Stress-dilatancy behaviour of frozen sand in direct shear

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1 Stress-diltncy behviour of frozen snd in direct sher Permfrost, Phillips, Springmn & Arenson (eds) 23 Swets & Zeitlinger, Lisse, ISBN N. Ysufuku Kyushu University, Fukuok, Jpn S.M. Springmn, L.U. Arenson & T. Rmholt Institute for Geotechnicl Engineering, Swiss Federl Institute of Technology, Zurich, Switzerlnd ABSTRACT: This pper ims to clrify the chrcteristics of the strength nd diltncy behviour oturted frozen snd in direct sher. A series of direct sher box tests were performed in cold room using sturted frozen fine snd smples with wide rnge ond volume frctions. The dependency of the strength nd diltncy behviour on the temperture, norml stress nd strin rte re discussed on the bsis of the experimentl results. It ws found tht the sher strength nd diltncy of the snd-ice mixture ws strongly dependent on the rte oher deformtion nd the volume frction ond. The ongoing diltion of most of the tests indictes tht the shering not only ffects thin sher plne, but lso influences strongly the djcent soil due to possible propgtion of crcks between the solid prticles. Furthermore, the sher strength ws quite sensitive to the temperture chnges in the rnges ner to C. 1 INTRODUCTION The importnce of high mountin permfrost s nturl hzrd is incresing, due to indictions of incresing rising globl tempertures (Cheng & Drmis 1992, Heberli et l. 1993, 1997, Knutti et l. 22). The melting of ice in the permfrost mtrix will reduce the interprticle stress nd hence sher strength. This my, in the presence of wter, quickly led to slope filure nd debris flows (Hefeli 1948, Iverson & Mjor 1986, Heberli et l. 1997, Arenson & Springmn 2). In Switzerlnd, the popultion in Alpine vlleys is quite dense nd debris flows cn cuse much dmge nd even loss of life (Heberli et l. 199, Zimmermnn 199). Hence, the potentil for instbility of Alpine permfrost hs been identified s being n issue of considerble importnce in Switzerlnd (Heberli et l. 1999). Although the dngers re known, the knowledge of the thermo-mechnicl behviour of Alpine permfrost is limited. Until now, Alpine permfrost reserch hs focused minly on issues such s geomorphologicl spects, mesurements of internl nd surfce movements nd tempertures, generl structure of the ground or ge of the permfrost (e.g. Heberli et l. 1998, Vonder Mühll et l. 1998, Kääb & Vollmer 2). Therefore, dvnced knowledge of the mechnicl properties of thwing permfrost is required for numericl modelling, nd to enble predictions of potentil slope instbilities due to temperture chnges. Bsed on mesurements of internl deformtion of creeping rock glciers in the Swiss Alps (e.g. Arenson et l. 22) distinct sher zone from some centimetres up to metres thick, where up to 97% of the rock glcier deformtion occurs, could be locted. Direct sher box tests hve been proposed in order to model this sher zone nd to determine the mobilised strength on plne. In the study presented in this pper, series of direct sher box tests were performed in cold room, using lbortory prepred sturted frozen fine snd smples with vrious snd contents. Temperture dependency between 3 nd 7 C, nd effects of norml stress nd strin rte dependency on the strength-diltncy behviour re discussed on the bsis of experimentl results nd microscopic observtions of the specimens fter shering. 2 MATERIALS AND TESTING PROCEDURES 2.1 Testing progrmme Tble 1 shows the test conditions of the direct shering under constnt norml stress on frozen Weicher fine snd. In order to clrify the effects of volume frction ond on the direct sher strength of frozen snds, ws vried from.5 to.63 in which is defined s 1/(1 e), with e s the voids rtio. Three horizontl deformtion rtes, i.e. horizontl deformtion velocities, dh/dt were pplied: 2. mm/ min,.2 mm/min nd.2 mm/min. Norml stresses v were selected from rnge between 2 kp nd 4 kp bsed on the recorded depths of in situ sher surfces. The testing tempertures were 6.5, 4.1 nd 3.1 C, respectively. Figure 1 shows the direct sher box, which ws kept in cold room t the specific test temperture within n ccurcy of.5 C. A sensor ws mounted in the lower hlf of the box, to mesure the temperture of the 1253

