IntroductionSilos with a substantial capacity in the cement industrymay cause large eccentricities during discharge due totheir individual bottom aeration sections. A large eccen-tricity is classed as when a discharge flow channel is morethan half the radius of a silo from the silo mid-point. Fromdifferent investigations1,2 it is known that horizontal pres-sures in a flow channel are smaller than in the bulk mate-rial outside the flow channel. This results in a reduction inhorizontal pressures in the zone in which the flow chan-nel contacts the wall, compared to the horizontal pres-sure on the remaining wall circumference thatcorresponds with the fill pressures. In the transition fromflow zone to static zone, horizontal pressures even higher than the fill pressure occur due to the load bal-ance. The result is an alternating pressure distributionwhen discharging large capacity silos, which could lead tocritical wall loads in certain cases.Corresponding views are included in thecurrent draft of European SiloStandards prEN 1991-4 and therevised German Silo Standards DIN1055-6, which fundamentally corre-sponds to prEN 1991-4 and will pre-sumably be introduced by the end of2004. Silos with bottom aeration aregenerally viewed as ‘slender’ silos.

Process engineering forsilo dischargingThe largest silos in the cement industryare built with diameters up to 30 m. Typical silos for storage of 20 000 t cement are, for example, 20 m in diameter and 60 m high.Although there are different designvariations by the leading suppliers,large capacity silos with diametersabove 12 m are mainly executed ascentral cone versions. The central conehas a material displacement function,which allows the material in the silo tocome into motion during discharge.

All silos with a central cone(Figure 1) are designed as quasi flatbottom silos, whereby the silo

bottom forms a ring space. This is divided into individualaeration sections that are slightly declined towards theoutlet by approximately 10°. The silo bottom isequipped with so-called fluidslides that have an air-per-meable fabric on the upper side. The aeration air isblown under the fabric in order to fluidise the bulkmaterial on the fabric. The percentage of coverage ofthe silo bottom with fluidslides varies between 35 and50% depending on system and requirements. In orderto ensure problem-free discharge of material, airamounts and aeration pressure must be adjusted toeach other. The air amounts increase roughly linearlyfrom a minimum air amount with the required dis-charge throughputs. As a rule, blowers with 500 mbarpressure are sufficient for aeration.

The silo bottom is aerated section by section, so thatall sections are aerated in a complete cycle. It is insignif-

icant whether two or more sections are con-nected for aeration. Correspondingly,

only the part of the bulk materialabove the actively aerated silo sectionis in motion, and a flow channel formsincreasing upwards (Figure 2), whichcan include almost the entire crosssection, depending on dischargeamount, silo height and aerationtime. Within the flow channel there isa convergent material flow. The gra-dient of flow is illustrated in the fig-ure by the increasing width of theblue and white material elements. Asonly the bulk material above the aer-ated section is in motion, no massflow will occur in the silo. With massflow the entire material in the silowould be in motion uniformly. Due tothe cyclic aeration of the ring zone,one section after another, the dis-charge process in the silo must bestrongly eccentric.

Wall loads duringdischarge with largeeccentricitiesFigure 3 shows the wall loads afterfilling according to prEN 1991-4

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D. Lippold, Peter und Lochner, BeratendeIngenieure für Bauwesen GmbH,Germany, and J. Harder, OneStoneConsulting Group GmbH, Germany,describe the silo aeration for the materialdischarge of large capacity silos in thecement industry and its influence on wall loads.

Figure 1. Silo with central cone for thecement industry.

