DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW

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1 TR 219 Technical Report 219 DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW Sherood C. Reed September 1974 OA TASK 1T62112A131 CORPS OF ENGINEERS, U.S. ARMY COLD REGIONS RESEARCH AND ENGINERING LABORATORY HANOVER, NEW HAMPSHIRE APPROVED FOR PUBLIC RELEASE; OISTRIBUTION UNLIMITED.

2 I.. DESIGN OF FOOTI-NG FOUNDATIONS ON PO.LAR SNOW Sherood C. Reed September DA TASK 1T62112A131 CORPS OF ENGINEERS, U.S. ARMY COLD REGIONS RESEARCH AND ENGINEERING LABORATORY HANOVER, NEW HAMPSHIRE APPFH)VF:O F()R PllBLIC RELEASE; DISTRIBUTION UNLIMITEC.

3 i i PREFACE This stdy as condcted by Mr. S.C. Reed, Sanitary Engineer, nder the general direction of Mr. Kenneth A. Linell, Chief; Experimental Engineering Division, and the immediate direction of Mr. Edard F. Lobacz, Chief, Con- -st.rction Engineering Branch; Experimental Engineering Division,.s. Army 'Ctlld Reg.fons Resea;ch and Engiheering Laboratory. Li'etenant Colonel John E. Wagner as Commanding Officer /Director of the Labc_>ratory dring the prep aration of this repot and Mr.:..K. Boyd a's Chief Engineer.. This report is pblished nder DA Project 1 T62112A13, Research in Military Aspects of Terrestrial Sciences, Task 1, 1J ilit[y Aspects of Cold ' '... ;... Regions Research. The athor is indebted to SP5 Allen VandenHoek for his essential assistance in the analytical development and the preparation of this rep9rt. Dr. Arnold Kerr and Mr. K.A. Lin ell technically revieed the report. '

4 iii It. "' ' CONTENTS Introdction.... Procedre Reslts and analysis Time dependence..._ Temperatre dependence Density dependence... _..... Effect or load intensity Effe"ct of size Effect of shape Combined effects Point-of tangency !... Conclsions... ; Literatre cited..._... :.... Appendix A. Design application... :... >. Abstract......_... ;.._.... Page ILLUSTRATIONS- Figre 1. Footing and gage pad constrction Typical settlement-time relationship Settlement rate vs average sno temperatre Depth-density nder rooting test no. 13 (1965 series) Settlement vs time at -1C Settlement rate, time to point of tangency, and intercept vs initial specific gravity..._ , Settlement vs time, effect of load Settlement rate vs load intensity Settlement intercept vs load intensity Effect of size-settlement vs time Settlement rate vs size... ;._ Settlement intercept vs size Settlement vs time - effect of shape, 1961 series... ; Settlement vs time - effect of shape, 1965 series. ; Settlementrate ratio vs shape factor ratio K vale vs temperatre : Actal vs compted settlement, test 1 and 2, Actal vs compted settlement, test 3 and 4, Actal vs compted settlement, test 5 and 7, Actal vs compted settlement, test 8 and 9, Actal vs compted settlement, test 4 and 5, Actal vs 9ompted settlement; test 13, 1965 and Test "B," Byrd Station, Antarctica Table I. Test details II. K vales TABLES 2 18

5 . DESIGN OF. FOOTING FOUNDATIONS ON POLAR SOW.by SherOOd C. Reed INTRODUCTION The design of fondation systems for large-scale ice cap facilities presents special problems becase. of the inherent instability of sno. Any object placed at a near thesrfaceofan ice cap moves donard ith time as a combined reslt of the natral densification of the sno and the penetration of the object.. Natral densification is a continos process inflenced by 'the normal overbrden load, and reslts in the gradal consolidation of the permeable sno to ice. The process nite varies,. ith locale becase of environmental parameters bt can be considered niform over a particlar site. Methods are available to predict this rate (Bader, 1962). Its effects mst be considered if the strctral fondations cannot be placed and maintained in a horizontal plane or if te abs olte elevation of a facility is critical. ' The penetration of ari object is of primary interest to the design engineer since differential movements can impose severe stresses in strctrl elements and disrpt tility connections. Observations have shon that ttiis penetration, or settlement, for spread footings on sno depe11ds on: time, sno density, sno temperatre, load intensity, footing size, and footing shape. It is the. prpose of this :report to examine these parameters and to present an empirical meth,od that c pe sed by the design engineer to estimate the tiehavior of spreadfootings on sno.,. ; : Field tests ere condcted for this investigation at Camp Centry, Greenland, from throgh 1965 (Ryan, 1966; Reed, 1966):. The design eqations developed in this report are based on the relts of these tests. In general, they apply only to spread footings on fine-grained dry snos common to cold polar snofields. 'fhese areas are characterized by gradal changes in dens ty and grain type ith depth, At tnose sites exhibiting significant discontinity (i.e. stratification of very hard and very soft layers, ice glands and pipes, depth hoar, etc.), it is necessary to place the footings at a depth here these effects are minimal. Sch discontinities are sally common to the nely deposited layers at or near the sno srface. These very nstable srface layers shold be avoided to eliminate the possibility of sdden collapse or excessive settleent (Linen et al )..... The nine tests in the 1961 series ere designed and the installations ere made by Major.T.F. Ryan of the British Army Royal Engineers; reslts ere reported in detail by eed (1966)... Three di.fferent locations ere sed for the test series to evalate the sno dnsity and environmental parameters; The 1961 test footings ere placedi jn the fel storage area, in trenches 13 and 14, at the main camp. of the Camp Centry complex. The 1963 test footings.ere installed in ti ench 33, a special trench located east of the main camp. The final test installations ere made dring the 1965 smmer on the srfe north of the main camp. :... The 1965' srface installations ere made possible throgh the developmentof a ne sno constrction techniqe by Mr. W. Tobiasson of U.S. Army Cold Regions Res earch.anderiginering Laboratory. The test area as enclosed ith sno alls formed of disaggregate(r srio cst in. place in a constrction process similar to that employed for concrete. Sffiblent. 1JO'nd1g dccrred