2 Tble 1. Test conditions. dh/dt 2 mm/min dh/dt.2 mm/min dh/dt.2 mm/min Norml Temp. stress T ( C) v (kp) X X X X X X X X X X 3 X X X X X X X X X 4 X X X X X X X X 4 =.5.1 =.45.5 Figure 3. Schemtic imges ond-ice specimens. Figure 1. percent finer (%) Figure Direct sher box, dimeter 6.5 cm grin size (mm) Grin size distribution of Weicher snd. specimen. Corresponding tempertures in the smple vried by.3 C. 2.2 Smple preprtion Weicher fine silic snd ws used s n inclusion mteril. The grin size distribution curve of this snd is given in Figure 2. The ngle of friction of dry Weicher snd is 32 in simple sher. The rtificilly mde snd-ice specimens were prepred s follows: ) known mount ond ws mixed uniformly with powdered ice, tht hd similr grin sizes to the snd, to prepre smple with fixed volume frction ond. b) the snd-ice mixture ws poured into the sher box nd lightly compcted in 4 to 8 lyers, depending on the volume frction ond. c) the snd-ice specimen ws sturted crefully by pouring de-ired wter t zero centigrde from the top within the cooling room in order to fill the ir voids without disturbing the pcking of the sndice mixture. d) fterwrds, the specimen ws kept in freezing box for bout 24 hr t temperture of 18 2 C (during the freezing process, the snd prticles remined in dispersed position). e) the frozen specimen ws plced in the direct sher pprtus nd left for t lest 3 hours until the temperture of the smple becme stble. Before shering, ll smples were left for one night fter pplying the norml stress. Smples with high snd concentrtions (.55) were prepred by plcing pre-cooled dry snd stright into the direct sher box, pouring pre-cooled wter crefully into the snd, nd freezing the mixture using method similr to d) nd e). The specimens hd dimeter of 6.5 cm nd height of bout 2. cm. Schemtic imges ond-ice specimens with low nd high snd volume frctions re given in Figure 3. 3 TEST RESULTS AND DISCUSSION Tble 2 summrises test conditions nd some key results. Tempertures, volume frction ond, pplied norml stress nd sher deformtion rte re shown, together with smple response, including the pek mobilised sher stress, the corresponding horizontl displcement nd the men ngle of the diltncy rte v tn 1 (dv/dh), where V is the verticl nd H the horizontl displcement. 1254

3 Tble 2. Summry of test conditions nd results. Temp. in dh/dt 1st pek sher dh t Pek sher Test no. specimen ( C) ( ) v (kp) (mm/min) stress (kp) 1st pek (mm) stress (kp) Men v ( ) Sher deformtion rte dependency The influence of the horizontl strin rte dh/dt, which ws vried from.2 to 2 mm/min, on the mobilised sher stress nd the verticl displcement dv of the ice-soil mixture is shown in Figures 4 nd 4b for reltively low volume frction ond (.17) t temperture of 4.1 C (Tests 31, 32, 33). Similr results were obtined for reltively high volume frction (.43.48; Tests 27, 34, 35). The stressdeformtion curve nd the diltncy behviour for the sme stress nd temperture conditions were found to be strongly dependent on dh/dt. The volume frction ond ppers to influence the pek mobilised sher stress in similr mnner to the dt shown in Figure 4, but the dditionl 25 3% ond leds to n increse of mximum sher strength of 2 3 kp under the previling norml stress field (Fig. 5). The mximum sher stress increses exponentilly with incresing dh/dt for the dt shown. The slope of this increse, however, seems not to be influenced by t T 4.1 C nd v 3 kp. For the sme temperture, the diltncy tends to increse with the incresing dh/dt (v 4.6, 12.4, 18.3 ). A close inspection of the sher zone with microscope (mgnifiction 8) did not indicte significnt expnsion of the voids, which my be expected for n unfrozen diltnt mteril (Fig. 6). In ddition, there ws no evidence of ny other form of dmge long the sher zone. If regeltion effect does ct round the prticles on the sher plne, there is sufficient free τ (kp) dv (mm) 5 v = 3 kp energy vilble to refreeze liquid wter once locl shering is complete. In essence, there is looser pcking in the sher zone due to smll diltive movements of the grins combined with self-heling. 