REINFORCED EXTENDED RING FOUNDATIONSFOR TOP-UNLOADING CONCRETE TOWER SILOS

J.E. Turnbull, H.A. Jackson, and D. Lowe

Engineering and Statistical Research Institute, Research Branch, Agriculture Canada, Ottawa, Ontario, KIA 0C6,ESRI contribution no. 596

Received 20 September 1978

Turnbull, J.E., H.A. Jackson, and D. Lowe. 1979. Reinforced ring foundations for top-unloading concrete tower silos. Can.Agric. Eng. 21: 111-116.

Weak soils require special foundation designsto spread the load of tall tower silos over sufficientsoil-bearingarea to maintainan adequate safety factor. Eccentricity of silo wall loads and soil reaction pressuresfrequently cause the annular ring footing torotate and break into sectors. In this design, the annular ring is reinforced with a flat continuous spiral of steel to resist rotation,and the majority of the footing width is located beyond the silowallto increasetotal bearingarea under the silo. Designcriteriawere based on the Canadian Farm Building Code (1977), and solutions were calculated for soils ranging from 72 to 288 kN/m2(1500 to 6000 lb/ft2) safe bearing pressures.

INTRODUCTION

As more and more large tower silos arebuilt on supporting soils of undeterminedbearing capacities, the number of cases ofsettled, leaning and overturned silos inCanada continues to increase. A previouspaper (Bozozuk 1974) dealt with factorswhich determine the safe allowable bearingpressures of clay soils under tower silofoundations. This paper deals with a designprocedure for silo foundations capable ofspreading the load of a single silo pluscontents over sufficient soil area for safe

support.A tower silo can easily overload the area

of soil directly under the silo cylinder andfloor. Then it is necessary to spread theweight of the silo and contents over abearing area considerably greater than thebase of the silo cylinder. The reinforcedextended ring foundation described here is amethod of increasing the foundation bearingarea beyond the wall of the silo cylinderwithout wasting unnecessary foundationconcrete and reinforcing steel under the silofloor.

NOMENCLATURE

rad

mm2

m

2 3

HEIGHT/DIAMETER RATIO (h/D)

Figure 1. Silage wall friction versus height/diameter ratio for concrete tower silos.

a = angle subtended by unit wallcircumference

Al = section area of rebars to resistlateral pressure

As = section area of rebars to resistmoment

B = breadth of footingC = centroid of a sector of footing ring

(see Fig. 2)D = silo inside diameter

5 = silage load at 70% moistured = footing depthe = eccentricity of silo wall load with

respect to c

F = silage friction load on wall perunit of circumference

fc = 28-day compressive strength ofconcrete

fs = steel safe working stressH = silo wall heighth = silage height = (H — 1.5)mk = cone height/diameter ratio = 4.72

(Code, 1977)

L = lateral silage pressure on silowalls

P = safe soil bearing pressure

M

kN/m*m

m

kN/m

MPa

MPa

m

m

kPa

kPa

P - steel/concrete area ratioR = soil reaction at centroid of footing

sector

S = silo dead load (wall + roof +unloader) per unit circumference kN/m

Ts = spiral steel tension force kNW = total silage load per unit of silo

circumference kN/m

REQUIREMENTS FORSILO FOUNDATIONS

The Canadian Farm Building Code,hereafter referred to as the "Code"

(Standing Committee on Farm BuildingStandards 1977) gives requirements for

tower silo foundations, summarized asfollows:

(1) The base of a tower silo intended forwhole-plant silage should have a floorand drainage system designed toprevent silage liquids from penetratingthe soil under the footing and floor(floor and drainage details as shown inFig. 2 are designed to satisfy thisrequirement).

(2) The footing should be designed to resistbending moments caused by silo walland soil reaction loads (mostfoundation failures to date have been

CANADIAN AGRICULTURAL ENGINEERING, VOL. 21, NO. 2, DECEMBER 1979 111

Figure 2. Section and plan of extended ring silo foundation.

accompanied by breakup of the footingring into segments, thereby causing aring of concentrated load to developdirectly under the silo walls.

