calculationofsilowallpressureconsideringthe...

Research ArticleCalculation of Silo Wall Pressure considering theIntermediate Stress Effect

Shanshan Sun Junhai Zhao and Changguang Zhang

School of Civil Engineering Changrsquoan University Xirsquoan 710061 China

Correspondence should be addressed to Changguang Zhang zcg1016163com

Received 11 February 2018 Revised 4 June 2018 Accepted 27 August 2018 Published 18 September 2018

Academic Editor Pier Paolo Rossi

Copyright copy 2018 Shanshan Sun et al+is 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

+e reasonable determination of wall pressure is critical for the design of silo structures In this study the primary objective is topresent four novel wall pressure coefficients based on four true triaxial strength criteria in the quasiplane strain state +ese fourstrength criteria are the Drucker-Prager (D-P) criterion the Matsuoka-Nakai (M-N) criterion the Lade-Duncan (L-D) criterionand the unified strength theory (UST) and they all consider the effect of the intermediate stress yet to different extent +esecoefficients have a wide application range and are readily used to predict the distribution of wall pressure for deep and squat silosComprehensive comparisons are made between the predictions from the wall pressure coefficients described herein and ex-perimental data reported in the literature as well as the results from the European American and Chinese silo standards or theRankine and the modified Coulomb theories It is found that the effect of the intermediate stress on the wall pressure is verysignificant for both deep and squat silos the wall pressure of the D-P criterion is underestimated whereas that of the Mohr-Coulomb (M-C) criterion is overestimated the L-D criterion is recommended to be adopted to calculate the soil wall pressure

1 Introduction

Silos are widely used for the storage handling and trans-portation of bulk solids in industries Since Janssenrsquosproposition in 1895 [1] silo behavior has been extensivelystudied in terms of wall pressure and flow for differentsituations such as filling storage and discharge Variousresearch methods including the theoretical analysis [2ndash6]experimental investigation [7ndash14] and numerical simulation[15ndash20] have been used Although much progress has beenmade some aspects of the silo structural design still lackgenerally accepted directives [21ndash23]

+e static pressure during the filling and storage con-stitutes the primary load acting on the silo wall +ere areseveral classical theories to predict static wall pressures[24ndash26] Earlier studies have shown that the wall pressureduring the filling and storage can be expressed as Janssenrsquosequation However a consensus with regard to the wallpressure coefficient k is not generally accepted

For deep silos most design standards are based on theJanssen theory but each of them uses different wall pressurecoefficients +e commonly used wall pressure coefficients

are the Rankine active earth pressure coefficient k

(1minus sinφ)(1 + sinφ) [27] the static earth pressure co-efficient k 1minus sinφ [28] the modified static earth pressurecoefficient and the wall pressure coefficient considering wallfriction [29ndash31] +e classical theories of wall pressure forsquat silos include the Rankine theory and the modifiedCoulomb theory [32 33] +ese two theories are based ontheMohr-Coulomb (M-C) criterion without considering theintermediate principal stress

In fact the materials stored in silos are in a quasiplanestrain state where three-dimensional unequal stresses existAs the influence of the intermediate principal stress on thematerial strength is in general significant theM-C criterionis not appropriate to predict such strength +e silo wallpressure using the M-C criterion is then overestimatedleading to a conservative silo design [34ndash38] Conse-quently choosing an appropriate true triaxial strengthcriterion such as the Drucker-Prager (D-P) criterion theMatsuoka-Nakai (M-N) criterion the Lade-Duncan (L-D)criterion or the unified strength theory (UST) can not onlyimprove silo quality and durability but also generateeconomic benefits

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 3673515 10 pageshttpsdoiorg10115520183673515

In this study the D-P criterion the M-N criterion theL-D criterion and the UST are adopted to derive four novelwall pressure coefficients in quasiplane strain to consider theintermediate stress effect +e applicability condition forthese coefficients is also provided Furthermore these co-efficients are used to calculate the wall pressure for deep andsquat silos Finally the calculated results are compared withseveral sets of experimental data and different standards ortheories

2 Principles and Basic Assumptions

21 Principles +e distribution of wall pressure depends onthe silo type According to the load characteristics silos areusually divided into deep silos and squat silos +ese twotypes of silos have different calculation methods [27]

For a deep silo (HDge 15 where H is the silo height andD is the silo diameter) as shown in Figure 1 the wallpressure Ph on the silo wall [6] is written as

Ph Chcρ 1minus eminusμksρ( 1113857

μ (1)

where Ch is the correction factor related to the calculatedheight and can be determined by GB50077-2003 [27] c is thegravity density of bulk solids ρ is the hydraulic radius of thenet horizontal cross section μ is the friction coefficientbetween the silo wall and bulk solids k is the wall pressurecoefficient and s is the depth from the material top or fromthe center of cone gravity to the calculation section

For a squat silo (HDlt 15) the wall pressure Ph [6] isexpressed as

Ph kcs (2)

When the Rankine theory is used the wall pressurecoefficient k is

k 1minus sinφ1 + sinφ

(3)

When the modified Coulomb theory is used the wallpressure coefficient k is

k cos2 φ

1 +sin(φ + δ)cos δ

1113968 (4)

where φ is the internal friction angle of bulk solids and δ isthe wall friction angle

It can be seen from Equations (1) and (2) that the key tocalculate the wall pressure for both deep and squat silos ishow to rationally determine the wall pressure coefficient kIn addition bulk solids are similar to granular materials+erefore the wall pressure coefficient k in the quasiplanestrain state can be determined from the analogy with thelateral earth pressure for sandy soils acting on retainingwalls

22 Basic Assumptions

(1) +e calculation of silo wall pressure can be regardedas a quasiplane strain problem [6] +e intermediate

stress in bulk solids could be considered approxi-mately as the intermediate principal stress σ2 equal tothe average value of the maximum principal stress σ1and the minor principal stress σ3 without significanterror [34ndash38] +is correlation is written as

σ2 12

σ1 + σ3( 1113857 (5)

(2) Bulk solids can be analogous to sandy soils +at is tosay the cohesion c of bulk solids is negligibleie c 0

(3) +e compressive stress is assumed to be positive andthe tensile stress is thus negative

3 Novel Wall Pressure Coefficients

31 D-P Criterion +e D-P criterion [39 40] known as thegeneralized Mises criterion makes the assumption that theintermediate principal stress and the minor principal stresshave an identical effect on the material strength +e D-Pcriterion is expressed as

J2

1113968

2 sinφ3

radic(3minus sinφ)

I1 +6c cosφ

3

radic(3minus sinφ)

(6)

where J2 is the second invariant of stress deviation and I1 isthe first invariant of stress tensor

J2 16

σ1 minus σ2( 11138572

+ σ2 minus σ3( 11138572

+ σ3 minus σ1( 11138572

1113960 1113961 (7)

