INTERNATIONAL SOCIETY FOR SOIL MECHANICS AND GEOTECHNICAL ENGINEERING
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This is an open-access database that archives thousands of papers published under the Auspices of the ISSMGE and maintained by the Innovation and Development Committee of ISSMGE. 4/63 Friction between Sand and Metal Surface
Friction entre Sable et Surface Metallique
Y. YOSHIMI Tokyo Institute of Technology, Tokyo, Japan T. KISHIDA Toa Harbor Works Co. Ltd., Yokohama, Japan
SYNOPS I S Large frictio n a l resistance is desirable for fric ti o n piles and reinforced earth, whereas low fric tio n is desirable fo r negative skin fric tio n and selfboring pressurem eters. To cope w ith the problems one needs quantitative inform atio n of fric tio n a l resistance as w ell as deform ation of so il near the contact surface because the normal stress may be sta tica lly indeterm inate. This paper presents the results of laboratory tests on f ric tio n between dry sand and m etal surface under constant normal stress conditions over a wide range of surface roughness and sand density. A ring torsion apparatus was used to achieve uniform stres s d istrib u tio n over the contact surface and w ithin the sand specimen. The deform ation in sand n ear the m etal surface was observed by means of X-ray radiography. In addition to the effects of su rface roughness on the ultim ate co e fficie n t of fric tio n , the relationship among m obilized fric tio n , shear strain and slip are discussed.
I NTR O DUCTI ON A PPARA TU S A ND TEST PROCEDURE
F rictio n between so il and structures often plays A ring torsion apparatus as shown in Fig. 1 was an im portant role in geotechnical engineering. used. Dry sand was rained into the annular Large fric tio n a l resistance is desirable for container lined w ith 0.3 -mm th ick rubber mem fric tio n piles, reinforced earth, or base of branes, and the top surface of the sand was retaining w alls; whereas one wants to m inim ize leveled w ith a suction device. A ring shaped fric tio n along the surface of so il samplers or m etal specimen was then placed on the sand, and selfboring pressurem eters, or point bearing sta tic torque was applied thereupon w hile a piles where negative skin fric tio n poses a prob constant ve rtica l load was applied w ith w eights. lem. Because frictio n is not sta tica lly deter The ve rtica l stress covered a range from 25 to m inate in many o f those problem s, one needs to 15 8 kPa (0.26't'1.61 kgf/cm 2) w ith 105 kPa used know not only maximum fric tio n a l resistance but for most tests. The torque was applied in such also friction-displacem ent relationship. The a way that the m etal surface mo ved at a rate o f need fo r re lia b le estim ates of fric tio n between about 0. 6 mm per m in. in circum ferential direc so il and solid surface has increased in recent tion. In addition to measurements of circum fer years w ith the development of analytical tech e n tia l and ve rtica l di splacem ents of the m etal niques and w ith the recognition of the negative ring, the deform ation of the sand and slippage skin fric tio n problem in which underestim ation at the soil -m etal contact were measured in some of fric tio n causes an error on the unsafe side. tests using X-ray radiography.
Based on d ire ct shear tests on skin fric tio n The ring torsion apparatus is essentially the between various so ils and three construction same as th a t reported by Yoshim i and Oh-oka m aterials (steel, wood, and concrete), Potyondy ( 1973). Compared w ith a d ire ct shear de vice the ( 1 961) identified four m ajor factors that de ring t orsion apparatus has the follow ing ad van term ined skin fric tio n , i.e ., "the m oisture tage s: ( 1 ) the stresses and strains w ithin the content of so ils, the roughness of surface, the specimen are nearly uniform , ( 2 ) because the com position of soils, and the intensity of nor specimen is endless it is free from progressi ve mal load." Esashi et al (1966) showed that skin fa ilu re that w ould in itia te at the ends of a fric tio n between sand and three construction d ire ct shear de vice, and (3) unlim ited circum m aterials (steel, wood, and concrete) could be fe re n tia l di splacem ent can be applied. Three correlated w ith quantified surface roughness sands as shown in Table I and three m etals, i.e . regardless of the type of m aterial. In both re stru ctu ra l steel, brass, and aluminum, were ferences, the d ire ct shear apparatus was used in tested. Eighty tests were carried out for va ri which stresses and strains could not be uniform ly ous com binations of the density of the sands and distributed and the physical significance of the the roughness of the m etal surface. The surface displacem ents could not be cle a rly established. roughness was expressed in term s of a maximum height, Rmax, that is the re la ti ve height be The object of the present paper is to quantify tween the highe st peak and the low est v a lle y the effects of the roughness of m etal surface along a surface p ro file o ver a gage length o f and the density of sand on the skin fric tio n 2.5 mm. The contact surfaces of the m etal rings between dry sand (three sands) and m etal sur were finished so that Rmax co vered a range fr om face (three m etals), using an apparatus in which 3 to 510 ym, which included w ith ample m argins stresses and strains are nearly uniform ly dis the range between 10 and 150 pm fo r ordinary trib u te d . construction m aterials. D etailed descriptions
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AB I T LE Pr oper t i es of Sands Test ed PLAN Hydr aul i c j ack Sand Toyour a Tonegawa Ni i gat a Met al 5 i men Mini mum voi d r at i o 0. 628 0. 717 0. 611 Wir e r ope Maxi mum voi d r at i o 1. 019 1. 157 0. 947 10 % si ze ( mm) 0. 16 0. 18 0. 18 Uni f or mit y coef f i ci ent 1. 31 1. 83 1. 64 0. 105 0. 105 0. 105 Grai n si ze r ange (urn) ^ 0. 25 ~ 0. 71 -v-0.71 fr Speci fi c gravi ty of sol i ds 2. 64 2. 76 2. 66 X- r ay sour ce Wat er cont ent (%) 0. 09 0. 51 0. 24 Sand speci Grai n shape Rounded Angul ar Subr ounded Grai n sur f ace Med i um Rough Smoot h
SECTION o f the te s t pr o cedure are given b y K ishida (1979).