(3) The foundation ring should bereinforced circumferentially towithstand the same lateral pressures asthe bottom of the silo wall (Bozozuk1974).

(4) The width of an annular footing ringshould be based on providing sufficientbearing area at the critical soil bearingsurface to support the silo roof,equipment, wall and footing, plusvertical wall friction.

(5) Total bearing area under footing plusfloor should be sufficient to safelysupport the total weight of silo,foundation and contents (this lastrequirement may or may not be met bysatisfying requirement (4) above,depending on the required proportionsof the silo and foundation ring).

The Code (1977) does not specificallymention design of silo foundations for windeffects. Although many concrete stave siloshave been demolished by wind, the wind-caused failures seen to date have not been

due to foundation or soil failure, but ratherto collapses of the empty walls or roofs.

To check wind effects on silo

foundations, a calculation was done toestimate the amount of "tilt" required of thesoil reaction diagram in order to balance theoverturning pressure of a "design"windstorm at Ottawa. For a 7.2 x 21.6-m

silo, with outside footing radius selected toload the soil to 96 kPa (2000 lb/ft2), theextreme increment of soil reaction pressuredue to wind would be only ± 5% of the meanbearing pressure. This small increment, plusthe remote possibility of a maximum windblowing from the most critical directionwhen the silo is filled, all seem to indicate thedesign of silo foundations for wind issuperfluous. In tall structures of lesser

weight, this would not necessarily be true.

Silage density and wall friction forestimating floor and wall loads

The 1977 Code gives an equation forestimating that part of the silage whichwould be supported by wall friction, asfollows:

Wh

' A.12D (1-h

14.16/)(1)

Equation 1 is based on the assumptionthat the silage-to-wall vertical friction F,accumulated to the base of the wall, is themass of silage contained above a rightcircular cone with base the floor of the siloand height h of 4.72 times the silo diameterat the silo vertical center line (see Fig. 1).

There are recent indications that Eq. 1reasonably estimates the wall friction loadfor 70% moisture of silage stored from 9 to24 m depth. M. Bozozuk (National ResearchCouncil, personal communication)calculated from measurements of vertical

soil stresses under one silo footing and floorthat about 50% of the silage weight wassupported by the wall. In this case, the floorload due to silage corresponded with a cone4.72 silo diameters in height, instead of 3.2silo diameters as per the 1975 code.

Negi et al. (1977) measured wall frictionexperimentally in a scale model silo withvarying height/diameter ratio; their resultswhen replotted also showed closeragreement with the "cone" concept when thecone height is adjusted to 4.72 silo diameters(see Fig. 1). Since the cone concept is easierto apply and seems to result in errors slightlyon the safe side with wider silos, this conceptwas used in calculations to determine

required footing widths.To apply the cone concept for estimating

wall friction loads, uniform silage densitythroughout the silage depth has beenassumed. Averaged silage densities weretaken from the Code (1977).

DESIGN ASSUMPTIONS

AND EQUATIONS

1. Estimating Silage Load, WTotal estimated silage vertical wall

friction was based on the cone concept (seeFig. 1) with cone height/diameter ratio k =4.72.

Total silage load in a cylinder isInD2h/4. The silage load Wenclosed by aunit sector of wall (1 metre of circumference)then becomes

W= dDh/4 (2)

2. Estimating Silage Friction Load onWall, F.

Combining Eqs. 1 and 2 gives

„ a218.88

(114.16D

(3)

3. Calculating Footing Width, BThe dead load (S) of silo wall plus roof

and equipment is a very significant part ofthe footing load with concrete silos. The wall

112 CANADIAN AGRICULTURAL ENGINEERING, VOL. 21, NO. 2, DECEMBER 1979

part was calculated on the basis of 63-mmthick concrete staves or 150 mm thick cast-in-place concrete, each at 23.56 kg/m3 (150lb/ft3). To this was added the weights ofroof, unloader, etc. based on manufacturers'shipping weights, all divided by nD to giveloads per unit of circumference.