I1 σ1 + σ2 + σ3 (8)

Substituting Equations (5) (7) and (8) into Equation (6)with c 0 the wall pressure coefficient based on the D-Pcriterion (ie kDP) is obtained as

kDP σ3σ1

3

3

radicminus(6 +

3

radic)sinφ

33

radic+(6 +

3

radic)sinφ

(9)

32M-NCriterion +eM-N criterion [41 42] is suitable forcohesionless materials and overcomes the singularity of theM-C criterion in a deviatoric plane as well as the condition of

Storing surface(f lat pile)

Storing surface(cone pile)

Center ofcone gravity

Calculationsection

D

ssH

PhPh

Figure 1 Mechanical model of silo wall pressure (no-funnel)(modified from Sun et al [37])

2 Advances in Civil Engineering

equal strength in tension and in compression of the D-Pcriterion It reflects the effect of the intermediate principalstress on the material strength to a certain extent +e M-Ncriterion is expressed as

I1I2

I3 9 + 8 tan2 φ (10)

where I2 and I3 are the second and third invariants of stresstensor respectively

I2 σ1σ2 + σ2σ3 + σ3σ1 (11)

I3 σ1σ2σ3 (12)

Substituting Equations (5) (11) and (12) into Equation(10) the wall pressure coefficient based on the M-N criterion(ie kMN) is obtained as

kMN σ3σ1

83tan2 φ + 1minus

43tanφ

4 tan2 φ + 31113969

(13)

33 L-D Criterion +e expression of the L-D criterion[43 44] is similar to the M-N criterion but the limit locus ofthe former in the deviatoric plane is slightly larger than thatof the latter +e L-D criterion is expressed as

I31I3

27 + 4 tan2 φ(9minus 7 sinφ)

(1minus sinφ) (14)

Substituting Equations (5) (8) and (12) into Equation(14) the wall pressure coefficient based on the L-D criterion(ie kLD) is obtained as

kLD σ3σ1

1 +4 tanφ

27(1minus sinφ)11138762 tanφ(9minus 7 sinφ)

minus

(9minus 7 sinφ) 27(1minus sinφ) + 4 tan2 φ(9minus 7 sinφ)1113858 1113859

1113969

1113877

(15)

34 UST With fully considering the intermediate principalstress effect and its interval the UST [45] covers the entireregion from the lower bound to the upper bound of allconvex strength criteria +e UST can thus be applied tovarious bulk solids with different tension-compressioncharacteristics and is expressed as1minus sinφ1 + sinφ

σ1 minusbσ2 + σ31 + b

2c cosφ1 + sinφ

when σ2 leσ1 + σ3

2minusσ1 minus σ3

2sinφ

(16a)

1minus sinφ(1 + b)(1 + sinφ)

σ1 + bσ2( 1113857minus σ3 2c cosφ1 + sinφ

when σ2 geσ1 + σ3

2minusσ1 minus σ3

2sinφ

(16b)

where b is the USTparameter which reflects the influence ofthe intermediate principal stress on the material strengthwith the range 0le ble 1 In addition there is a positivecorrelation between the parameter b and the intermediateprincipal stress effect In other words the greater the pa-rameter b the higher the strength of bulk solids achieveddue to considering the intermediate principal stress effectAlso b is a parameter for choosing different strength criteriaFor instance the UST becomes the M-C criterion whenb 0 the twin-shear stress criterion is obtained when b 1a series of new strength criteria are set up when 0lt blt 1

From Equation (5) it is found that the quasiplane straincondition satisfies Equation (16b) for sin(φ)ge 0 SubstitutingEquation (5) into Equation (16b) the wall pressure co-efficient based on the UST (ie kUST) is obtained as

kUST σ3σ1

(2 + b)(1minus sinφ)

2 + b +(2 + 3b) sinφ (17)

35 Applicable Conditions Substituting Equations (9) (13)(15) and (17) into Equations (1) and (2) four novel for-mulations of wall pressure corresponding to four true tri-axial strength criteria are presented for deep silos and squatsilos respectively +e application of these wall pressurecoefficients (and thus the corresponding wall pressure for-mulations) is very simple and convenient

According to the silo wall pressure theory [6] the wallpressure coefficient should be nonnegative and thus theapplicable condition is given by

ki ge 0 i DPMN LDUST (18)

In addition the wall pressure coefficients presentedherein are only associated with the internal friction angle φof bulk solids Accordingly φ should fulfill Equation (18)which means that φle 4222deg for the D-P criterion whereasthe other three strength criteria impose no restrictions on φand therefore have a wider applicable range

36 Comparisons of Wall Pressure Coefficients Figure 2 il-lustrates the values of kDP kMN kLD and kUST (b 0 12 and1) as well as the wall pressure coefficients from the Europeansilo standard (EN1991-4) American silo standard (ACI313-97) and Chinese silo standard (GB50077-2003) for differentvalues of the internal friction angle φ Equation (4) of themodified Coulomb theory is not shown in Figure 2 in thatthe wall friction angle δ needs to be known

From Figure 2 it can be seen that the wall pressurecoefficients all decrease with increasing the internal frictionangle of bulk solids and their relative values are (from biggerto smaller) EN1991-4 ACI313-97 GB50077-2003 the UST(b 0) the UST (b 12) theM-N criterion the UST (b 1)the L-D criterion and the D-P criterion +e European silostandard using the modified static earth pressure coefficientas 11times (1minus sinφ) is the most conservative while theAmerican silo standard using the static earth pressure co-efficient as 1minus sinφ is slightly smaller +e Chinese silostandard using the Rankine active earth pressure coefficient

Advances in Civil Engineering 3

from the M-C criterion expressed as in Equation (3) isconsistent with that of the UST when b 0

Meanwhile the wall pressure coefficients for differentstrength criteria have significant differences due to thedifferent influence of the intermediate stress +e wallpressure coefficient based on the USTwhen b 0 is relativelylarger due to not considering the intermediate stress effectOn the contrary the kDP of the D-P criterion for φle 4222deg isthe smallest due to the large influence of the intermediatestress

4 Comparisons and Discussions

To demonstrate the applicability and differences of the fourtrue triaxial strength criteria to calculate the silo wallpressure when considering different effects of the in-termediate stress the corresponding four wall pressureformulations are used for deep (HDge 15) and squat silos(HDlt 15) respectively +ese formulations are comparedwith several sets of experimental data as well as with theresults from three standards and two theories

Note that the experimental data involved here are allspecific measured values rather than mean ones

41 Deep Silos Liu and Hao [7] Zhang et al [8] Ruiz et al[11] andMunch-Andersen et al [12] carried out model teststo measure the wall pressure distribution of deep silos +eratio of silo height to its diameter is always greater than 15+e geometric data and material properties of the test silosare listed in Table 1

