Scaling of supersaturation by a simple test

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1 Permafrot, Phillip, pringman & Arenon (ed) 2003 et & Zeitlinger, Lie, IBN caling of uperaturation by a imple tet M. Dyli oil Mechanic Laboratory of the i Federal Intitute of Technology, Lauanne, itzerland ABTRACT: The term uperaturation i ued to define permafrot that contain a volume of ice greater than the volume of pore ater before the freezing of the oil. In engineering practice, the aturation of a oil i alay numerically defined, but thi i not yet the cae in the permafrot cientific community. uperaturation ith regard to hat? Thi hort paper propoe a imple method for the numerical definition of the uperaturation of a permafrot baed on a ell-knon civil engineering tet. 1 INTRODUCTION The term uperaturation or uperaturated permafrot are ued to define permafrot that contain a volume of ice greater than the volume of pore ater before the freezing of the oil (for intance: French 1996 p. 87, Haeberli 1996), hoever thee term are not yet commonly ued. Of more ignificance, the degree of uperaturation i not numerically defined in the permafrot cientific community a the degree of aturation i in oil mechanic. uperaturation ith regard to hat? Thi hort paper attempt to rectify thi omiion. It define hat i meant by aturation in oil mechanic, for unfrozen a ell a for frozen oil. It then goe on to define uperaturation and the degree of uperaturation. Finally, it propoe a imple mean for the quantification of degree of uperaturation for frozen oil. 2 ELEMENTARY BUT COMPULORY DEFINITION In oil mechanic, the aturation of unfrozen oil i defined by the degree of aturation r (Fig. 1): r r e r v r rd ( r r ) r d (1) here i the volume of ater, v i the volume of void, i the ater content M /M, r i the denity of olid particle M /, r d i the denity of dry oil M /, r i the denity of ater and e i the void ratio v / (r r d )/r d. The degree of aturation r cannot exceed 1 ( a 0). Thu, an unfrozen oil cannot be uperaturated. In Figure 1, the to ytem that contain volume or mae of oil are aid to be cloed, i.e. they are ytem from hich the ater preent cannot ecape and into hich additional ater cannot enter. Figure 1. olume and mae for unfrozen and frozen oil in a cloed ytem. The aturation in ice of frozen oil i defined by the degree of aturation in ice ri : (2) here i i the volume of ice, vf i the volume of frozen void ( vf v becaue r i r ), i i the ice content M i /M, r i i the denity of ice and e f i the void ratio of frozen oil vf /. The aturation relative to the unfrozen ater of frozen oil i defined by the degree of aturation in unfrozen ater ru : ri ru i i r e r vf u vf f u r e r f i (3) 223

2 here u i the volume of unfrozen ater and u i the unfrozen ater content M u /M. Finally, the total degree of aturation (ice and unfrozen ater) for frozen oil i: r i u rf ri ru e r r f i (4) In frozen oil (not in very fine oil), the volume of the unfrozen ater i mall in relation to the ice volume. The effect of thi unfrozen ater i, hoever, very important. In addition, the difference beteen e and e f i mall and, a the value of the void ratio i alay approximate, e can aume that e e f. A for the other degree of aturation, hich are defined ith repect to volume, thi total degree of aturation cannot exceed 1. 3 THE UPERATURATION The adjective uperaturated define a permafrot that contain a volume of ice greater than the volume of pore ater before the freezing of the oil. More exactly, the volume of pore ater before the freezing hould be equal to the ater content of the aturated oil ( r 1). Hoever, and epecially in mountain permafrot, the oil before freezing are not uually aturated but nearly o. The degree of aturation defined above alay refer to a contant volume of oil if the mall difference beteen the volume of the ice and that of the ater i neglected. During the formation of permafrot or of eaonal frot, there i, hoever, addition of ater (ice) by gravity or by thermo-uction (in thi cae, the ice i alo termed egregated ice). We are, therefore, in the preence of an open ytem, i.e. a ytem from hich the ater preent can ecape and into hich additional ater can enter. If aturation refer to a cloed ytem, ith no external ater upply and hich cannot exceed 1, uperaturation of a permafrot or of a eaonal frot rp i defined a the ratio beteen the volume ip (Fig. 2) of the ice and of the unfrozen ater after the formation of the permafrot, and the volume v of void before the formation of the permafrot or of the eaonal frot. Neglecting the unfrozen ater, hoe the volume i mall, the degree of uperaturation of the permafrot rp i given by Equation (5) and Figure 2: rp ip v ip r e r i (5) here ip i the volume of ice after the formation of the permafrot (or of the eaonal frot), v i the volume Figure 2. olume and mae for unfrozen and frozen oil in an open ytem. of void before the formation of the permafrot, ip M ip /M i the ice content after the formation of the permafrot, r the denity of olid particle, e i the void ratio before the formation of the permafrot and r i i the denity of the ice ( t m 3 near 0 C). A a function of the volumetric ice content u ip ip / p, Equation (5) become: rp ip v ( ) uip 1 ep uip r e e r u r ( p ip i) (6) here e p i the void ratio of the permafrot and r p the denity of the oil after the formation of the permafrot, meaured, for intance, by mean of a gamma gamma logger. Thi degree of uperaturation can exceed 1 and thu the prefix uper i correct. For permafrot, Equation (6) i the mot important. In the above analyi, it a aumed that the oil before freezing a formed by depoit, rock-fall or any other geological proce and that it a only ubjected to freezing afterard. In actual fact, the oil of a mountain permafrot i often formed at the ame time that freezing occur. Thu, the time limit defined by before the formation of the permafrot and after the formation of the permafrot i often a little abtract. 224

