 PPT15 and PPT20 wereat the upstream side while PPT16 PPT17 PPT18 and PPT21were at the downstream side of the dam PPT19 was placeddirectly below the core It was found that the EPWPdecreasedslightly with the increase of the water storage level in theupstream upper layer of the foundation while the EPWP didnot change with the water storage level in the downstreamfoundation layer However the EPWP ratio for PPT18 wasgreater than 10 for all values of upstream water storage levelthis was due to the small overburden pressure at this pointand hence suggested that the ground here would be unstable

The EPWP generated in the middle layer of the MLfoundation did not seem to approach the critical value atwhich liquefaction would occur (Figure 9(f)) PPT22 andPPT23 at the upstream side have negative relationship withthe increment of the water storage level while PPT24 andPPT25 at the downstream side have positive relationship withthe increment of the water storage level The ratio for PPT25located to the furthest right increased from60 to 80of theinitial effective stress for the range of the water storage levelstudied

The relationship between the EPWP normalized by theinitial vertical stress of all the 28 pore-water pressure moni-toring points and the initial hydrostatic pore-water pressureis plotted in Figure 10 Some of the normalized EPWP ratioswere greater than 10 at locations near to the ground surfacewith hydrostatic pore-water pressure of less than 30 kPaFor places with 100 to 250 kPa of hydrostatic pore-waterpressure in particular those below the dam core and in thedownstream foundation layer their EPWP ratio was higherthan 80 of the initial vertical stress The soil mass here wassusceptible to liquefaction and therefore their stability is aconcern

6 Conclusion

A series of dynamic finite element analysis under a syntheticearthquake was conducted using a two-dimensional programin this study The computer program DIANA-SWANDYNEII and the soil model adopted in this study were firstcalibrated by simulating the response of a model earthdam under an earthquake excitation in the centrifuge Thefollowing conclusions can be made

The amplification of the earthquake wave as it was trans-mitting to the top of dam and the response of the EPWPswerecaptured and compared between the centrifuge test resultand the numerical result Good agreement has been achievedbetween both sets of result indicating the reliability of thechosen program and soil model

The silty-sand filter layer placed on the right shoulder ofthe core and the bottom of the downstream transition shellwas effective in dissipating almost all the EPWPs generated atthe end of the excitation

The result of the analysis revealed that the EPWP near thetop-third of the upstream outer shell was becomingmore andmore negative (suction) until the water level reached 75 of


minus14

minus10

minus06

minus02

02

06

03 04 05 06 07 08 09 1

EPW

P ra

tio

Water storage leveldam height

Upstream outer shell (SM)

PPT1PPT6PPT10

(a)

minus06minus04minus02

000204060810

03 04 05 06 07 08 09 1

EPW

P ra

tio


Upstream transition shell (ML)

PPT2PPT7PPT11

(b)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Core (CL)

PPT3PPT8PPT12

(c)

minus05

minus03

minus01

01

03

05

03 04 05 06 07 08 09 1

EPW

P ra

tio


Downstream shells (ML and SM)

PPT4PPT5PPT9

(d)

00

02

04

06

08

10

12

14

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (SM)

PPT13PPT14PPT15

PPT19PPT20PPT16

PPT17PPT18PPT21

(e)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (ML)

PPT22PPT23PPT24

PPT25

(f)

Figure 9 EPWP ratio versus normalized water storage level from FE analysis

dam height indicating that this region will be in a stable stateas no liquefaction is possible during excitation

The results from dynamic analysis with five differentwater storage levels suggested that the zone just above theinterfaces between the foundation soil and the upstream ML

transition shell and the CL core was susceptible to lique-faction if the level of the upstream water storage was closeto the dam height In addition it was observed that EPWPbuilt up quickly in the middle ML layer of the downstreamfoundation


00

02

04

06

08

10

12

14

0 50 100 150 200 250 300 350 400

EPW

P ra

tio

Hydrostatic water pressure (kPa)

zH = 085

zH = 075

zH = 062

zH = 050

zH = 037

Figure 10 Normalized EPWP versus hydrostatic PWP

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors are grateful to the financial support providedby Taiwan Water Corporation for conducting the abovecentrifuge tests

