Discusion on Failure Mechanism of Piping

Transcription

1 1051 A publcaton of CHEMICAL ENGINEERINGTRANSACTIONS VOL. 51, 016 Guest Edtors:Tchun Wang, Hongyang Zhang, Le Tan Copyrght 016, AIDIC Servz S.r.l., ISBN ; ISSN The Italan Assocaton of Chemcal Engneerng Onlne at DOI: /CET Zhechao Fan *a,b, Jun Sun a Dscuson on Falure Mechansm of Ppng a Department of Cvl Engneerng, Chongqng Three Gorges Unversty, Chongqng , Chna b ey Laboratory of Hydraulc and Waterway Engneerng of the Mnstry of Educaton, Chongqng Jaotong Unversty, Chongqng , Chna fanzhechao@163.com Supposng that the layer s conssted of two deal elastc spheres wth dfferent dameters, the permeablty coeffcent of the layer can be calculated. After ppng takng place and small grans beng carred away, the permeablty coeffcent wll change. The ppng model s made to quantfcatonally calculate the permeablty coeffcent and hydraulc head of any pont. The model explans the causes of ppng and the development of concentrated passage, and t provdes theoretcal bass for preventon of dam ppng. 1. Introducton Dam break s mostly caused by permeablty deformaton, and slope sldng accdents are also caused by seepage, whch are n the references of Evans et al.(000), Lu (01), Zhao et al. (015), and Fread (1996). The dam of Yangtze Rver bursted n 1998, whch were mostly caused by permeablty deformaton such as ppng. The study of ppng has been studed by many former, such as the lteratures of Awal et al. (01), Awal et al. (008), and Meyer et al. (1994). But the damage cause of the layer whch s caused by ppng has been done lttle. The only way s to study the law of the grans movng n the layer after ppng takng place. So the damage to the around layer whch s caused by the ppng can be studed further, and then renforcng engneerng for the dam can be guded. The mechansm of the seepage passage whch s caused by ppng has been studed qualtatvely, and has been valdated by Chen (000). After the ppng takng place, the groundwater well theory can be ntroduced to study the ntal seepage feld durng ppng. Ppng can be approxmately regarded as artesan well, and the rver can be looked as half no-boundary wth fxed water level. Steady flow theory or unsteady flow theory can be appled to study the dstrbuton and the varety of the seepage feld durng the early perod of ppng. The complex nteracton of the seepage water and sol determnes the seepage tme, whch s a non-lnear dynamc problem. The layer s predgested to be conssted of two deal elastc spheres wth dfferent dameters, and the coheson s gnore. The permeablty coeffcent can be equvalent as the average permeablty coeffcent of the layer consstng of two spheres wth dfferent dameters. So the varaton rules of the permeablty coeffcent, crtcal surface, water grads, and so on can be calculated quantfcatonally after ppng takng place.. Model of permeablty coeffcent of the layer after ppng takng place.1 Permeablty coeffcent of the layer The actual layer s very complex, and the layer whch may conduce ppng s not well sorted. In order to establsh the quanttatve seepage model, we should start from smple model, and then nduce the more complex sorted layer. Supposng the layer s conssted of two spheres wth dfferent dameters, and the small partcles are all taken out of the bg partcles, the dam wll be damaged because of the sde force. We manly dscuss the form of the large partcles lable to move whle the small partcles are carred away. The permeablty coeffcent of the layer whch s conssted of two knds of grans can be shown: J 1 J A1 J A Two sdes of the equaton can be smplfed: Please cte ths artcle as: Fan Z.C., Sun J., 016, Dscuson on falure mechansm of ppng, Chemcal Engneerng Transactons, 51, DOI: /CET