The ring footing was arbitrarily set withinside radius a constant 0.3 m less than theradius of the silo (see Fig. 3). Thus totalbearing area under a sector of the ringfooting corresponding to one unit of wallcircumference becomes

compression to balance the spiral steeltension; a steel/concrete area ratio p =0.009was chosen to ensure an underreinforcedbeam section. This gives

As = 9000 5 (d- 0.1) (6)

D(B+D-.6)

Beyond the basic requirement thatfooting width B must be sufficient to supportthe silo, plus silage-on-wall friction loads, Bmust be further increased to support theconsiderable load of the footing itself. Aconvenient way to do this is to reduce theallowable unit bearing pressure of the soil byan amount equal to the load of the footing,which is in turn the density of reinforcedconcrete times the depth d. Net allowablebearing pressure thus becomes P — 23.56d.

This method is based on the assumptionthat the soil reaction pressure is uniformunder the whole area of the footing ring.This is not necessarily true, but theassumption of uniform reaction pressure issimpler and is on the safe side, from thestandpoint of footing design. Furtherresearch will hopefully indicate a morerealistic distribution of reaction pressuresand permit future economies in the design ofextended ring footings.

The equation for footing width B can bewritten thus:

F + S= —(B+D- .6)(P- 23.56tf)

(4)

4. Calculating Eccentricity, eThe extended ring foundation (see Fig.

2), when loaded, rotates outwards at thebottom, and without reinforcement it canbreak into separated sectors due to theeccentricity e of the resultant soil reaction Rwith respect to the wall loads (F+ S). Withproper circumferential reinforcement toresist this rotation, the ring becomesanalogous to a concrete beam where thespiral steel As acts in tension near thebottom and is balanced by concrete acting incompression at the top. It can be shown thatthis eccentricity is:

..§»3— +

B

|~2 D/2-31 3L2+_? J '

D/2 - 0.3

(5)

5. Steel/Concrete Area RatioEquation 4 above has two unknown

terms, B and d\ therefore additionalequations are required. Footing depth dmust provide enough concrete in

6. Spiral Steel Area (As) to Resist FootingRotation

In Fig. 2, the eccentricity e of wall loads F+ S in relation to soil reaction R develops acouple which tends to rotate any sector ofthe footing ring outwards at the bottom andinwards at the top. In this, the footing ring issomewhat analogous to a beam stressed inbending; rotation of any sector defined by asmall horizontal angle dd) is resisted by the"beam" action of concrete acting incompression in the top of the ring, and by aflat-wound continuous spiral of steel actingin circumferential tension near the bottom.

The steel is placed as a continuous spiralusing the longest rebar lengths obtainable,to minimize and randomize the end-laps.

For any sector of footing defined bysmall angle d0, the wall load is (F+ S) D/2dd, and the "load" moment developed bythis eccentric load is M - e(F + S) D/2 d6.

The resisting moment to balance this isdeveloped by the radial component ( TssindO) of the steel tension, acting about pointC, the assumed centroid of thecircumferential compression forces in thetop part of the concrete ring. Using workingstress design methods (CSA Standard A23.3, 1970), the effective depth of the steel isabout 0.857 (d — 0.1), and the resistingmoment Mr developed by steel/concreteinteraction is

Mr = Tssindd (0.857)(rf - 0.1).