References

[1] United States Geological Survey (USGS)M63 Eastern TaiwanEarthquake of 31 October 2013 Earthquake Hazards ProgramReport 2014 httpearthquakeusgsgovearthquakeseqar-chivesposter201320131031php

[2] Water-Watch Non-Governmental Organization (Mandarin)2010 httpwaterwatchngoorgtw

[3] Z-M Zhang ldquoAchievements and problems of geotechni-cal engineering investigation in Chinardquo Journal of ZhejiangUniversitymdashScience A (Applied Physics amp Engineering) vol 12no 2 pp 87ndash102 2011

[4] R W Clough and A K Chopra ldquoEarthquake stress analysis inearth damsrdquo ASCE Journal of Engineering Mechanics Divisionvol 92 no 2 pp 197ndash211 1966

[5] H B Seed P de Alba and F I Makdisi ldquoPerformance of earthdams during earthquakesrdquo Journal of the Geotechnical Engineer-ing Division vol 104 no 7 pp 967ndash994 1978

[6] H B Seed ldquoConsiderations in the earthquake-resistant designof earth and rockfill damsrdquoGeotechnique vol 29 no 3 pp 215ndash263 1979

[7] O C Zienkiewicz C T Chang and E Hinton ldquoNonlinearseismic response and liquefactionrdquo International Journal forNumerical and Analytical Methods in Geomechanics vol 2 no4 pp 381ndash404 1978

[8] O C Zienkiewicz and Z Mroz ldquoGeneralized plasticity for-mulation and application to geomechanicsrdquo in Mechanics ofEngineering Materials pp 655ndash680 John Wiley amp Sons 1985

[9] M Pastor O C Zienkiewicz and A H C Chan ldquoGeneralizedplasticity and the modelling of soil behaviourrdquo International

Journal for Numerical and Analytical Methods in Geomechanicsvol 14 no 3 pp 151ndash190 1990

[10] A R Khoei A R Azami and S M Haeri ldquoImplementation ofplasticity basedmodels in dynamic analysis of earth and rockfilldams a comparison of Pastor-Zienkiewicz and cap modelsrdquoComputers and Geotechnics vol 31 no 5 pp 384ndash409 2004

[11] C Wu C Ni and H Ko ldquoSeismic reaction of earth and rockfilldam centrifuge modeling test and numerical simulationrdquoChinese Journal of Rock Mechanics and Engineering vol 26 no1 pp 1ndash14 2007

[12] M W Gui and H T Chiu ldquoSeismic response of renyitan earth-fill damrdquo Journal of GeoEngineering vol 4 no 2 pp 41ndash502009

[13] G R Martin W D L Finn and H B Seed ldquoFundamentalsof liquefaction under cyclic loadingrdquo Journal of GeotechnicalEngineering Division ASCE vol 101 no 5 pp 423ndash438 1975

[14] S-L Chen C-F Lin and C-K Ni ldquoEarthquake damage assess-ment on Jen-Yi-Tan earth dam in Taiwanrdquo Disaster Advancesvol 5 no 4 pp 1626ndash1631 2012

[15] M A Biot ldquoTheory of propagation of elastic waves in a fluid-saturated porous solidrdquo Journal of the Acoustical Society ofAmerica vol 28 pp 168ndash178 1956

[16] M Pastor A H C Chan P Mira D Manzanal J A F Merodoand T Blanc ldquoComputational geomechanics the heritage ofOlek Zienkiewiczrdquo International Journal for Numerical Methodsin Engineering vol 87 no 1ndash5 pp 457ndash489 2011

[17] O C Zienkiewicz and T Shiomi ldquoDynamic behavior of satu-rated porous media the generalized Biot formulation and itrsquosnumerical solutionrdquo International Journal for Numerical andAnalytical Methods in Geomechanics vol 8 no 1 pp 71ndash961984

[18] O C Zienkiewicz A H C ChanM Pastor B A Schrefler andT ShiomiComputational GeomechanicsWith Special Referenceto Earthquake Engineering John Wiley amp Sons West SussexUK 1999