3.2 Norml stress dependency dh/dt = 2 mm/min dh/dt =.2 mm/min dh/dt =.2 mm/min 3 b dh/dt = 2 mm/min 2 1 Tests t different vlues of v showed tht there is no significnt influence of v on the sher response (Fig. 7, Tests 31, 38, 39). However, rpid heve ws mesured t the beginning of the shering for the dh/dt =.2 mm/min dh/dt =.2 mm/min Figure 4. Dependency of deformtion rte on strength nd diltncy behviour due to sher. 1255

4 τ pek(kp) v = 3 kp = = τ pek (kp) dh/dt =.2 mm/min (.39) (.43) (.42) (.15) (.17) (.18) dh/dt (mm/min) Figure 5. Strength properties of frozen snd relted to deformtion rte. ( ): norml stress, n (kp) Figure 8. Pek sher strength dependency relted to the norml stresses. Closed circles:.41, open tringles: = τ (kp) Figure 6. Typicl cross section opecimen fter shering (Test 46:.36). τ (kp) 15 1 dv (mm) 5 dh/dt =.2 mm/min τ vo = 4 kp f =.18 s vo = 3 kp f =.17 s vo = 2 kp = b vo = 3 kp 2 f vo = 2 kp s = =.15 vo = 4 kp.5 =.18 dh/dt =.2 mm/min, T = 4.1 C Figure 7. Dependency of () sher stress-displcement nd (b) diltncy behviour on the norml stresses. lowest v (Fig. 7b) nd this levelled off to constnt vlue of bout 1.5 mm, wheres the behviour under higher norml stresses is very similr t 4.1 C nd dh/dt.2 mm/min. The tests shown in Figure 7 (Tests 31, 38, 39) re plotted gin in Figure 8 with n equivlent series t.41.2 (Tests 27, 36, 37) s pek sher strength ginst norml stress. A slight increse of the sher strength cn be determined for.41, wheres no influence or even decrese ws recorded for.17. However, the reltively high pek for test No. 38 (.15) my be ttributed to externl work done ginst the verticl stress s the smple diltes. dv (mm) dh/dt =.2 mm/min, T = -6.5 C = Volume frction dependency Figure 9. Effect of the volume frction ond on () the sher stress-deformtion nd (b) the diltion-deformtion reltionships. Six tests with different volume frctions ond (Tbles 1 & 2: Tests 46 51) were shered under norml stress of 3 kp with deformtion rte of.2 mm/min t temperture of bout 6.5 C. The soil prticles strongly influenced the response to shering for.3 (Fig. 9). The yield nd the pek sher strength is very similr for low nd is reched within bout 2 mm deformtion. However, n upper yield region (e.g. Andersen et l. 1995) develops for higher vlues of, nd strin hrdening effect cn be observed for the rest of the test. The diltncy lso chnges for different vlues of. Except for test No. 51 (.5), n increse in diltion, nd hence v, ws recorded with incresing (v 8.5, 5.4, 1.2, 15.6, 15.6, 18.3 ). It is thought tht the greter strength of ice seeded with reltively few solid prticles is due to the crcks generted t yield pssing from prticle to prticle, but requiring dditionl energy to initite new crck. b 1256

5 However, for such low vlues of.5, the brittle behviour indicted in Figure 9 is confirmed by the degree of diltion observed in Figure 9b. Equivlent behviour ws lso mesured for the tests t 4.1 C (Tests 25, 27, 28, 3, 31) with v 11.3, 12.4, 14., 14., 16.7 respectively. The ongoing diltion shown in Figure 9b is most probbly n effect of the crck propgtion. In contrst to unfrozen soils, where sher zone of 5 to 1 grin dimeters might be typicl, the sher zone within these frozen smples develops to be much lrger nd therefore more verticl displcement occurs. Stress concentrtions tht occur round the solid