6 2 DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW in the material to prodce self-spporting alls ithin 24 hors, permitting rapid stripping of the - plyood forms. A c<x'rgated steel roof spported on open-eb steel joints and covered ith a 1 ayer of procesed so completed the enclosre. Thi noical sno strctre providd the'. necessary protection from storms a.nd drifting sno. al)d tne test area as. still accessible in A detailed report on thls. techniqe is in preparation by Mr. Tobias son. ' Permanent copper-constantan thermocople strings ere installed at each location to monitor sno temperatre conditions dring the test period. Data ere collected continosly 'from 196'1 throgh early 1963 for the first test grop. PROCEDURE. - :.::.AU test footings ere composed of timber and plyood and ith the e,xception of the circlar and rctanglar nits ere constrcted _as shon in Figre 1.. The circl.ar footings ere bilt-p plyood sheets and the rectanglar footings ere a single timber of the dimensions given in Table I. Table I smmarizes details of te field tests condcted for this investigation. At least for dial. gages (;in. increment, 2-in. range) ere fixed to each _test footing. and. impi:nged on small pads locat.ed Ol) the adjacent sno srface. PeriOdic observation of these gages. indicated the settlement or penetration of the footings ith respect to the adjcent ndis- : trbed srface. The load sorce for all tests as a predetermined eight of pig iron symmetrically placed. OQ a pallet. This pallet asjoyrered onto the test footing ith mechanical ja.gks..for the 1961 and 1963 tests to approximate instantaneos loading. The 1965 tests ere incrementally loaded in place s_ince space limitations prevented the se of. mechanical jacks. Loading operations-ere.complete ithin :1 min for these tests. From late 1963 throgh 1966, Camp Centry as. closed dring the inter months; this permitted data collection only dring,the spring and smmer for tests condcted in this period. Since t.he dial gages fnctioned continosly it as possible to record the total settlement that occrre d!jring the inter. Table I. Test details. Initial* Tern per atre*r (- C) specific Long-term Test Test Series Size Load Shape gravity Constrction average dration (ft) (kips/ft 2 ) (days) * Sqare (diam) 1 Circle Sqare Sqare : Sqare X Rectangle ;11 3.D.5 Sqare Sqare Sqare Sqare Sqare Sqare o.5oot (diam) i Circle o.5oot 14 2C 39 H.I X 3,6 1 Rectangle: o.5oot Sqare Within a depth eqalto b/2 t. On processed sno.

7 DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW_ ,., "\' 3. Step Step Step <D Figre 1. Footing and gage pad constrction. Mixed nits (c.g.s. and English system) repeatedly appear in the development of this report. Glaciological data sch as sno density and sno temperatre are sally reported in metric linits. The adoption of specific gravity G as a parameter instead of density in the e9ations to.follo permits the direct tilization. of metric field density data i a dimensionless forin. Time dependence RESULTS AND ANALYSIS All the settlement-time plots have a similar configration hich is characteristic of the. viscoelastic stress-strain relationship described by Mellor (1964) for the creep of sno nder sstained load. Upon the application of load an essentially instantaneos strain as exhibited by all tests. This as folloed ithin mintes by a decreasing rate hich gradally approached a nearly constant vale.

8 4 DESIGN OF FOOTING FQUNDATfONS ON POL.ARNOW TIME, days J I If) Q.l..c c.4!--'" z _J (f) Oo TEST I ftsq,lksf.o 1.2 Figre 2. Typical settlement-time relationship. Figre 2 is a typical settlement-time plot for test 1. The settlement rate as essentially linear after a finite time period ith the exception of flctations that ere shon to be tempera. tre dependent (Reed, 1966). A simplified eqivalent of this plot cold be adeqately described by the slope and intercept of the linearportion and an estimated location of the initial point of tangency. The inflences of the varios parameters on these qantities ere examined separately and then combined. The traditional soils engineering approach sing ratios that compare the performance of a knon reference test to the desired nknon qantity as adopted in this analysis. The test reslts plotted on Figre 2 ere chosen as the reference case. To adjacent tests having this configration ere installed in 1961 and prodced practically identical reslts dring the 2 1 h years of observation (Reed, 1966). This dplication spports the validity of the reslts shon in Figre 2 and jstifies their selection as the reference case. Temperatre dependence The temperatre dependence :of rate processes is sally described by some modification of th relationship developed by S.A.. Arrhenis (Mellor, 1964 )": The effect ()f U;mperatre on the creep rate of sno has been described by Mellor as: here T temperatme, K referebct rem per at r at hich T has been mea rtd gas co11stant. (.98) cal/mole degree (1)