[19] A Borowiec ldquoNumerical analysis of wave propagation in two-phase soil mediumrdquo in Proceedings of the GeoShanghai Interna-tional Conference Soil Dynamics and Earthquake EngineeringM S Huang X Yu and Y Huang Eds Geotechnical SpecialPublication no 201 pp 252ndash262 June 2010

[20] J A F Merodo M Pastor P Mira et al ldquoModelling of diffusefailuremechanisms of catastrophic landslidesrdquoComputerMeth-ods in Applied Mechanics and Engineering vol 193 no 27ndash29pp 2911ndash2939 2004

[21] Y N Ge Y Bao and H Y Ko ldquoDynamic centrifuge modeltesting of Renyitan damrdquo Tech Rep Department of CivilEnvironmental and Architectural Engineering University ofColorado Boulder Colo USA 2004

[22] Y Jafarian A Ghorbani S Salamatpoor and S SalamatpoorldquoMonotonic triaxial experiments to evaluate steady-state andliquefaction susceptibility of Babolsar sandrdquo Journal of ZhejiangUniversitymdashScience A (Applied Physics amp Engineering) vol 14no 10 pp 739ndash750 2013

[23] M Pastor O C Zienkiewicz and K H Leung ldquoSimple modelfor transient soil loading in earthquake analysis II Non-associative models for sandsrdquo International Journal for Numer-ical and Analytical Methods in Geomechanics vol 9 no 5 pp477ndash498 1985

[24] G D Bouckovalas and A G Papadimitriou ldquoNumerical eval-uation of slope topography effects on seismic ground motionrdquoSoil Dynamics and Earthquake Engineering vol 25 no 7ndash10 pp547ndash558 2005


[25] A J Brennan and S P GMadabhushi ldquoAmplification of seismicaccelerations at slope crestsrdquo Canadian Geotechnical Journalvol 46 no 5 pp 585ndash594 2009

[26] G P Cimellaro A M Reinhorn A DrsquoAmbrisi and M De Ste-fano ldquoFragility analysis and seismic record selectionrdquo Journal ofStructural Engineering vol 137 no 3 pp 379ndash390 2011

[27] J J Bommer and A B Acevedo ldquoThe use of real earthquakeaccelerograms as input to dynamic analysisrdquo Journal of Earth-quake Engineering vol 8 no 1 pp 43ndash91 2004

[28] Y H Yeh and Y B Tsai ldquoCrustal structure of central Taiwanfrom inversion of P-wave arrival timesrdquo Bulletin of the Instituteof Earth Sciences Academica Sinica vol 1 pp 83ndash102 1981

[29] S S Lai ldquoAssessment of design response spectrum of nuclearpower plant no 2rdquo Tech Rep CT 85075 ER 8502 NationalTaiwan Institute of Technology 1985 (Mandarin)

[30] BA Bolt ldquoDuration of strong groundmotionrdquo inProceedings ofthe 5th World Conference on Earthquake Engineering pp 1304ndash1313 Rome Italy 1974

[31] E H Vanmarcke G A Fenton and E Heredia-ZavoniSIMQKE-II Conditioned Earthquake GroundMotion SimulatorUserrsquos Manual Version 21 Princeton University Princeton NJUSA 1999

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


the dynamic responses of an earth dam Gui and Chiu[12] simulated the dynamic response of Renyitan earth damusing the Finn model [13] provided in the two-dimensionalfinite difference program FLAC All of these studies yieldedconvincing results

When an earth dam is subjected to a seismic load pore-water pressure responded faster than the deformation at thetop of damThus for safety management of earth dam pore-water pressure response is an important indicator This studyaims at investigating the influence of the upstream waterstorage level on the pore-water pressure response in the bodyof an earth dam subjected to synthetic earthquake excitationExperimental results from a dynamic centrifuge test were firstused to calibrate the appropriate use of the chosen constitu-tive law for the following numerical simulation Subsequentlyeffective stress analysis was conducted to evaluate the safetyof the study earth dam under the synthetic seismic loading