411 Comparisons of the Results from Different CriteriaA total of six sets of experimental data are compared with theresults from six strength criteria as shown in Figure 3 +esesix strength criteria are the D-P criterion the M-N criterionthe L-D criterion and the UST (b 0 12 and 1)

It can be found from Figure 3 that the differences of thewall pressure for deep silos calculated by different strengthcriteria are obvious +e effect of the strength criterion onthe wall pressure results significant +e values of the wallpressure corresponding to six strength criteria are as followsthe UST (b 0)gt the UST (b 12)asymp the M-N criteriongt theUST (b 1)gt the L-D criteriongt the D-P criterion For thethree groups of model tests from Liu and Hao [7] the av-erage ratios of the Ph obtained with the six strength criteriato the experimental data are (from larger to smaller) 121110 107 103 097 and 070 For the model test fromZhang et al [8] the ratios of the Ph obtained with the sixstrength criteria to the experimental data are (from larger tosmaller) 132 121 119 115 109 and 080 For the modeltest from Ruiz et al [11] the ratios of the Ph obtained withthe six strength criteria to the experimental data are (fromlarger to smaller) 141 126 122 117 105 and 061 For themodel test fromMunch-Andersen et al [12] the ratios of thePh obtained with the six strength criteria to the experimentaldata are (from larger to smaller) 153 145 143 140 129and 043

From the above analyses we can conclude that the Ph ofthe L-D criterion agrees best with the experimental data thePh of the UST when b 12 is similar to that of the M-Ncriterion +e Ph using the UST when b 0 (ie the M-Ccriterion not considering the intermediate stress effect) is thelargest on the contrary the Ph of the D-P criterion is thesmallest since the intermediate stress effect is exaggeratedlyconsidered to be the same as theminor principal stress effect

412 Comparisons of the Results from the Standards+e six sets of experimental data for deep silos are once againcompared with the results from the European Americanand Chinese silo standards and the UST (b 0) in which theintermediate stress effect is null as well as the D-P criterionin which the effect of the intermediate stress is the greatestas shown in Figure 4

Figure 4 presents the changes of the wall pressure inmagnitude from three standards and two strength criteriaEN1991-4gtACI313-97gtGB50077-2003 the UST (b 0)gt the D-P criterion For the three groups of model tests fromLiu and Hao [7] the average ratios of the Ph calculated by thethree standards and the two strength criteria to the exper-imental data are (from larger to smaller) 170 161 121 121and 070 For the model test from Zhang et al [8] the ratiosof the Ph calculated by the three standards and the twostrength criteria to the experimental data are (from larger tosmaller) 178 170 132 132 and 080 For the model testfrom Ruiz et al [11] the ratios of the Ph calculated by thethree standards and the two strength criteria to the exper-imental data are (from larger to smaller) 222 205 141 141and 061 For the model test from Munch-Andersen et al[12] the ratios of the Ph calculated by the three standardsand the two strength criteria to the experimental data are(from larger to smaller) 176 173 153 153 and 043

From the above results we find that the three standardsare all more conservative than the strength criterion con-sidering the effect of the intermediate stress (ie the D-P

10 15 20 25 30 35 40 4500

02

04

06

08

10W

all p

ress

ure c

oeffi

cien

t k

EN1991-4ACI313-97UST (b = 0)(GB50077-2003)UST (b = 12)

M-NUST (b = 1)L-DD-P

Internal friction angle φ (deg)

Figure 2 Comparisons of the wall pressure coefficient


criterion) +e results of the UST (b 0 ie the M-C cri-terion) are consistent with those of the Chinese silo stan-dard +e experimental data are basically distributed in theregion between the results from the UST (b 0) and the D-Pcriterion All this means that overall the effect of the in-termediate stress should be considered accurately to cal-culate the wall pressure for deep silos

42 Squat Silos Yuan [13] carried out several field tests tomeasure the wall pressure distribution of squat silos (No 4No 7 and No 8) from Xuzhou National Grain Reserve

Chen [14] carried out similar field tests to measure the wallpressure distribution of squat silos (No 4) from HenanNational Grain Reserve In this case the stored height h ofbulk solids is considered to be the silo height H and thenhDlt 15 +e geometric data and material properties arepresented in Table 2

Due to similar variations of the wall pressure for dif-ferent stored heights only some field experimental data fromYuan [13] (No 4 and No 7 silos for the first and secondgroups as well as No 8 silo for the first group) and fromChen [14] (No 4 silo for the first group) are adopted to makethe following comparisons

00 01 02 03 04 05 0600

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Pa)

Depth from material top to calculation section s (m)

UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

(a)

Wal

l pre

ssur

e P h (k

Pa)

00 01 02 03 04 05 06Depth from material top to calculation section s (m)

UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

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(b)

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Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

00

07

14

21

28

35

(c)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (8)

00 02 04 06 08 10 1200

15

30

45

60

75

Wal

l pre

ssur

e P h (k

Pa)

(d)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (11)

00 05 10 15 200

2

4

6

8

Wal

l pre

ssur

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Pa)

(e)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (12)

00 05 10 15 20 25 30 35 400

2

4

6

8

Wal

l pre

ssur

e P h (k

Pa)

(f )

Figure 3 Comparisons of the results from six strength criteria with experimental data for deep silos (a) Experimental data with coal fromLiu and Hao [7] (b) Experimental data with wheat from Liu and Hao [7] (c) Experimental data with dry sand from Liu and Hao [7] (d)Experimental data with standard sand from Zhang et al [8] (e) Experimental data with wheat from Ruiz et al [11] (f ) Experimental datawith dry sand from Munch-Andersen et al [12]

Table 1 Geometrical data and material properties of deep silos

References Model materials H (mm) D (mm) HD Bulk solids c (kNm3) φ (deg) μ

Liu and Hao [7] Plexiglass 600 300 20Coal 10 33 045Wheat 8 28 04

Dry sand 16 325 043Zhang et al [8] Plexiglass 1200 500 24 Standard sand 174 311 043Ruiz et al [11] Stainless steel 2000 1000 20 Wheat 838 3422 02Munch-Andersen et al [12] Epoxy 5000 700 714 Dry sand 15 40 067


421 Comparisons of the Results from Different CriteriaFigure 5 compares the six sets of experimental data with theresults from six strength criteria for squat silos For bothcone piles and flat piles the differences of the wall pressurefor squat silos using different strength criteria are found tobe significant +e values of the wall pressure correspondingto the six strength criteria are the UST (b 0)gt the UST(b 12)asymp the M-N criteriongt the UST (b 1)gt the L-Dcriteriongt the D-P criterion+is scale is the same as that fordeep silos