prticles result in crcks between the grin bond with the ice mtrix tht propgte from prticle to prticle similr to Griffith s (1921) model of frcture for solid mterils. The zone ffected by these crcks depends on the volume frction of snd, resulting in vrious, but pronounced, diltncy responses, which seem to question the concept of constnt volume for criticl stte strength (Schofield & Wroth 1968) for frozen soil. Even though constnt vlue oher strength ws reched for dh 1 mm the smple height increses, indicting ongoing crck propgtion throughout the smple. However, the uthors ssume tht for lrger strins, even under the conditions presented, the stress concentrtion dissiptes, stopping further frcturing nd constnt vlue of dv would be ttined. This is lso geometricl effect cused by the limittion of the sher box. During initil phses ohering (Fig. 1), the sher zone extends primrily from prticle to prticle over depth of pproximtely 1 2 mm. However, s the vlue of dh increses, the sher zone increses in thickness due to mobilistion of the ice grnules nd prticles cting nd dilting together (Fig. 1b). This effect cn be described s rubblistion (e.g. Tke & Bolton 22). Even though the mount of unfrozen wter might be less thn.5 Vol.-% (Willims 1967, Stähli & Stdler 1997), it my hve n dditionl influence on the behviour of the smple. The smll mount ond prticles in test No. 51 results in very little unfrozen wter nd therefore supports the concept of brittle behviour, in contrst to the other tests tht showed ductile tendency. This would lso explin why the sher response of this test is higher thn the response of test No.47 (.14) nd why there is difference in the diltncy. Similr results could be observed for tests t the two other tempertures, 3.1 C nd 4.1 C, respectively. Figure 11 shows the effect of on pek strength of the snd-ice mixture with reference to temperture T. There is only slight increse in the pek strength with decresing temperture for low. A much steeper increse cn be observed for.3 nd n even steeper increse for.5, nd this is more pronounced for lower tempertures. Different mechnisms seem to be relevnt for the vrious volume frctions of b Figure 1. τ pek (kp) snd. Severl other uthors hve described this effect. Ting et l. (1983) showed similr results for frozen Ottw snd t temperture of 7.6 C under unixil compression, suggesting tht only the strength of the ice is responsible for the sher strength t low vlues of. Structurl hindrnce cn be tken into ccount for volume frctions lrger thn.4, since the solid prticles strt to come into contct with ech other. Crck propgtion through the ice-prticle mixtures, however, lso chnges with incresing volume frction ond nd influences the sher response within the filure plne. Despite the temperture dependency of the ice strength itself, unfrozen wter lso influences the sher response t wrmer tempertures nd therefore much lower vlues for pek strength were mesured. Due to the increse of unfrozen wter with incresing, more gentle increse of the sher response with incresing volume frction ond occurs. 4 CONCLUSIONS 1-2 mm 5-1 mm Development oher zone. 55 v = 3 kp =.5.57 dh/dt =.2 mm/min -6.5 C -4.1 C -3.1 C < 2 mm ~1 mm volume frction ond, Figure 11. Effect of on pek strength ond-ice mixture with reference to the temperture of the specimen. A series of direct sher box tests were performed on snd-ice mixtures to investigte the effect of volume frction onds, norml stresses, strin rte nd tempertures between 3.1 nd 6.5 C on the diltncy nd strength ouch mixtures. The min conclusions cn be summrised s follows: the verticl deformtion due to shering in direct sher box ws minly diltive nd ws strongly dependent on the rte oher deformtion, on the volume frction ond s well s on the temperture. 1257