2 Governing Equations

Total stress analysis yields only the deformation of soil fromthe given stress-strain relationship but provides no informa-tion on the changes in excess pore-water pressure (EPWP)when the soil is subjected to excitation Thus the use ofthe total stress analysis for liquefaction study is insufficientBiot [15] incorporated Darcyrsquos law for the representation ofthe fluids flow in the soil to the linear elastic solid mechanicsframework and thus formulated the so-called two-phasemix-ing theory to deal with the pore-water pressure issues that thetotal stress analysis failed to handle The equations of motionfor elastic porous media saturated with a pore fluid consistof two variablesrsquo fields (i) pore pressure 119901 and (ii) skeletondisplacements 119906 A simplified numerical framework knownas the 119906-119901 formulation was formulated by assuming Darcyrsquosflow rule (laminar flow) and neglecting the fluid inertia [716ndash18] By denoting was the flow rate of the fluid we thushave the overall balance or momentum equilibrium equationof soil-liquid mixture as [19]

[M 00 0]

u

+ [0 0

QT S]

u

+ [

K minusQ0 H]

u119901 =

f119906

f119901

(1)

whereM andK are the total mass and total stiffness matrixesQ is the discrete gradient operator coupling the soil andfluid phase H is the permeability matrix and S is the com-pressibility matrix Vectors f119906 and f119901 represent the effect ofbody forces along with prescribed boundary conditions forthe solid-fluid mixture and fluid phases

The model used to simulate the dynamics behavior of thesoil is the Pastor-Zienkiewiczmark III (P-Z III) model whichhas been recognized as the model most suitable for modelingmaterials susceptible to liquefaction [19] The model wasproposed in 1985 by Pastor et al for saturated sands subjectedto dynamic excitation and liquefaction was imminent Themain advantage of the theory is that neither the yield surfacenor the plastic potential surface needs to be explicitly definedsee for example Merodo et al [20] and Khoei et al [10]

Detailed description of the theory and constitutive relationfor P-Z III can be found in for example Merodo et al [20]Khoei et al [10] Borowiec [19] Zienkiewicz and Mroz [8]they are thus not repeated here

3 Calibration of Soil Model and FE Program

To calibrate the appropriateness of the soil model chosen forthis study it is necessary to calibrate the result obtained fromthe finite element analysis with that of a well-instrumentedexperimental test

31 Centrifuge Model A dynamic centrifuge test performedat the University of Colorado at Boulder was selected forthis purpose [11 14 21] The centrifuge model test selectedfor this study was one of the three tests performed in theUniversity of Colorado to obtain data for safety assessment ofa dam in Taiwan that was rocked by a strong earthquake on21 September 1999 The soil used in the construction of themodel dam was taken within the reservoir of the dam so thata better representation of the behavior of the prototype damcould be simulated in the centrifuge The centrifuge hasa maximum capacity of 400 g-ton and equipped with anelectrohydraulic shaking tableThus the shockwavewas gen-erated by this in-flight electrohydraulic shaker table whichis a displacement-controlled system [21]

For all the three centrifugemodels tested at theUniversityof Colorado the slope at the upstream and downstream sideswas 1 3 and 1 35 respectively Model I of the earth dam wasbuilt entirely using the prototype core material which is thelow-plasticity clay (CL) and it was founded directly on theimpervious and rigid base of the aluminum model container[21] Model II was analogous toModel I but with a 33m thicklow-plasticity silt (ML) foundation Model III was built tomimic the actual section of the prototype dam as shown inFigure 1 The materials used to construct the model damincluded low-plasticity clay (CL) for the core low-plasticitysilt (ML) for the upstream and downstream slopes and silty-sand (SM) for the 33m thick foundation All the models werescaled down 150 times from the actual dam the models werethen subjected to 150 g of gravitational acceleration to repli-cate the field stress state as in the actual dam [21] Model IIIis the subject of this study

To provide a better representation and understanding ofthe responses of the dam during excitation a number ofaccelerometers pore-water pressure transducers and linearvariable differential transformers were installed in the bodyof the model dam as shown in Figure 1 Specifically eightaccelerometers and six pore-water pressure transducers wereinstalled to measure the time-history responses of horizontaland vertical accelerations and the EPWP respectively duringthe seismic excitation of the dam In addition four linear vari-able differential transformers (LVDTs) were installed at thedam crest and the shoulder of the downstream slope to mon-itor both the horizontal and vertical displacements of theselocations during excitation