For all six groups of field tests the average ratios of the Phusing these six strength criteria to the experimental data are(from larger to smaller) 121 109 107 101 100 and 082It is demonstrated that the Ph based on the UST when b 0(ie the M-C criterion) is the largest the Ph based on theUST when b 12 is also close to that based on the M-Ncriterion the Ph using the UST when b 1 is close to thatusing the L-D criterion Furthermore the Ph on the basis ofthe L-D criterion is shown to be very consistent with theexperimental data for the average ratio being 100

422 Comparisons of the Results from the eories Forsquat silos all standards make use of the same formulation

expressed in Equation (2) to calculate the wall pressure+ere are two classical theories which have been adopted bydifferent standards to determine the wall pressure co-efficient k [32 33] One is the Rankine theory +e other isthe modified Coulomb theory

Figure 6 presents the six sets of experimental data forsquat silos that are now once again compared with the Phcalculated by the Rankine theory the modified Coulombtheory and the UST (b 0) in which the intermediate stresseffect is null as well as the D-P criterion in which the in-termediate stress effect is the greatest+e Ph calculated by thetwo theories and the two strength criteria are as follows (fromlarger to smaller) the modified Coulomb theorygt the Ran-kine theory the UST (b 0)gt the D-P criterion For the sixgroups of field tests the average ratios of the Ph using the twotheories and the two strength criteria to the experimental dataare (from larger to smaller) 156 121 121 and 082

From the above results it is demonstrated that theRankine theory and the modified Coulomb theory are moreconservative than the strength criterion considering theintermediate stress effect (ie the D-P criterion) +e resultsof the UST when b 0 (ie the M-C criterion) are the sameas those of the Rankine theory +e experimental data arealso generally located in the region between the results from

00 01 02 03 04 05 0600

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15

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30


Wal

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Pa)

EN1991-4ACI313-97GB50077-2003

UST (b = 0)D-PTest (7)

(a)W

all p

ress

ure P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00

05

10

15

20

25

(b)

Wal

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EN1991-4ACI313-97GB50077-2003


0

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(c)

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Pa)


EN1991-4ACI313-97GB50077-2003


00 02 04 06 08 10 120

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EN1991-4ACI313-97GB50077-2003


00 05 10 15 200

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all p

ress

ure P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 05 10 15 20 25 30 35 400

2

4

6

8

10

(f )

Figure 4 Comparisons of the results from three standards and two strength criteria with experimental data for deep silos (a) Experimentaldata with coal from Liu and Hao [7] (b) Experimental data with wheat from Liu and Hao [7] (c) Experimental data with dry sand from Liuand Hao [7] (d) Experimental data with standard sand from Zhang et al [8] (e) Experimental data with wheat from Ruiz et al [11] (f )Experimental data with dry sand from Munch-Andersen et al [12]


the UST (b 0) and the D-P criterion+is ordering is a clearindication that the wall pressure for squat silos is not ac-curately calculated if the intermediate stress effect is notconsidered rationally

5 Conclusions

+rough this study some primary conclusions can be drawnas follows

(1) Based on the principles and basic assumptions of silowall pressure four novel wall pressure coefficientsare presented for the D-P criterion the M-N crite-rion the L-D criterion and the UST to consider theeffect of the intermediate stress For the D-P crite-rion the internal friction angle of bulk solids cannotbe greater than 4222deg whereas the other threestrength criteria are not restricted +ese four co-efficients are readily used to predict the wall pressure

Table 2 Geometrical data and material properties of squat silos

References Test location Silo number h (m) Pile type D (m) Bulk solids c (kNm3) φ (deg) δ (deg)

Yuan [13] Xuzhou National Grain Reserve

No 4 1343 Cone

15 Wheat 788 25 218No 4 1371 FlatNo 7 993 ConeNo 7 1377 FlatNo 8 635 Cone

Chen [14] Henan National Grain Reserve No 4 730 Cone 26 Wheat 822 25 218

0 2 4 6 8 10 12 140

9

18

27

36

45


Wal

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Pa)

UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

(a)

Wal

l pre

ssur

e P h (k

Pa)

0 2 4 6 8 10 12 14Depth from material top to calculation section s (m)

UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0

9

18

27

36

45

(b)

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UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 2 4 6 8 100

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(c)

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0 2 4 6 8 10 12 140

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UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

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UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (14)

0 2 4 6 80

5

10

15

20

25

(f )

Figure 5 Comparisons of the results from six strength criteria with experimental data for squat silos (modified from Sun et al [37]) (a)Experimental data of No 4 silo for the first group from Yuan [13] (cone pile) (b) Experimental data of No 4 silo for the second group fromYuan [13] (flat pile) (c) Experimental data of No 7 silo for the first group from Yuan [13] (cone pile) (d) Experimental data of No 7 silo forthe second group from Yuan [13] (flat pile) (e) Experimental data of No 8 silo for the first group from Yuan [13] (flat pile) (f ) Experimentaldata of No 4 silo for the first group from Chen [14] (cone pile)


for both deep and squat silos and their predictionsare compared with several sets of experimental dataand the results from three national standards as wellas two theories

(2) For the wall pressure of deep silos the Europeanstandard is the most conservative one followed bythe American one +e results of the Chinese stan-dard are the same as those of the USTwhen b 0 theresults of the USTwhen b 12 are close to that of theM-N criterion For the wall pressure of squat silosthe modified Coulomb theory is the most conser-vative +e results of the Rankine theory are equal tothose of the UST when b 0 the results of the USTwhen b 12 are also close to that of the M-N cri-terion the results from the UST when b 1 and theL-D criterion are nearly equivalent

(3) +e effect of strength criterion on the wall pressurefor both deep and squat silos is found to be verysignificant It is indicated that the intermediate stresseffect is in fact dealt with distinctly by the differentstrength criteria +e wall pressure using the UST

when b 0 is overestimated since it does not considerthe intermediate stress effect On the contrary thewall pressure based on the D-P criterion is under-estimated due to the overestimation on this criterionof the effect of the intermediate stress Overall thewall pressure generated by the L-D criterion agreeswell with the experimental data due to rationalconsideration that it makes use of the intermediatestress effect Accordingly the L-D criterion is rec-ommended to be adopted to calculate the silo wallpressure

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

0 2 4 6 8 10 12 140

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Wal

l pre

ssur

e P h (k

Pa)

CoulombRankineUST (b = 0)

D-PTest (13)

(a)W

all p

ress

ure P h (k

Pa)



D-PTest (13)

0 2 4 6 8 10 12 140

10

20

30

40

50

60

(b)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 2 4 6 8 100

6

12

18

24

30

36

42

(c)

0

10

20

30

40

50

60

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

(d)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

25

(e)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (14)

0 2 4 6 80

5

10

15

20

25

30

(f )