9 DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW 5 \. I 8 >. 6.c. 4 c <[ :: z _.J I I (/) (/) / 4 -L---L _j TEMPERATURE, C Figre 3; Settlement rate vs average sno temperatre;. f T strain rate at temperatre T Q activation energy, cal/ mole. The activation energy Q varies ithin the. rang 7, to 25,. cal/mole, ith 14, sggested as a fair niean for analytical prposes (Mellor, 1964). The performance of the reference case as examined to test the applicability of this relationship.. The settlement rates dring short time intervals verss the average sno temperatres ; ithin a 2. 5-ft depth dring the same time intervals are plotted on Figre. 3. The settlement rates are from. the linear portion (after 15 days ±) of Figre 2 only. There is some scatter bt the data can be adeqately described by,. s O.o489 e.182t (2) here s settlement rate, in./day T temperatre, C. sing a linear regressin program. Similar reslts ill.be prodced by.eq l if te aqtiyation. nergy is.taken as 22,. This is highr than te sggested ean bt ithin the reportedrange... qation 1 as theref.ore adopted for se ith an actiyation energy of 14, cal/mole since one;.test. '... '. 1..,., is insfficient evidence to spport the general valiity of the indicated 22, cal;triole....!. Eqation. 1 as sed in. this.analysis to convert test reslt- to a common -1C base for examination of-other parameters. Application of the methods.developed in this stdy. therefore re-. qires a readjstment from the base temperatre to: the ambient GOnditiops nder conderation... /

10 6 DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW so Figre 4. Depth-density nder footing test no. 13 ( 1965 series). Density dependence The creep of sno nder sstained load has been shon by many investigators to be strongly dependent on density (Mellor, 1964 ). A variety of exponential relationships relating creep and density are available in the literatre (Mellor, 1 964)., A density relationship for design prposes mst be ritten in terms of the initial in-sit density of the spporting material since these are the only data that ill be available. It is therefore necessary to determine the finite depth over hich the density ill be considered. A previos analysis of the 1961 test data hdicated that most of the densification cold be acconted for ithin a depth eqal to 1;2 the idth or diameter of a particlar footing (Reed, 1966). Frther evidence is shon on Figre 4 here inore recent test reslts give the same indication. A dept'h eqal to b/2, here b is the footing idth or diameter as thereforeselected as the effec., tive depth for this analysis. This same vale has been sggested and sed by othrs (Mellor, 1 969; Tobiasson, 197). ' Three -of the footing tests (1961, , , Table l) ere eqivalent in all physical respects except temperatre and the initial density of the spporting sno ithin the effective depth. The settlement-time relationships for these three tests, adjsted to a common

11 DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW TIME, days 7.26 lit tl).s::. c: 2 3 t- z 4 _J t- 't Cb (/) I = intercept, o =-specific gravity,' S =settlement rate. Fisre 5. Settlement. vs time at.. loc. 7 lit 6 > D t; 5 z C> z 4... z 3 a.. 2 :,; i= :1 6 5 lit CD..c: c:.--_ 4... a.. 3 z... 2 G =.35 to.55 s=.o323j.575-gi.6 D.5 i c: :::....3 :f _J.2 (/).1 (/) INITIAL SPECIFIC GRAVITY Figre 6. Settlement rate, time.to point of tan,ency, and intercept vs initial. specific lf8viiy. temperatre of -loc are shon on Figre 5. It is apparent that the intercept, slope, d point of. tangency for the linearized versions are dependent on the density, or specific gravity, of the spporting sno. These qantities are plotted vs the initial average specific.gravity (G) ithin the effective depth on Figre. 6. It as fond that the intercept and slope relationships cold be

12 8 DEIGN OF. FOOTING FOUNDATIONS ON POLAR SNOW adeqately described by a modified first order hyperbolic eqation. Sbstittion of appropriate vales and)e.rrangement of terms prodce: Intercept In ( GnlGR.) IR. - Gn!GR :. 784 (3) here In = intercept for nknon footing IR. = intercept for 'reference footing Gn IG R ;; rado of specific gravities. A straight line fitted by the method of least sqares as fond to give the best representation of slope and point of tangency data: Sn slope 3.85 ( 1.25:... Gn) GR (4) SR here Sn settlement rate for nknon. SR settlement rate for reference. The time reqired to reach the point of tangency as a fnction of the initial density can be approximated by: (5) here tn = time for nknon (days) tk = time for reference test (days). Sbstittion of reference test data prodces: Intercept In siope :sn.52- Gn).795 ( Gn-.359 (in.)..323 (.575- Gn) (in. /day) (3a) (4a) Point of tangency tn.'2855 (.5 Gn) (days) (5a) ith nits as defined previosly. The apparent limiting specific gravity of.575 as indicated by eq 4a is not a completely valid bondary condition as secondary creep ill occr at higher vales. Hoever, creep as det'ined here ill approach zero as- the specific gravity approaches the ltimate vale of ice (.918). To permit an approximation of creep at the higher densities, a specific gravity of.55 as arbitrarily chosen as the pper limit for eq 4a. A conservative estimate of settlement rate in the range.55 to.918 is given by: S =.245( G) (6) ith terms as defined previosly.

