Tower silo design loads for wet silages J.C. JOFRIET1, Z. YAO2 and S.C. NEGI1 1 School ofEngineering and 2Food Science Department, University of Guelph, Guelph, ON, Canada NIG 2W1. Received 3 October 1991; accepted 11 June 1992. . Jofriet, J.C, Yao, Z. and Negi, S.C. 1992. Tower silo design loads for wet silages. Can. Agric. Eng. 34:375-381. Wet silage stored in tower silos may become saturated if sufficiently consolidated. If this occurs, liquid pressures will result in the saturated silage zone. This paper briefly reviews a comprehensive study of the magnitude of liquid pressures and of the extent of the saturated silage zone.The latter is a function of silo size and of the moisture content of the silage. On the basis of the results of the recent study, recommenda tions are made for determining the height of the saturated zone for both silos with and without adequate drains. The recommended saturation heights are greaterthan those in the 1990CFBC.It also is proposed that the CFBC wall loadrecommendations are suitable for silos withoutadequate drains. For those with drains, the wall loads could be reduced considerably in the lower part of the silo. Specific design formulae are provided. L'ensilage humide approvisionne dans les silos-tours pourrait devenir sature s'il se consolide suffisamment. Si cela arriverait, des pressions liquides resulteraient dansla zonesaturee de l'ensilage. La presentation revise une etude comprehensive de la grandeur des pressions liquides et de l'etendue de la zone saturee de l'ensilage. Celui-ci est une fonction des dimensions du silo et de l'humidite de l'ensilage. A basedes resultats de 1'etuderecente, on faitdes recom- mandations pour determiner 1'hauteur de la zone saturee pour les silos dans deux etats, avec et sans des drains suffisantes. Les hauteurs de saturationrecommandees sont plus grandesque celles du CCCBA de 1990. On propose aussi que les recommandations CCCBA ac- tuelles(de 1990)sur les chargesdes murs sontconvenables aux silos sans des drains suffisantes. Pour ceux avec drains, on pourrait reduire considerablement les charges des murs de la partie inferieuredu silo. On foumit aussi des formules specifiques de dessein. INTRODUCTION A direct consequence of storing wet material in a tower silo is the build-up of liquid pressure in the bottom, especially if the hydraulic conductivity of the material is low. The liquid pressure is superimposed onto the effective wall pressure (pressure transmitted through the particulate skeleton), and the total lateral pressure is usually considerably greater than fordry materials because of the relatively large magnitude of the liquid pressure. 't Hart et al. (1979) observed that liquid pressures were three times the effective pressure in a steel silo filled with corn silage. Therefore the prediction of liquid pressure is essential for silo design. If it is neglected or underestimated in a cast-in-place concrete silo, or other type with impervious walls, a collapse or serious damage may result. There are several silo design codes in force in Europe and North America. Design standards for silos storing relatively dry material (M < 65% w.b.) are fairly well established. However, the standards for silos filled with wet silage (mois ture content > 65%) vary greatly from code to code. The Canadian Farm Building Code (NRC 1990) classifies top-unloading farm tower silos intended for wet silage as class II. In class II silos saturation is expected when: M> 80 - 0.5(// + D) (1) where: M- moisture content on a wet basis (%), H = silo height (m), and D = silo diameter (m). For design, it is assumed that the silo can be filled to the top, hence silo height and filling height are considered equal. The pressure in Class II silos above the saturation level is represented by a bilinear function based on the well-known Janssen's (1895) theory (NRC 1990). Below the saturation level the total (effective plus hydrostatic) pressure is given by: Pt = Ps + (z-zs)(lL0- ^ Ps) where: z = depth from the top of silo (m), zs = depth to saturated zone (m), \i = friction coefficient, K = pressure ratio, Pt = pressure at depth z (kPa), and Ps = pressure at depth zs (kPa). An empirical equation: • z*=160-2M-D is used to calculate the depth from the top of the silo to the saturated zone. The British Standard Institution suggests in the standard BS 5061 (BSI 1974) that the lateral pressure Pt at depth z in drained cylindrical silage tower silos is: Pt = 9.8 + 0.75(9.8 -^ )(z -3) zs<z<H (2) (3) z >3m (4) The factor 0.75 in the second term of Eq. 4 is changed to 1.0 if the crop is ensiled in a watertight silo. The German Standard DIN 1055 (Deutsche Normen 1977) simply relates pressure Pt to silage depth z: Pt = 4.0z (5) CANADIAN AGRICULTURAL ENGINEERING Vol. 34, No. 4 October/November/December 1992 375
Transcript
Tower silo design loads for wet silagesJ.C. JOFRIET1, Z. YAO2 and S.C. NEGI1
1School ofEngineering and 2Food Science Department, University ofGuelph, Guelph, ON, Canada NIG 2W1. Received 3October 1991; accepted 11 June 1992. .