Figure 6 Comparisons of the results from two theories and two strength criteria with experimental data for squat silos (modified from Sunet al [37]) (a) Experimental data of No 4 silo for the first group from Yuan [13] (cone pile) (b) Experimental data of No 4 silo for thesecond group from Yuan [13] (flat pile) (c) Experimental data of No 7 silo for the first group from Yuan [13] (cone pile) (d) Experimentaldata of No 7 silo for the second group from Yuan [13] (flat pile) (e) Experimental data of No 8 silo for the first group from Yuan [13] (flatpile) (f ) Experimental data of No 4 silo for the first group from Chen [14] (cone pile)


Acknowledgments

+e financial support provided by the Natural ScienceFoundation of China (Grant nos 51708035 and 51878056)the Fundamental Research Fund for the Central Universities(Grant nos 310828173402 310828171012 300102288109and 310828171003) and the Research Fund for the DoctoralProgram of Higher Education (Grant no 20110205130001)is gratefully acknowledged

References

[1] H A Janssen ldquoVersuch uber getreidedruck in sillozellenrdquoZeitschrift des Vereins Deutscher Ingenieure vol 39 no 35pp 1045ndash1049 1895

[2] M L Reimbert and A M Reimbert ldquoSilos theory andpracticerdquo Journal of ought vol 5 no 3 pp 141ndash156 1976

[3] G Abdelsayed and F Monasa ldquoCold-formed steel farmstructures part I grain binsrdquo Journal of Structural Engi-neering vol 111 no 10 pp 2065ndash2089 1985

[4] J Y Ooi Bulk solid behavior and silo wall pressure PhDthesis University of Sydney Sydney Australia 1990

[5] Z Zhong J Y Ooi and J M Rotter ldquo+e sensitivity of siloflow and wall stresses to filling methodrdquo Engineering Struc-tures vol 23 no 7 pp 756ndash767 2001

[6] J B Fu Lateral wall pressure analysis and three-dimensionalfoundation consolidation analysis of large diameter silo PhDthesis Dalian University of Technology Dalian China 2012

[7] D H Liu and J P Hao ldquoStudy on wall pressure of RC silordquoJournal of Building Structures vol 16 no 5 pp 57ndash63 1995

[8] D Y Zhang Q K Xu S M Wang and X P LiangldquoSimulation and experimental validation of silo wall pressureduring dischargerdquo Transactions of the Chinese Society ofAgricultural Engineering vol 33 no 5 pp 272ndash278 2017

[9] C J Brown E H Lahlouh and J M Rotter ldquoExperiment ona square planform steel silordquo Chemical Engineering Sciencevol 55 no 20 pp 4399ndash4413 2000

[10] A Couto A Ruiz and P J Aguado ldquoDesign and in-strumentation of a mid-size test station for measuring staticand dynamic pressures in silos under different conditions-part I descriptionrdquo Computers and Electronics in Agriculturevol 85 pp 164ndash173 2012

[11] A Ruiz A Couto and P J Aguado ldquoDesign and in-strumentation of a mid-size test station for measuring staticand dynamic pressures in silos under different conditions-part II construction and validationrdquo Computers and Elec-tronics in Agriculture vol 85 pp 174ndash187 2012

[12] J Munch-Andersen V Askegaard and A Brink Silo ModelTests with Sand SBI Bulletins No 91 Danish Building Re-search Institute Hoslashrsholm Denmark 1992

[13] F Yuan Analysis of bulk-solid pressure on curve walls and itsengineering application PhD thesis Dalian University ofTechnology Dalian China 2004

[14] C B Chen Bulk-solid pressures on silosrsquo walls PhD thesisHefei University of Technology Hefei China 2006

[15] J Y Ooi and J M Rotter ldquoWall pressure in squat steel silofrom simple finite element analysisrdquo Computers and Struc-tures vol 37 no 4 pp 361ndash374 1990

[16] J F Chen J M Rotter and J Y Ooi ldquoA review of numericalprediction methods for silo wall pressuresrdquo Advances inStructural Engineering vol 2 no 2 pp 119ndash135 1999

[17] M A Martinez I Alfaro and M Doblare ldquoSimulation ofaxisymmetric discharging in metallic silos Analysis of the

induced pressure distribution and comparison with differentstandardsrdquo Engineering Structure vol 24 no 12 pp 1561ndash1574 2002

[18] Y Wang Y Lu and J Y Ooi ldquoFinite element modeling ofwall pressures in a cylindrical silo with conical hopper usingan Arbitrary Lagrangian-Eulerian formulationrdquo PowderTechnology vol 257 no 5 pp 181ndash190 2014

[19] Y Wang Y Lu and J Y Ooi ldquoA numerical study of wallpressure and granular flow in a flat-bottomed silordquo PowderTechnology vol 282 no 24 pp 43ndash54 2015

[20] J Horabik P Parafiniuk and M Molenda ldquoExperiments anddiscrete element method simulation of distribution of staticload of grain bedding at bottom of shallow model silordquoBiosystems Engineering vol 149 pp 60ndash71 2016

[21] F Ayuga Some Unresolved Problems in the Design of SteelCylindrical Silos CRC Press-Taylor Francis Group BocaRaton FL USA 2008

[22] A Dogangun Z Karaca A Durmus and H Sezen ldquoCause ofdamage and failures in silo structuresrdquo Journal of Performanceof Constructed Facilities vol 23 no 2 pp 65ndash71 2009

[23] A Jansseune W D Corte and J Belis ldquoElastic failure oflocally supported silos with U-shaped longitudinal stiffenersrdquoKSCE Journal of Civil Engineering vol 19 no 4 pp 1041ndash1049 2015

[24] P C Arnold A G Mclean and A W Robert Bulk SolidsStorage Flow and Handling Tunra Bulk Solids HandlingResearch Associates University of Newcastle CallaghanNSW Australia 1980

[25] A G Bishara Interaction of Bin and Stored Bulk Solids Designof Steel Bins for the Storage of Bulk Solids University ofSydney Sydney Australia 1895

[26] E H Gaylord and C N Gaylord Design of Steel Bins forStorage of Bulk Solids Prentice Hall Englewood Cliffs NJUSA 1984

[27] GB50077-2003 Code for Design of Reinforced Concrete SilosNational Standards Compilation Group of Peoplesrsquo Republicof China Beijing China 2003

[28] ACI313-97 Standard Practice for Design and Construction ofConcrete Silos and Stacking Tubes for Storing Granular Ma-terials American Concrete Institute Indianapolis MI USA1997

[29] EN1998-4-2007 Eurocode 8 Design of Structure for Earth-quake Resistance Part 4 Silos Tanks and Pipelines EuropeanCommittee for Standardization 2007

[30] DIN1055 Design Loads for Buildings Loads in Silo BinsDeutsches Institut fur Normung Berlin Germany 1987

[31] AS3774-1996 Loads on Bulk Solids Containers StandardAssociation of Australia Sydney Australia 1996