2 105 1 A1 A (1) Where 1 s the permeablty coeffcent of the layer conssted of large grans; s the permeablty coeffcent of the layer conssted of small grans; A 1 s the area rato of the large grans to the layer; A s the area rato of the small grans to the layer. Mao (003) gave the expresson of the permeablty coeffcent of the layer conssted of one knd of gran. n w d (1 n) () Where β s form coeffcent (β=π/6 for sphere); n s porosty; λ s the effect coeffcent of of the adjonng grans; d s dameter of the sphere; γ w s the densty of water; μ s coeffcent of vscosty of the flud. When the porosty of large partcles s flled wth small partcles, permeablty coeffcent s determned by the area rato of small partcles to the layer. When small partcles are all carred away, permeablty coeffcent s determned by the area rato of large partcles to the layer. So permeablty coeffcent n any cell n the layer s determned by part of large partcles and small partcles, shown n Fgure 1. Fgure 1: Equvalent permeablty coeffcent after small grans carred away When the overlay s penetrated by the hydraulc water after the ppng takng place, the statc hydraulc pressure releases, water effusng from the ppng well. The streamlnes and the equpotental lnes around the ppng well redstrbute. We can use the theory about steady flowng of a well n confned aqufer to approxmately determne the streamlnes. We can regard the ppng as artesan well. The length between the artesan well and the replenshment rver s a, the dscharge Q. Durng the process of ppng, the hydraulc head of the replenshment boundary doesn t change. We can replace the rechargng boundary wth a rechargng mage well. The rver s regarded as rechargng source, flow n the early perod of the ppng can be consdered as lamnar flow. The y coordnaton s parallel to the dam, and x coordnaton s through ppng well and perpendcularty to y coordnaton. By the method of mages appled to the well, Lu (001) expressed the drawdown S at any pont (x,y): Q ( x a) y S ln T ( x a) y (3) Where T s the coeffcent of transmssblty. Let ( ) 4 ( x a) y Q x a y TS exp( ) c, so the followng equaton can be obtaned: (1 c) a c a ( x ) y 1 c (1 c) (4) Supposng dfferent values to S, we can dvde the flow feld accordng to the values of S. Frst the dscharge of the early perod of the ppng was calculated, and then overall dscharge can be assgned to any cell. In the perod tme of t, the permeablty coeffcent doesn t change, and the permeablty coeffcent n the cell s constant. We can calculate flow velocty and actual velocty by permeablty coeffcent, hydraulc gradent and so on. If the flow velocty can carry small partcles to move, small partcles can be carred out of the cell. Supposng that the capacty of small grans transport reles on velocty n the porous medum, and the volume of the small grans transport from the no. cell s V, from Eq(1) the followng equaton can be expressed: V t V t 1 (1 ) S L M S L M (5)

3 Where S s the length of the cell; L s the wdth of the cell; M s thckness of the layer. The dscharge of the ppng Q can be obtaned accordng to water level of the rver and ground elevaton around the ppng after ppng takng place, and hydraulc loss h can be calculated as follows: h C Q (6) Where C s well loss constant, and can be determned by experment. When water s confused flow, hydraulc loss wll be drect rato to square of dscharge. From H=H 0- h, hydraulc head of the ppng well can be calculated, where H 0 s statc hydraulc head. We can calculate the ntal dscharge of the ppng ( H0 H ) M Q a ln( ) r w (7) Where r w s radus of ppng well, M s the thckness of the aqufer. In the early perod of the ppng the flow qualty through each cell s equalty. We take the radal cells for example, shown n Fgure. Flow quantty through ths cell s q. There s no recharge from the adjonng cells, q 1=q =q. Lu (006) and Chen et al. (1999) calculated the hydraulc gradent of the seepage passage n the early perod by the mage method. aq ( a y x ) 4x y J( x, y) J x J y M x a y x a y 0 [( ) ][( ) ] (8) Fgure : The part of cell. The permeablty coeffcent of the layer after ppng takng place After ppng takng place, hydraulc gradent near ppng well s maxmal. The crtcal hydraulc gradent can be calculated as follows: s d Jc ( 1)(1 n) (9) d sk Where d s the dameter of the lost partcle; d sk s equvalent dameter; γ s s unt weght of sol grans; γ s unt weght of sol; α s shape coeffcent of sol grans. When the velocty reaches startng velocty of the small grans, small grans wll move, the startng velocty of small grans can be calculated as follows: BV MV N 0 (10) 6 Av(1 n) Where M, d sk 1 N ( 1). For velocty of lamnar flow s s small, B=0, so V. 6 M S 3 N n gd s After small grans move, the qualty of movng grans n each cell s dfferent. Cell s nearer to the ppng well, the more small grans are carred away. We can use the qualty model to work out reduced small grans n the cell, and then calculate the permeablty coeffcent. In Fgure, consderng the no. cell, n the perod of t the decrement of small grans n the cell can be calculated as follows: V V V 1 (11) Where V t s the volume of small grans carred away from cell, V -1 s the volume of small grans carred nto cell. So we can calculate the small grans decrement n each cell n perod of t accordng to flow velocty. From Eq(1) and () we also can calculate permeablty coeffcent n each cell. For the permeablty coeffcent n each cell has changed, we can t use Eq(7) or Eq(8) to calculate the dscharge and hydraulc gradent n next t. To calculate the dscharge, we should calculate the radal equvalent permeablty coeffcent, and then sum up each permeablty coeffcent n each group. So the average permeablty coeffcent of the layer wll be