Jofriet, J.C, Yao, Z. and Negi, S.C. 1992. Tower silo design loadsfor wet silages. Can. Agric. Eng. 34:375-381. Wet silage stored intower silos may become saturated if sufficiently consolidated. If thisoccurs, liquid pressures will result in the saturated silage zone. Thispaper briefly reviews a comprehensive study of the magnitude ofliquid pressures and of the extent of the saturated silage zone. Thelatter is a function of silo size and of the moisture content of thesilage. On the basis of the results of the recent study, recommendations are made for determining the height of the saturated zone forboth silos with and without adequate drains. The recommendedsaturation heights are greaterthanthose in the 1990CFBC.It also isproposed that the CFBC wall loadrecommendations are suitable forsilos withoutadequate drains. For those with drains, the wall loadscould be reduced considerably in the lower part of the silo. Specificdesign formulae are provided.
L'ensilage humide approvisionne dans les silos-tours pourraitdevenir sature s'il se consolide suffisamment. Si cela arriverait, despressions liquides resulteraient danslazonesaturee de l'ensilage. Lapresentation revise une etude comprehensive de la grandeur despressions liquides et de l'etendue de la zone saturee de l'ensilage.Celui-ci est une fonction des dimensions du silo et de l'humidite del'ensilage. A basedes resultats de 1'etuderecente, on faitdes recom-mandations pour determiner 1'hauteur de la zone saturee pour lessilos dans deux etats, avec et sans des drains suffisantes. Les hauteursde saturationrecommandees sont plus grandesque celles du CCCBAde 1990. On propose aussi que les recommandations CCCBA ac-tuelles(de 1990)sur les chargesdes murs sontconvenables aux silossans des drains suffisantes. Pour ceux avec drains, on pourrait reduireconsiderablement les charges des murs de la partie inferieuredu silo.On foumit aussi des formules specifiques de dessein.
INTRODUCTION
A directconsequence of storing wet material in a tower silois the build-up of liquid pressure in the bottom, especially ifthehydraulic conductivity of the material is low. The liquidpressure is superimposed onto the effective wall pressure(pressure transmitted through the particulate skeleton), andthe total lateral pressure is usually considerably greater thanfordrymaterials because of therelatively large magnitude ofthe liquid pressure.
't Hart et al. (1979) observed that liquid pressures werethree times the effective pressure in a steel silo filled withcorn silage. Therefore the prediction of liquid pressure isessential for silo design. If it is neglected or underestimatedin a cast-in-place concrete silo, or other type with imperviouswalls, a collapse or serious damage may result.
There are several silo design codes in force in Europe andNorth America. Design standards for silos storing relativelydry material (M < 65% w.b.) are fairly well established.However, the standards for silos filled with wet silage (mois
ture content > 65%) vary greatly from code to code.The Canadian Farm Building Code (NRC 1990) classifies
top-unloading farm tower silos intended for wet silage asclass II. In class II silos saturation is expected when:
M > 80 - 0.5(// + D) (1)
where:
M - moisture content on a wet basis (%),
H = silo height (m), andD = silo diameter (m).
For design, it is assumed that the silo can be filled to thetop, hence siloheight andfilling height areconsidered equal.The pressure in Class II silos above the saturation level isrepresented by a bilinear function based on the well-knownJanssen's (1895) theory (NRC 1990). Below the saturationlevel the total (effective plus hydrostatic) pressure is givenby:
Pt =Ps +(z-zs)(lL0- ^ Ps)where:
z = depth from the top of silo (m),zs = depth to saturated zone (m),
\i = friction coefficient,K = pressure ratio,Pt = pressure at depth z (kPa), andPs = pressure at depth zs (kPa).
An empirical equation: •
z*=160-2M-D
is used to calculate the depth from the top of the silo to thesaturated zone.
The British Standard Institution suggests in the standardBS 5061 (BSI 1974) that the lateral pressure Pt at depth z indrained cylindrical silage tower silos is:
Pt =9.8 +0.75(9.8 -^ )(z -3)
zs<z<H (2)
(3)
z > 3 m (4)
The factor 0.75 in the second term of Eq. 4 is changed to 1.0if the crop is ensiled in a watertight silo.