(2004 version) in a large capacity silowithout displacement cone. The hor-izontal pressure phf increases withthe height according to the Janssenformula3 based on an e-functiontowards the silo bottom, and besidethe diameter, it is dependent on thespecific weight of the bulk material,the wall friction coefficient of bulkmaterial and wall material, as well asthe horizontal pressure ratio.Accordingly, calculation guidelinesexist for the wall friction pwf and thevertical load pvft in the depth z. Forthe discharge of silos with largeeccentricities, design loads are givenin the prEN 1991-4 for the case thatthe discharge eccentricity eo exceedsthe critical value of e o,cr = 0.25 dc,with dc as the silo diameter. Twocases were differentiated dependingon silo size (Figure 4):� ‘Assessment class 3’ (general

process for silos with a fill capaci-ty greater than 1000 t): if the sizeof a flow channel cannot be pre-dicted from the discharge system,calculations must be implement-ed with different approaches forthe diameter of the flow channel.This allows the horizontal pres-sure within and outside of theflow channel and the associatedcircumferential angle θc for thecontact zone of the flow channelat the wall for any case to bedetermined.

� ‘Assessment class 2’ (generalprocess only for silos with a fillcapacity of less than 1000 t): Theflow channel contacts the wallwith a circumferential angle θc of35° and the horizontal dischargepressure in the flow zone can be

set with phce = 0 and outside the flowzone with phse = phf as well as phae = 2phf. This view is simplified and theresults are on the safe side; the appli-cation of general processes forassessment class 3 remains optional.To allow a better prediction of thesize of a flow channel for largecapacity silos in the cement industry,in the following, an attempt is madeto give a qualitative estimation uponthe formation of flow channels.

Formation of flow channelsFigure 5 shows the flow channel for-mation with large eccentricities in acement silo, where a lower andupper flow channel part have to beseparated. While the upper part isonly formed by the gradient of theslope at the surface of the materialwith practically no influence on thehorizontal pressures, the lower partis formed by the flow within thematerial, because of the bottom aer-ation. The momentary aerated silosection can be located at the righthand side. The flow channel can bedifferentiated by a slightly darkercolour than the rest of the material.

As the momentary flow channel hasno contact with the silo wall, the cir-cumferential angle θc = 0. Since θc isdependent on the silo height, for silodimensions it would be useful todetermine θc approximately at theheight of the cone tip and not at thematerial surface.

Figure 6 schematically shows theflow channel formation for three dif-ferent times. At the initial aeration,only the material close to the outletbecomes fluidised and a flow channel

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Figure 2. Flow channel during eccentric discharge.

Figure 3. Filling loads in a silo.

Figures 4a and b. Influencing variables during eccentric discharge. Left: Flow channel geometry and right: pressures.

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is formed where θc = 0 (t1). With ongoing aeration theflow length for the bulk material along the fluidslidesincreases, and also the size of the flow chan-nel increases until the first material at thesilo wall becomes fluidised. This meansthat the material at the silo wallcomes into motion. θc becomes > 0(t2). When all the material abovethe aeration section is in motion(t3), with longer aeration timethe flow channel size and θc willfurther increase until a maximumθc,limit is reached. The circumferen-tial angle θc and maximum θc,limit

are proportional to the size of theaeration section and the area onwhich the bulk material is in motion.Correspondingly, for a section number of16, for example, the circumferentialangle θc is at least > 22.5° (360°/16)when the bulk material above it iscompletely in motion.

It can be assumed, that not only the size of an aera-tion section, but also the arrangement of the fluidslidesystem and the flow control have an influence on theflow channel formation, as there are radial and tangen-tial fluidslide arrangements. Thus, in practice, the cir-cumferential angle θc is influenced by a number ofparameters, including the aeration system, the numberof aeration sections, the aeration time, the dischargecapacity per time, the storing time without movementand the specific bulk materials characteristics such asbulk density, internal angle of friction and wall frictionangle.

For an actual comparison of different discharge sys-tems with regard to the wall load, the size of the activeaeration section is most significant. Generally, the num-ber of aeration sections increases with increasing silodiameter in order to keep the active aeration surfacesfrom becoming too large. Correspondingly, the circum-ferential angle θc decreases in silos with a larger diame-ter and a higher number of aeration sections. Thecircumferential length lc of the flow channel at the wallthat has an effect on bending moments, however,

increases with a constant number of aeration sectionsand increasing silo diameter.