4 1054 got. The equvalent average permeablty coeffcent s used to replace the permeablty coeffcent of the layer whose permeablty coeffcent has changed. Consderng one group n radal, the unt wdth dscharge through the cell s q : L q S (1) Where H s hydraulc head dfference of the no. cell; L s average length of no. cell along equpotental lne; S s average length of the seepage lne. The dfference of hydraulc head H of the cell can be calculated: q S H L (13) For the dscharge along the streamlne through each cell s the same, the dfference of hydraulc head equals to the sum of the dfferences of hydraulc head of each cell: (14) Supposng the average permeablty coeffcent along the streamlne s, so the dscharge can be expressed approxmately as follows: ( H0 H ) T q a m ln( ) r w (15) Where m s the number of cells around the crcle. From Eq(1), (13),average permeablty coeffcent can be expressed as follows: S L S L (16) The average coeffcent of the next streamlne can be got usng the same method, and then the total average permeablty coeffcent n the feld can be calculated. Supposng the average permeablty coeffcent along the no. streamlne s, and dscharge s q, so q L S (17) The total dscharge n the seepage feld s Q. Q q L (18) S From Eq(15), (16) and 1, the total average permeablty coeffcent can be got: L S L S (19) Supposng the hydraulc head of the rver s constant, the second hydraulc head can be got by H H H, where hydraulc head has ncluded knematc hydraulc head. By ths way, hydraulc, t 1, t, t t head and permeablty coeffcent of each pont n the feld can be studed, and the total dscharge can be calculated. The dscharge of each cell q can be dstrbuted by the total dscharge, q Q. So the teratve calculate can be performed, and the new dscharge after the perod of t can be calculated.

5 3. Case Study Supposng the layer s conssted of two dfferent dameters, the dameter of the large gran s 5mm, the dameter of small gran of 0.6mm. The permeablty coeffcent of the large grans s 38cm/s, and the permeablty coeffcent of the small grans s 0.019cm/s. The water head of the rver s 150m. The ground elevaton around the ppng well s 145m, and the length between the ppng well and the rver s 10m. The radus of the ppng well s 0.5m. 3.1 Hydraulc head near the ppng well after ppng takng place The dfference of hydraulc head before and after ppng n the model can be calculated. Before ppng takng place permeablty coeffcent n the layer s the same, and the dstrbuton of hydraulc head s shown n Fgure 3(a). Hydraulc gradent near the rver changes more sgnfcantly. Wth the development of ppng, more and more small grans s carred away, permeablty coeffcent of the layer changes. The nearer the pont to the ppng s, the larger permeablty coeffcent s. The dstrbuton of hydraulc head s shown n Fgure 3(b). From Fgure 3(b), hydraulc head near the ppng s larger than before, and permeablty coeffcent near the rver s sgnfcantly larger. When the dscharge s steady after ppng takng place, the dstrbuton of hydraulc head s shown n Fgure 3(c). Small grans near the rver are all carred out, and form the ppng passage eventually (a) (b) (c) Fgure 3: Dstrbuton of hydraulc head n dfferent process of the ppng (a) ntal perod of ppng (b) durng the process of ppng (c) the later perod of the ppng 3. Relaton among ppng, permeablty coeffcent and flow velocty By the calculaton, we fnd that there s no rgorous lmt among ppng and permeablty coeffcent. For cohesonless sol when the overlyng s penetrated, small grans are all able to be carred away and ppng well forms. When 1=36cm/s (D=5mm), =0.019cm/s (d=0.6mm), and a=10m, the permeablty coeffcent curve can be got, shown n Fgure 4(a). The dfference of permeablty coeffcent n the zone s large. The zone of gushng grans s lke a crcle whose center s ppng well. There s a gap besde the rver. Permeablty coeffcent ranges from.0-4.0cm/s. From Fgure 4 we can fnd that there s an obvous crtcal surface. When hydraulc head n the ppng well s rsng durng the development of the ppng, hydraulc gradent descend, and the crtcal surface shrnks, shown n Fgure 4(b). The gushng gran mostly come from the dam sde. Permeablty coeffcent n the new crtcal surface s larger than before, and t descends toward to the dam. The ppng passage forms eventually, shown n Fgure 4(c). (a) (b) (c) Fgure 4: Dstrbuton of permeablty coeffcent n dfferent process of the ppng (a) ntal perod of ppng forms (b) durng the medum process of ppng (c) the perod after the ppng passage