[32] W J M Rankine ldquoOn the stability of loose earthrdquo Philo-sophical Transactions of the Royal Society of London vol 147pp 9ndash27 1857

[33] C A Coulomb Essai sur une Application des Regles deMaximis et Minimis a Quelques Problems de Statique Relatifsa la Architecture 1973

[34] S Q Xu and M H Yu ldquo+e effect of the intermediateprincipal stress on the ground response of the circularopenings in rock massrdquo Rock Mechanics and Rock Engi-neering vol 39 no 2 pp 169ndash181 2006

[35] S S Sun J H Zhao C G Zhang and Y Cui ldquoWall pressureof large squat silos based on the unified strength theoryrdquoEngineering Mechanics vol 30 no 5 pp 244ndash249 2013

[36] S S Sun J H Zhao C G Zhang and K Yang ldquoNew solutionfor lateral pressure of silos and bunkersrdquo Journal of GuangxiUniversity vol 43 no 1 pp 168ndash177 2018


[37] S S Sun J H Zhao and C G Zhang ldquoLateral pressurecalculation for silos considering intermediate principal stresseffectrdquo Journal of Architecture and Civil Engineering vol 35no 3 pp 71ndash78 2018

[38] J L Shang Y L Gui and Z Y Zhao ldquoBroad-spectrumfracture toughness of an anisotropic sandstone under mixed-mode loadingrdquo eoretical and Applied Fracture Mechanicsvol 96 pp 556ndash575 2018

[39] L R Alejano ldquoDrucker-Prager criterionrdquo Rock Mechanicsand Rock Engineering vol 45 no 6 pp 995ndash999 2012

[40] H Jiang and Y L Xie ldquoA note on the Mohr-Coulomb andDrucker-Prager strength criterionrdquo Mechanics ResearchCommunication vol 38 no 4 pp 309ndash314 2011

[41] M C Liu Y F Gao and H L Liu ldquoA nonlinear Drucker-Prager and Matsuoka-Nakai unified failure criterion forgeomaterials with separated stress invariantrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 50 no 2pp 1ndash10 2012

[42] C G Zhang Q Yan and C L Zhang ldquoA unified solution ofcritical filling height for embankment considering in-termediate principal stress and its comparisonsrdquo ChineseJournal of Rock Mechanics and Engineering vol 35 no 7pp 1466ndash1473 2016

[43] L Q Guo Q P Cai and X Q Peng ldquoEffect of strengthcriterion on design of strip coal pillarrdquo Rock and Soil Me-chanics vol 35 no 3 pp 777ndash782 2014

[44] H Jiang ldquoExpressing strength criterion in principal stressplane base on equivalent Mohr-Coulomb friction anglerdquoJournal of Central South University (Science and Technology)vol 43 no 8 pp 3216ndash3221 2012

[45] M H Yu Twin Shear eory and Its Application SciencePress Beijing China 1998


International Journal of

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Active and Passive Electronic Components

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Shock and Vibration


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Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

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Submit your manuscripts atwwwhindawicom

In this study the D-P criterion the M-N criterion theL-D criterion and the UST are adopted to derive four novelwall pressure coefficients in quasiplane strain to consider theintermediate stress effect +e applicability condition forthese coefficients is also provided Furthermore these co-efficients are used to calculate the wall pressure for deep andsquat silos Finally the calculated results are compared withseveral sets of experimental data and different standards ortheories

2 Principles and Basic Assumptions

21 Principles +e distribution of wall pressure depends onthe silo type According to the load characteristics silos areusually divided into deep silos and squat silos +ese twotypes of silos have different calculation methods [27]

For a deep silo (HDge 15 where H is the silo height andD is the silo diameter) as shown in Figure 1 the wallpressure Ph on the silo wall [6] is written as

Ph Chcρ 1minus eminusμksρ( 1113857

μ (1)

where Ch is the correction factor related to the calculatedheight and can be determined by GB50077-2003 [27] c is thegravity density of bulk solids ρ is the hydraulic radius of thenet horizontal cross section μ is the friction coefficientbetween the silo wall and bulk solids k is the wall pressurecoefficient and s is the depth from the material top or fromthe center of cone gravity to the calculation section

For a squat silo (HDlt 15) the wall pressure Ph [6] isexpressed as

Ph kcs (2)

When the Rankine theory is used the wall pressurecoefficient k is

k 1minus sinφ1 + sinφ

(3)

When the modified Coulomb theory is used the wallpressure coefficient k is

k cos2 φ

1 +sin(φ + δ)cos δ

1113968 (4)

where φ is the internal friction angle of bulk solids and δ isthe wall friction angle

It can be seen from Equations (1) and (2) that the key tocalculate the wall pressure for both deep and squat silos ishow to rationally determine the wall pressure coefficient kIn addition bulk solids are similar to granular materials+erefore the wall pressure coefficient k in the quasiplanestrain state can be determined from the analogy with thelateral earth pressure for sandy soils acting on retainingwalls

22 Basic Assumptions

(1) +e calculation of silo wall pressure can be regardedas a quasiplane strain problem [6] +e intermediate

stress in bulk solids could be considered approxi-mately as the intermediate principal stress σ2 equal tothe average value of the maximum principal stress σ1and the minor principal stress σ3 without significanterror [34ndash38] +is correlation is written as

σ2 12

σ1 + σ3( 1113857 (5)

(2) Bulk solids can be analogous to sandy soils +at is tosay the cohesion c of bulk solids is negligibleie c 0

(3) +e compressive stress is assumed to be positive andthe tensile stress is thus negative

3 Novel Wall Pressure Coefficients

31 D-P Criterion +e D-P criterion [39 40] known as thegeneralized Mises criterion makes the assumption that theintermediate principal stress and the minor principal stresshave an identical effect on the material strength +e D-Pcriterion is expressed as

J2

1113968

2 sinφ3

radic(3minus sinφ)

I1 +6c cosφ

3

radic(3minus sinφ)

(6)

where J2 is the second invariant of stress deviation and I1 isthe first invariant of stress tensor

J2 16

σ1 minus σ2( 11138572

+ σ2 minus σ3( 11138572

+ σ3 minus σ1( 11138572

1113960 1113961 (7)

I1 σ1 + σ2 + σ3 (8)

Substituting Equations (5) (7) and (8) into Equation (6)with c 0 the wall pressure coefficient based on the D-Pcriterion (ie kDP) is obtained as

kDP σ3σ1

3

3

radicminus(6 +

3

radic)sinφ

33

radic+(6 +

3

radic)sinφ

(9)

32M-NCriterion +eM-N criterion [41 42] is suitable forcohesionless materials and overcomes the singularity of theM-C criterion in a deviatoric plane as well as the condition of

Storing surface(f lat pile)

Storing surface(cone pile)

Center ofcone gravity

Calculationsection

D

ssH

PhPh

Figure 1 Mechanical model of silo wall pressure (no-funnel)(modified from Sun et al [37])



