SEEPAGE AND EROSION MECHANISMS OF OF SANDY GROUND DUE TO AIR BUBBLES

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1 C-14 Fourth Internatonal Conference on Scour and Eroson 28 SEEPAGE AD EROSIO MECHAISMS OF OF SADY GROUD DUE TO AIR BUBBLES Hrotaka SAKAI 1 and Kench MAEDA 2 1 Member of JGS, Dept. of Cvl Eng., agoya Insttute of Technology (Gokso-cho, Showa-ku, aoya , Japan) E-mal: cgt1853@stn.ntech.ac.p 2 Member of ISSMGE, Assocate Professor, Dept. of Cvl Eng., agoya Insttute of Technology (Gokso-cho, Showa-ku, aoya , Japan) E-mal: maeda.kench@ntech.ac.p Seepage falure of sol and/or ground causes mportant geotechncal problems such as damage of dyke under flood, eroson of sol structure and ground nearby ocean and rver and so on. Moreover, generaton of gas and blow-out of ar bubbles have been seen before seepage falure occurred n many cases. The sources of ar bubbles could be thought to be ar phase entrapped by seepage front and oversaturated ar n pore water. The generaton and the development of ar bubble, therefore, play a very mportant role on seepage falure n nature. The ar bubbles must, therefore, ncrease the rsk of sol falure and eroson. In ths paper, we focused the evoluton effect of ar bubbles n pore water on seepage falure. We performed model test, and developed a new numercal smulaton method accountng for flowage deformaton and sold-water-ar bubbles nteractons by Smoothed Partcle Hydrodynamcs. And smulaton results were verfed by comparson wth model test results. Key Words : seepage falure, ar bubble, three phase couplng, PIV, SPH 1. ITRODUCTIO Large flowage deformatons and hydraulc collapse of ground ppng whch nduces eroson are nduced by permeaton of water through ground. That plays mportant roles n the destablzaton of ground durng floods, lquefacton, eroson and so on. It s necessary to model progressve seepage falure n the sol to analyze these phenomena more precsely. Some Reports have found mportant roles for nteractons among all three phases n solds, lquds and gases. In partcular, Kodaka and Asaoka s paper 1) mght be the frst artcle whch revealed mportance of dynamcs of ar bubbles n geoengneerng. Indeed, when the Toka flood dsaster attacked agoya regon on 11 th Sept. 2, a man saw the process of dke falure. He mentoned n a newspaper that after a crack generated on the surface of the dke, whte bubbles water blew out from the dke and then dke gradually faled for about three hours. Ths knd of phenomena has been seen many tmes snce old tme. Ths blowng ar bubbles before seepage falure was called frog blows bubbles by elderly people. The hydraulc falure wthout ar bubbles was defned and dscussed by Terzagh 2). In ths study, we conducted model test and developed a new numercal smulaton method for the seepage falure wth ar bubbles. Dscrete analyss (e.g. DEM) s adapted to abrupton, falure and flowage, but unsutable procedure to analyss doman of large scale. Contnuum analyss (e.g. conventonal FEM) has opposte propertes to that. The smoothed partcle hydrodynamcs method (SPH) 3), 4), a completely mesh-free technque, was used to obtan the combned benefts of both dstnct and contnuum methods. In ths study 5)-7), SPH wth a new method for calculatng densty, surface tenson and mult-phases couplng was proposed. In ths paper, the smulaton results, moreover, were verfed by comparson wth model test results ncludng velocty of ground and pore water pressure at falure

2 2. MODEL TEST WITH IMAGE AALY- SIS (1) Model test procedure In model tests, we observed the deformaton-falure around sheet-ple n sand ground submerged by two knd of water; one was water wth low DO (demand oxygen), and another was water wth hgh DO and over-saturated ar; referred to Fg.1. In the latter, ar bubble was easy to generate. 飽和溶存酸素量 DO ( mg / l) dssolved oxygen, DO (%) 水温と水中飽和溶存酸素量の関係 8 6 Super-saturaton state of oxygen 過飽和状態 ar s unstable for dssolve. saturaton curve 未飽和状態 Un-saturaton state of oxygen 水温 ( ) Water temperature Fg. 1 DO (dssolved oxygen) saturaton curve. water tank thermo regulator DO meter follow the test apparatus shown n Fg.2 and test condton as experments performed by Kodaka and Asaoka 1). Toyoura sand was employed. The dssolved oxygen (DO), water temperature, and permeable water volume of the ground were measured. A tensometer pressure sensor was equpped at the 5mm rght horzontally from the tp of the sheet-ple n the down-stream. (2) Model test results and dscussons Fg.3 and Fg.4 show the typcal deformaton-falure behavours around sheet-ple for lower DO and hgher DO cases, respectvely. Fg. 5 shows the relatve appled