research article dynamic active earth pressures of the

Research ArticleDynamic Active Earth Pressures of the Retaining Piles withAnchors under Vehicle Loads

Hong-zhi Qiu12 Ji-ming Kong1 and Ren-chao Wang12

1Key Laboratory of Mountain Hazards and Earth Surface Processes Institute of Mountain Hazards and EnvironmentChinese Academy of Sciences Chengdu Sichuan 610041 China2University of Chinese Academy of Science Beijing 100049 China

Correspondence should be addressed to Hong-zhi Qiu hnqhz126com and Ji-ming Kong jimingkimdeaccn

Received 17 July 2015 Revised 23 October 2015 Accepted 4 November 2015

Academic Editor Sundararajan Natarajan

Copyright copy 2016 Hong-zhi Qiu 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

The pile-anchor supporting structure is widely used in foundation pit engineering then knowledge of active earth pressure onpiles is very important for engineers In this paper based on the pseudodynamic method and considering the vehiclersquos vibrationcharacteristic a method to calculate the earth pressure on piles under vehicle load is presented At the same time the constraintof anchor is simplified relation of lateral deformation of piles in present method Effects of a wide range of parameters like ruptureangle vibration acceleration coefficient wall friction angle and soil friction angle on active earth pressure have been studiedResults are presented in terms of coefficients in the figures and comparison of the test data and the earth pressure calculated byM-Omethod and present studyThe result shows that the measured earth pressure is accordant with the theoretical analysis so themethod in this paper is an effective basis for the calculation of earth pressure on piles under vehicle loads

1 Introduction

In design and construction of the excavation the calculationproblemof earth pressure has been encountered by engineersThere are a lot of deep excavations in center area of thecity where dense urban roads traffic is heavy In particularthe project of urban road expansion during construction ofthe road keeps working When foundation pit is close todriving roads it can cause the damage of retaining structurefor underestimating the vehicle vibration on the impact offoundation pit supporting structure (see Figure 1) Usuallythese typical examples can be commonly found in large- andmedium-size cities in China Therefore calculating the earthpressure on retaining piles close to road in the design andconstruction of foundation pit we must consider the impactof vehicle loads

In the past few decades though the calculation methodof earth pressure on retaining structure has been greatlydeveloped achievements are mainly focused on the dynamicresponse of the structure subjected to dynamic loads such asearthquake and vehicle loads [1 2] Under earthquake loadsthe methods have been developed to evaluate the seismic

earth pressure on a rigid retaining structure being knownas the pseudostatic method first used by Okabe [3] andMononobe and Matsuo [4] Pseudostatic method is anextension of the Coulomb sliding wedge theory which waslater recognized as famous Mononobe-Okabe method [5]Steedman and Zeng [6] proposed a pseudodynamic methodwhich assumes that the walls and high seismic accelerationversus time were sinusoidal variation and the shear modulusand shear wave velocity are also identified as a limited valuethe study shows that the pseudodynamic method is closedactually Then Zeng and Steedman [7] also show that theearth pressure in pseudodynamic method is in agreementwith the centrifugal modeling results confirming that theproposed method is correct

Pseudodynamic method is used to calculate the earthpressure on retaining walls under earthquake the results aremore accurate compared to the static method [8ndash12] Studyon supporting structure under the vehicle load is mainly inthe dynamic characteristics of the supporting structures [1314] and the stability of supporting structures [15] However inthe calculationmethod of earth pressure behind the support-ing piles effects of vehicle vibration characteristics are rarely

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 4023827 8 pageshttpdxdoiorg10115520164023827

2 Shock and Vibration

Pavement crack

CrackPile destruction

Current position

Previous position

Pavement crack

Figure 1 Typical example of pit destruction [16]

taken into account In addition there is no considerationof the constraint of anchor structures in solution of earthpressure on retaining piles

In the past solving the earth pressure on supportingstructure is based on static method [17 18] and vehicle loadsare simplified equal static load results of calculation showthat the error is relatively large and cannot reflect the soilpressure in practice Thus in this work a distribution ofearth pressure on supporting structure under vehicle loadis presented we have considered the contribution of anchorstructures on earth pressure on piles Moreover effectsof a wide range of parameters like vibration accelerationcoefficient wall friction angle soil friction angle and theweight of the soil on active earth pressure have been studiedFinally comparison of the earth pressure is calculated byM-Omethod and present study and test data a suggestion has beengiven to calculate earth pressure on pile under vehicle loads

2 Method of Analysis

21 Response Acceleration The growth of heavy vehicle loadsposes a threat to the safety of infrastructure Dynamicstress and acceleration response analysis is important fordesign and assessment of structure [19 20] Accelerationinduced by vehicle loads was obtained by experiment [2122] The experimental results show that characters measuredacceleration response versus time is similar to accelerationinduced by earthquakeTherefore this paper assumes that thevehicle generates shear and primary waves

Pseudodynamicmethod assumes that the rockmass shearmodulus 119866 does not change over vertical position of theslope namely 119866 is a constant Supporting piles at depth 119911by horizontal and vertical vibration accelerations is definedas 119886ℎ(119911 119905) and 119886119881(119911 119905) respectively where 119911 is depth belowthe surface of the soil vibration acceleration at time 119905 for thefollowing equation [6]

119886ℎ (119911 119905) = 119896ℎ119892 sdot sin [120596(119905 minus119911

119881119904

)]

119886119881 (119911 119905) = 119896119881119892 sdot sin[120596(119905 minus119911

119881119901

)]

(1)

where 119896ℎ is the horizontal vibration acceleration coefficient119896119881 is the vertical vibration acceleration coefficients 119911 is

a

b

c

d

B

C

W

F

z

x

z

Vehicleq

A

Ni

120573

Pa

H

120579

120593

Vs Vp

dzQh

Q

120572

Figure 2 Model for computation earth pressure on piles undervehicle loads

the depth of the underground 120596 is the angular frequency ofthe wave vibration and 119881119904 and 119881119901 are the velocity of shearwave and vertical wave respectively

119881119904 = radic119866

120588

119881119901 =radic119866 (2 minus 2120583)

120588 (1 minus 2120583)

(2)

where 119866 is the shear modulus of soil and 120588 and 120583 are thedensity of pile soil and Poissonrsquos ratio respectively

For themajority of geological material119881119901119881119904 = 187 [23]and vibration cycle is 119879 = 2120587120596 = 4119867119881119904 [24]