But Ts = AsfSf fs = 165.5 mPa for grade50 000 steel, and sin dd = dd for very smallangles, therefore

Mr = 165.5As. dd (0.857)(rf - 0.1)

For equilibrium, equate load moment M toresisting moment Mr\ therefore

e (F +S)- d6 = 165.5As. dd (0.857)(d - 0.1)

from which

Ax = -103 De(F +S)

2(165.5)(0.857)(</-0.1)(7)

Note that the bearing line of silo wallloads F + S was taken at the inside wall

circle, to allow for the unknown silagepressures acting vertically on the inside heelof the footing.

7. Calculating Footing Depth DCombining Eqs. 6 and 7 gives

9000 5 (d- 0.1)De (F + S)

2(165.5)(d-0.1)

De (F + S)(tf-0.ir -

25535= 0 (8)

In practice, Eq. 8 is solved for d, and thisis fed back into Eq. 4 to adjust the allowablebearing pressure of the soil (see P — 23.56c/).

CANADIAN AGRICULTURAL ENGINEERING, VOL. 21, NO. 2, DECEMBER 1979

Figure 3. Diagram of footing ring withexaggerated rotation and displacementdue to eccentric loading.

A process of iteration is used to obtain amore exact value for depth d, then Eq. 7 issolved to obtain the spiral steel area, As.

8. Reinforcing for Lateral Pressure InsideFooting Ring

Additional spiral steel is required to resistlateral pressure on the footing ring resultingfrom the silage load on the floor. The exactnature of this soil pressure is not known, butit is assumed here that it is equal to thelateral pressure of the silage at depth h.

For lateral silage pressure L at silagedepth //, the Code gives

L =4.785 + 0.579/z (D - 0.6)oss

Since this pressure is applied to the insideof the footing ring, the diameter reduces toD — 0.6, and the required extra spiral steelarea Aj^ at safe working stress is therefore

AL =\0* d{D-0.6)

2(165.5)[4.785 +0.579/2

(D - 0.6)0.55

G (9)

The location of this extra steel is subjectto some judgment. One approach would beto arrange it vertically near the inside edge ofthe footing, corresponding to thecircumferential steel in the silo wall above.

However, only a few turns of steel arerequired to provide area Al, and to beeffective it should be located where tensile

strain approaches a maximum in the footingring. Figure 3 shows a section diagram of thefooting ring, with rotation under loadexaggerated to show displacement effects.At the beginning of loading the neutral axisof the concrete "beam" is assumed to be a

horizontal line (n to a) above which theshaded portion of the concrete is undercompression. With rotation under fulleccentric loads, the neutral axis rotatesthrough a smaller angle (a n a") than does thesection as a whole (angle bfhr). Thecompression concrete towards the outer

113

FOOTING BREADTH B (m)

1.0 1.5 2.0 2.5

DEPTH d (m) AL (mm*)500 1000 03.0 0.2 0.4 0.6 0.8 0

I I, I , I L 1,1

Ag (mm2)5 000 10000

2 3 4 5 6 7 8 9 10 0.5 1.0 15 2.0 25 0 05 1.0 15 0

FOOTING BREADTH B (ft) DEPTH d (ft) AL (in2) As (in2)

Figure 4. Design requirements of extended ring foundations for cast-in-place concrete tower silos. Numbers at top end ofdiameters, ft (m).

each curve are nominal silo

perimeter of the footing assumes a greatershare of the circumferential compressionforces.

Similarly the innermost turns ofcircumferential steel are displaced outwardsmore than the outermost steel (A/>A<?)and the inner turns of steel are thereforeunder higher tensile strain and stress. On thisbasis the additional steel area 04/,) requiredto resist lateral pressure L should be locatedas shown in Fig. 2.

114

9. Average Bearing Pressure UnderFooting and Floor

The above analysis may or may notsatisfy the fundamental requirement that thetotal soil area under footing plus floor mustbe sufficient to support the total weight ofthe silo, foundation and contents. Withweaker soils and taller silos this lastrequirement tends to apply. Thus theimportant dimension is the outside footingradius (D/2 + 5 — 0.3), and the area under a

sector corresponding to a unit of silo wallcircumference is therefore (D/2 + B-0.3)2/Z). A calculation is required to findif

* "" (10){D/2 +B - 0.3)2 > W+SP-23.56d

If not, an iterative procedure is requiredto increase B and recalculate d in steps untilEq. 10 is just satisfied, then recalculate Asand Al.