The German Standard DIN 1055 (Deutsche Normen 1977)simply relates pressure Pt to silage depth z:
Pt = 4.0z (5)
CANADIAN AGRICULTURAL ENGINEERING Vol. 34, No. 4
October/November/December 1992
375
Equation 5 applies to a silo height of 20 m or less andsilage moisture contents ranging from 60 to 77% (w.b.). Thestandards of the International Silo Association (ISA 1981) donot consider wet silage and the possibility of hydrostaticpressures.
The objective of this paper is to use the results of previousresearch related to the effect of silage saturation in tower silos(Lau and Jofriet 1988; Tang and Jofriet 1989; Yao and Jofriet1991) to formulate design loading recommendations fortower silos that may be subjected to liquid pressures. Bothdrained and undrained structures will be discussed.
BACKGROUND RESEARCH
Tang and Jofriet (1989) and Yao and Jofriet (1991) havepresented a simulation procedure for predicting numericallythe lateral pressures (liquid and effective pressures) in silosfilled with high moisture content material. Three time dependent processes were modelled in the simulation computerprogram: filling, consolidation, and drainage. Previously Lauand Jofriet (1988) had shown that excess pore pressures areinsignificant in the silo filling/silage draining process.
The numerical models were verified against an experimentconducted by 't Hart et al. (1979) in the Netherlands. The testwas carried out in a 6.19 x 18.15 m glass lined steel farm silo.The simulation was carried out for a period of 30 days. Thesimulated results for the total and liquid lateral pressures at7, 14, 21, and 30 days were compared with those of 't Hart.Figure 1 shows the comparison at 14 days. The pressurescompared well at all time steps. The settled silage height waswithin 0.25 m of the experimental value at 7 days and virtually equal to it at 30 days.
Subsequently, Yao and Jofriet (1991) carried out a parametric study of farm silos filled with alfalfa silage. Itaddressed the three most important parameters that affectwall pressures: silo height, silo diameter, and silage moisturecontent. Most analyses assumed adequate drainage in thebottom of the silo. A limited number of analyses were carriedout with undrained silos. The results of the parametric studyare relevant to silos intended for alfalfa and grass. They willbe conservative for corn silage because it has a lower bulkdensity and drains faster (Tang and Jofriet 1989).
Four diameters ranging from 3.7 to 9.1 m were chosen.For the 3.7 m diameter, silo heights of 9.1, 12.2, and 15.2 mwere investigated to represent small, medium, and large siloaspect ratios. The silo heights for the 4.9 m diameter were15.2, 18.3, and 21.3 m and for the 6.1 m diameter 18.3, 21.3,and 24.4 m. The large diameter silos were 9.1 x 24.4 m,9.1 x 27.4 m, and 9.1 x 33.5 m. This range of sizes covers thesilo sizes used by Canadian farmers today. Moisture contents(w.b.) of 60%, 65%, 70%, and 75% were chosen for theparametric study.
The results of the 48 analyses of drained silos are shownin Table I. For each analysis, Table I presents in column 4 themaximum saturation height measured from the silo bottom,in column 6 the average bulk density, and in columns 8 and9 the maximum liquid and total pressures on the silo wall.For comparison, the tables include the CFBC values of saturation height determined with Eq. 3 (column 5); the averagebulk density suggested by the CFBC (column 7); and in
376
12
10
£ 8LUCO<CD
LU> 6offi<111o
(0
5
MEASURED SETTLED HEIGHT
SIMULATED
MEASURED
TOTAL PRESSURE
MEASURED
EFFECTIVE PRESSURE
SATURATION HEIGHT
60
PRESSURE (kPa)
Fig. 1. Comparison of simulated lateral pressures withexperimental data by 't Hart et al. (1979) forgrass silage in a 6.19 x 18.15 m glass-lined steelsilo; t = 14 days.
column10and the maximumpressureas per the CFBCusingEqs. 2 and 3 (column 10).
Figure 2 illustrates the maximum pressures for a 3.7 x 12.2m silo; maximum total pressures for 65%, 70%, and 75%moisture content silage are shown. Figure 3 has the sameplots for a 9.1 x 27.4 m silo.
The effect of not providing adequate drainage was determined for three silo sizes and for three moisture contents(65%, 70%, and 75% w.b.). The saturation height, the bulkdensity, and the maximum liquid pressures and total pressures are presented in Table II, together with correspondingvalues calculated from the CFBC. The CFBC values areexactly the same as those in Table I because this code doesnot differentiate between silos with and without adequatedrains.