I1I2

I3 9 + 8 tan2 φ (10)


I2 σ1σ2 + σ2σ3 + σ3σ1 (11)

I3 σ1σ2σ3 (12)


kMN σ3σ1

83tan2 φ + 1minus

43tanφ

4 tan2 φ + 31113969

(13)


I31I3


(1minus sinφ) (14)


kLD σ3σ1

1 +4 tanφ


minus


1113969

1113877

(15)



2c cosφ1 + sinφ


2minusσ1 minus σ3

2sinφ

(16a)




2minusσ1 minus σ3

2sinφ

(16b)



kUST σ3σ1


2 + b +(2 + 3b) sinφ (17)




















10 15 20 25 30 35 40 4500

02

04

06

08

10W

all p

ress

ure c

oeffi

cien

t k










00 01 02 03 04 05 0600

05

10

15

20

25

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

(a)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

00

05

10

15

20

(b)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

00

07

14

21

28

35

(c)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (8)

00 02 04 06 08 10 1200

15

30

45

60

75

Wal

l pre

ssur

e P h (k

Pa)

(d)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (11)

00 05 10 15 200

2

4

6

8

Wal

l pre

ssur

e P h (k

Pa)

(e)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (12)

00 05 10 15 20 25 30 35 400

2

4

6

8

Wal

l pre

ssur

e P h (k

Pa)

(f )













00 01 02 03 04 05 0600

05

10

15

20

25

30


Wal

l pre

ssur

e P h (k

Pa)

EN1991-4ACI313-97GB50077-2003


(a)W

all p

ress

ure P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00

05

10

15

20

25

(b)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


0

1

2

3

4

5

(c)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 02 04 06 08 10 120

2

4

6

8

10

(d)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 05 10 15 200

2

4

6

8

10

12

(e)W

all p

ress

ure P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 05 10 15 20 25 30 35 400

2

4

6

8

10

(f )




5 Conclusions






No 4 1343 Cone



0 2 4 6 8 10 12 140

9

18

27

36

45


Wal

l pre

ssur

e P h (k

Pa)

UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

(a)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0

9

18

27

36

45

(b)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 2 4 6 8 100

4

8

12

16

20

24

28

32

(c)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 2 4 6 8 10 12 140

9

18

27

36

45

(d)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

(e)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (14)

0 2 4 6 80

5

10

15

20

25

(f )







Data Availability




0 2 4 6 8 10 12 140

10

20

30

40

50

60


Wal

l pre

ssur

e P h (k

Pa)


D-PTest (13)

(a)W

all p

ress

ure P h (k

Pa)



D-PTest (13)

0 2 4 6 8 10 12 140

10

20

30

40

50

60

(b)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 2 4 6 8 100

6

12

18

24

30

36

42

(c)

0

10

20

30

40

50

60

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

(d)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

25

(e)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (14)

0 2 4 6 80

5

10

15

20

25

30

(f )



Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



I1I2

I3 9 + 8 tan2 φ (10)


I2 σ1σ2 + σ2σ3 + σ3σ1 (11)

I3 σ1σ2σ3 (12)


kMN σ3σ1

83tan2 φ + 1minus

43tanφ

4 tan2 φ + 31113969

(13)


I31I3


(1minus sinφ) (14)


kLD σ3σ1

1 +4 tanφ


minus


1113969

1113877

(15)



2c cosφ1 + sinφ


2minusσ1 minus σ3

2sinφ

(16a)




2minusσ1 minus σ3

2sinφ

(16b)



kUST σ3σ1


2 + b +(2 + 3b) sinφ (17)




















10 15 20 25 30 35 40 4500

02

04

06

08

10W

all p

ress

ure c

oeffi

cien

t k










00 01 02 03 04 05 0600

05

10

15

20

25

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

(a)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

00

05

10

15

20

(b)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

00

07

14

21

28

35

(c)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (8)

00 02 04 06 08 10 1200

15

30

45

60

75

Wal

l pre

ssur

e P h (k

Pa)

(d)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (11)

00 05 10 15 200

2

4

6

8

Wal

l pre

ssur

e P h (k

Pa)

(e)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (12)

00 05 10 15 20 25 30 35 400

2

4

6

8

Wal

l pre

ssur

e P h (k

Pa)

(f )













00 01 02 03 04 05 0600

05

10

15

20

25

30


Wal

l pre

ssur

e P h (k

Pa)

EN1991-4ACI313-97GB50077-2003


(a)W

all p

ress

ure P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00

05

10

15

20

25

(b)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


0

1

2

3

4

5

(c)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 02 04 06 08 10 120

2

4

6

8

10

(d)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 05 10 15 200

2

4

6

8

10

12

(e)W

all p

ress

ure P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 05 10 15 20 25 30 35 400

2

4

6

8

10

(f )




5 Conclusions






No 4 1343 Cone



0 2 4 6 8 10 12 140

9

18

27

36

45


Wal

l pre

ssur

e P h (k

Pa)

UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

(a)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0

9

18

27

36

45

(b)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 2 4 6 8 100

4

8

12

16

20

24

28

32

(c)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 2 4 6 8 10 12 140

9

18

27

36

45

(d)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

(e)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (14)

0 2 4 6 80

5

10

15

20

25

(f )







Data Availability




0 2 4 6 8 10 12 140

10

20

30

40

50

60


Wal

l pre

ssur

e P h (k

Pa)


D-PTest (13)

(a)W

all p

ress

ure P h (k

Pa)



D-PTest (13)

0 2 4 6 8 10 12 140

10

20

30

40

50

60

(b)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 2 4 6 8 100

6

12

18

24

30

36

42

(c)

0

10

20

30

40

50

60

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

(d)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

25

(e)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (14)

0 2 4 6 80

5

10

15

20

25

30

(f )



Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














10 15 20 25 30 35 40 4500

02

04

06

08

10W

all p

ress

ure c

oeffi

cien

t k










00 01 02 03 04 05 0600

05

10

15

20

25

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

(a)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

00

05

10

15

20

(b)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

00

07

14

21

28

35

(c)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (8)

00 02 04 06 08 10 1200

15

30

45

60

75

Wal

l pre

ssur

e P h (k

Pa)

(d)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (11)

00 05 10 15 200

2

4

6

8

Wal

l pre

ssur

e P h (k

Pa)

(e)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (12)

00 05 10 15 20 25 30 35 400

2

4

6

8

Wal

l pre

ssur

e P h (k

Pa)

(f )













00 01 02 03 04 05 0600

05

10

15

20

25

30


Wal

l pre

ssur

e P h (k

Pa)

EN1991-4ACI313-97GB50077-2003


(a)W

all p

ress

ure P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00

05

10

15

20

25

(b)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


0

1

2

3

4

5

(c)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 02 04 06 08 10 120

2

4

6

8

10

(d)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 05 10 15 200

2

4

6

8

10

12

(e)W

all p

ress

ure P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 05 10 15 20 25 30 35 400