Soil type 119872119892

119872119891

119870ev0119888 (MPa) 119870es0119888 (MPa) 1198670

1198671198800

(MPa) 120574 119867DM 1199011015840 (kPa)

CL 150 13 95 210 200 125 4 8 1962ML 154 13 30 318 280 300 8 4 1962SM 154 14 30 155 150 400 4 10 1962


3

1 35

PPT2PPT5

PPT4PPT3PPT6

PPT1 ACC5ACC6

ACC7ACC8

ACC2

ACC3ACC4

ACC18250m 9550m

26

m3315

m

Upstream

5615m

LVDT4LVDT3

LVDT2 LVDT1

9m

SM

ML MLCL

65m 175m175m 78m

Downstream2

1

1

























119889The










ACC1

ACC2

ACC3

ACC4

ACC5

ACC6

ACC7

ACC8

CentrifugeNumerical

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

0

02

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

0

0

02

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02



119889cor-


0 5 10 15 20 25 30 35

02040 PPT1

PPT2

PPT3

PPT4

PPT5

EPW

P (k

Pa)

Time (s)

0 5 10 15 20 25 30 35

02040

EPW

P (k

Pa)

Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

CentrifugeNumerical








05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(a)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(b)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(c)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(d)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(e)

EPWP (kPa)05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(f)


11

11

124 12 23 34

6

6

5



Upstream

Downstream2

125

12 12

131

493m

32m

9m

32m1206m

32m

86

m203

m97

m137

m



Upstream

Downstream

PPT1

PPT6PPT10

PPT2PPT7

PPT3PPT8PPT11

PPT14PPT12

PPT15

PPT4 PPT9 PPT5

PPT16 PPT17PPT19

PPT20 PPT21


PPT13

PPT26

PPT18

PPT28

152m173m

102m127m

76m


minus1

minus05

0

05

1

0 5 10 15 20 25 30 35

Time (s)

Acce

lera

tion

(g)

0

05

1

15

2

25

3

35

4

0 05 1 15 2 25 3

Frequency (1s)

Acce

lera

tion

spec

trum

(g)











zH = 037

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(a)

zH = 05

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(b)

zH = 07560

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(c)


















6 Conclusion






minus14

minus10

minus06

minus02

02

06

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT1PPT6PPT10

(a)


000204060810

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT2PPT7PPT11

(b)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Core (CL)

PPT3PPT8PPT12

(c)

minus05

minus03

minus01

01

03

05

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT4PPT5PPT9

(d)

00

02

04

06

08

10

12

14

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (SM)

PPT13PPT14PPT15

PPT19PPT20PPT16

PPT17PPT18PPT21

(e)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (ML)

PPT22PPT23PPT24

PPT25

(f)






00

02

04

06

08

10

12

14

0 50 100 150 200 250 300 350 400

EPW

P ra

tio


zH = 085

zH = 075

zH = 062

zH = 050

zH = 037




Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Soil type 119872119892

119872119891

119870ev0119888 (MPa) 119870es0119888 (MPa) 1198670

1198671198800

(MPa) 120574 119867DM 1199011015840 (kPa)

CL 150 13 95 210 200 125 4 8 1962ML 154 13 30 318 280 300 8 4 1962SM 154 14 30 155 150 400 4 10 1962


3

1 35

PPT2PPT5

PPT4PPT3PPT6

PPT1 ACC5ACC6

ACC7ACC8

ACC2

ACC3ACC4

ACC18250m 9550m

26

m3315

m

Upstream

5615m

LVDT4LVDT3

LVDT2 LVDT1

9m

SM

ML MLCL

65m 175m175m 78m

Downstream2

1

1

























119889The










ACC1

ACC2

ACC3

ACC4

ACC5

ACC6

ACC7

ACC8

CentrifugeNumerical

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

0

02

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

0

0

02

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02



119889cor-


0 5 10 15 20 25 30 35

02040 PPT1

PPT2

PPT3

PPT4

PPT5

EPW

P (k

Pa)