The effect of drainage is illustrated in Fig. 4 in which twosets of pressures are plotted for the 4.9 x 18.3 m silo filledwith 70% moisture content alfalfa silage, one with and onewithout a drain. The simulation of the silo with the floordrains showed pressures reaching a maximum at about 4days. The silo without drains had pressures increasinguntil t= 18.8 days.
DISCUSSION OF SIMULATION RESULTS ANDDESIGN LOAD RECOMMENDATIONS
At a moisture content of 60%, saturation [Tang et al. (1988)saturation criterion] occurred in the simulation analysis only
JOFRIET, YAO and NEGI
Table I. Simulated saturation heights and maximum pressures in drained silos
Saturation Bulk Maximum pressure Saturation Maximum* Ratio
M = moisture content(w.b.); H = silo height; liq = liquid; tot = total; D = diameterof silosimul = simulationbLateral pressure calculated with the saturation height from Eq. 7 (col. 11)
(m). Both M and H are significant at the 1% level. Zero andnegative values forHs from Eq.6 should be interpreted as nosaturation. Table I shows the values calculated with Eq. 6 incolumn 11.Figure 5 shows a plot of Hsdetermined with Eq.6 versus the simulated values (Table I, col. 4).
The pressures in silos in whichno saturation occurred arefairly typical Janssen (1895) typecurves. Indrained silos(seeFigs. 2 and 3)thepressures from those simulation analyses inwhich saturation of the silage was indicated are significantlydifferent below the saturation level because of the addition oftheliquid pressure. The total pressure curves below the saturation level have common characteristics. Just below thesaturation level the pressures increase at a rate of about 10kPa/m, the increase due to liquid pressure plus the relativelysmall rate of increase in effective pressure. The rate of increase in pressure reduces fairly quickly withdepthdown tothe point of the maximum pressure which lies typically between one half to one third of the saturation height from thebottom of the silo. Below the point of maximum pressure theliquid pressure quickly reduces to zeroand the totalpressureto the value of the effective pressure.
In undrained silos the effective pressure is about the sameas in drained silos. However, the hydrostatic pressure, andhence thetotalpressure, is significantly greater andthemaximum occurs near the silo bottom (see Fig. 4). Table II showsthe maximum total pressures from the simulation without adrain in column 9. The maximum liquid pressures are shownin column 8. As well, the saturation height (col. 4) tends tobe somewhat greater than for drained silos. It can be estimated reasonably well by:
Hs = H + 0.9M - 70 65%<M<75%
2.5 < HID < 4 (7)
Table II includes the values of saturation height calculatedwithEq. 7 in column 11. As well, Table II shows in column12the maximumpressurescalculated from the CFBC recom-
mendation(Eq. 2) using the silage densities recommendedbythat code but using saturation heights determined by Eq. 7.Both Eq. 2 and the simulations show the maximumpressureto occur at the silo floor.
Acomparison of thevalues ofmaximum pressure from thesimulations (column 9, Table II) with those predicted withEq. 2 (column 12, Table II) shows that this expression isfairly good for undrained silos. The ratio of predicted oversimulated maximum pressures is shown in column 13 ofTable II. The ratios range from a value of 0.81 to 1.21; themean of the ratios for the nine analyses is 0.93, the standarddeviation is 0.15. Thus, the continued use of Eq. 2 for undrained silos seems to err somewhat on the unsafe side,assuming of course that the simulations are realistic. However, the authors consider that Eq. 2 is adequate for design,bearing in mind that no silo is fully watertight.
The maximum pressures in a drained silo occur somewhere between the saturation level and the silo floor. Whena silo is properly drained, no increase in liquid pressureoccurs below a point about halfway between the saturationlevel (Eq. 6) and the bottom of the silo. The authors recommend that for adequately drained silos, Eq. 2 be used tocalculate lateral pressures down to halfway between saturation level and the silo bottom. It is also recommended thatbelow that level the total pressure be kept constant. Thus:
Pt =Ps +(z-Zs)(U.0-^- Ps)zs < z < (// + zs)l2
Pt = Ps + 0.5(H-Zs)(U.O4\&
D
(// + zs)l2 <z<H
Ps)
(8)
(9)
The resultingmaximumpressures are includedin column12 of Table I. The agreement of these recommended maximum pressures with the total pressures from analyses of the
CANADIAN AGRICULTURAL ENGINEERING Vol. 34, No. 4
October/November/December 1992
379
OUJ
<cc
5
g5UJKQ.
Fig. 5.