Generally it should be noted that at adefined silo size the resulting wall stresses

due to discharging become smaller as thecircumferential angle of flow channels

at the silo wall becomes smaller.Accordingly the wall stressesbecome smaller as the pressure dif-ferences in the silo become smaller: these depend on the sizeand eccentricity of the flow chan-nels. One possible means of reduc-ing the formation of flow channels

is, for example, using smaller aera-tion sections and not connecting

neighbouring aeration sections toge-ther for silo discharging.

Practical calculationexamplesA practical example of a cement silowith 17.2 m inner diameter and a fill-

ing height of 40 m shows what effects the horizontalpressure distribution from the described flow channelshas on the stress resultants and dimensions of the silowall. The silo wall is stiffened at the upper and loweredge by adjoining components; the assumed wall thick-ness is 30 cm. The design loads and relevant stress resul-tants for two flow channels with the radii rc = 0.35 r and0.5 r are shown. Since loads and stress resultants changewith the height, the section is viewed at half filledheight (z = 20 m) for simplification, which can be seen asrepresentative for the ratio on the entire wall height. Inaddition, a direct comparison with the design based onthe DIN 1055 part 6 standard (May 1987, currently stillvalid) is possible for this height section.

Figure 7 shows the horizontal pressure distributionalong the wall circumference. A larger contact zone atthe wall circumference results for the larger flow chan-nels with 0.5 r compared to the smaller flow channelwith 0.35 r, while the pressure differences along the cir-cumference are lower with the larger flow channeldiameter. This can be seen in the view of the flow chan-nel as ‘silo in the silo’. Thus, with increasing flow chan-nel diameter, the pressures also increase and approachthe pressures in the surrounding static bulk material (ascan be compared in Figure 8).

Figure 9 shows the bending moment at half height ofthe silo wall in circumferential direction. Characteristicsfor the established pressure distribution are the bendingmoments that create considerably higher tensile stresseson the inner side than the outer side of the wall. Thelarger flow channel diameter produces the appropriatelylarger bending moment. Simultaneously, these bendingmoments are considerably larger with tension on thewall inner side than those in the design with patch loadstowards the outside. This use of patch loads was the rel-evant load case based on DIN 1055 part 6 (May 1987) todate for the load from the bulk material pressures, andshould now as before be viewed as an additional loadcase. The ring tensile forces are almost constant over thesilo circumference and practically the same for both flowchannel diameters, which is why no presentation is

Figure 5. Formation of flow channels in acement silo.

Figure 6. Formation of flow channels for different aeration timest3>t2>t1.

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made here. They can be sufficiently accurately deter-mined from the fill pressure of the resting material viathe so-called container formula at nx = phf x r = 106 x 8.6= 912 kN/m. Compared to load approaches with patchload, they are considerably less, since larger dischargeloads are anticipated.

The shear forces in circumferential direction areshown in Figure 10 as additional internal forces. Withthe silo design typical up until now, corresponding shearforces also resulted from the patch loads in principle;however, these were previously not seen as relevant forwall design, and therefore they were not considered(this is compared below). Please note that the designloads shown according to the drafts of standards areonly simplifications of what in reality are very complicated conditions in the silos shown, and in prac-tice, their conversion for each application must beappropriately critically scrutinised.

Results of the wall designFor the ring reinforcement at the outer side of the wallthere are practically no changes compared to previous

designs, since here, as before, the approach with patchloads is significant. However, deviations can result asmathematical effects through negligibly changedparameters and modified formulas; nevertheless theyshould not exceed 10 - 15% in normal cases. The ringreinforcement at the wall inner side is clearly increaseddue to the high bending moment compared to previousdesigns, a significant result of the design load with flowchannel. This indicates that the decisive load on a cylin-drical silo wall in addition to the absolute size of themaximum pressure is very strongly influenced by thepressure distribution, and that not only localised pres-sure increases, but also a pressure decrease, brings prob-lems. Table 1 shows a comparison of the required ringreinforcement based on ‘old’ and ‘new’ standards.