13 DESIGN OF FOOTING FQUNDATIONS ON POLAg-Sl)!OW -, : :1,.,... 1 Q & IC?J 1&1..J 1=c- l&.l {I).,, f'ooting DIN$1N$: " 111., Figre 7. Settlement vs time, effect of load. Eqations 4 and 4a are considered valid beteen G =.35 and G =.55, hich is tha range of primary _interest to the design engineer. The apparent pper limits of eq 3 and 5 are con sidered valid since test reslts ere observed near these vales. A direct comparison beteen these eqations and the reslts of other investigators is not' possible becase of the different treatment of the density parameters. The eqations in this stdy.alays refer to the initial specific gravity at time zero hile other methods are based on longrange average or instantaneos conditions. rn:oo& o locdl IDlISIDlUy Settlement of the five tests in this grop is plotted verss time on.fligre 7. All test fen& ings ere the same size and shape and ere exposed to similar environmental conditions. The initial specific gravity varied from.449 for test 9 to.55 for test 5 (1963). It is-6bvios abn&. both the slope and the intercept of tire linearized versions old be depand mton load intensity. Eqations 3 and 4 ere sed to adjst these data to a common initial specific gravity to elimin&me density dependence. A common vale of.458 as chosen since this as the initial SP8Cifi<! gravity for the reference case..

14 1 DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW 6 o Measred vales Adjsted to.458 specific gravity ; eqation 4 >. 'U... VI Q) c.. LLJ t- <1: ::... z LLJ LLJ _j UJ-. (f) (f) LOAD INTENSITY, lb/ft 2 Figre 8. Settlement rate vs load in tensity. These adjsted vales for settlement rate and intercept are plotted on Figmes 8 and 9, respectively. A linear relationship beteen settlement rate and load intensity is sggested by the data, at least p to 2 lblft\ A moe complex form is necessary to inclde higher loads and the folloing closely approximates all of the'adjsted data: (7) here s PIA settlement rate,. in./day load itensity, ksf. Sbstittion of vales for the reference case prodces the specific form:. ( (P/A)N ) SN = (p/a)n (7a) The settlement intercept verss load intensity data sggest an expone-ntial relationship. primarily becase of the position of the adjsted reslts (to specific gravity of.458) of test 5

15 DESIGN OF FOOTING FOUNDATIO!is ON POLAR SNOW 6. o Measred vales Adjsted to.458 specific gravity., "' 5.1: C...t 4 a.. L&.l : 3 L&.l z Where: 1 2 = Intercept at 1 lb/ft2 and G= I. 2 3 LOAD INTENSITY, lb/ft 2 Figre 9. Settlement intercept vs load intensity. (1963).. lf eq 3 and 4 ere not sed to adjst to a common density an approximately linear.depiid... ency old be indicated. The folloing crvilinear expression adeqately describes the adjted data bt shold be considered valid for loads p to 2 lb/ft 2 only:... 4(1?/ A)p/(.P! A) R 5- [(PIA)n/(PIA)R] (8} here In IR (PI A)ni(PI A)R ratio of intercepts for nknoit. footing and reference test ratio of load intensities. This expression can be sed as first approximation for loads in excess of 2 lbift 2 bt i.ts real validity in this range can only be established by frther investigation. E,fft qf size The reslts from for identically-loaded tests are shon n Figre 1. Except for initial discrepancies beteen tests 3, 4 and 5 the settlement rate is clearly depe.ndent orifootirig size. The smallest footing in these tests (test 3) shoed the highest settlement rate dring the initial period of primary creep. This cold be de to.s.lll'face irregij].arities nder the test installation

16 12 DESIGN OF FOOTING FOUNDATIONS ON folar,snj)w. i I.4 FOOTING NUMBERS 1961 Test Series DIMENSIONS. FOOTING LOAD:.1 psf TIME, days Figre 1: Effect of'size-set'tlement vs time. casing stress concentrations and a temporary increase in settlement rate. This is believed to be the IJlOSt proable cas since dring the lopg-range secondary ereep test performances refleced footjg size as,expected. ',.. '.. - Obviosly, the inflence of size is an expression of the magnitde of the pressre blb beneath the footing.' As the size increase.s the volme of material and deformable voids in the pres S].ll'e blb increases correspondigly. A preliminary analysis of these data (Reed, 1966) sggested the Jolloing eqation to express the relationship beteen settlement rate and size: (9) here S2/S 1 bl.. b2 ratioof settlement rates of to footings, in./day idth or diameter of footings, ft. An identical eqation is sed in soils fondation engineering; based on- the ork of Kogler, it relates the settlement of any footing to the movement of a plate 1 ft sqare (b 1 = l) (Terzaghi and Peck, 1948). Eqation 9 is graphically presented on Figre 11, sing test l as a reference,. here the secondary creep rates of the fortests. are plotted directly and, after adjstment ith eq3, to a common initial specific gravity.. Th eqation gives a reasonable fit fo the range of vales shon. It obviosly is deficient for very narro footings; as the idth approaches,zero one old expect the settlement to increase rapidly nder the- inflence of.the predominant edge effects.

17 DESIGN OF FOOTING FOUNDATIONS. ON POLAR SNOW 4xlo >.. 't:l... Cll Q).r; 3. c.. UJ <X a: 2 t- z :E I- I- (/) o Measred vales Adjsted to.458 specific gravity. 2 S=O.Ol33[ 1. 7 bb] g (/) b FOOTING WIDTH; feet Figre 11. Settlement rate vs size. 5.5 /(/I Q).r; c.4 a...3 a: z.2 :E _J_ --.1 (/) Measred vales Adjsted to.458 specific gravity b FOOTING WIDTH.,, feet Figre 12. Settlement intercept vs size. 5 ', The ettlement intercep_ts adjsted to a common initialspecific gravity (OA58) are!:;hoq._on Fig_r 12.' The scatter is believed d to the effect of SW"face irreglarities discssed previosly. These inconsistencies prevent a rig oro.s analysis, bt as a first approximation it is assed the ' intercpt is dependenton s1ze in a manner similar to that established for settlemen_tate.: '... ' ;,.' :. 2''34. ('. ' b21bt...,. )'.. :; L33 + b 2 /b 1.. (9a) atio of settlmentinterc.ept for to 'footings..._, t ' : '.: ',i :