4 8 12 16 20 24 28
SIMULATED SATURATION HEIGHT (m)
Simulated saturation height versus predictedsimulated saturation heights (Eq. 6) for allsilos with adequate drainage that experiencedsaturation
CO<CD
UJ
8CD<HIOz
g
20
15
10
\ •\ N
\\\ \\ X ,
\ X\ \
Undrained §Uos
r
EQ. 2 \
•
N
X
\ x\ X
\\
\
Drained Silos
EOS. a* 9 ^*i
20 40 60 80
PRESSURE (kPa)
100
Fig. 6. Recommended design pressures for 4.9 x 18.3 mconcrete silos, with and without drainage, for70% moisture content whole plant silage
drained silos (column 9, Table I) is remarkably good. Incolumn 13 the ratio of predicted (Eqs. 8 and 9) over simulatedmaximum lateral pressures (column 9) are shown. The ratiosrange from a low of 0.97 to a maximum value of 1.66. Themean of the ratios is 1.18, the standarddeviation0.17. Onlyseven of the 48 ratios are less than 1.0 (i.e. unsafe predictions). Figure 6 shows an exampleof the pressurediagramsproduced with Eqs. 2 and 7 for undrained silos and Eqs. 6, 8,and 9 for silos with adequate drains.
380
Drains in the bottom of a silo have to be adequately largeto carry away the silage juice that flows downward throughthe silage mass. The rate of flow is a function of the silagetype, silo size, and of the moisture content of the silage. Inmost silos the density of silage near the floor is in the orderof 900 - 1100 kg/m . At these densities the vertical hydraulicconductivity of the silage will be of the order of 10" to 10m/s (Tang and Jofriet 1991). It is obvious from these lowvalues that the rates of flow will usually be small and thecommon provisions made today by silo builders are as a ruleadequate providing they are kept in working order.
The hydrostatic pressures against a silo wall will, ofcourse, develop only if the wall is watertight. It is thereforenot necessary to use the design pressures proposed in thispaper for stave silo walls providing the owner is prepared tohave silage juice draining through the joints between staves;however, this will shorten the life of a stave silo because ofcorrosion of the staves and the steel hoops.
SUMMARY
The results of an extensive parametric study of silo wall loadsdue to wet silages were used to formulate some improvements to the present provisions of the 1990 Canadian FarmBuilding Code (NRC 1990). This code has provisions fordealing with wet silages. However, the height of the saturation zone appears to be underestimated. Two newexpressions, Eqs. 6 and 7, are proposed for estimating thesaturation height in tower silos with and without drainage.The CFBC does not provide for the considerable reduction inliquid pressure resulting from floor drains. A simple modification to the present code is recommended (Eqs. 8 and 9).
ACKNOWLEDGEMENTS
The funding for this project was provided by the NaturalSciences and Engineering Research Council of Canada andthe Ontario Ministry of Agriculture and Food.
REFERENCES
BSI. 1974. Specifications for cylindrical forage tower silosand recommendations for their use. BS 5061. BritishStandards Institution, London, England.
Deutsche Normen. 1977. Design loads for buildings; loadson silo bins. DIN1055, Blatt 6.
't Hart, C, A.H. Bosma and M.G. Telle. 1979. Physicalproperties of ensiled grass and corn, silo capacities andsilage pressures in cylindrical tower silos. ResearchReport 79-3. Institute of Agricultural Engineers, IMAG,Wageningen, The Netherlands.
ISA. 1981. ISA recommended practice for the design andconstruction of top unloading monolithic concrete farmsilos. International Silo Association, Des Moines, IA.
Janssen, H. A. 1895. Versuch uber Getreidedruck inSilozellen. Zeitschrift des Verein Deutscher Inginieurs39:1045-1049.
Lau, A. and J.C. Jofriet. 1988. Silage pressures at saturationin tower silos. Canadian Agricultural Engineering30(l):83-92.
JOFRIET, YAO and NEGI
NRC. 1990. Canadian Farm Building Code (CFBC). Tang, J., J.C. Jofriet and B. LeLievre. 1988. A saturationNational Research Council of Canada, Ottawa, ON. criterion for ensiled plant materials. Canadian
Tang, J. and J.C. Jofriet. 1989. Simulation of consolidation Agricultural Engineering 30(l):93-98.and liquid flow in a farm tower silo. Canadian Yao, Z. and J.C. Jofriet. 1991. Simulation of liquid pressuresAgricultural Engineering 31:167-174. in farm tower silos. Journal ofAgricultural Engineering
Tang, J. and J.C. Jofriet. 1991. Hydraulic conductivity of Research 49:35-50.whole plant corn silage. Canadian AgriculturalEngineering 33(1): 161-167.
CANADIAN AGRICULTURAL ENGINEERING Vol. 34, No. 4 381October/November/December 1992