6 the sher zone expnded with sher deformtion due to crck propgtion nd rubblistion resulting in pronounced diltncy tht did not level off even t horizontl deformtions of more thn 1 mm. the sher strength of the snd-ice mixture ws lso dependent on the rte oher deformtion nd volume frction ond. the observed trends were more evident with decresing temperture: higher pek sher strength ws mobilised nd proportionlly more so t higher. Mechnisms tht re responsible for the sher nd the diltncy behviour chnge with different nd tempertures. Only the ice controls the response for low. Despite brittle behviour with pek sher vlue t smll strin for smples with very low (.1), minly ductile behviour with strin hrdening nd continuous verticl heve ws observed for smples with.1. Crck propgtion might be the min influence tht controls the sher nd deformtion response s function of the volume frction ond, since the solid prticles within the ice-soil-mtrix control the length nd direction of the crcks. In ddition, structurl hindrnce results in higher sher responses nd more pronounced diltncy. Unfrozen wter tht might lso be present under these test conditions hs n dditionl effect tht supports ductile response. An upper yield region develops for smll strins nd higher. Criticl vlues of, which initite chnge of mechnism, is temperture sensitive, but lies between.3 nd.5. Norml stress seems not to influence the mechnisms significntly. The presented tests, however, demonstrte the sensitivity of frozen soil response to vrious effects, such s temperture, deformtion rte nd volume frction ond. Even though direct sher tests hve proved to be very suitble for the testing of frozen ice-snd mixtures, further investigtions on the chnge of mechnisms s function of temperture nd grin size distributions re recommended for the future. ACKNOWLEDGEMENT The uthors wish to cknowledge with grtitude the ssistnce of IGT/ETHZ personnel with the experiments, prticulrly D. Bystricky, E. Bleiker nd M. Schärer nd Professor F. Bucher for fruitful discussions. The first uthor lso thnks Prof. H. Ochii nd Dr. K. Omine of Kyushu University for supporting him during the sbbticl in Switzerlnd. REFERENCES Andersen, G.R., Swn, C.W., Ldd, C.C. & Germin, J.T Smll-strin behvior of frozen snd in trixil compression. Cndin Geotechnicl Journl 32: Arenson, L. & Springmn, S.M. 2. Slope stbility nd relted problems of Alpine permfrost. Proc. Int. Workshop Permfrost Engng., Longyerbyen: Arenson, L.U., Hoelzle, M. & Springmn, S.M. 22. Borehole deformtion mesurements nd internl structure oome rock glciers in Switzerlnd. Permfrost nd Periglcil Processes 13: Cheng, G. & Drmis, F Distribution of mountin permfrost nd climte. Permfrost nd Periglcil Processes 3: Griffith, A.A The phenomen of rupture nd flow in solids. Philos. Trns. Roy. Soc. London, Ser. A 221: Heberli, W., Rickenmnn, D. & Zimmermnn, M Debris flows 1987 in Switzerlnd: generl concept nd geophysicl soundings. Hydrology in Mountin Regions. II-Artificil Reservoirs; Wter nd Slopes, IAHS Publiction: Heberli, W., Cheng, G., Gorbunov, A.P. & Hrris, S.A Mountin permfrost nd climte chnge. Permfrost nd Periglcil Processes 4: Heberli, W., Wegmnn, M. & Vonder Mühll, D Slope stbility problems relted to glcier shrinkge nd permfrost degrdtion in the Alps. Ecloge Geologice Helvetice 9: Heberli, W., Hoelzle, M., Kääb, A., Keller, F., Vonder Mühll, D. & Wgner, S Ten yers fter drilling through the permfrost of the ctive rock glcier Murtèl, estern Swiss Alps: Answered questions nd new perspectives. Proc. 7th Int. Conf. on Permfrost, Yellowknife: Heberli, W., Kääb, A., Hoelzle, M., Bösch, H., Funk, M., Vonder Mühll, D. & Keller, F Eisschwund und Nturktstrophen im Hochgebirge. Zürich: vdf, Hoch-schulverlg n der ETH. Hefeli, R The stbility olopes cted upon by prllel seepge. 2nd Int. Conf. On Soil Mech. nd Fdn Engng 1: Iverson, R.M. & Mjor, J.J Groundwter seepge vectors nd potentil for hillslope filure nd debris flow mobiliztion. Wt. 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