22 Analytical Model Based on the character of the researchproblem the active earth pressure behind retaining pileshas been analyzed by using pseudodynamic approach undervehicle loads According to practical engineering problemsanalysis model is shown in Figure 2

The soil behind the piles from an equilibrium stateto another equilibrium state in Figure 3 and the position119860119861 moves to a new location 11986010158401198611015840 so a slight angle 120575 isgenerated at the same time the pile shows a slight lateraldeformation Δ119897 We assume that the lateral deformationof pile is approximately equal to the elongation of anchorstructure and the tensile force of anchor is Δ119873 determined

Shock and Vibration 3

Pile

Anchor structure

B

A

z

H

Ni120579

Δl

120575

A998400

B998400

Figure 3 Lateral deformation of pile-anchor support structure

by the elongation of anchor which distributed continuouslywith the depth

Δ119897 = (119867 minus 119911) 120579 (3)

where119867 is a length of cantilever retaining pilesAccording to the principle of force equilibrium the

tensile force acting on the piles in depth 119911 is given by

Δ119873 = Δ119897119864119860119886 = (119867 minus 119911) 120579119864119860119886 (4)

where 119864 is elastic modulus of anchor structure and 119860119886 issectional area of the anchor structure

Tension generated by anchor structure is assumed to beevenly distributed along the length of pile and then the totalforce can be expressed as

119873 = int

119867

0

Δ119873119889119911 =1

21198672120579119864119860119886 (5)

From Figure 2 in the limit equilibrium soil wedge ABCtaking 119889119911 thickness analysis unit body as an object

119886119888 = (119867 minus 119911) cot120572

119887119889 = (119867 minus 119911 minus 119889119911) cot120572(6)

Then the area of the horizontal bar 119889119911 is

119878119886119888119889119887 =1

2(119887119889 + 119886119888) 119889119911 (7)

The quality of the horizontal bar 119889119911 is

Δ119898 = 120588119878119886119888119889119887 = 120588 (119867 minus 119911) cot120572119889119911 (8)

The weight of the soil wedge is

119882 = int

119867

0

120588119892 (119867 minus 119911) cot120572119889119911 = 121205741198672 cot120572 (9)

where 120574 is the unit weight of the soil 120574 = 120588119892

The total horizontal inertia force acting within the failurezone is given by

119876ℎ (119911 119905) = int

119867

0

Δ119898119886ℎ (119911 119905)

=120582119904120574119896ℎ cot120572

2120587

sdot [120582119904

2120587(sin120596119905 minus sin120596120578) minus 119867 cos120596119905]

(10)

where 120582119904 is the transverse wavelength 120582119904 = 119881119904119891 and theangular frequency 120596 = 2120587119891 making 120578 = 119905 minus 119867119881119904

Similarly the total vertical inertial force acting on thefailure wedge is given by

119876119881 (119911 119905) = int

119867

0

Δ119898119886119881 (119911 119905)

=120582119901120574119896119881 cot120572

2120587[120582119901


(11)

where 120582119901 is the longitudinal wave 120582119901 = 119881119901119891119881119901120596 = 1205821199012120587making 120585 = 119905 minus 119867119881119901

According to the equilibrium of the forces on piles inFigure 2 the total active thrust can be obtained so 119875119886 can beexpressed as follows

119875119886

=cos (120572 minus 120593)119876ℎ + sin (120572 minus 120593)119876119881 + sin (120572 minus 120593)119882

cos (120572 minus 120593 minus 120573)

+cot120572 sin (120572 minus 120593) 119902119867 + cos (120572 minus 120593 + 120579)119873

cos (120572 minus 120593 minus 120573)

(12)

Assuming that the coefficient of active earth pressure is119870119886

119870119886 =2119875119886

1205741198672 (13)

Substituting for 119876ℎ and 119876119881 in (13) an expression for 119870119886in terms of 119876ℎ 119876119881119882 and119873 can be derived

119870119886 =cos (120572 minus 120593) cot120572119896ℎ21205872 cos (120572 minus 120593 minus 120573)

119879119881119904

1198671198861

+sin (120572 minus 120593) cot12057211989611988121205872 cos (120572 minus 120593 minus 120573)

119879119881119901

1198671198862

+cot120572 sin (120572 minus 120593)cos (120572 minus 120593 minus 120573)

+2119902 cot120572 sin (120572 minus 120593)120574119867 cos (120572 minus 120593 minus 120573)

+cos (120572 minus 120593 + 120579) 120579119864119860119886120574 cos (120572 minus 120593 minus 120573)


1198861 =119879119881119904

119867[sin 2120587 ( 119905

119879) minus sin 2120587( 119905

119879minus119867

119879119881119904

)]

minus 2120587 cos 2120587 ( 119905119879)

1198862 =119879119881119901

119867[sin 2120587 ( 119905

119879) minus sin 2120587( 119905

119879minus119867

119879119881119901

)]

minus 2120587 cos 2120587 ( 119905119879)

(14)

From (14) it can be analyzed that active earth pressurecoefficient is the function of 120572 119905119879 119867119879119881119904 and 119867119879119881119881In most geological materials 119867119879119881119904 and 119867119879119881119901 values are025 and 0134 respectively And then we can take the partialderivative with respect to 119875119886(119911 119905) as distribution of earthpressure with depth

119901119886 (119911 119905) =120597119875119886 (119911 119905)

120597119911

=cos (120572 minus 120593) 119879119881119904

cos (120572 minus 120593 minus 120573) 2120587120574119896ℎ (cot120572) 1198871

+sin (120572 minus 120593) 119879119881119901

cos (120572 minus 120593 minus 120573) 2120587120574119896119881 (cot120572) 1198872

+sin (120572 minus 120593) cot120572119902cos (120572 minus 120593 minus 120573)

+sin (120572 minus 120593) 119911120574 cot120572cos (120572 minus 120593 minus 120573)

+cos (120572 minus 120593 + 120579) 119911120579119864119860119886

cos (120572 minus 120593 minus 120573)

1198871 = [cos 2120587(119905

119879minus119911

119879119881119904

) minus cos 2120587 ( 119905119879)]

1198872 = [cos 2120587(119905

119879minus119911

119879119881119901

) minus cos 2120587 ( 119905119879)]

(15)

According to (15) dynamic active earth pressures on pilesfor foundation pit contain three parts

119901119886 (119911 119905) = 119901119886119889 + 119901119886119904 + 119901119886119905