18 14 z.8 UJ...J UJ (/) 1.2 DESiGN OF FOOTING FOUNDATIONS. ON: POLAR SNOW,.._, 1961 FOOTING LOAD: 1 psf. \ FOOTING NUMBERS -, 1961 Test Series WITH DIM:ENSIONS ::--- =---:..._ " x 43.25" RECTANGULAR I' 72 Figre 13. Settlel'llellt vs time -' effect of shape, 1961 series. TIME, days Vl Q).c c z _J (/) Shape, R 1 1 S in/day --- _!Conge _9.:_11 ' '..::::.::::-e Circie - ""-- _ 2_:142 --: L L- Figre 14. Settlmen(vs' time - effect of shape, 165 series. Effect of shape Aithogn this. parameter is not as significant 's those. previsly discssed it does 'prodce masrable inflence on settle.ment. Th t.heories. of Bossinesq and Westergaard sho that the depth of.significant stress in,flence increases a the shape is changed from a rectangle,to a sqare and then to a circle of eqal area. Similar conchisioris can be deriv,ed from the ork of :S. Hosel (1929),ho assmes that footing load is distribted to the fondation material thrq\.lgh a combination of compressive stress nder the footing and shear stresses arondthe primeter. Three differently shaped footings in the 1961 test grop (Fig.. 13) ere designed to examine this parameter. Inconclsive reslts preve11t a rigoros analysi,s so the examination as tra11s ferred to a similar grop of tests installed in 1965' on a thick layer of 'disaggregated processed sno. Figrre 14 shos that the total settlement of these tests as significantly greater than that

19 " ' DESIGN OF FOOTING FOUNDATIONS ON "POLAR SNOW 15. _: ( ;...' 1.5 <t ::: t-, : c::t ::: t- 1. z _j (/).5.j.;.n.5 1. ' L2f.fii2 --- SHAPE FACTOR RAJIO.. L1/.fi1 Figre 15. Settlement rate ratio vs shape factor ratio.. :, of the previos grop hich had been spported on natral ndistrbed sno. These differences are attribted to. the altered properties of the disaggregated material. Hoever, the reslts of these tests are believed to demonstrate the effect of shape on settlement. The res.lts of these three.tests indicate that for a: given area' the. sttiemeht ill decrease as the perimeter increa ses. Determination of a shape factor to describe this phenomeric:m mst reflect the geometric relationship beteen perimeter and area and mst be invariant ith size for a particlar.shape. The only sitable relationship to satsfy these conditions is: Shape factor here L perimeter A area. Figre 15 gives a plot of settlement rate against the shape facor for these tests. Data. are plotted as ratios ith the sqare footing test chosen s, the r_efereee.' :A 'straight line, fitted by the method of least sqares, gives the folloing relationship: ; '. (1). ; ; J The dght side of this' eqation redces t9 a constarit'for'reglar geometric.sh?-pes and satisfies the reqirement that it be invariant With size:.:t

20 16 DESIGN OFFOOTING F_QUNDATIONS ON POLAR SNOW Combined effects The final orking eqations ere prodced by combining the separate treatments of the individal parameters and ith sbstittion of vales for the reference case (test 1, 1961 series) to. prodce: settlement rate S, shon to be dependent on initial specific gravity, load intensity, size, shape and temperatre (eq 4, 7, 9, 1, and 11) and evalated for the reference case: ;()()384 (8.4) ( G) (26.3)_(. PI A )(2. 'Jj)( (1.43)( L) [ (7. 46) (PIA). 1 + i,}. _ 17 exp va. T since, (8.4) (263) (2. 79) (1.43) (. 384) Then: let K l = (3.38) exp[26.8 (746/T)]., Then, combining and rearranging terms: here S = i (.57S- G)( LJff K q VA - b/ s settlement rate, in./day q load intensity (PI A:4,ksf p footing load, kips (1 kip= 1 lb) A contact area, fe L perimeter, ft b footing idth or diameter, ft G. initial. specific gravity of spporting sno ithi a depth eqlto.. b/2...k constant, dependent on temperatre and, for ponvenience, illclding the combined coefficients from the reference case. (11) Vales for the constant K are shon in Table II for temperatres from -5C (23F) to -5C (-58F) and are plotted graphically on Figre 16. Extrapolation fortemperatres approaching OC (32F) is not recommended. The ratio L/yA is constant for circles and sqares so for these reglar shapes eq 11 re dces to: Sqares s = (o. 7) i (o575 G)L!!_f K q \1 + b/ Circles 2. S = (. 735) i ( G)f_l!_ \. K q \1 + bl (11a) (11b) It is necessary to conform. to the specified nits in eq 11, since dimensional qantities for the reference case have bee inclded in the K-factor '.. '

21 .,,... :; DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW t-:, :.s "- ' -2 TEMPERATURE, oc TEMPERATURE, C Figre 16. Kvale vs temperatre (see eq 11 for definition of K). Intercept I as shon to be strongly dependent on size, density, load and temperatre. The effect of shape is minor and is therefore neglected. _I_. = (2.34)(-b-)(1.59)( 52 -G.)(4.)( P/ A ) ex (746/T).6 2+b. G (P/A) p if K- 1 = (3.38) exp[26.8- (746/T)].. Then \. I = _(2.65).(-_ b ) K 2 + b 5 :- q G )(.52- G) (12) here I = settlement intercept, in., and other tems are as defined previosly. Point of tangency This vale gives an estimate of lhe time reqired for the onset of a linear settlement rate of secondary creep. A :sitable approximation can be obtained by considering only the specific