FRI CTI ON-DIS PLACEMENT RELATI ONSHIP
Fig. 2 shows a typical set of te st results for Wei ght s the Tonegawa sand ha ving an in itia l relative den s it y of 60 %. The circum ferential displace ment is expressed in a dim ensionless form by d i viding it b y the in itia l height of the sand (22 mm). As one would expect, the maximum coef Met al speci fic ie n t of fric tio n increases w ith the surface roughness. Note a w ell defined "stick -s lip " phenomenon fo r Rmax<.5 pm (F ig. 2(a)), and marked dilatancy fo r Rmax>.220 ym (Fig. 2(b)). Rubber On the other hand, the in itia l portion of the Sand speci men friction-displacem ent curves is p ra ctica lly un Acryl i c ri (9 ^ 42 mm hi gh) affected by the surface roughness as shown in Load cel l F ig. 2 (a'). This is attributed to the fact that For r adi ogr aphy —► For st andar d t est s w ithin a certain lim it (in th is case, x/h< 1.5% o r T S / Ov < 0 .4 ), n o s lip devel o p s at the c o n ta ct F ig. 1 T e s t Apparatu s s u rface even f o r the s m o o th e s t s u rface; there f o re the di s placem ent s are w h o ll y accounted fo r EFFECTS OF SANDS AND SURFACE MATERIALS ON THE by the deform ation of the sand its e lf (Fig. 6 ). FRICTI ONAL RESISTANCE The data of Fig. 2 contradicts the pre v i ous a ssu m pti o n that the in itia l tangent m o dulu s i s A s s h ow n in Fig. 3 the c o e ffic ie n t o f fric ti o n p r o p o rti o nal t o the ultim ate fric ti o n a l re s i s t i s e s s e n tia ll y go verned b y the surface roughness ance (e.g.. Sm ith (I960)). w ith the re la ti ve den s it y of the sand and the
(*)
- 0. 5
0. 0
0.5
Fi g. 2 Typi cal Test Resul ts of Steel and Tonegawa Sand
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T------r To.y oura Sand A Steel Dr = 40 ! 40° Steel 60 Steel 90 Brass 65 Al umi num 65 30° *% 0. 4 Soma Sand 20 ° • Steel Usual r ange f or Wood 0. 2 - ■ C oncr et e const r act i on 10° mat er i al s Machinist's symbol . 0. 0 10 20 50 100 200 500 1000 Sur f ace Roughness, Rmax (y m) Sur f ace Roughness, Rmax (y m)
Fig. 3 E ffects of Sand Density and Surface F ig. 4 E ffects of Kind of Sand on Coef M aterial on C oefficient of F riction fic ie n t of F riction surface m aterial playing a negligibly m inor part. shear stress ra tio . On the basis of the obser The data points fo r Soma sand (Esashi et a l, vation by Oda and Konishi (1974) that the shear 1966) which include tests on wood and concrete stress ra tio at the horizontal surface of a speci as w ell as steel appear to agree w ith the au men of rod mass during sim ple shear is propor thors' test results. Fig. 4 shows that the kind tio n a l to the tangent of the angle between the of sand has little influence on the co efficie nt ve rtica l axis and the d irection of the maximum of fric tio n if Rmax exceeds about 20 uni. For a principal stress, and on the basis of the postu sm oother surface (Rmax < 20 vim) , however, the la te by O chiai (1975) that the maximum shear kind of sand seems to make some difference, in stress ra tio during la te ra lly confined compres th a t the Tonegawa sand having angular, rough sion of granular mass is equal to tan^y, one can grains has larger co efficient of fric tio n than derive from statics the follow ing relationship: the Toyoura sand w ith rounded, medium rough J.__r _ 2 l/sin
The values of Smax computed by Eq.(l) are in LOWER AND UPPER LI MITS OF FRICTI ONAL ANGLE fa irly good agreement w ith the observed values as shown in Fig. 5. Although under favorable conditions it is possi -i------T1------r ble to obtain extrem ely smooth m etal surface 4 whose Rmax is as sm all as 0.1 ym, a minimum obser ved f r om pl ane pul t value of Rmax in geotechnical applications is strai n compr essi on t est 1.2 probably about 2 ym. According to Lambe and <“ 50' (d comput ed f r om ^ i t anc* $y W hitm an (1969), the frictio n a l angle of a very e e ■o
As shown in Fig. 5, the fric tio n a l angle, 6 m ax, F ig s. 6 (b), (d), (f) show typical results of X- fo r a very rough surface (Rmax = 510 ym) appears ray observations during fric tio n tests using somewhat lower than the ultim ate angle of in te r steel and medium dense Tonegawa sand. Each sym nal fric tio n ,
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ded in the s and. T h u s , the h o riz o ntal di s tance between the t o p s ymbol and the symbol w ith an arrow shows the amount of s lip at the sand-m etal interface, xs, as shown in the key sketch.