CANADIAN AGRICULTURAL ENGINEERING, VOL. 21, NO. 2, DECEMBER 1979

100

FOOTING BREADTH B (m)

OS 1.0 1.5 2.0 2.5 3.0

SAFE SOIL

BEARING

PRESSURE

P=4000 lb/ft'

= 191 kPa

SAFE SOIL

BEARING

PRESSURE

P=3000 lb/ft2=144 kPa

j^i x- :SAFE SOIL

BEARING

PRESSURE

P=2000 lb/ft2= 96 kPa

DEPTH d ( mm' )0.2 0.4 0.6 0.8 0

A. ( mm )

2 3 4 5 6 7 8 9 10 0.5 1.0 1.5 2.0 2.5 0 0.5 1.0 1.5 0

FOOTING BREADTH B (ft) DEPTH d (ft) AL(in2)

Ac <mm )

10 15 20 30

As(in2)

Figure 5. Design requirements of extended ring foundations for concrete stave tower silos. Numbers at top end of each curve are nominal silo diameters, ft(m).

10. Shear Through Footing DepthA shear check by the method required by

CSA Std. A23.3 (1970) shows that safeconcrete shear stresses are likely to beexceeded only with very tall silos on veryweak soils. This situation applies beyond thelimits of Figs. 4 and 5. Since the equationsfor checking shear are rather complicated inthis case, they were omitted for brevity.

To support the spiral steel As duringplacing of the footing concrete, and toensure that the concrete develops therequired shear resistance, radial rebars arerecommended. Rebars (Size 10M) spaced at0.6 m can be supported on dowels or stakesdriven into the bottom of the footing trench.This forms a platform for wiring the spiral

rebars in place and centered 100 mm abovethe trench bottom.

DESIGN RESULTS

Figures 4 and 5 show curves derived fromcomputer calculations to give theengineering requirements of extended ringfoundations; Fig. 4 is for cast-in-placeconcrete, and Fig. 5 is for concrete staves.Three soil bearing strengths were assumed ineach case.

Referring to the curves for footingbreadth /?, the lower parts of each curve werederived from Eq. 4 based on wall loads andfooting bear area. Footing widths plottedabove each dot in the curve were based on

CANADIAN AGRICULTURAL ENGINEERING, VOL. 21, NO. 2, DECEMBER 1979

Eq. 10 which relates the total base area(footing plus floor) to the total silo load.Note that this latter requirement controls fortaller silos on weaker soils; the dots shiftupwards and vanish off the top of the curvesas soil bearing pressure P increases. In somecases (Fig. 5, 9.1-m diameter silos on P= 144kPa (3000 psf) soil, for example), the curvesbreak below the dot; the computer checkedat 1.5-m height intervals but there theextrapolated curves intersected about 1 mbelow the checkpoint dot. Note that BonHis a curved function below the dots, but thatB is a linear function of H above the dotswhere total silo base area controls.

Footing breadth B was arbitrarily set at0.76 m minimum for the cast-in-place

115

concrete silos and 0.61 m for the

lighterweight silos made with concretestaves (see Figs. 4 and 5, respectively). Thesedimensions were considered to be practicalminima for excavation with a small

backhoe; they also prevent a negative valuefor eccentricity dimension e (Fig. 2) andcorresponding negative steel requirement.

Note that circumferential steel area 04/,)to resist lateral pressure is typically less than5% of the steel area (As) to resist footingbending moments.