22 18 DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW TaMe D. K valaea.. K K i ' ; o.4rl2853. g:uajfi (] as '73 1( * See eq 11 for definition. TIME, ft sqare, I ksf G=.458, T 1 =-16 C, T 5 =...,2CC Test dration: 698 days Total settlement Actal: I. 2 in. Predicted: I. 2 in. cn.8 Q).r:. c TEST I L-----L L :e _J en.4 8 TEST ft dla, circlar, I ksf G=.463, T 1 =-16 C, Ts =-2 C Test dration: 699 days Test settlement o o Actal: 1.1 in. o Predicted: 1.21n.. i,' Figre 17. Actal vs compted settlement, test 1 and 2, 1961.

23 DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW TIME, ft sqare, I ksf G=.455, Tr=-I6 C, T 5 =-:-2 C Test droti on: 7 I days ) Ill Q).c. g 2.._:- z. _J. I I (/) 1. TEST ft. sqare 1 ksf G=.455, T 1 =-I6 C, Ts= -2 C. Test dration: 693 days Total settlement Actal : 2.3 in. Predicted:2.4 in. 2. Figre 18. Actal vs compted settlem.ent, test 3 and 4, TIME, 1. en Q) -B 2. c:.,..: z _J I I (/) TEST ft sqare,.5 ksf G=.455, T 1 =-I7 C, T 5 =-2 C Test dro t. ion: 69 4 days Total settlement Actal :.9 in. Predicted :.9 in. Figre 19. Actal vs compted settlement, test 5 and 7, gravity dependence, so other factors ere neglected. Its primary vale is to enable the graphical estimation of a time-settlement plot to be made. Having compted and plotted intercept and settlement rate, a smooth crve from the origin to this point of tangency ill give. a reasonable approximation of primary creep: t = (2855)(.5G) (13) here t =- Plapsed time to poit of tangency, dys. and other terms are as defined previosly.

24 2 DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW.1, 3. ft sqare, 1. kif G=.453, T 1-11 c, T; -2 c Test dra.tlon: 12 do.p Total settlement Actal :2.4 ln. Predicted :2.1 ln. 2. II).,.c....: z 3. L!J 2 L!J...J L!,J' en \o TEST \ ' ' '- Oo I,. TEST Oo.o o oo 3. ft. sqare, 2 ksf G=.449, Tr=-17 c, Ts=-2e>-C Test dration: 63 days Total settlement_ Actal :J.5 in. Predicted ;3,6 ln. Figre 2. Actal vs compted settlement, test 8 and 9, TEST ft sqare, lklf. G.59 T 1 -ll c, Ts-2 c Test dration: 29 days Total settlement Actal :Q.21n. Predlcted:.21n. : or r ft sqare, 4 ksf G=.55, Tr=-II C; Ts -2o c Test dration: 429 days Toto I settlement.c. c.,.: z L!J..:J I- I- L!J.. en 2. 'o. Actal :4.11n. Predicted:3. 91n TEST Figre 21. Actal vs compted settlement, test 4 and 5, 1963.

25 DES,.IGN OF FOOTING FOUNDATIONS ON POLAR SNOW days 21 VI Q).I::. c " z t--"" 2. "... Cb "- :!: ' ft sqi.jdre, 1 ksf oc G=.384 T 1 = 14 C, Ts =,-2 Test dration: 3 2 days Total settlement Acta I :4:2 in. Predicte.d :4. 1 ln. 4 o r ,tes5-rfll33,.,.;..:_;:;-.::. --=-.=-:-:.=:...=::...:==-==-= =?-=.ao."o"no... : d (/) 1965 VI Q)..c c.2 :!:...J r-.4 (/) 5 TEST"B" Byrd Station, Antarctica 1962 TIME, days 1 ' ft sqare, lksf G =.48, T= variable.-17 to..,. 9 t Test dr:oti9n: 21 days Total settlement ' Actal ;.36 in. Predicted :.34 in. ---:--:.--- Figre 22. Actal vs compted settlement, test 13, 1965 and Test" B," Byrd Station, Antarctica. The reslts of eq 11, 12 and 13 are. compared graphically ith the actal settlement of the test footings on Figres 17-22, The black dots indicate the compted point of tangency. The compted reslts are completely adeqate for engineering prposes in every case. The measred average smmer temperatre as sed to compte the intercept and the measred average annal temperatre to compte the settlement rate,. A closer intermediate fit ith field data cold.have been obtained by incremep.ting eq 11 ith actal average temperatre vales: for s_rrialler time periods,. Figre 22, test B, shos the analysis of a test footing installed at Byrd Station, Antarctica (Mellor and Morelli, 1962). The average sno temperatre in 25-day increments as sed in sccessive applications of eq 11 to prodce the crvilinear form shon. Initial sno density measrements at this locale hoed a vry.erratic pattern varying from.46 g/cm 3 to.5'3 g/cm 3 ithin the significant depth. A vale of.48 g/cm 3 as sed in the an.alysis presented in this stdy. The sccessfl application of the eqations to this test indicate that the approach is not.limited by locale. Application of these techniqes to a design sitation is illstrated in Appendix A. CONCLUSIONS 1. The settlement of spread roofings on sno is dependent on: time, sno density, temperatre, load intensity, footing size and shape. Empirical eqations relating these parameters have been developed in this report. These eqations permit the calclation of the linear secondary. settlement rate S, and an intercept I and point of tangency t for plotting prposes. These eqations are: Settle.ment rate S =.!!_ (.575- G) (l _.5L) (-b-)2 K q y A 1 + b