119901119886119889 =cos (120572 minus 120593) 119879119881119904


+sin (120572 minus 120593) 119879119881119901


119901119886119904 =cot120572 sin (120572 minus 120593) 119902cos (120572 minus 120593 minus 120573)

+sin (120572 minus 120593)

cos (120572 minus 120593 minus 120573)119911120574 cot120572

119901119886119905 =cos (120572 minus 120593 + 120579) 119911120579119864119860119886

cos (120572 minus 120593 minus 120573)

(16)

119901119886119889 is the dynamic earth pressure created by vehicle loads119901119886119904is the static earth pressure created by the weight of soils andthe static load on the ground 119901119886119905 is the tensile force producedby anchor structure

23 Computation of Rupture Angle (120572) It can be shownfrom (15) that earth pressure distribution function 119901119886(119911 119905) isrelated to the following parameters 120593 120573 120574 119896ℎ 119896119881 and 119891119886And test shows that the soil pressure after pile varies withtime and different depth 119911 When the sliding mass attainslimiting equilibrium condition the active earth pressure afterpile 119875119886(119911 119905) reached a maximum Thus the angle of slidingsurface inclination and also the angle of rupture can beobtained by partial differential equation 120597119875119886(119911 119905)120597120572 = 0After simplifying

[minus sin120573 cot120572

cos2 (120572 minus 120593 minus 120573)minus

cos (120572 minus 120593)cos (120572 minus 120593 minus 120573) sin2120572

]120582119904120574119896ℎ

2120587

sdot 1198981 + [cos120573 cot120572

cos2 (120572 minus 120593 minus 120573)

minussin (120572 minus 120593)

cos (120572 minus 120593 minus 120573) sin2120572]120582119881120574119896119881

21205871198982

+1205741198672

2[

cos120573 cot120572cos2 (120572 minus 120593 minus 120573)


cos (120572 minus 120593 minus 120573) sin2120572] + 119902119867[

cot120572 cos (120572 minus 120593)cos (120572 minus 120593 minus 120573)


cos (120572 minus 120593 minus 120573) sin2120572] minus

sin (120573 + 120579)11986721205751198641198601198862cos2 (120572 minus 120593 minus 120573)

= 0

1198981 =120582119904

2120587[sin 2120587 ( 119905

119879) minus sin 2120587( 119905

119879minus119867

119879119881119904

)] minus 119867

sdot cos 2120587 ( 119905119879)

1198982 =120582119881

2120587[sin 2120587 119905

119879minus sin 2120587( 119905

119879minus119867

119879119881119901

)] minus 119867

sdot cos 2120587 ( 119905119879)

(17)

Equation (17) is a function of the time 119905 and the inclina-tion angle 120572 of the slide surface abbreviated as 119891(119905 120572) = 0Therefore the angle of rupture will be obtained by drawing


00 01 02 03 04 05

10

08

06

04

02

00

pa120574H

120572 = 28∘

120572 = 32∘

120572 = 36∘

120572 = 40∘

120572 = 45∘

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025

zH

HTVp = 0134

Figure 4 Active earth pressure distribution for different values ofrupture angle 120572

the soil pressure distribution curve since corresponding angle120572119894 at any time will all work out

3 Results and Discussion

31 Effect of Rupture Angle (120572) Figure 4 shows the distri-butions of active earth pressure for values of rupture angle120572 with 119896119881 = 05119896ℎ 119896ℎ = 005 120593 = 223

∘ 120573 = 1205932120574 = 188 kNm3 119867119879119881119904 = 025 and 119867119879119881119901 = 0134With the increasing of rupture angle 120572 active earth pressureincreased Plots show that when 120572 change from 28∘ to 32∘the active earth pressure increases by 1629 kN namely wheneach degree increases in rupture angle 120572 the active earthpressure increased by 407 kPa

Similarly when 120572 change from 32∘ to 36∘ a total of theactive earth pressure increases by 1081 kPa and the averageof active earth pressure increased by 27 kPa for each degreeThe value of increment in active earth pressure decreasedwith increase at the same angle (120572) Therefore the greaterthe rupture angle the smaller the impact range on theearth pressure The dotted line represents the dynamic earthpressure produced by vehicle loads the solid line representsthe static earth pressure in Figure 5 Results show that thevalue of rupture angle decreases with increase in proportionof dynamic earth pressure Moreover the greater the ruptureangle the smaller the dynamic earth pressure

In Figure 6 the solid line represents the dynamic earthpressure produced by the horizontal inertia force and thedotted line represents the dynamic earth pressure producedby the vertical inertial force comparing the two values resultsshow that the vertical inertial force has a marginal effect

00 01 02 03 04 05

10

08

06

04

02

00

Dynamic earth pressure

Static earth pressure

pa120574H

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134

120572 = 28∘

120572 = 28∘

120572 = 32∘120572 = 32∘

120572 = 36∘

120572 = 36∘

120572 = 40∘120572 = 40∘

120572 = 45∘

120572 = 45∘

zH

Figure 5 Comparisons of static and dynamic soil pressure

on the dynamic earth pressure and thus contributions todynamic earth pressure are mainly horizontal inertia force

32 Effect of 119896ℎ and 119896119881 According to the definition of theacceleration coefficient 119896ℎ can indirectly reflect the value ofinertial force by dynamic loads

Figure 7 shows a plot of the distributions of active earthpressure for values of 119896ℎ with 119896119881 = 05119896ℎ 120593 = 223

∘ 120573 = 1205932120574 = 188 kNm3119867119879119881119904 = 025 and119867119879119881119901 = 0134Theplotshows that at more than half the height of the pile the impacton the earth pressure is very small and active earth pressuredecreases with the increase of coefficient 119896ℎ At less than halfthe height of the pile earth pressure is greatly influenced by119896ℎ and active earth pressure increases with the accelerationcoefficient increase

33 Effect of Soil Friction Angle (120593) Figure 8 shows thedistributions of active earth pressure for values of soil frictionangle 120593with 119896119881 = 05119896ℎ 119896ℎ = 005 120573 = 1205932 120574 = 188 kNm

3119867119879119881119904 = 025 and 119867119879119881119901 = 0134 When 120593 change from18∘ to 26∘ active earth pressure changes from 15267 kPa to10569 kPa which decreases by about 3077 In other wordseach degree increased in the soil friction angle 120593 and thenactive earth pressure decreases by 59 kPa

34 Effect of Wall Friction Angle (120573) Figure 9 shows thedistributions of active earth pressure for values ofwall frictionangle 120573 with 119896119881 = 05119896ℎ 119896ℎ = 005 120593 = 20