The shear forces are another very significant aspectin the circumferential direction which result from thedesign loads described above. When using the previ-ously valid standard, DIN 1045 (July 1988), relativelysmall shear stresses occur, which cannot lead to conclu-sions about any problems. In the future, the proof ofthe established shear resistance without shear rein-

Table 1. Comparison of the required ring reinforcement at mid-height (z=20 m)Outside silo wall Inside silo wall Silo wall totalcm2/m cm2/m cm2/m

Internal forces and bending moments35.8 23.6 59.4

due to DIN 1055 part 6 (May 1987)Internal forces and bending moments

37.1 24.7 61.8κ-method, due to DIN 1055 part 6(May 1987) distribution outside/inside 60/40%Internal forces and bending moments

23.8 33.7*according to flow channel method due todraft prEN 1991-4 respectively DIN 1055-6r=0.5rc

70.8Due to standard design 37.1* 24.7*Relevant for the design

Figure 8. Horizontal pressures depending on height.Figure 7. Horizontal pressure distribution in a silo due to a flowchannel.

forcement must be shown based on DIN 1045-1,whereby the axial forces in the section must be consid-ered. The ring tensile force in the silo wall drasticallyreduces the incorporated shear resistance. In theexample described, this leads to an inadequate shearresistance of the silo wall for the calculated shearforces of a reinforced wall without post-tensioningwith typical dimensions based on DIN 1045-1. Simplystated: no adequate shear forces can be transmittedvia open cracks in silo walls.

The fact that the design formula listed in 1045-1 isnot applicable to the typically large tensile forces in silowalls, and the lack of information about the limit of thescope of validity also presents a problem at present.Based on current knowledge, it cannot be expected thatproof can be given in a different manner. The applica-tion of shear reinforcement fails due to the same obstacle. The insufficiently researched influence of cycli-cally alternating loads from the circulating aeration ofthe discharge sections is also of significance. Previouslyimplemented model design calculations clearly indicatethat the inadequate shear resistance of the silo wallunder tension could be the main cause for severe damages.

Reducing a too high ring tensile stress in the silo wallis a useful solution for critical cases. This leads to the useof post-tensioning in the circumferential direction asalready successfully used for many years for silos andstores with a diameter of 20 m and more. Although thisis a more technologically demanding solution, it doesnot need to be more expensive than a wall withoutpost-tensioning. In addition, the post-tensioning brings

well-known advantages for limiting the width of cracks,which is an important aspect for the durability of thewall. Post-tensioning could already be used withconsiderably smaller diameters than previously typical,in order to avoid long-term damage.

Conclusions and recommendationsIt has been shown that the silo discharge system has aconsiderable influence on the size and eccentricity ofthe flow channel formation and the resulting wall loadsin silos with a central cone. Depending on the dischargesystem, the number of aeration sections and dischargequantities, critical cases can occur with regard to wallloads. Generally, such critical cases should undergo anextensive analysis that includes the ideas presented. If itis decided that the case must be considered critical, post-tensioning in circumferential direction may be a solution.________________________________________�

Literature1. JOHNSTON, T., ‘Pressure Measurement During Flow in a 23.4 m

Diameter x 66.7 m High Raw Meal Blending Silo at a Cement

Plant’, Bulk Solids Handling, Vol. 21, No. 2 March/April 2001,

pp. 149-152.

2. SADLER, J. E. et al, ‘Designing Silo Walls for Flow Patterns’, ACI

Structural Journal, March/April 1995, pp. 219-228.

3. ROTTER, J. M., Guide for the economic design of circular metal

silos, SPON PRESS, London and New York.

4. JANSSEN, H., ‘Versuche über Getreidedruck in Silozellen, [Tests

regarding grain pressure in silo cells]’, VDI Zeitschrift, Vol. 39,

August 1985, pp. 1045-1049.

Figure 9. Bending moments depending on circumference. Figure 10. Shear forces depending on circumference.