Dependence of new-snow density on slope angle

Transcription

1 Annals f lailgy Inernainal Glailgial Siey Dependene f new-snw densiy n slpe angle YASOI HI E N DO, Y U]I K OMINAMI, SHOU]I NIWANO Thkamahi Experimen Sain, Fres1) and Fres Prdus Researh Insiue, Thkamahi iy, Niigaa 948, Japan ABSTRAT. The mass per uni hriznal area, verial heigh and densiy f new snw aumulaed n varius slpes f 75 we re measured. Alhugh he mass f new snw n hese slpes was nearly he same, verial heigh inreased and densiy de reased wih inrease f slpe angle. Differenes in heighs and densi ies f new snw due slpe angle were explained by nsidering bh aumulain and densifiain presses n he slp es. INTRODUTION Under windless ndiins, mass per uni hriznal a rea, verial heigh and densiy f new snw aumulaed n slpes are usually nsidered be equal hse n a hriznal surfae. I was fund fi rs by Takahashi and Ngami (1952) a nd nfirmed by Shidei (1952) ha he ver ial heigh f new snw n a slpe inreases wih slpe angle and densiy dereases wih slpe angle, hugh he mass per uni hri znal area is nearly he same wheher n a slpe r n a hri znal surfae. H wever, his res ul did n reeive muh aenin and was frgen. The dependene f heigh a nd densiy n slpe angle is n nly essenial as basi knwl edge bu m ay als play an impra n par in avalanhe frmain. H ene, we re-invesigaed his de E u > '-" 3 S Z I ) '+- 1 U G " Fig. 1. Relain beween mass H N TV f new snw jjer uni hriznal area and slpe angle e. pendene in a fi eld experi men. Here, he resuls a re shwn and he auses a re explained. METHOD OF FIELD EX PERIMENT In rder measure mass, verial heigh and densiy f new snw n varius slpes, we nsrued six wden slpes 9 m lng a nd 6 m wide inlined a, 15, 3, 45, 6 and 75 n fl a grund a he Thkamahi Experimen Sain. T hey were surrunded by a shee 3 m high redue irregular aumulain f new snw due srng winds r sunshine. Measuremens f m ass H NW per uni hriznal a rea and verial heigh H N f new snw aumulaing n he slpes during inervals f 3 24 hurs were made using snw samplers and measuring rulers, u s hey were parallel he slpe when insered verially in he snw. Mean densiies p f new snw were alulaed by p = H N W / H N. This experimen was arried u during he winers f , and inthkamahi. RESULTS OF FIELD EXPERIMENT All m asses H NW measu red during he h ree winers were pled agains slpe angle e in Figure 1, where pen irles nneed by a slid line represen H N W f new snw aumulaed n eah slpe during a measuring inerval. Va r iains f H N V-V are small n slpes belw 45 bu derease n slpes abve 6, beause f sliding and rlling f snw pariles. If snw fall s veriall y under windless ndiins and aumulaes n a slpe wihu slipping dwn, H NW shuld be independen f slpe angle. In rder sudy he dependene f heigh and densiy n slpe angle, we needed invesigae new snw whih had aumulaed unifrmly n a slpe wihu he influene f wind, sunshine r sliding. We herefre seleed ases where he rai f H N W n a slpe ha n a hriznal surfae was wihin 1 ± 5%, a nd pled densiies p f new snw agains slpe angle e. Figure 2 shws ha he densiy p f new snw n a slpe dereases 14

2 End and hers: De/mzdmu if new-snw densiy n slpe angle..-.. "7 E u l... - /) ;J:.15 --r ' ,--,.1 '+-.5 >- :!:: /) /)...1 ;J: 4- >-.5. /) P e (g m- 3 ) e Fig. 2. ReLain beween densil) P if new snw and sl/le angle e Densiy f snw n a hriznal surfae Fig.