∘ 120574 = 188 kNm3119867119879119881119904 = 025 and 119867119879119881119901 = 0134 Active earth pressureshows relatively marginal decrease with the increase in wallfriction angle 120573 When 120573 change from 0∘ to 1205932 the active


000 002 004 006 008 010 012

10

08

06

04

02

00

Produced by vertical inertial force

Produced by horizontal inertia force

zH

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134

120572 = 28∘

120572 = 28∘

120572 = 32∘120572 = 32∘

120572 = 36∘

120572 = 36∘

120572 = 40∘120572 = 40∘

120572 = 45∘

120572 = 45∘

pa120574H

Figure 6 Comparisons of dynamic earth pressures produced by thehorizontal inertia force and the vertical inertial force

earth pressure decreases by 348 and when 120573 change from0∘ to 120593 the active earth pressure decreases by 365

From (12) it can be learned that the generation of activeearth pressure on retaining structure consists of three partsincluding inertia force generated by vehicle loads tensionof anchor and the gravity of soil wedge The wall frictionangle has no effect on the total earth pressure In additionthe wall friction angle in the formula is only a denominatorcalculating the distribution of earth pressure with depthThe denominator is a function of three angles one of theangles changes and the others change as well Therefore therelation between all angles is to ensure that the denominatoris positive and the effect of the wall friction angle 120573 is notworth mentioning

35 Comparison of Results In order to certify that presentstudy method is effective Figure 10 shows the comparisonof the test data and the active earth pressure calculated byMononobe-Okabe method and present study with 119896119881 =

05119896ℎ 119896ℎ = 004 120593 = 223∘ 120573 = 1205932 120574 = 188 kNm3

119867119879119881119904 = 025 and 119867119879119881119901 = 0134 the above parametersare obtained by experience

It is evident from Figure 10 that active earth pressurecalculated by present study is close to the test data resultobtained by Mononobe-Okabe method is relatively largeWhat ismore distributions of active earth pressure calculatedby present study and test data show clearly nonlinear vibra-tion of vehicle loads It is also clear from Steedman and Zeng[6 7] that the dynamic earth pressure distribution along theheight is nonlinear

00 01 02 03 04 05 06

10

08

06

04

02

00

zH

pa120574H

kh = 0005

kh = 001

kh = 002

kh = 003

kh = 004

kh = 005

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134 120572 = 36∘

Figure 7 Active earth pressure distribution for different values of119896ℎ with 119896119881 = 05119896ℎ

00 01 02 03 04 05 06 07

10

08

06

04

02

00

pa120574H

zH

120593 = 18∘

120593 = 20∘

120593 = 22∘

120593 = 24∘

120593 = 26∘

k = 05kh kh = 005 120573 = 1205932 120574 = 188 kNm3HTVs = 025HTVp = 0134 120572 = 36∘

Figure 8 Active earth pressure distribution for different values ofsoil friction angle 120593

4 Conclusions

Pile-anchor retaining structure is the type of deep foundationpit retaining system most frequently used in China In thiswork based on the pseudodynamic method a solution waspresented for calculating active earth pressures on piles in


00 01 02 03 04 05 06

10

08

06

04

02

00

zH

pa120574H

120573 = 0∘

120573 = 1205932120573 = 120593

k = 05kh kh = 005 120593 = 20∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134 120572 = 36∘

Figure 9 Active earth pressure distribution for different values ofwall friction angle 120573

00 01 02 03 04 05

10

08

06

04

02

00

Mononobe-Okabe methodPresent studyTest data

pa120574H

zH

Figure 10 Typical comparison results for 119896ℎ= 004 119896

119881= 002

120593 = 223∘ 120573 = 111∘ and 120574 = 188 kNm3

deep pits The proposed solution incorporates vibration ofvehicle loads retaining structure deformations and materialproperties The following are the main conclusions of thestudy

(1) In present method by considering the effect of vehicleloads and the constraint of anchor structures the solution

to calculate the active earth pressure on piles under vehicleloads is obtainedThe paper presents effects of parameters onearth pressure such as rupture angle horizontal and verticalvibration coefficient soil friction angle and wall frictionangle

(2) The results of present analysis show that the earthpressure increases with the increase in rupture angle 120572 andhorizontal and vertical vibration coefficient 119896ℎ and 119896119881 whichhave a great influence on the earth pressure on piles Theactive earth pressure is highly sensitive to the friction angle ofthe soil120593 and comparatively less sensitive to the wall frictionangle 120573

(3)The typical results of distribution of the earth pressureon piles show the high nonlinearity Under the influenceof many factors the distribution of dynamic earth pressuregenerated by vehicle loads with depth is nonlinear whichhave a great contribution to the active earth pressure onpiles In comparison of the test data and the results calculatedby present study and Mononobe-Okabe method the resultsshow that the earth pressure gained by the proposed methodcoincides well with the test dataThiswork provides amethodto calculate earth pressure on piles required for the designpurpose

Nomenclature

119866 Shear modulus of soil119886ℎ(119911 119905) Horizontal vibration acceleration119886119881(119911 119905) Vertical vibration acceleration119896ℎ Horizontal vibration acceleration coefficient119896119881 Vertical vibration acceleration coefficients119911 Depth of the underground120596 Angular frequency of the wave vibration119867 Height of the retaining piles119881119904 Shear wave velocity of vibration wave119881119901 Vertical wave velocity of vibration wave120588 Density of soil wedge120583 Poissonrsquos ratio119864 Elastic modulus of anchor structure120574 Unit weight of the soil120582119904 Transverse wavelength120582119901 Longitudinal wave120572 Rupture angle120593 Soil friction angle120573 Rupture angle120579 Horizontal angle anchor

Conflict of Interests

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

Acknowledgments

This research was supported by National High TechnologyResearch andDevelopment Program of China (ldquo863rdquo Projectno 2012AA121302) In addition NetEase News providedimage information for this work


References

[1] K S Subba Rao andD Choudhury ldquoSeismic passive earth pres-sures in soilsrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 131 no 1 pp 131ndash135 2005

[2] A-H Soubra ldquoStatic and seismic passive earth pressure coef-ficients on rigid retaining structuresrdquo Canadian GeotechnicalJournal vol 37 no 2 pp 463ndash478 2000

[3] S Okabe ldquoGeneral theory of earth pressurerdquo Journal of JapanSociety of Civil Engineers vol 12 no 1 1926 (Japanese)