Time (s)

0 5 10 15 20 25 30 35

02040

EPW

P (k

Pa)

Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

CentrifugeNumerical








05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(a)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(b)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(c)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(d)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(e)

EPWP (kPa)05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(f)


11

11

124 12 23 34

6

6

5



Upstream

Downstream2

125

12 12

131

493m

32m

9m

32m1206m

32m

86

m203

m97

m137

m



Upstream

Downstream

PPT1

PPT6PPT10

PPT2PPT7

PPT3PPT8PPT11

PPT14PPT12

PPT15

PPT4 PPT9 PPT5

PPT16 PPT17PPT19

PPT20 PPT21


PPT13

PPT26

PPT18

PPT28

152m173m

102m127m

76m


minus1

minus05

0

05

1

0 5 10 15 20 25 30 35

Time (s)

Acce

lera

tion

(g)

0

05

1

15

2

25

3

35

4

0 05 1 15 2 25 3

Frequency (1s)

Acce

lera

tion

spec

trum

(g)











zH = 037

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(a)

zH = 05

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(b)

zH = 07560

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(c)


















6 Conclusion






minus14

minus10

minus06

minus02

02

06

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT1PPT6PPT10

(a)


000204060810

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT2PPT7PPT11

(b)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Core (CL)

PPT3PPT8PPT12

(c)

minus05

minus03

minus01

01

03

05

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT4PPT5PPT9

(d)

00

02

04

06

08

10

12

14

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (SM)

PPT13PPT14PPT15

PPT19PPT20PPT16

PPT17PPT18PPT21

(e)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (ML)

PPT22PPT23PPT24

PPT25

(f)






00

02

04

06

08

10

12

14

0 50 100 150 200 250 300 350 400

EPW

P ra

tio


zH = 085

zH = 075

zH = 062

zH = 050

zH = 037




Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
























119889The










ACC1

ACC2

ACC3

ACC4

ACC5

ACC6

ACC7

ACC8

CentrifugeNumerical

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

0

02

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

0

0

02

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02



119889cor-


0 5 10 15 20 25 30 35

02040 PPT1

PPT2

PPT3

PPT4

PPT5

EPW

P (k

Pa)

Time (s)

0 5 10 15 20 25 30 35

02040

EPW

P (k

Pa)

Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

CentrifugeNumerical








05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(a)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(b)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(c)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(d)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(e)

EPWP (kPa)05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(f)


11

11

124 12 23 34

6

6

5



Upstream

Downstream2

125

12 12

131

493m

32m

9m

32m1206m

32m

86

m203

m97

m137

m



Upstream

Downstream

PPT1

PPT6PPT10

PPT2PPT7

PPT3PPT8PPT11

PPT14PPT12

PPT15

PPT4 PPT9 PPT5

PPT16 PPT17PPT19

PPT20 PPT21


PPT13

PPT26

PPT18

PPT28

152m173m

102m127m

76m


minus1

minus05

0

05

1

0 5 10 15 20 25 30 35

Time (s)

Acce

lera

tion

(g)

0

05

1

15

2

25

3

35

4

0 05 1 15 2 25 3

Frequency (1s)

Acce

lera

tion

spec

trum

(g)











zH = 037

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(a)

zH = 05

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(b)

zH = 07560

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(c)


















6 Conclusion






minus14

minus10

minus06

minus02

02

06

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT1PPT6PPT10

(a)


000204060810

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT2PPT7PPT11

(b)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Core (CL)

PPT3PPT8PPT12

(c)

minus05

minus03

minus01

01

03

05

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT4PPT5PPT9

(d)

00

02

04

06

08

10

12

14

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (SM)

PPT13PPT14PPT15

PPT19PPT20PPT16

PPT17PPT18PPT21

(e)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (ML)

PPT22PPT23PPT24

PPT25

(f)






00

02

04

06

08

10

12

14

0 50 100 150 200 250 300 350 400

EPW

P ra

tio


zH = 085

zH = 075

zH = 062

zH = 050

zH = 037




Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










ACC1

ACC2

ACC3

ACC4

ACC5

ACC6

ACC7

ACC8

CentrifugeNumerical

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

0

02

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

0

0

02

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02

0

Acce

lera

tion

(g)