2

4

6

8

10

(f )




5 Conclusions






No 4 1343 Cone



0 2 4 6 8 10 12 140

9

18

27

36

45


Wal

l pre

ssur

e P h (k

Pa)

UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

(a)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0

9

18

27

36

45

(b)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 2 4 6 8 100

4

8

12

16

20

24

28

32

(c)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 2 4 6 8 10 12 140

9

18

27

36

45

(d)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

(e)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (14)

0 2 4 6 80

5

10

15

20

25

(f )







Data Availability




0 2 4 6 8 10 12 140

10

20

30

40

50

60


Wal

l pre

ssur

e P h (k

Pa)


D-PTest (13)

(a)W

all p

ress

ure P h (k

Pa)



D-PTest (13)

0 2 4 6 8 10 12 140

10

20

30

40

50

60

(b)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 2 4 6 8 100

6

12

18

24

30

36

42

(c)

0

10

20

30

40

50

60

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

(d)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

25

(e)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (14)

0 2 4 6 80

5

10

15

20

25

30

(f )



Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






00 01 02 03 04 05 0600

05

10

15

20

25

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

(a)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

00

05

10

15

20

(b)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (7)

00

07

14

21

28

35

(c)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (8)

00 02 04 06 08 10 1200

15

30

45

60

75

Wal

l pre

ssur

e P h (k

Pa)

(d)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (11)

00 05 10 15 200

2

4

6

8

Wal

l pre

ssur

e P h (k

Pa)

(e)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (12)

00 05 10 15 20 25 30 35 400

2

4

6

8

Wal

l pre

ssur

e P h (k

Pa)

(f )













00 01 02 03 04 05 0600

05

10

15

20

25

30


Wal

l pre

ssur

e P h (k

Pa)

EN1991-4ACI313-97GB50077-2003


(a)W

all p

ress

ure P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00

05

10

15

20

25

(b)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


0

1

2

3

4

5

(c)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 02 04 06 08 10 120

2

4

6

8

10

(d)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 05 10 15 200

2

4

6

8

10

12

(e)W

all p

ress

ure P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 05 10 15 20 25 30 35 400

2

4

6

8

10

(f )




5 Conclusions






No 4 1343 Cone



0 2 4 6 8 10 12 140

9

18

27

36

45


Wal

l pre

ssur

e P h (k

Pa)

UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

(a)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0

9

18

27

36

45

(b)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 2 4 6 8 100

4

8

12

16

20

24

28

32

(c)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 2 4 6 8 10 12 140

9

18

27

36

45

(d)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

(e)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (14)

0 2 4 6 80

5

10

15

20

25

(f )







Data Availability




0 2 4 6 8 10 12 140

10

20

30

40

50

60


Wal

l pre

ssur

e P h (k

Pa)


D-PTest (13)

(a)W

all p

ress

ure P h (k

Pa)



D-PTest (13)

0 2 4 6 8 10 12 140

10

20

30

40

50

60

(b)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 2 4 6 8 100

6

12

18

24

30

36

42

(c)

0

10

20

30

40

50

60

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

(d)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

25

(e)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (14)

0 2 4 6 80

5

10

15

20

25

30

(f )



Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








00 01 02 03 04 05 0600

05

10

15

20

25

30


Wal

l pre

ssur

e P h (k

Pa)

EN1991-4ACI313-97GB50077-2003


(a)W

all p

ress

ure P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00

05

10

15

20

25

(b)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


0

1

2

3

4

5

(c)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 02 04 06 08 10 120

2

4

6

8

10

(d)

Wal

l pre

ssur

e P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 05 10 15 200

2

4

6

8

10

12

(e)W

all p

ress

ure P h (k

Pa)


EN1991-4ACI313-97GB50077-2003


00 05 10 15 20 25 30 35 400

2

4

6

8

10

(f )




5 Conclusions






No 4 1343 Cone



0 2 4 6 8 10 12 140

9

18

27

36

45


Wal

l pre

ssur

e P h (k

Pa)

UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

(a)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0

9

18

27

36

45

(b)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 2 4 6 8 100

4

8

12

16

20

24

28

32

(c)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 2 4 6 8 10 12 140

9

18

27

36

45

(d)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

(e)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (14)

0 2 4 6 80

5

10

15

20

25

(f )







Data Availability




0 2 4 6 8 10 12 140

10

20

30

40

50

60


Wal

l pre

ssur

e P h (k

Pa)


D-PTest (13)

(a)W

all p

ress

ure P h (k

Pa)



D-PTest (13)

0 2 4 6 8 10 12 140

10

20

30

40

50

60

(b)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 2 4 6 8 100

6

12

18

24

30

36

42

(c)

0

10

20

30

40

50

60

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

(d)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

25

(e)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (14)

0 2 4 6 80

5

10

15

20

25

30

(f )



Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



5 Conclusions






No 4 1343 Cone



0 2 4 6 8 10 12 140

9

18

27

36

45


Wal

l pre

ssur

e P h (k

Pa)

UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

(a)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0

9

18

27

36

45

(b)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 2 4 6 8 100

4

8

12

16

20

24

28

32

(c)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 2 4 6 8 10 12 140

9

18

27

36

45

(d)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

(e)

Wal

l pre

ssur

e P h (k

Pa)


UST (b = 0)UST (b = 12)M-NUST (b = 1)

L-DD-PTest (14)

0 2 4 6 80

5

10

15

20

25

(f )







Data Availability




0 2 4 6 8 10 12 140

10

20

30

40

50

60


Wal

l pre

ssur

e P h (k

Pa)


D-PTest (13)

(a)W

all p

ress

ure P h (k

Pa)



D-PTest (13)

0 2 4 6 8 10 12 140

10

20

30

40

50

60

(b)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 2 4 6 8 100

6

12

18

24

30

36

42

(c)

0

10

20

30

40

50

60

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

(d)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

25

(e)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (14)

0 2 4 6 80

5

10

15

20

25

30

(f )



Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Data Availability




0 2 4 6 8 10 12 140

10

20

30

40

50

60


Wal

l pre

ssur

e P h (k

Pa)


D-PTest (13)

(a)W

all p

ress

ure P h (k

Pa)



D-PTest (13)

0 2 4 6 8 10 12 140

10

20

30

40

50

60

(b)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 2 4 6 8 100

6

12

18

24

30

36

42

(c)

0

10

20

30

40

50

60

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

(d)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (13)

0 1 2 3 4 5 60

5

10

15

20

25

(e)

Wal

l pre

ssur

e P h (k

Pa)



D-PTest (14)

0 2 4 6 80

5

10

15

20

25

30

(f )



Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Acknowledgments


References



















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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