When the m etal is very smooth (Figs. 6 (a), (b) ) , the sand is sheared uniform ly w ithout developing a shear zone; therefore the circum ferential dis placem ent of the m etal consists m ostly of s lip . The phenomenon resem bles that of so lid -to -so lid fric tio n in that dynamic fric tio n is sm aller than static frictio n . This is reflected in Fig. 6 (b ') in which the shear strain in the sand de creases as the s lip distance increases. When the m etal is slig h tly rough (Figs. 6 (c), (d) ) , a shear zone develops near the m etal surface im m ediately a fte r a slip occurs. The shear zone begins to form when the shear stress ra tio ex ceeds about 75 percent of the co e fficie n t of fric tio n . When the m etal is very rough (Figs. 6 (e), (f)), on the other hand, a shear zone develops in the sand w ithout a slip . This con d itio n corresponds to the upper lim it of co e ffi cient of fric tio n . The thickness of the shear zone fo r the present te st series was 3 Rmax to 5 Rmax or 5 to 8 tim es the mean grain size.
CONCLUSI ONS
The follow ing conclusions may be made on the basis of the laboratory tests on fric tio n be tween three sands and three m etals under con stant normal stress conditions:
1. The fric tio n a l resistance between sand and m etal surface was p rim a rily governed by roughness of the m etal surface irrespective of the kind of m etal and the density of sand.
2. The fric tio n a l angle fo r a very smooth m etal surface was less than one h alf of the par- tic le -to -p a rtic le fric tio n angle,
3. The fric tio n a l angle for a very rough surface could be expressed as a function of the ultim ate angle of internal fric tio n , ifult and the p a rticle -to -p a rticle fric tio n angle, (j)p.
4. According to radiographical observations of the sand no s lip occurred at the contact surface when the shear stress ra tio was less than 70 to 80 percent of the co e fficie n t of fric tio n , irrespective of the surface rough ness . F ig . 6 Deform ation of Sand Observed by Ra diography (S teel and Tonegawa Sand)
REFERENCES Found.Engg., (15), 4, 93-100 (in Japanese).
Esashi, Y ., Kataoka, T ., and Yasuda, M. (1966). Oda, M ., and K onishi, J. (1974). Rotation of U p lift resistance of piles: Part 1, Cohe- principal stresses in granular m aterial sionless so il. Report of C entral Research during sim ple shear. S oils and Foundations, In stitu te of E le ctric Power Industry (14), 4, 39-53. [66037], 1-60 (in Japanese). P otyondy, J.G. (1961). Skin fric tio n between Kishida, T. (1979) . Fundamental Studies of various soils and construction m aterials. F rictio n a l Resistance between Sand and G eotechnique, (11), 4, 339-353. M etal Surface. Doctoral D issertation, S m ith, E.A.L. (1960). P ile-driving analysis by Tokyo In s titu te of Technology, Tokyo, 235pp. the wave equation. ASCE, J.S o il Mech. (in Japanese). Found.D iv., ( 86 ), SM4, 35-61. Lam be, T.W., and W hitman, R.V. (1969). Soil Yoshim i, Y. and Oh-oka, H. (1973). A ring tor M echanics, John W iley & Sons, New York, pl44. sion apparatus fo r sim ple shear tests. O chiai, H. (1975). The behavior of sands in d i P roc. 8 th In t. Conf. S oil Mech. Found. Engg., rect shear tests. J.Jap.Soc.Soil Mech. (1.2), 501-506, Moscow.
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