Time (s)0 5 10 15 20 25 30 35

minus02

02



119889cor-


0 5 10 15 20 25 30 35

02040 PPT1

PPT2

PPT3

PPT4

PPT5

EPW

P (k

Pa)

Time (s)

0 5 10 15 20 25 30 35

02040

EPW

P (k

Pa)

Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

02040

EPW

P (k

Pa)

0 5 10 15 20 25 30 35Time (s)

CentrifugeNumerical








05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(a)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(b)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(c)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(d)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(e)

EPWP (kPa)05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(f)


11

11

124 12 23 34

6

6

5



Upstream

Downstream2

125

12 12

131

493m

32m

9m

32m1206m

32m

86

m203

m97

m137

m



Upstream

Downstream

PPT1

PPT6PPT10

PPT2PPT7

PPT3PPT8PPT11

PPT14PPT12

PPT15

PPT4 PPT9 PPT5

PPT16 PPT17PPT19

PPT20 PPT21


PPT13

PPT26

PPT18

PPT28

152m173m

102m127m

76m


minus1

minus05

0

05

1

0 5 10 15 20 25 30 35

Time (s)

Acce

lera

tion

(g)

0

05

1

15

2

25

3

35

4

0 05 1 15 2 25 3

Frequency (1s)

Acce

lera

tion

spec

trum

(g)











zH = 037

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(a)

zH = 05

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(b)

zH = 07560

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(c)


















6 Conclusion






minus14

minus10

minus06

minus02

02

06

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT1PPT6PPT10

(a)


000204060810

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT2PPT7PPT11

(b)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Core (CL)

PPT3PPT8PPT12

(c)

minus05

minus03

minus01

01

03

05

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT4PPT5PPT9

(d)

00

02

04

06

08

10

12

14

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (SM)

PPT13PPT14PPT15

PPT19PPT20PPT16

PPT17PPT18PPT21

(e)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (ML)

PPT22PPT23PPT24

PPT25

(f)






00

02

04

06

08

10

12

14

0 50 100 150 200 250 300 350 400

EPW

P ra

tio


zH = 085

zH = 075

zH = 062

zH = 050

zH = 037




Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(a)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(b)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(c)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(d)

EPWP (kPa)

05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(e)

EPWP (kPa)05

10

15

20

25

30

35

40

45

50

minus5

minus10

minus15

minus20

(f)


11

11

124 12 23 34

6

6

5



Upstream

Downstream2

125

12 12

131

493m

32m

9m

32m1206m

32m

86

m203

m97

m137

m



Upstream

Downstream

PPT1

PPT6PPT10

PPT2PPT7

PPT3PPT8PPT11

PPT14PPT12

PPT15

PPT4 PPT9 PPT5

PPT16 PPT17PPT19

PPT20 PPT21


PPT13

PPT26

PPT18

PPT28

152m173m

102m127m

76m


minus1

minus05

0

05

1

0 5 10 15 20 25 30 35

Time (s)

Acce

lera

tion

(g)

0

05

1

15

2

25

3

35

4

0 05 1 15 2 25 3

Frequency (1s)

Acce

lera

tion

spec

trum

(g)











zH = 037

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(a)

zH = 05

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(b)

zH = 07560

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(c)


















6 Conclusion






minus14

minus10

minus06

minus02

02

06

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT1PPT6PPT10

(a)


000204060810

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT2PPT7PPT11

(b)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Core (CL)

PPT3PPT8PPT12

(c)

minus05

minus03

minus01

01

03

05

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT4PPT5PPT9

(d)

00

02

04

06

08

10

12

14

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (SM)

PPT13PPT14PPT15

PPT19PPT20PPT16

PPT17PPT18PPT21

(e)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (ML)

PPT22PPT23PPT24

PPT25

(f)