-/. Relain beween densiy P ifnewsnw n a sl/je alld densil)' P n a hriznal suljae. as he slpe inreases. nsequenly, he verial heigh HN, being inversely prprinal densiy P fr similar masses H NW, inreases as he slpe inreases. DEPENDENE OF HEIGHT AND DENSITY ON SLOPE I n Figures 3 and 4, verial heighs H Ne and densiies P f' new snw n a slpe f angle e are pled respeively agains heighs H N and densiies P n a hriznal surfae e = O. These fi gures shw ha HNe and P respei\'ely are well apprximaed by he fllwing sraigh lines HNe = (l/b)hn and P = Bp H ere, he mean values f B bained frm he sraigh lines /) 5 l.. en 4 g 3 en ' ) I e HN(m) Heigh f snw n a hriznal surfae Fig. 3. Relain beween verial heigh H N ifnew snw n n a s//je and heigh H N n a hriznal su/jae. in Figures 3 and 4 are.975 fr e = 15",.917 fr e = 3,.84 fr e = +5 and.687 fr e = 6. Then, pling he bained va lu es f lg B agains lg( s e), we bain ed he fll wi ng rlain B = pe / p = H N/H Ne = (se (1) wih a =.57 fr new snw aumulaed during measuring inerva ls f 3-2+ hurs. T he slid urve in Figure 5 is he pl f Equain (I), while pen i rles are he pls f B (!).8 )( ;;;;;,:;: >::)(.... a'.... r :::.7 B=(s e ).57 /... )( Fig. 5. Relain beween he rai P / P and s//je angle e. Open irles are he values B bainedfrm sraigh lines in Figures 3 and 4; rsses mark he rais po/ P fr he 3-7 hur inervals; slid irles llosefr he 17-24hllr inervals. The slid urve is he pl f Equain (1); he brken urve a he pl if p/ P mpuedfr a = ver an inervalql7 hurs; and brken ZlrlJes a, band (Ihe /J/s if pe/ P fr a =,.3 and.5 ver a 24 hollr inlerval. 15

3 End and hers: Dependene f new -snw densiy n slpe angle agains e. As shwn in Figure 5, he values f B are well apprximaed by Equain (1). T invesigae he influene f he lengh f he measuring inerval, we pled he rais pe/ p bained fr eah measuring inerval agains 8 in Figure 5, where rsses are fr he inervals [3-7 hurs; and slid irles are fr hse f hurs. Alhugh he daa fr he inervals f 3-7 hurs a re few, ms are disribued abve he pl r Equain (I). T ha is, he value a fr he shr inlervals f 3-7 hurs, ranging frm a =.2.5, is smaller han he value fr hse f hurs. Suh an inrease f a wih he lengh f measuring inerval suggess ha he dependene f densiy n slpe is aused parly by differenes in snw densifiai n n slpes. DENSIFIATION OF SNOW ON SLOPES Sudies based n visus mpressin mdels esimae he densiy prfil e ra snw ver have been ndued suessfully by Kj ima (1967), End (1992) a nd hers. We mpued densiies f new snw n varius slpes mpare wih measured values, using he fllwing empirial relain beween mpress ive vissiy TJ and densiy P fund fr snw wih a densiy range f beween 4-3 kg m -3 by E nd and hers (199): TJ = p (2) where.392 Pa s (kg m -3) - n and n 4.. Fig. 6. Mdel qf a snw ver n a slpe. Nw we nsider a hin snw layer alled i layer whih is aumulaed a ime i, as shwn in Figure 6. Le hi( ) and Pi () be verial hikness and densiy f i layer a ime, and Wi( ) be weigh per uni hriznal a rea f snw lying n i layer a ime. Then, nrmal sress and shear sress exered n i layer are respeively (J" = W;()(s e)2 a nd T = Wi()s 8 sine. The i layer is mpressed in he nrmal direin by (J", and sheared parallel he slpe by T whih des n affe a hikness f i layer. If i layer is mp ressed by (J" have a hikness hi - dh; and a densiy Pi + dpi in a shr ime inerval d, a mpressive srain rae E: in he direin nrmal i layer is given by E: = -(I / hj )(dhi/d) = (1/ pi)(dpd d ). As snw is a vis- us mpressive maeri al, we ass ume ha he relain be ween (J" and E: is given by (J" = TJ E:. Then, we have Wi()(s 8)2 = TJ(I/ Pi)(dp;jd ). (3) Subsiuing Equain (2) in Equain (3) and inegraing bh sides afer sepa raing he variables, we have as an equain giving he ime variain f snw densiy where Pi,O( ) is he snw densiy fi layer n a slpe e a ime, Pini,e he iniial densiy n a slpe e, and i (i' ) he ime-inegrain f weigh per uni hriznal area f snw lying n i layer frm ; : i(i, ) = J Wi() d = J,, = J, ( - s)dws ( - s)q(s)gds where Wi() is a weigh per uni hriznal area f snw lying n i layer a