[4] N Mononobe and H Matsuo ldquoOn the determination of earthpressure during earthquakesrdquo in Proceedings of the WorldEngineering Conference vol 9 pp 177ndash185 Tokyo Japan 1929

[5] R V Whitman ldquoSeismic design of earth retaining structuresrdquoin Proceedings of the 2nd International Conference on RecentAdvances in Geotechnical Earthquake Engineering and SoilDynamics pp 1767ndash1778 St Louis Mo USA March 1991

[6] R S Steedman and X Zeng ldquoThe influence of phase on thecalculation of pseudo-static earth pressure on a retaining wallrdquoGeotechnique vol 40 no 1 pp 103ndash112 1990

[7] X Zeng and R S Steedman ldquoOn the behaviour of quay walls inearthquakesrdquo Geotechnique vol 43 no 3 pp 417ndash431 1993

[8] D Choudhury and S S Nimbalkar ldquoPseudo-dynamic approachof seismic active earth pressure behind retaining wallrdquoGeotech-nical and Geological Engineering vol 24 no 5 pp 1103ndash11132006

[9] Z-K Wang T-D Xia and W-Y Chen ldquoPseudo-dynamicanalysis for seismic active earth pressure behind rigid retainingwallrdquo Journal of Zhejiang University (Engineering Science) vol46 no 1 pp 46ndash51 2012 (Chinese)

[10] P Ghosh ldquoSeismic passive earth pressure behind non-verticalretaining wall using pseudo-dynamic analysisrdquo Geotechnicaland Geological Engineering vol 25 no 6 pp 693ndash703 2007

[11] S Ghosh ldquoPseudo-dynamic active force and pressure behindbattered retaining wall supporting inclined backfillrdquo SoilDynamics and Earthquake Engineering vol 30 no 11 pp 1226ndash1232 2010

[12] A Azad S S Yasrobi and A Pak ldquoSeismic active pressuredistribution history behind rigid retaining wallsrdquo Soil Dynamicsand Earthquake Engineering vol 28 no 5 pp 365ndash375 2008

[13] C Lin Y-F Luo and S-P Wang ldquoMonitoring and effect ofmoving load to foundation excavation support configurationrdquoJournal of Wuhan University of Technology vol 29 no 11 pp112ndash114 2007 (Chinese)

[14] J C Yue H Z Qiu and L J Zhang ldquoAnalysis on dynamicresponse of the foundation pit supporting structure undertraffic loadsrdquo Chinese Journal of Underground Space and Engi-neering vol 9 no 6 pp 1320ndash1325 2013 (Chinese)

[15] X D Zhang C G Zhang and J S Liu ldquoAnalysis on stabilityof deep foundation pit supporting structure under traffic loadrdquoThe Chinese Journal of Geological Hazard and Control vol 22no 2 pp 125ndash129 2011 (Chinese)

[16] Netease news ldquoThe supporting structure of pit fracture and thesubway construction site collapsed inWuhan city Chinardquo 2012httpnews163comphotoview00AN000130678html

[17] J-J Wang and H-J Chai ldquoActive earth pressure induced bysaturated sub grade under vehicle loadrdquo Chinese Journal ofGeotechnical Engineering vol 30 no 3 pp 372ndash378 2008(Chinese)

[18] Specifications for Design of Highway Asphalt Pavement(JTGD50-2006) China Communication Press Beijing China2006 (Chinese)

[19] H Zhang X Xie J Q Jiang andM Yamashita ldquoAssessment ontransient sound radiation of a vibrating steel bridge due to trafficloadingrdquo Journal of Sound and Vibration vol 336 pp 132ndash1492015

[20] Y L XuQ Li D JWu and ZWChen ldquoStress and accelerationanalysis of coupled vehicle and long-span bridge systems usingthe mode superposition methodrdquo Engineering Structures vol32 no 5 pp 1356ndash1368 2010

[21] H Aied A Gonzalez and D Cantero ldquoIdentification of suddenstiffness changes in the acceleration response of a bridge tomoving loads using ensemble empirical mode decompositionrdquoMechanical Systems and Signal Processing vol 66-67 pp 314ndash338 2016

[22] H Z Qiu J M Kong R CWang et al ldquoAnalyzing the effects ofactive earth pressure on supporting piles under vehicle loadsrdquoChinese Journal of Geotechnical Engineering 2015 (Chinese)

[23] D Choudhury and S Nimbalkar ldquoSeismic passive resistance bypseudo-dynamicmethodrdquoGeotechnique vol 55 no 9 pp 699ndash702 2005

[24] S L Kramer Geotechnical Earthquake Engineering PrenticeHall Upper Saddle River NJ USA 1990

International Journal of

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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



Pavement crack

CrackPile destruction

Current position

Previous position

Pavement crack

Figure 1 Typical example of pit destruction [16]

taken into account In addition there is no considerationof the constraint of anchor structures in solution of earthpressure on retaining piles

In the past solving the earth pressure on supportingstructure is based on static method [17 18] and vehicle loadsare simplified equal static load results of calculation showthat the error is relatively large and cannot reflect the soilpressure in practice Thus in this work a distribution ofearth pressure on supporting structure under vehicle loadis presented we have considered the contribution of anchorstructures on earth pressure on piles Moreover effectsof a wide range of parameters like vibration accelerationcoefficient wall friction angle soil friction angle and theweight of the soil on active earth pressure have been studiedFinally comparison of the earth pressure is calculated byM-Omethod and present study and test data a suggestion has beengiven to calculate earth pressure on pile under vehicle loads

2 Method of Analysis

21 Response Acceleration The growth of heavy vehicle loadsposes a threat to the safety of infrastructure Dynamicstress and acceleration response analysis is important fordesign and assessment of structure [19 20] Accelerationinduced by vehicle loads was obtained by experiment [2122] The experimental results show that characters measuredacceleration response versus time is similar to accelerationinduced by earthquakeTherefore this paper assumes that thevehicle generates shear and primary waves

Pseudodynamicmethod assumes that the rockmass shearmodulus 119866 does not change over vertical position of theslope namely 119866 is a constant Supporting piles at depth 119911by horizontal and vertical vibration accelerations is definedas 119886ℎ(119911 119905) and 119886119881(119911 119905) respectively where 119911 is depth belowthe surface of the soil vibration acceleration at time 119905 for thefollowing equation [6]

119886ℎ (119911 119905) = 119896ℎ119892 sdot sin [120596(119905 minus119911

119881119904

)]