head loss h/h cr ndcatng safety aganst ppng wth elapsed tme after h was ncreased and/or held. In the case of lower DO n the normal ppng test, ppng occurred at h/h cr =1 accordng to the defnton. However, n the case of hgher DO, even though h s than h cr, ar bubbles were generated as shown n Fg. 4, and consequently, falure occurred n holdng test. When the water level was ncreased after holdng the smaller water level dfference h for a long tme, the falure tended to occur even before the water level dfference reached the crtcal level h cr : h/h cr < 1; t s smlar to creep falure n a materal under constant load smaller than the strength. Ths mples that ar bubbles n ground brng strength degradaton. The relatonshp between the ar bubble generaton and DO and the nfluence of ar bubbles on the ground were nvestgated n the followng sectons. h=12~17 6 Sheet ple sand ground 6 (mm) Fg. 2 Model test apparatus for seepage falure. (upstream) (downstream) Two types of tests were conducted; one was normal ppng test wth lower DO and another was holdng test. In the former test, a dfference n water level h whch was head loss appled to ground was ncreased to a crtcal head loss h cr n whch ppng occurred n a ground; h ncreased wthn 1-2 hours gradually wth a set of small ncrement of h and 5 mnute holdng. In the later test, head loss h appled was held untl ppng occurred. If ppng dd not occur even through much elapsed tme passed, h was ncreased agan to generate ppng. We can measure the velocty feld of ground usng PIV (Partcle Image Velocmetry) mage analyss and calculate the stran rate felds from mage analyss results. We Fg. 3 Ppng wth water of lower DO and wthout ar bubbles n normal ppng test: ncreasng head loss h to h cr. (start of holdng test) (elapsed tme after holdng: 94hr) Fg. 4 Deformed ground ust before ppng wth water of hgher DO n holdng test: holdng head loss h =.8 h cr

3 relatve head loss, h / h cr falure pont [ wthout bubbles (ncreasng h to h cr ) ] normal ppng test [ wth bubbles (holdng and ncreasng h<h cr ) ] holdng test medum loose duraton tme, t (hr.) Fg. 5 Decrease n safety aganst ppng due to ar bubbles. In seepage falure wthout ar bubbles as shown n Fg.6, ground subsdence (scour) at the upstream sde and ground uplft (roll-up) at the downstream sde occur contnuously when h/h cr >.9. However, n the case wth ar bubbles as shown n Fg.7, the ground surface at the downstream sde was dsplaced ntermttently. Ths must be related to the dynamcs of ar bubble such as the generaton and development, movement, and eecton of ar bubbles from the ground. Fg.8 shows both of change n amount of ar bubbles at the downstream sde whch was calculated by mage analyss and change n vod rato estmated by assumng that vod changed due to only ar bubbles. Here, the rapd descend ponts mean the bubble eecton wth rapd subsdence of ground. Moreover, snce the accumulated amount of ar bubbles was lmted as shown n Fg.8, the ground surface at the downstream sde was not dsplaced for a whle followng the eecton of large ar bubbles. On the other hand, the ground surface at the upstream sde was not dsplaced for a whle, but t was suddenly dsplaced after a perod of tme; we can observe ths vsually n Fg.9. Consequently, the dsplacement n the ground at the downstream sde gradually propagated to the ground at the upstream sde, passng below the sheet ple, accompaned by the ntermttent eectons of ar bubbles accumulated n the ground at the downstream sde. Ths resulted n the ground surface subsdence at the upstream sde h/h cr normal Ppng test wthout bubbles -2 Upstream Downstream.2 Dense Dsplacement of ground, δ (mm) Duraton tme, t (hour) Fg. 6 Dsplacement of ground surfaces n upstream and down stream for normal ppng test wthout ar bubbles due to applcaton head loss. Appled head loss, h/h cr 3 47 Dsplacement of ground, δ (mm) 1. 3 h/h cr [ holdng test wth bubbles ].2 Upstream Downstream Dense holdng tme, t (hour) Fg. 7 Dsplacement of ground surfaces n upstream and down stream for holdng test wth ar bubbles due to applcaton head loss. area of ar bubbles, S (mm 2 ) area of ar bubbles, S holdng tme, t (hour) Fg. 8 Changes n amount of ar bubbles n downstream around sheet-ple and n vod rato calculated accordng to Fg.7. L tme = hour L 1 tme = 56.8 hours L 2 tme = 88.5 hours vod rato e (a-) (a-1) (a-2) Appled head loss, h/h cr vod rato, e (b-1) (b-2) Fg. 9 Varatons of length of seepage around sheet-ple and maxmum shear stran rate dstrbuton, referred to Fg.7. Those dynamcs of ar bubbles brng frequent change n vod rato. Snce the crtcal hydraulc gradent cr of ground s calculated by cr = (G s -1) / (1+e) where G s s sol partcle specfc weght 2), as shown n Fg. 1. From the photographs, seepage dstances L around sheet-ple can be calculated. Before ground subsdence at the upstream occurs, L becomes longer;