26 2! DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW here S = )etlment rate, in./.day q load intensity, ksl A contact area, ft 1 L perimeter. ft b = idth or diameter, ft G :::z initial specific gravity of spporting sno ithin a depth eqal to b/2 K dimensionless constant, dependent on temperatre, evalated in Table II. The ratio L/VA redces to a constant for reglar geometric shapes: Sqares S = O. 7!( G)(-. b \2. K q l + b} I Circles S (;735)!!.( G)f_E_f.. K q \i + b/ Intercept I = 2.65 (.52- G)( q ) ( b ) T G q 2 + b I here r = intercept, in. t and other terms are defined previosly. Point of tangency here t ::;:. time,. days. t = (2855)(.5 G) 2. These eqations predicted the performance of the 12 test footings discssed in this report ith an accracy sitable for engineering prposes. To ensw'e a comparable ac9racy in design applications the folloing limits are sggested for inpt data: G =.35 to.55 Temperatre =:= 5C to -5C; Load intensity q = to 2 ksf; Sizeb :t: 1 ft loer limit. Since most ice cap sitations fall ithin these limits no severe restrictions are placed on the designer. 3. Field measrements reqired consist only of in-sit sno dens1ty and temperatres beneath the proposed location. For very critical facilities a more extensive investigation inclding field testing old be advantageos. If time permits, the observation of an 18-in. sqare test footing, loaded to 1 ksf old provide referenc data similar to data sed in the development of the eqations presented in this stdy. If reqired, this old permit modification,of the eqations to reflect particlar local conditions. 4. It mst be remembered that the reslts predicted by the eqations represent only the penetration of the footing into the sno. If total absolte settlement is of interest. the portion de to. natral densification of the spporting sno mst be inclded. 5. As stated previosly, the approach developed here is entirely empirical. Its major advantage is believed to be its relative simplicity compared ith previosly developed empirical

27 DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW 23 approaches. Becase of its emf:>il"ical nat.re; the techniqe does not provide any real insight into the fndamental stress-strain relationships involved. Theoretical treatments of footing behavior on viscoelastic materials by Kerr (1962) offer an approach to the fndamental processes. A combination of the techniqe described here and Kerr's treatment old provide a more rational basis for a ider variety of design applications. Work in this direction has been initiated and its contination is recommended. LITERATURE CITED Arctic Constrction and Frost Effects Laboratory (1947) Investigation of constrction and maintenance of airdromes on ice Report of Engineer Observers on Project Snoman of Atlantic Division, ATC, Ne England Division, Corps of Engineers, Technical Report 15 (AD ).. Bader, H. (1962) Theory of densification of dry sno on high polar glaciers,..s. Army Cold Regions Research and Engineering Laboratory (USA CRRE L) Research Report. 18 (AD ). Hosel,.s. (1929) A practical method for the selection of fondations based on fndamental research in soil mechanics. University of Michigan, Engineering Research Blletin no. 13. Kerr, A.D. (1962) Settlement and tilting of footings on a viscos fondation. USA CRREL Research Report 81 (AD ). Mellor,.M. (1964) Properties of sno. Cold Regions Research and Engineering (F,J. Sanger, Editor), USA CRREL Monograph II A1 (AD 61123). Mellor, M. (1969) Fondations and sbsrface strctres onsno. Cold RegionsResearch and Engineering (F.J. Sanger, Editor), USA CRRE L Monagraph III-A2c (AD ). Mellor, M. and Morelli, P. (1962) Stdies in applied glaciology, Antarctica Report sbmitted nder National Science Fondation Grant G Reed, S.C. (1966) Spread footing fondations on sno. USA CRREL Technical Report 175 (AD ). Ryan, J.F. ( 1966) Footing tests on dry sno (Camp Centry, Greenland), USA CRRE L Internal Report 2 (npblished). Terzaghi, K. and Peck, R.B. Soil mechanics in engineering practice. Ne York: John Wiley and Sons. Tobiasson,.N. (197) Stresses developed on strctres bried in sno. Thayer School of Engineering, Dartmoth College, Gradate Thesis.