119886119881 (119911 119905) = 119896119881119892 sdot sin[120596(119905 minus119911

119881119901

)]

(1)

where 119896ℎ is the horizontal vibration acceleration coefficient119896119881 is the vertical vibration acceleration coefficients 119911 is

a

b

c

d

B

C

W

F

z

x

z

Vehicleq

A

Ni

120573

Pa

H

120579

120593

Vs Vp

dzQh

Q

120572

Figure 2 Model for computation earth pressure on piles undervehicle loads

the depth of the underground 120596 is the angular frequency ofthe wave vibration and 119881119904 and 119881119901 are the velocity of shearwave and vertical wave respectively

119881119904 = radic119866

120588

119881119901 =radic119866 (2 minus 2120583)

120588 (1 minus 2120583)

(2)

where 119866 is the shear modulus of soil and 120588 and 120583 are thedensity of pile soil and Poissonrsquos ratio respectively

For themajority of geological material119881119901119881119904 = 187 [23]and vibration cycle is 119879 = 2120587120596 = 4119867119881119904 [24]

22 Analytical Model Based on the character of the researchproblem the active earth pressure behind retaining pileshas been analyzed by using pseudodynamic approach undervehicle loads According to practical engineering problemsanalysis model is shown in Figure 2

The soil behind the piles from an equilibrium stateto another equilibrium state in Figure 3 and the position119860119861 moves to a new location 11986010158401198611015840 so a slight angle 120575 isgenerated at the same time the pile shows a slight lateraldeformation Δ119897 We assume that the lateral deformationof pile is approximately equal to the elongation of anchorstructure and the tensile force of anchor is Δ119873 determined


Pile

Anchor structure

B

A

z

H

Ni120579

Δl

120575

A998400

B998400



Δ119897 = (119867 minus 119911) 120579 (3)



Δ119873 = Δ119897119864119860119886 = (119867 minus 119911) 120579119864119860119886 (4)



119873 = int

119867

0

Δ119873119889119911 =1

21198672120579119864119860119886 (5)


119886119888 = (119867 minus 119911) cot120572

119887119889 = (119867 minus 119911 minus 119889119911) cot120572(6)


119878119886119888119889119887 =1

2(119887119889 + 119886119888) 119889119911 (7)


Δ119898 = 120588119878119886119888119889119887 = 120588 (119867 minus 119911) cot120572119889119911 (8)


119882 = int

119867

0

120588119892 (119867 minus 119911) cot120572119889119911 = 121205741198672 cot120572 (9)



119876ℎ (119911 119905) = int

119867

0

Δ119898119886ℎ (119911 119905)

=120582119904120574119896ℎ cot120572

2120587

sdot [120582119904


(10)



119876119881 (119911 119905) = int

119867

0

Δ119898119886119881 (119911 119905)

=120582119901120574119896119881 cot120572

2120587[120582119901


(11)



119875119886


cos (120572 minus 120593 minus 120573)


cos (120572 minus 120593 minus 120573)

(12)


119870119886 =2119875119886

1205741198672 (13)



119879119881119904

1198671198861


119879119881119901

1198671198862





1198861 =119879119881119904

119867[sin 2120587 ( 119905

119879) minus sin 2120587( 119905

119879minus119867

119879119881119904

)]

minus 2120587 cos 2120587 ( 119905119879)

1198862 =119879119881119901

119867[sin 2120587 ( 119905

119879) minus sin 2120587( 119905

119879minus119867

119879119881119901

)]

minus 2120587 cos 2120587 ( 119905119879)

(14)


119901119886 (119911 119905) =120597119875119886 (119911 119905)

120597119911

=cos (120572 minus 120593) 119879119881119904


+sin (120572 minus 120593) 119879119881119901




+cos (120572 minus 120593 + 120579) 119911120579119864119860119886

cos (120572 minus 120593 minus 120573)

1198871 = [cos 2120587(119905

119879minus119911

119879119881119904

) minus cos 2120587 ( 119905119879)]

1198872 = [cos 2120587(119905

119879minus119911

119879119881119901

) minus cos 2120587 ( 119905119879)]

(15)


119901119886 (119911 119905) = 119901119886119889 + 119901119886119904 + 119901119886119905

119901119886119889 =cos (120572 minus 120593) 119879119881119904


+sin (120572 minus 120593) 119879119881119901



+sin (120572 minus 120593)


119901119886119905 =cos (120572 minus 120593 + 120579) 119911120579119864119860119886

cos (120572 minus 120593 minus 120573)

(16)






]120582119904120574119896ℎ

2120587

sdot 1198981 + [cos120573 cot120572

cos2 (120572 minus 120593 minus 120573)



21205871198982

+1205741198672

2[








= 0

1198981 =120582119904

2120587[sin 2120587 ( 119905

119879) minus sin 2120587( 119905

119879minus119867

119879119881119904

)] minus 119867

sdot cos 2120587 ( 119905119879)

1198982 =120582119881

2120587[sin 2120587 119905

119879minus sin 2120587( 119905

119879minus119867

119879119881119901

)] minus 119867

sdot cos 2120587 ( 119905119879)

(17)



00 01 02 03 04 05

10

08

06

04

02

00

pa120574H

120572 = 28∘

120572 = 32∘

120572 = 36∘

120572 = 40∘

120572 = 45∘

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025

zH

HTVp = 0134








00 01 02 03 04 05

10

08

06

04

02

00



pa120574H

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134

120572 = 28∘

120572 = 28∘

120572 = 32∘120572 = 32∘

120572 = 36∘

120572 = 36∘

120572 = 40∘120572 = 40∘

120572 = 45∘

120572 = 45∘

zH











000 002 004 006 008 010 012

10

08

06

04

02

00



zH

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134

120572 = 28∘

120572 = 28∘

120572 = 32∘120572 = 32∘

120572 = 36∘

120572 = 36∘

120572 = 40∘120572 = 40∘

120572 = 45∘

120572 = 45∘

pa120574H





05119896ℎ 119896ℎ = 004 120593 = 223∘ 120573 = 1205932 120574 = 188 kNm3



00 01 02 03 04 05 06

10

08

06

04

02

00

zH

pa120574H

kh = 0005

kh = 001

kh = 002

kh = 003

kh = 004

kh = 005

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134 120572 = 36∘


00 01 02 03 04 05 06 07

10

08

06

04

02

00

pa120574H

zH

120593 = 18∘

120593 = 20∘

120593 = 22∘

120593 = 24∘

120593 = 26∘



4 Conclusions



00 01 02 03 04 05 06

10

08

06

04

02

00

zH

pa120574H

120573 = 0∘

120573 = 1205932120573 = 120593



00 01 02 03 04 05

10

08

06

04

02

00


pa120574H

zH


119881= 002

120593 = 223∘ 120573 = 111∘ and 120574 = 188 kNm3






Nomenclature




Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Pile

Anchor structure

B

A

z

H

Ni120579

Δl

120575

A998400

B998400



Δ119897 = (119867 minus 119911) 120579 (3)