4 L < L 1. And then L becomes shorter; L 2 < L 1. Consequently, the hydraulc gradent ncreases, expressed n Fg.1, even through head loss h s constant. ormally, ordnate seepage falure occurs when the seepage force ncreases due to an ncrease n head loss. However, even though the head loss was held, the resdence aganst ppng cr decreased and seepage load ncreased due to the abovementoned mechansm, and consequently, seepage falure occurred. hydraulc gradents, and cr cr appled head loss, h/h cr h holdng tme, t (hour) Fg. 1 Changes n hydraulc gradents due to generaton of ar bubbles and deformaton of ground evoluton of ar bubbles even wth constant head loss, accordng to Fg UMERICAL AALYSIS: SPH (1) Analyss procedure Superposton of smooth functons SPH s a partcle-based Lagrangan method. Ths method was orgnally developed by Gngold & Monaghan 3) and Lucy 4) n astrophyscs to solve motons of galaxes. Then, ths method was appled to vscd flows and falure of solds. The SPH s ntended not for treatng the actual sol gran but for solvng partcle as sol mass (Fg. 11), whose radus s h. Smlarly water partcle s a fnte volume of water but not a molecule. These partcles can overlap. Snce ths method s Lagrangan, t can also express sldng, contact, separaton, and two or three phase nteractons. The spatal averaged value < f(x)> of physcal quantty f(x) at pont x s gven by Eq. (1). Partcles x' wth f(x') are located wthn the zone of nfluence of the frst partcle (2h). The physcal quantty s nterpolated usng a smoothng functon W (see Fgs. 11). f =< f ( x ) > = 1 m f W ( r, h) where r = x x and W s defned by, (1) 1 = W ( r, h) dx' (2) In ths paper, 3 rd B-splne functon was employed as W, and r = r and S = r /h are used, S + S S < W S 2 = ( 2 S ) 2 7 π h 6 2 < S The densty of partcle s replaced wth f, m W = = 1 = 1 (3) = m W (4) x 2 Partcle: x Smooth functon (kernel) for each partcle Smoothed partcle r x Partcle: However, ths descrpton shows large error n denstes calculated by orgnal theory around the nterface. We mproved ths pont by normalzaton and lmted summaton for a materal focused (e.g. materal a) Materal a = = 1 Materal a = 1 Materal a m W m W for materal a; (5) o 2h x 1 h The SPH descrpton for partcle n moton equaton can be explaned as follows. Fg. 11 Partcle and smoothng functon n SPH dv σ σ = m + dt 2 =1 2 + Π I W + f (6) where σ and f are stress tensor and body force, respectvely. The matrx I s unt matrx, and Π s the artfcal vscosty. For the purpose of couplng, the sol and the fluds

5 of water and ar were handled on dfferent layers (see Fg. 12). The frctonal body forces resultng from velocty dfferences between two phases, vs and vf were employed wth the Bot s mxture theory8). The forces can be expressed as follows: f sf = n f g k (v s ) v f, f fs = n f g k (v f vs ) usng clusters of SPH gas partcles. We nvolved surface tenson effect by addng force term. 5m (7) Ar bubbles 5m Here, porosty n, permeablty k, flud densty f and gravty acceleraton g are ncluded. Fg. 15 Analyss of bubbles n water. Fgure 16 shows an SPH model of the experment shown n Fg. 3 wthout ar bubbles. Ths model can smulate characterstcs of seepage falure well not only durng deformaton but also after the falure. Interacton body force f fs Superposton of flud-sold layers Layer of Flud Layer of Sold f sf Ar Porous materal, sol Sheet ple Water Heavng up and cave downward.3m.15m Curlng up Ground surface.15m Total volume fracton: 1 = (Volume fracton: n) + (Volume fracton: 1-n) Scourng Ground.2m Fg. 16 Seepage falure analyss around sheet ple wthout ar bubbles; generaton of falure of ground when h=hcr. Fg. 12 Interacton force to couplng between sold-lqud-gas. The boundary was reproduced by creatng an array of vrtual boundary partcles. The leap-frog method wth tme step was used holdng the CFL condtons. We can see not only the concentraton of flow around the tp of the sheet-ple but also the exstence of hgh speed n the downstream sde due to curlng nduced by the eroson. Fg.17 and Fg.18 show comparsons between model test results and numercal smulaton results for velocty feld and for pore water pressure n the ground around the sheet-ple at ppng falure. The velocty of ground measured by PIV s shown n Fg.17(a) and the velocty at the 5mm rght horzontally from the sheet-ple tp n the down-stream after the falure s about.3m/s, whch mght be same as the