ime, dws = q(s)gds a weigh f s layer aumulaed frm ime is s + d s, q( s ) an aumulai n rae a ime s, and 9 is graviainal aelerain. nsequenly, if hurly preipiai n frm ime i up is knwn, we an mpue numerially he densiy pi,e() f i layer n a slpe 8 a ime frm Equains (4) and (5). Sine he verial hikness hi,( ) f i layer n a slpe e a ime is given by q( i)di;j Pi,e( i ), he verial heigh H Ne f new snw aumulaed n a slpe e frm ime ; is given by HN = J (5) {q (s)/ps,e()}ds (6), and he mean densiy P f he new snw n a slpe e bemes Pe = [J q( s)dsl/ H N. (7) I, Nw nsider a ease ha i (i' ) saisfi es he fllwing ndiin: i(ii, )>> ( / n)(s e)- \ pi l1i,. (8) Then, Equain (4) bemes? 1. pi,e( ) = { (n / ) (s e ; ( i, i))" = (s e)"pi,o( ) where p;,( i) is a densiy f i layer n a hri znal surfae e = a ime. If ms new snw layers aumulaed frm ime ; saisfy Equain (8), he rai pe/ P fr he mean densiy f he snw is given by B = po/p = H N/HN = (s e). (9) This resul indiaes ha he value f po/p apprahes Equain (9) unrelaed he iniial snw densiy, as he measuring inerval is lng. Sine he value n is abu 4 arding End and hers (199), Equain (9) is nearly equal Equain (1) bained fr he measuring inervals f 3-24 hurs. Hwever, i is n erain wheher ur measuremens saisfy Equain (8). In rder sudy ha relainship, we mpued mean densiies PO f new snw aumulaed under nsan raes 16

4 End and hers: DejJelldene if new-snw densiy Oil slpe angle n varius slpes. In he mpuains, we ass umed ha he iniial densiy Pin i,e was relaed he iniial densiy Pini,O n a hrizna l surfae by Pini,e / Pini,O = (s e)"," (1) where a is a fr he iniial densiy, using he fll wing values: q( s ) = 1. kg m 2 h I (= 1. mm waer h - \ Pilli,O = 5 kg m 3, a =,.3 and.5, ime inerval equals 7 and 24 hurs. The mpued rais pe/p are shwn by brken urves in Fig ure 5, where he urve a' represens he relain fr a = ver a 7 hur inerva l and he urves a, b a nd represen relains fr a =,.3, and.5 ver an inerval f 24 hurs. As shwn in Figure 5, he bse rved daa are bes represened by he brken urves b and fr a =.3 a nd.5, and hene we an say ha he bserved differene f snw densiy due slpes an be explained by he press f snw densifiain in ases where a ranges frm.3.5, bu n in ases where a = O. When a =, he iniial snw densiy jus afer aumulain des n vary wih slpe angle. DIFFERENE OF INITIAL SNOW DENSITY DUE TO SLOPE In rder invesigae differenes f iniial snw densiy n varius slpes, we measured densiies f he surfae snw lying up 3 m belw he surfae direly wih a snw sampler, 3 m high, 6 m wide and 5.5 m lng. The resuls are shwn by pen irles in Figure 7, where he numeral in pa r enheses by he pen irle shws he ime whih passed frm aumulai n f snw is measuremen. Fi gure 7 indiaes ha densiies f new snw aumulaed befre I r 5 hurs depend n slpe angle; and he values f a range frm.2.5. Suh a dependene jus afer snw aumulai n mus be aused by he press f aumulain f snw rysals r snw fl akes n he slpes. Frm hese res uls, we an say ha he dependene f snw densiy n slpe angle riginaes in he press f bh aumulain and densifiain f snw n he slpes; he value f a, ranging frm.2.5 fr he iniial snw densiies jus afer aumulain, mes abu.56 fr he mean densiies f new snw aumulaed during abu I day. Thereiall y, he value a is nsidered apprah wih n equa l abu 4, as he lapse f ime is lng enugh saisfy Equain (8). ---(!) U :: L-L. -L-_--'- -L-_ ---'-_---" Fig. 7 ReLain beween le rali P / P and slpe angle e fr he su1jae snw jus afer aumulain. like rysals is equal H N. H ene, d ivid ing he heigh f new snw n a hriznal In-fae in w pars f plae-like and sphere-like rysals, and dening a rai f plae-like rysals al heigh ex', we have he fll wing equai ns as hse giving he differene f heigh