6 Concluson Ppng s a random phenomenon, and t s affected by gran sort, gran composton, dfference hydraulc head, etc. Permeablty coeffcent of the layer s determned mostly by small grans before ppng occurrng. Once ppng happens, and small grans wll be carred away, permeablty coeffcent of the layer wll be asymmetry. Permeablty coeffcent of the layer becomes to be determned by large grans, and dangerous ppng passage may eventually form. In ths paper, the layer s supposed conssted of two spheres wth dfferent dameters. The flow feld s be dvded nto cells under the assumpton of the layer s homogenous. When the small grans are carred away, permeablty coeffcent becomes asymmetry. For the cell s lttle, permeablty coeffcent of the cell s constant. By the Darcy law, we can calculate the dscharge, hydraulc head, etc. Though the model studes the two deal sphere, t can be appled to actual stratum. Ths model has taken specfc pont n flow feld nto account, and so t reflects that absolute passage has effecton on ppng. From the analyss of ths model we can conclude that ppng s lable to happen n the normal drecton to the dam. References Awal R., Nakagawa H., awake., 01, Expermental study on ppng falure of natural dam, Journal of Japan Socety of Cvl Engneers Ser B1, 67, Awal R., Nakagawa H., awake., Baba Y. and Zhang H., 008, Expermental study on predcton of falure mode of landslde dams, Proceedngs of Fourth Internatonal Conference on Scour and Eroson (ICSE-4), Chen J.S., Wang Y., 1999, The sotope tracer method for study on seepage flow n fssured rock, Journal of Hydraulc Engneerng, (11), 0-, DOI: /j.cnk.slxb Chen J.S., 000, Study of ppng causng concentrated leakage passage mechansm, Journal of Hydraulc Engneerng, (9), 48-54, DOI: /j.ssn: Evans J.E., Mackey S D, Gottgens J F, 000, Lessons from a dam falure, Oho Journal of Scence, 100 (5), Fread D.L., 1996, Dam-breach floods, Water Scence and Technology Lbrary, 4, 85-16, DOI: / _5. Lu J.G., 001, Calculaton and analyss for seepage deformaton to bank foundaton, Journal of Yangtze Rver Scentfc Research Insttute, 18 (6), 37-39, DOI: /j.ssn Lu Y., 01, Predcton methods to determne stablty of dam f there s ppng, Ier Proceda, 1 (11), , DOI: /j.er Lu T.H., 006, Andvanced sol mechancs, Chna Machne Press. Mao C.X., 003, Seepage Calculaton Analyss and Control, Water Conservancy and Water Electrcty Press. Meyer, W., Schuster, R.L. and Sabol, M.A., 1994, Potental for seepage eroson of landslde dam, Journal of Geotechncal Engneerng, 10 (7), , DOI: /(ASCE) (1994)10:7(111). Zhao L., Jang L.F., 015, A Data Feld Clusterng Method for Classfcaton of Concrete Dam Cracks, Chemcal Engneerng Transactons, 46, , DOI: /CET