3 4 HOW TO MEAURE THE UPERATURATION OF PERMAFROT It i neceary, firt of all, to kno the ice content of the permafrot. Different method exit, hoever, a borehole or an excavation i almot alay neceary, a a minimum of 15 kg of material i needed to carry out the tet hich permit the evaluation of the void ratio before the formation of the permafrot. We ill not dicu the determination of the ice content of permafrot here, a ubtantial literature exit already on thi topic. The denity of ice r i i knon and r may be eaily etimated. Typical value of r for mot oil range from 2.5 to 2.8 t m 3. Clayey oil have a value of r beteen 2.65 and 2.80 t m 3, depending on the predominant mineral in the oil (quartz ha a r of 2.65 t m 3 ). Concerning the void ratio e before the formation of the permafrot, thi i here the civil engineering tet come into play. It i ell knon that mot gravity-compacted natural oil have a denity cloe to a value obtained by a tandard tet called the Proctor tet (Table 1). During thi tet, a ample i compacted in a tandard mold 102 mm in diameter and 117 mm in height Table 1. alue of denity r in t m 3, of void ratio e (before the formation of the permafrot) and of optimum denity r dopn in t m 3, for coare oil from Alpine region, orted according to UC. tandard deviation. Thee average value come from a tatitical tudy involving about 6000 ample (Dyli & Rybiar 1992, Dyli 1995, Dyli 2001). r r dopn e UC GW ell-graded gravel; ell-graded gravel ith and GP poorly-graded gravel; poorly-graded gravel ith and GM ilty gravel; ilty gravel ith and GW-GM & GP-GM gravel ith ilt; gravel ith ilt and and GC clayey gravel; clayey gravel ith and GW-GC & GP-GC gravel ith clay (or ilty clay); gravel ith clay and and GC-GM ilty, clayey gravel; ilty, clayey gravel ith and W ell-graded and; ell-graded and ith gravel P poorly-graded and; poorly-graded and ith gravel M ilty and; ilty and ith gravel W-M & P-M and ith clay; and ith clay and gravel C clayey and; clayey and ith gravel W-C & P-C and ith clay (or ilty clay); and ith clay and gravel C-M ilty, clayey and; ilty, clayey and ith gravel 225