28 AIPI?l&WBJKX A: DESRGN APIPLKCATKON Minimm reqirements for design inclde a temperatre profile to a depth of 1 m (32.8 ft). belo the sno srface and accrate depth-density data at the footing location. Techniqes for obtainingthese data are described by Mellor (1964). It can be assmed that the temperatre observed a the m d_epthtn an ndistrbed area is very close to the mean annal temperatre_ for the ste (Mellor, 1964). This is sitable for design prposes if the intended fondations are plac'ed 15 ft belo the srface and are protected from sbseqent heat sorces. Design of fooings.31t shall.?er depths mst reflect the cyclic temperatre changes. If exact data are- not available K is sggested that smmer temperatres at the desired depth be assmed to exist for for moths' and the' mean annal temperatre for eight months in the design calclations. Any heat losses from the proposed facility mst also be considered. The presence of ice lenses in the sno mass ithin the effective depth (b/2) has a direct effect on inpt data for the eqations. Since this material cannot densify rther it shold not be inclded in a determination of average specific gravity. Only material ithin the effective depth having a specific gravity less than. 9 shold be consideed. Since ice lenses might be discontinos over a given area a sbsrface exploration at or near each footing is necessary to insre homogeneity of spporting material to avoid differential settlements.. The eqations are.all based on 'the assmption that.:_each footing acts independently. A spacing, edge-to edge of adjacent footings, at least eqal tcdhe idth of the largest as indicated by the performance of these test foot1ngs (Reed, 1966), shold be adeqate. ':! A hypothetical example is given belo to illstrate the application of the design eqations. As shon belo, the design procedre is a series of trial.;.and.. error operations for size determination. Example: Colmn load Footing elevation Design life. 3 kips 1 ft belo srface 5 years Design footing to limit settlement to not more than 2 in. /year. Field measrements: Depth Specific Temp J!!L_ gravity (-oc) ;) '.5 1 (), 15 1 (i HLO Assme b/2 = approximately 2.5 ft. Then: G (<l\trage) "".49; T (smmer) T (mean annal) = -19.C. From Tablr II, for T (smtr., i l. K -.525: for T(inten. K -15.5C;.76:3.

29 26 APPENDIX A I,,:. Time to po1nt of tangeacy: t 2855(.5 G) = 57 days. Assme constrction to occr dring early smmer; so intercept I calclation to be based on smmer temperatres. I (2.65).( b )( q )(.52- G') = K 2 + b 5- q G Sbstitting then ( 2.65)( b )( q )( ) = b 5- q = (1.155) (-b)(-. q ). 2+b 5-q Try a 4-ft sqare footing b = 4. \ 3 q = - = ksf 16 I = (-b)(- q ) 2+b 5-q b 4. q I.473 in. and s = (o. 7)!!.. (.o:s7s - a\(_e_)2. K q J l + b For a 4.-ft sqare footing ith q = 1:875.,.264 s == --- K.264 In smmer months, :s =.55 in./day In inter months, S = ==.346 in./day..763 Total settlement: 1st year I + St (smmer}+ St (inter)

30 APPENDIX A 27 1st year (.473) + (.55) (12) + (.346)(245).. i,!-r :.< i<..,1 Jit.. t.o in. is less than 2 in. Therefore the 4-ft footing is sitable. Thei!Ao each remaining year in. is less than 2 in. Recheck density and temperatre assmptions: b/2 = 2. ft then, and, S<i: G (average) T (smmer) K (smmer).49 in..49 hich eqals original assmption -15.4C.519. and S (smmer) in./day. Total settlement: 1st year.49 + (.59) (12) + (.346) (245) in. - O.K. to se 4-ft sqare footing. A sqare as arbitrarily adopted in the example bt similar calclations for other shapes are also possible. The first year settlement controls in the example since 2 in./year as set as a limiting vale. If in the actal facility some adjstment ere inclded to compensate for primary creep, the design cold be based on the loer steady-state creep rate and a footing size smaller than 4 ft old be sitable. The folloing procedre is recommended to limit differential settlement among a grop of footings here total settlement is not especially critical: 1. Determine the size for the most heavily loaded colmn so that bearing pressre is abot 2 ksf, then compte settlement. abov-e. 2. Determine the size of other footings to prodce the same settlements as compted

31 Unclassified Secnty ClassificatiOn DOCUMENT CONTROL OAT A R & D (Secrity classilicstion of 1/rle, body ofabiltrsct and index.ln annotation mst be entered hen the overall report Is claaolfle 1 ORIGINATING ACTIVITY (Corporate athor) 2a. REPORT SECURITY CLASSIFICATION.s. Army Cold Regions Research and Unclassified Engineering Laboratory 2b. GRoP Hanover, Ne Hampshire 375r:; 3 REPORT TITL DESIGN OF FOOTING FOUNDATIONS ON POLAR SNOW 4. DESCRIPTIVE NOTES (Type of report and Inclsive dates) !> AU THORIS) (First name, middle initial, last name) t Sherood C. Reed e-sr;r-a-;r , e.TOTALNO.O;AGES. 17b.NO_O_F_R-F-S l CON:rRACT OR GRANT NO. 91J. ORIGINATOR'S REPORT Nl.IM'BER(S) t. f'f;cjec T NO. c. DA Project 1 T62112Al3 Task 1 d. I C. D I S 1 R I B U T I "' S T A T EM EN T Technical Report 219 lib. OTHER REPORT NO(S) (Any other nmbers that may be assllfled this report) Approved for pblic release; distribtion nlimited I-,. _S_U_P_P L_E_M_E_N_T_A_R_V_N_O_T'"""E_S ,-2.-S-P_O_N-SO_R_I_N_G_M_I_L I_T_A_R_V_A_C_T_I.,.-V-1 T-'1'-----: US. Army Materiel Command 13.. ABSTRACT Settlement of spread footings on sno is dependent on time, sno density, sno temperatre, load intensity, footing size and footing shape. Empirical eqations,. based on field test reslts at Camp Centry, Greenland, relating these parameters are developed in this report. The eqations are ritten to permit simple hand calclations so they do not reqire a complex mathematical techniqe or compter application. 14. KEY WORDS Footing fondations Greenland sno Sno density Sno temperatre I. llltiiislacill DO srorm I UI. I JAN 84, WHICH 18 OB8LiiTiil.. OR ARMY USfl. Unclassified secrity cteirtcation

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