00

02

04

06

08

10

12

14

0 50 100 150 200 250 300 350 400

EPW

P ra

tio


zH = 085

zH = 075

zH = 062

zH = 050

zH = 037




Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Upstream

Downstream

PPT1

PPT6PPT10

PPT2PPT7

PPT3PPT8PPT11

PPT14PPT12

PPT15

PPT4 PPT9 PPT5

PPT16 PPT17PPT19

PPT20 PPT21


PPT13

PPT26

PPT18

PPT28

152m173m

102m127m

76m


minus1

minus05

0

05

1

0 5 10 15 20 25 30 35

Time (s)

Acce

lera

tion

(g)

0

05

1

15

2

25

3

35

4

0 05 1 15 2 25 3

Frequency (1s)

Acce

lera

tion

spec

trum

(g)











zH = 037

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(a)

zH = 05

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(b)

zH = 07560

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(c)


















6 Conclusion






minus14

minus10

minus06

minus02

02

06

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT1PPT6PPT10

(a)


000204060810

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT2PPT7PPT11

(b)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Core (CL)

PPT3PPT8PPT12

(c)

minus05

minus03

minus01

01

03

05

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT4PPT5PPT9

(d)

00

02

04

06

08

10

12

14

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (SM)

PPT13PPT14PPT15

PPT19PPT20PPT16

PPT17PPT18PPT21

(e)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (ML)

PPT22PPT23PPT24

PPT25

(f)






00

02

04

06

08

10

12

14

0 50 100 150 200 250 300 350 400

EPW

P ra

tio


zH = 085

zH = 075

zH = 062

zH = 050

zH = 037




Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












zH = 037

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(a)

zH = 05

60

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(b)

zH = 07560

50

40

30

20

10

0

0 20 40 60 80 100 120 140 160 180

43

38

33

28

65 70 75 80 85 90 95 100 105 110

(c)


















6 Conclusion






minus14

minus10

minus06

minus02

02

06

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT1PPT6PPT10

(a)


000204060810

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT2PPT7PPT11

(b)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Core (CL)

PPT3PPT8PPT12

(c)

minus05

minus03

minus01

01

03

05

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT4PPT5PPT9

(d)

00

02

04

06

08

10

12

14

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (SM)

PPT13PPT14PPT15

PPT19PPT20PPT16

PPT17PPT18PPT21

(e)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (ML)

PPT22PPT23PPT24

PPT25

(f)






00

02

04

06

08

10

12

14

0 50 100 150 200 250 300 350 400

EPW

P ra

tio


zH = 085

zH = 075

zH = 062

zH = 050

zH = 037




Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















6 Conclusion






minus14

minus10

minus06

minus02

02

06

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT1PPT6PPT10

(a)


000204060810

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT2PPT7PPT11

(b)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Core (CL)

PPT3PPT8PPT12

(c)

minus05

minus03

minus01

01

03

05

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT4PPT5PPT9

(d)

00

02

04

06

08

10

12

14

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (SM)

PPT13PPT14PPT15

PPT19PPT20PPT16

PPT17PPT18PPT21

(e)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (ML)

PPT22PPT23PPT24

PPT25

(f)






00

02

04

06

08

10

12

14

0 50 100 150 200 250 300 350 400

EPW

P ra

tio


zH = 085

zH = 075

zH = 062

zH = 050

zH = 037




Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










minus14

minus10

minus06

minus02

02

06

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT1PPT6PPT10

(a)


000204060810

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT2PPT7PPT11

(b)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Core (CL)

PPT3PPT8PPT12

(c)

minus05

minus03

minus01

01

03

05

03 04 05 06 07 08 09 1

EPW

P ra

tio



PPT4PPT5PPT9

(d)

00

02

04

06

08

10

12

14

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (SM)

PPT13PPT14PPT15

PPT19PPT20PPT16

PPT17PPT18PPT21

(e)

00

02

04

06

08

10

03 04 05 06 07 08 09 1

EPW

P ra

tio


Foundation (ML)

PPT22PPT23PPT24

PPT25

(f)






00

02

04

06

08

10

12

14

0 50 100 150 200 250 300 350 400

EPW

P ra

tio


zH = 085

zH = 075

zH = 062

zH = 050

zH = 037




Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










00

02

04

06

08

10

12

14

0 50 100 150 200 250 300 350 400

EPW

P ra

tio


zH = 085

zH = 075

zH = 062

zH = 050

zH = 037




Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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