4 uing a hammer. The compactive effort i contant, but the tandard define to different value: 0.6 MJ m 3 for the tandard (normal) tet and 2.7 MJ m 3 for the modified tet. For the determination of the void ratio before the formation of the permafrot, the tandard tet hould be ued (0.6 MJ m 3 ). Thi tet allo the determination of the optimum denity of dry oil r dopn and the optimum ater content opn. The void ratio e i given by the Equation: e r r r dopn dopn (7) ariou tandard precribe the tet procedure: AFNOR P , ATM D 698, B /3, DIN and N The void ratio given by thi tet may eventually be replaced by thoe found in the literature a a function of oil type, for example thoe given in the i tandard N or thoe in Table 1. In addition, the void ratio may be corrected if the mode of oil formation before freezing i knon. For example, a urcharge or deiccation might have overconolidated the oil. In thi cae, the void ratio ould be le than that determined by the Proctor tet. Whatever the method ued for the determination of the void ratio, the degree of uperaturation i approximate. 5 EXAMPLE OF THE COMPUTATION OF THE DEGREE OF UPERATURATION OF PERMAFROT We ill conider a a numerical example the mountain permafrot of the Gruben rockglacier in itzerland into hich a borehole ith extenive intrumentation a placed in June 1976 (Barch et al. 1979). We have choen thi not o recent example becaue grain ize ditribution ere publihed even though Proctor tet reult are lacking (Barch 1996 p. 70 or Barch et al p. 219). In the layer beteen the depth of 4 and 6 m, the volumetric ice content u ip of the permafrot i, on average and very approximately (the calibration in u of the neutron neutron logger a made by back calculation ) 0.6 and the denity of oil r p i 1.6 t m 3 (gamma gamma logging). A Proctor reult are lacking, the grain ize ditribution allo an etimation of the void ratio through the ue of the Unified oil Claification ytem (UC ATM D 2487). Thi oil can be claified a an M, that i a ilty and. The tandard N give, for thi oil, a void ratio of (0.35 tandard deviation) and an optimum dry denity r dopn of Calculated ith the r dopn, the void ratio e i equal to A value of 0.40 a choen. Finally, the degree of uperaturation of thi permafrot can be calculated uing Equation (6): rp /0.40 ( ) Before the formation of the permafrot, denity of the oil r could be about 2.10 t m 3 (Table 1). With thi value, the degree of aturation r a CONCLUDING REMARK I the quantification of the uperaturation of permafrot ueful? From a cientific point of vie, if thi term i ued, it mut be defined exactly. For thi reaon, thi quantification i more than elcome. In addition, the degree of uperaturation permit a general and relatively precie comparion of different example or form of permafrot, baed on the relative importance of the ice ith repect to ater content before freezing. Obviouly thi degree of aturation remain approximate, hoever an approximate value i better than none at all! Beide, ince permafrot often form at the ame time a freezing occur, the quantification of uperaturation i often a little abtract. Hoever, e propoe a imple method baed on the initial unfrozen condition, defined by the Proctor tet, to compute the degree of uperaturation uing Equation (6). YMBOL The unit are given a an example; other unit are poible. e void ratio (unfrozen oil) e f void ratio of the frozen oil (in cloed ytem) e p void ratio of the permafrot r degree of aturation in ater rf total degree of aturation in frozen oil ri degree of aturation in ice rp degree of uperaturation of the permafrot ru degree of aturation in unfrozen ater ater content (ma) i ice content (ma) ip ice content of a permafrot (ma) opn optimum ater content (ma) (Proctor) u unfrozen ater content (ma) u ater content (volume) u ip ice content of the permafrot (volume) r denity of the oil t m 3 r d denity of dry oil t m 3 r dopn optimum denity of dry oil (Proctor) t m 3 226

5 r i denity of ice t m 3 r p denity of the oil after formation of the permafrot t m 3 r denity of olid particle t m 3 r denity of ater t m 3 REFERENCE Barch, D., Fierz, H. & Haeberli, W hallo core drilling and borehole meaurement in permafrot of an active rock glacier near the Grubengletcher, Walli, i Alp. Art. Alp Re 11: Barch, D Rockglacier. Berlin Heidelberg Ne York: pringer-erlag. Dyli, M. & Rybiar, J tatitique ur le caractéritique de ol uie. Rapport de recherche no 244, Office Fédéral de Route, Berne. Dyli, M tatitical analyi of glacial oil. Proc. of the XI European Conf. on oil Mech. and Foundation Engineering, Copenhagen 1: Dyli, M Recherche bibliographique et ynthèe de corrélation entre le caractéritique de ol. Rapport de recherche no. 496, Office Fédéral de Route, Berne. French, H.M The periglacial environment. Harlo: Longman. Haeberli, W On the characteritic and poible origin of ice in rock glacier permafrot. Z. Geomorph. N.F., uppl.-bd 104, Berlin-tuttgart: tandard: AFNOR P ol: Reconnaiance et eai Détermination de caractéritique de compactage d un ol par l eai Proctor normal et Proctor modifié (French tandard). ATM D 698 Laboratory compaction characteritic of oil uing tandard effort (U tandard). ATM D 2487 Claification of oil for engineering purpoe (Unified oil Claification ytem) (U tandard). B 1377 Method for tet for oil for civil engineering purpoe: Part 4: Compaction related tet: Claue 3: Determination of dry denity/moiture content relationhip (Britih tandard). DIN Baugrund; Unteruchung von Bodenproben Proctorveruch (German tandard). N Bodenkennziffern/Coefficient caractéritique de ol (i tandard). N Frothebungveruch und CBR-eruch nach dem Auftauen/Eai de gonflement au gel et eai CBR aprè dégel (i tandard). N erdichtung nach AAHTO/Compactage elon AAHTO (i tandard). 227

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