Δ119873 = Δ119897119864119860119886 = (119867 minus 119911) 120579119864119860119886 (4)



119873 = int

119867

0

Δ119873119889119911 =1

21198672120579119864119860119886 (5)


119886119888 = (119867 minus 119911) cot120572

119887119889 = (119867 minus 119911 minus 119889119911) cot120572(6)


119878119886119888119889119887 =1

2(119887119889 + 119886119888) 119889119911 (7)


Δ119898 = 120588119878119886119888119889119887 = 120588 (119867 minus 119911) cot120572119889119911 (8)


119882 = int

119867

0

120588119892 (119867 minus 119911) cot120572119889119911 = 121205741198672 cot120572 (9)



119876ℎ (119911 119905) = int

119867

0

Δ119898119886ℎ (119911 119905)

=120582119904120574119896ℎ cot120572

2120587

sdot [120582119904


(10)



119876119881 (119911 119905) = int

119867

0

Δ119898119886119881 (119911 119905)

=120582119901120574119896119881 cot120572

2120587[120582119901


(11)



119875119886


cos (120572 minus 120593 minus 120573)


cos (120572 minus 120593 minus 120573)

(12)


119870119886 =2119875119886

1205741198672 (13)



119879119881119904

1198671198861


119879119881119901

1198671198862





1198861 =119879119881119904

119867[sin 2120587 ( 119905

119879) minus sin 2120587( 119905

119879minus119867

119879119881119904

)]

minus 2120587 cos 2120587 ( 119905119879)

1198862 =119879119881119901

119867[sin 2120587 ( 119905

119879) minus sin 2120587( 119905

119879minus119867

119879119881119901

)]

minus 2120587 cos 2120587 ( 119905119879)

(14)


119901119886 (119911 119905) =120597119875119886 (119911 119905)

120597119911

=cos (120572 minus 120593) 119879119881119904


+sin (120572 minus 120593) 119879119881119901




+cos (120572 minus 120593 + 120579) 119911120579119864119860119886

cos (120572 minus 120593 minus 120573)

1198871 = [cos 2120587(119905

119879minus119911

119879119881119904

) minus cos 2120587 ( 119905119879)]

1198872 = [cos 2120587(119905

119879minus119911

119879119881119901

) minus cos 2120587 ( 119905119879)]

(15)


119901119886 (119911 119905) = 119901119886119889 + 119901119886119904 + 119901119886119905

119901119886119889 =cos (120572 minus 120593) 119879119881119904


+sin (120572 minus 120593) 119879119881119901



+sin (120572 minus 120593)


119901119886119905 =cos (120572 minus 120593 + 120579) 119911120579119864119860119886

cos (120572 minus 120593 minus 120573)

(16)






]120582119904120574119896ℎ

2120587

sdot 1198981 + [cos120573 cot120572

cos2 (120572 minus 120593 minus 120573)



21205871198982

+1205741198672

2[








= 0

1198981 =120582119904

2120587[sin 2120587 ( 119905

119879) minus sin 2120587( 119905

119879minus119867

119879119881119904

)] minus 119867

sdot cos 2120587 ( 119905119879)

1198982 =120582119881

2120587[sin 2120587 119905

119879minus sin 2120587( 119905

119879minus119867

119879119881119901

)] minus 119867

sdot cos 2120587 ( 119905119879)

(17)



00 01 02 03 04 05

10

08

06

04

02

00

pa120574H

120572 = 28∘

120572 = 32∘

120572 = 36∘

120572 = 40∘

120572 = 45∘

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025

zH

HTVp = 0134








00 01 02 03 04 05

10

08

06

04

02

00



pa120574H

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134

120572 = 28∘

120572 = 28∘

120572 = 32∘120572 = 32∘

120572 = 36∘

120572 = 36∘

120572 = 40∘120572 = 40∘

120572 = 45∘

120572 = 45∘

zH











000 002 004 006 008 010 012

10

08

06

04

02

00



zH

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134

120572 = 28∘

120572 = 28∘

120572 = 32∘120572 = 32∘

120572 = 36∘

120572 = 36∘

120572 = 40∘120572 = 40∘

120572 = 45∘

120572 = 45∘

pa120574H





05119896ℎ 119896ℎ = 004 120593 = 223∘ 120573 = 1205932 120574 = 188 kNm3



00 01 02 03 04 05 06

10

08

06

04

02

00

zH

pa120574H

kh = 0005

kh = 001

kh = 002

kh = 003

kh = 004

kh = 005

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134 120572 = 36∘


00 01 02 03 04 05 06 07

10

08

06

04

02

00

pa120574H

zH

120593 = 18∘

120593 = 20∘

120593 = 22∘

120593 = 24∘

120593 = 26∘



4 Conclusions



00 01 02 03 04 05 06

10

08

06

04

02

00

zH

pa120574H

120573 = 0∘

120573 = 1205932120573 = 120593



00 01 02 03 04 05

10

08

06

04

02

00


pa120574H

zH


119881= 002

120593 = 223∘ 120573 = 111∘ and 120574 = 188 kNm3






Nomenclature




Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1198861 =119879119881119904

119867[sin 2120587 ( 119905

119879) minus sin 2120587( 119905

119879minus119867

119879119881119904

)]

minus 2120587 cos 2120587 ( 119905119879)

1198862 =119879119881119901

119867[sin 2120587 ( 119905

119879) minus sin 2120587( 119905

119879minus119867

119879119881119901

)]

minus 2120587 cos 2120587 ( 119905119879)

(14)


119901119886 (119911 119905) =120597119875119886 (119911 119905)

120597119911

=cos (120572 minus 120593) 119879119881119904


+sin (120572 minus 120593) 119879119881119901




+cos (120572 minus 120593 + 120579) 119911120579119864119860119886

cos (120572 minus 120593 minus 120573)

1198871 = [cos 2120587(119905

119879minus119911

119879119881119904

) minus cos 2120587 ( 119905119879)]