velocty of water n mxed. The SPH smulaton result for velocty at the tp of the sheet ple n Fg.17(b) s.28m/s, and ths s almost same as that of the model test. The pore water pressure at the same pont measured by the tensometer s shown n Fg.18(a) and the value at the falure state s around 25Pa. And the pressure dstrbutons around the above are of ground n the down-stream are nfluenced by the curlng flow due to the eroson. The pressure value analyzed n the down-stream around the tp n Fg.18(b) s almost same as that of model test. The analyss results show good agreement wth model test results. The analyss show good performance qualtatvely and quanttatvely. (2) Analyss results and dscussons Fgures 13 and 14 show the results of the analyses for the collapse of columns of water and frctonal materal, respectvely. The fnal surface of water column broken becomes flat, but the surface n Fg.14 s nclned. These tendences agree wth actual flows. 2m 1m 5m upward Water column: (water partcles) Fg. 13 Collapse analyss of water column (dam break). Fg. 14 Collapse analyss of frctonal materal column. Fgure 15 shows analyss result of the rse process of ar bubbles n water. The bubbles were smulated 5 472

6 (a) model test (unt: mm/hr) (b) smulaton (unt: m/s) Fg. 17 Comparson n velocty dstrbutons around sheet-ple wthout ar bubbles; PIV mage of ground velocty for model test; (b) water velocty for SPH smulaton. Pore Pressure (Pa) falure state Tme (s) (unt: Pa) (a) model test (b) smulaton Fg. 18 Comparson n pore water pressure around sheet-ple wthout ar bubbles at ppng; (a) from tensometer pressure sensor n model test; (b) from SPH smulaton. Fg. 19 shows a SPH predcton of seepage falure around sheet ple wth ar bubbles under 8% of water heght dfference n Fg.16. In ths analyss, ar phase was replaced forcedly wth another phases at ntal state; the generaton of ar bubbles wll be able to be nvolved concernng entropy and enthalpy n the future work. The falure of ground s nduced by ar bubbles rse as same as experments. We can fnd that the movement of ar bubbles nduces the local deformaton of the ground. Ar bubbles entrapped ntally Fg. 19 Seepage falure analyss wth ar bubbles; generaton of local falure occurs at local even when h=.8 h cr. 4. COCLUSIOS From model test results by usng PIV mage analyss, t was revealed that the dynamcs of ar bubbles n the ground caused the degradaton of the ground. Even though the head loss was held to be constant value less than crtcal head loss, the resdence aganst ppng cr decreased and seepage load ncreased. In next stage, we wll reveal the nteracton detal mechansm between the degradaton of the ground and the evoluton of ar bubbles. Ths paper proposed a newly developed method of SPH to solve three-phase systems (sold, lqud and gas). Ths paper showed clearly the valdaton and usefulness of SPH to be applcable for problems three phase. The analyss performance s qualtatvely hgh. Some analyss results were verfed wth model test results and we found the accuracy of ths proposed analyss procedure although we conducted the verfcaton n only some data. The procedure wll be able to be developed to smulate seepage falure from the generaton of the bubbles to the evoluton. ACKOWLEDGMET: The authors are grateful to the Japan Socety for the Promoton of Scence for ts fnancal support wth Grants-n-Ad-for Scentfc Research (B) REFERECES 1) Kodaka, T. and Asaoka, A.: Formaton of ar bubbles n sandy sol durng seepage process, Journal of JSCE, Vol. 487 (III-26), pp (n Japanese), ) Terzagh, T.: Theoretcal sol mechancs, ohn Wler and Sons, IC., ) Gngold, R.A. and Monaghan, J.J.: Smoothed partcle hydrodynamcs: theory and applcaton to non-sphercal stars, Monthly otces of the Royal Astronomcal Socety, Vol.181, pp , ) Lucy, L. B.: A numercal approach to the testng of the fsson hypothess, Astronomcal Journal, Vol.82, pp , ) Maeda, K. and Saka, M.: Development of seepage falure analyss procedure of granular ground wth Smoothed Partcle Hydrodynamcs (SPH) method, Journal of Appled Mechancs, JSCE, Vol.7, pp (n Japanese), 24. 6) Maeda, K., Saka, H. and Saka, M.: Development of seepage falure analyss method of ground wth smoothed partcle hydrodynamcs, Jour. of Structural and earth-quake engneerng, JSCE, Dvson A, Vol.23, o.2, pp , 26. 7) Saka, H. and Maeda, K.: A study on seepage falure of sand ground wth account for generaton and development of ar bubbles, Proc. of 13 th Asan Regonal Conference on Sol Mechancs and Geotechncal Engneerng, pp , 27. 8) Bot, M. A.: General theory of three dmensonal consoldaton, Journal of Appled Physcs, Vol.12, ,