and densiy jus a fer snw aumula i n H N = {(1 - a') + a'/ sb} H N (s B)- n'hn PO = {(I - a') + a' / s er 1 P (s e)"" P. (11) Takahashi and Ngami (1951) bserved snw rysals f abu 1 piees falling a 1 h and 16 h every day during he winer f inthkam ahi, and shwed ha 38% f he rysals were plae-like inluding needle-like rysals. Thugh he rai f plae-like rysals is high in number, he rai a' f hse he al heigh f new snw may be less PROESS OF SNOW AUMULATION ON SLOPES H ere we disuss he dependene f iniia l snw densiy n slpe angle. The shape f new snw an be lassified in plae-like rysals suh as plaes and sellar rysals, needlelike rysals suh as needles a nd lumns and sphere-like rysals suh as spaial dendries and graupel. A umulai n f plae-like and needle-li ke rysals n slpes is nsidered be differen frm ha f sphere-like rysals. As shwn in Figure 8, plae-like rysals end aumulae parallel a slpe under windless ndiin. Then, if we assume ha all plae-l ike rysals (inluding needl es ) aumulae parallel slpes, he relain beween verial heigh H Ne and H N f new snw mpsed f plae-li ke rysals is given by HNe = (1/ s B)H N. On he her hand, sphere-like rysals are nsidered aumulae n slpes a randm unrelaed slpe angle, H N fr sphere- Fig. 8. PLae-Like rysals aumulaed parallel a slpe. Ph by Eizi Akiaya. 17

5 End and hers: Dependene if new -snw densiy n sl/je angle Snwflakes The dependene f iniial snw densiy n slpe angle is nsidered be aused by he aumulain presses f new snw as menined abve. ONLUSIONS Ra in h/s9 Shear Fig. 9. Suppsed aumulain press if snwflakes by rain and shear difrmain. han. 1 beause he hikn ess f pl ae-like rysals is muh smaller han he diameer f sphere-li ke rysals. In Thkamahi, snw fa lls as snwfl akes mre han as individual snw rysals. Ofen large snwflakes fall hriznally hrugh he air. Thugh snw fl akes fen break when landing n a slpe, hey and heir fragmens are nsidered li e parallel he slpe by heir rain and shear defrmain, as shwn in Figure 9. When all snwfl akes li n slpes by heir rain, he relain beween H N and H N is given by H N = (1/ s B)H N- In he press f shear defrmain, H Ne is equal H N. Then, if he prbabiliy i f rain n a slpe is given, he dependene f heigh and densiy jus afer he aumulain is given by Equain (11). Hwever, i is unknwn wh eher rain and shear defrmain ake plae n a slpe r n. We have nfi rmed ha he verial heigh f new snw n a slpe inreases wih inreasing slpe angle and densiy dereases wi h slpe a ngle. The weigh f new snw per uni hri znal area des n vary muh wih slpe. In addiin, we have shwn ha he rai f snw densiy n a slpe ha n a hriznal surfae an be expressed as a pwer funin f he sine f he slpe angle and ha suh a dependene f snw densiy n slpe angle is aused by he presses f bh aumulain and densifiain f snw n he slpe. REFERENES End, Y T ime variai n f sabi li y index in new snw n slpes. I II Preedings. Japall - Us. Wrkshp n Snw AvaLanhe, Landslide, Debris FLw Prediin and nrl, 3 Sepember - 2 Ober 1991, Tsukuba, J apan. Siene and Tehnlgy Ageny. Nai nal Researh Insiue fr Earh Siene and Disaser Prevenin, End, y., Y. Ohzeki and S. i'<iwan [Relain beween mpressive vissiy and densiy f lw-densiy snw.] Seppy, J Jpn. S. Snw Ie, 52 (4), [InJapanse wih E nglish summary.] Kj ima, K Densi i alin f seasnal snw ver. [n Gura, H., ed. Phys;s(J/snw and ie. V/. J, Par 2. Sappr, Hkkaid Uni versi y. Insiue f LwTemperaure Siene, Shidei, T [Snw ver n slpes.] Ringy Shikenj Kenkyu Hkku { Bullein if he Fresry and Fres Prdus Researh Insiue} 54, [lnjap a nes.] Ta ka has hi, K. and K. Ngami [Obse rvain f snw rysals in Thkamahi.J Yi'ki, 7, [lnjapanes.] 'la kahas hi, K. and K. Ngami r Meamrphism f snw n slpes.] luki, 1, (lnjapanese.] 18