DISCUSSION

Builders of cast-in-place concrete siloshave concrete, reinforcing steel and asteel-bender on site. For these builders, thereinforced extended ring foundationdescribed here poses no particular problems.Concrete stave silo builders, however, preferthe usual plain concrete footing placed into acircular trench in the ground. The trench isfilled with concrete up to grade line wherethe first ring of wall staves begins. Thisrequires considerably more concrete, butallows simplicity and reduced labor. Onsofter soils, the resulting plain footing isseldom as wide and never reinforced as goodengineering would require.

Silo builders have asked for designs forplain footings balanced under the silo wall,in preference to the reinforced extendedring. However, until more is known aboutthe distribution of silo floor loads and soil

reaction pressures, it is not possible toproportion a plain footing so that norotational moments can develop. The plainfooting also lacks reinforcing to resisttangential bending moments due to theconcentrated line load of the silo wall (Code,requirement (2) above), and lateral soil

116

expansion forces due to silage pressure onthe floor (Code, requirement (3) above).

The reinforced extended ring foundationdesigns given here (Figs. 4 and 5) have beencompared with earlier designs for"balanced" ring foundations with radialreinforcing published in the AgriculturalMaterials Handling Manual (NationalCommittee on Agricultural Engineering1964). The two methods give very similaroutside footing diameters. The extendedring design requires slightly more steel andconcrete than the "balanced" footing withradial reinforcing since circumferentialreinforcing is somewhat less efficient forresisting tangential moments.

This paper develops designs based on the"working stress" method of reinforcedconcrete design (CSA, A23.3, 1970). Acomparison with the newer "limit states"method (CSA, A23.3, 1973) showed that inone example, spiral steel area As could bereduced by 20%. This suggests that futurepreparation of the metric versions of plansresulting from this work should be based onthe more economical limit states method.

SUMMARY

A series of equations is developed fordesign of a family of extended concrete ringfoundations for cast-in-place and concretestave tower silos, based on a range of soilbearing strengths from soft to firm. Tominimize risks of silos overturning, a majorpart of the required footing bearing area islocated outside the silo wall circumference.

To resist footing moments developed bythe eccentricity of the silo wall loads withrespect to the centroid of the soil reactionpressure, and to resist lateral expansionpressures from the soil compressed under

the silo floor, circumferential steel is placednear the bottom of the footing.

Curves of design parameters to satisfy arange of silo sizes and soil bearing strengthsare included with this paper. More completeand convenient tabular design parametersbased on this paper are published as CanadaPlan Service leaflets 7411 Reinforced

Extended Ring Foundation for 6-inch Cast-in-place Concrete Tower Silos, and 7412Reinforced Extended Ring Foundation for2'/$-inch Concrete Stave Tower Silos.

REFERENCES

BOZOZUK, M. 1974. Bearing capacity of claysfor tower silos. Can. Agric. Eng. 16(1): 13-17.

JOINT CSA/NBC COMMITTEE ONREINFORCED CONCRETE DESIGN.

1970. Code for the design of plain orreinforced concrete structures. CSA Standard

A23.3, Canadian Standards Association,Rexdale, Ont.

JOINT CSA/NBA COMMITTEE ONREINFORCED CONCRETE DESIGN.

1973. Code for the design of concretestructures for buildings. CSA StandardA23.3-1973, Canadian StandardsAssociation, Rexdale, Ont.

NATIONAL COMMITTEE ON AGRICULT

URAL ENGINEERING. 1964. Agriculturalmaterials handling manual. Section 6.2types of storages. Queen's Printer, Ottawa,Ont. pp. 43—50.

NEGI, S.C., J.R. OGILVIE, and E.R. NORRIS.1977. Silage pressures in tower silos. Part 3.Experimental model studies and comparisonwith some silo theories. Can. Agric. Eng.19(2): 107-110.

STANDING COMMITTEE ON FARM

BUILDING STANDARDS. 1977. Canadian

farm building code. NRCC No. 15564,National Research Council of Canada,

Ottawa, Ont. p. 6.

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