1198872 = [cos 2120587(119905

119879minus119911

119879119881119901

) minus cos 2120587 ( 119905119879)]

(15)


119901119886 (119911 119905) = 119901119886119889 + 119901119886119904 + 119901119886119905

119901119886119889 =cos (120572 minus 120593) 119879119881119904


+sin (120572 minus 120593) 119879119881119901



+sin (120572 minus 120593)


119901119886119905 =cos (120572 minus 120593 + 120579) 119911120579119864119860119886

cos (120572 minus 120593 minus 120573)

(16)






]120582119904120574119896ℎ

2120587

sdot 1198981 + [cos120573 cot120572

cos2 (120572 minus 120593 minus 120573)



21205871198982

+1205741198672

2[








= 0

1198981 =120582119904

2120587[sin 2120587 ( 119905

119879) minus sin 2120587( 119905

119879minus119867

119879119881119904

)] minus 119867

sdot cos 2120587 ( 119905119879)

1198982 =120582119881

2120587[sin 2120587 119905

119879minus sin 2120587( 119905

119879minus119867

119879119881119901

)] minus 119867

sdot cos 2120587 ( 119905119879)

(17)



00 01 02 03 04 05

10

08

06

04

02

00

pa120574H

120572 = 28∘

120572 = 32∘

120572 = 36∘

120572 = 40∘

120572 = 45∘

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025

zH

HTVp = 0134








00 01 02 03 04 05

10

08

06

04

02

00



pa120574H

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134

120572 = 28∘

120572 = 28∘

120572 = 32∘120572 = 32∘

120572 = 36∘

120572 = 36∘

120572 = 40∘120572 = 40∘

120572 = 45∘

120572 = 45∘

zH











000 002 004 006 008 010 012

10

08

06

04

02

00



zH

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134

120572 = 28∘

120572 = 28∘

120572 = 32∘120572 = 32∘

120572 = 36∘

120572 = 36∘

120572 = 40∘120572 = 40∘

120572 = 45∘

120572 = 45∘

pa120574H





05119896ℎ 119896ℎ = 004 120593 = 223∘ 120573 = 1205932 120574 = 188 kNm3



00 01 02 03 04 05 06

10

08

06

04

02

00

zH

pa120574H

kh = 0005

kh = 001

kh = 002

kh = 003

kh = 004

kh = 005

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134 120572 = 36∘


00 01 02 03 04 05 06 07

10

08

06

04

02

00

pa120574H

zH

120593 = 18∘

120593 = 20∘

120593 = 22∘

120593 = 24∘

120593 = 26∘



4 Conclusions



00 01 02 03 04 05 06

10

08

06

04

02

00

zH

pa120574H

120573 = 0∘

120573 = 1205932120573 = 120593



00 01 02 03 04 05

10

08

06

04

02

00


pa120574H

zH


119881= 002

120593 = 223∘ 120573 = 111∘ and 120574 = 188 kNm3






Nomenclature




Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










00 01 02 03 04 05

10

08

06

04

02

00

pa120574H

120572 = 28∘

120572 = 32∘

120572 = 36∘

120572 = 40∘

120572 = 45∘

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025

zH

HTVp = 0134








00 01 02 03 04 05

10

08

06

04

02

00



pa120574H

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134

120572 = 28∘

120572 = 28∘

120572 = 32∘120572 = 32∘

120572 = 36∘

120572 = 36∘

120572 = 40∘120572 = 40∘

120572 = 45∘

120572 = 45∘

zH











000 002 004 006 008 010 012

10

08

06

04

02

00



zH

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134

120572 = 28∘

120572 = 28∘

120572 = 32∘120572 = 32∘

120572 = 36∘

120572 = 36∘

120572 = 40∘120572 = 40∘

120572 = 45∘

120572 = 45∘

pa120574H





05119896ℎ 119896ℎ = 004 120593 = 223∘ 120573 = 1205932 120574 = 188 kNm3



00 01 02 03 04 05 06

10

08

06

04

02

00

zH

pa120574H

kh = 0005

kh = 001

kh = 002

kh = 003

kh = 004

kh = 005

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134 120572 = 36∘


00 01 02 03 04 05 06 07

10

08

06

04

02

00

pa120574H

zH

120593 = 18∘

120593 = 20∘

120593 = 22∘

120593 = 24∘

120593 = 26∘



4 Conclusions



00 01 02 03 04 05 06

10

08

06

04

02

00

zH

pa120574H

120573 = 0∘

120573 = 1205932120573 = 120593



00 01 02 03 04 05

10

08

06

04

02

00


pa120574H

zH


119881= 002

120593 = 223∘ 120573 = 111∘ and 120574 = 188 kNm3






Nomenclature




Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










000 002 004 006 008 010 012

10

08

06

04

02

00



zH

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134

120572 = 28∘

120572 = 28∘

120572 = 32∘120572 = 32∘

120572 = 36∘

120572 = 36∘

120572 = 40∘120572 = 40∘

120572 = 45∘

120572 = 45∘

pa120574H





05119896ℎ 119896ℎ = 004 120593 = 223∘ 120573 = 1205932 120574 = 188 kNm3



00 01 02 03 04 05 06

10

08

06

04

02

00

zH

pa120574H

kh = 0005

kh = 001

kh = 002

kh = 003

kh = 004

kh = 005

k = 05kh 120593 = 223∘ 120573 = 111∘ 120574 = 188 kNm3HTVs = 025HTVp = 0134 120572 = 36∘


00 01 02 03 04 05 06 07

10

08

06

04

02

00

pa120574H

zH

120593 = 18∘

120593 = 20∘

120593 = 22∘

120593 = 24∘

120593 = 26∘



4 Conclusions



00 01 02 03 04 05 06

10

08

06

04

02

00

zH

pa120574H

120573 = 0∘

120573 = 1205932120573 = 120593



00 01 02 03 04 05

10

08

06

04

02

00


pa120574H

zH


119881= 002

120593 = 223∘ 120573 = 111∘ and 120574 = 188 kNm3






Nomenclature




Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










00 01 02 03 04 05 06

10

08

06

04

02

00

zH

pa120574H

120573 = 0∘

120573 = 1205932120573 = 120593



00 01 02 03 04 05

10

08

06

04

02

00


pa120574H

zH


119881= 002

120593 = 223∘ 120573 = 111∘ and 120574 = 188 kNm3






Nomenclature




Acknowledgments



References



























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










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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