Study of seepage for small homogeneous earth dams

Transcription

1 Study of seepage fo small homogeneous eath dams Maius Lucian Botos Abstact Constucted in ode to egulate the wate level in one section of a ive, dams, egadless of thei type, ae subjected to the pemanent o non-pemanent action of wate. Eath fill dams coss section geomety is designed based on the study of stability fo the upsteam and downsteam slope. he design is influenced by seveal factos; type of soil used; dainage solution; and in paticula the seepage. he calculation of seepage is detemining the delimitation of the satuated soil fom the unsatuated one. In the paticula case of small dams the wate level in the esevoi vaies quickly in time, hence seepage is influenced by this vaiation, as well as by the type of soil used, and the pesence o lack of a dainage system. Cuent pape pesents the esults of eseach caied out to detemine seepage chaacteistics fo diffeent exploitation stategies of such esevois, evolution of satuated aea if the maximum wate level is maintained constant fo a long peiod of time. Using esults fom such a study shows that seepage has an impotant ole when evaluating the slope stability o when eadings at piezometes ae used to evaluate behavio of existing dams. Keywods seepage, slope stability, small dam. I. INRODUCION N Romania thee is cuently geat potential to incease Ithe volume of fesh wate stoed in esevois without the need fo new dams constuction. Issues elated to envionmental potection and pivate popety in ecent yeas cause this type of constuction to be inceasingly moe difficult to stat with. An impotant numbe of non-pemanent stoage dams ae cuently with a single usage: flood wave attenuation. Adding new use by pemanent accumulation poses a numbe of poblems elated to the behavio of the dam to the new conditions. Non pemanent stoage dams fall into the categoy of small dams [], in Romania 9% of them ae eath fill homogeneous dams with heights up to metes []. o undestand in detail the behavio of this type of woks, this pape pesents a compehensive study on the changes, which occu fom seepage point of view, fo most cases possible in pactice. Undestanding behavio on seepage opens the way to solve poblems elated to the stability of slopes. Most of studies on unsteady seepage though eath dams focus on lage dams with coes made of clay, subject to slow M. L. Botos. is with the echnical Univesity of Cluj-Napoca, Faculty of Civil Engineeing, 4, Cluj-Napoca (phone: ; maius.botos@mecon. utcluj.o). vaiations of the wate levels up and downsteam. Small dams ae chaacteized by small heights and/o small stoage volumes. Vaiation of wate level in the lake is difficult to contol and geneally flood is attenuated without pefoming maneuves o pe emptying. hought to take and mitigate floods in the supeio basins of ives, chaacteized by hydogaphs with shot gowth times, causing apid vaiations flow and levels. his type of load automatically imposes, that the seepage has to be modeled consideing the unsteady unsatuated case. II. GOVERNING EQUAIONS he pesent poblem to be solved consists in a homogeneous eath isotopic dam founded on a laye of soil with same chaacteistics as the embankment. he impevious laye is placed at same depth as the dam s height. he poe pessue based fomulation of Richads equation fo two dimensional flow of wate though a homogeneous unsatuated soil is accoding to (): k x + x x y k ψ k ψ, k ψ x y ( ) k ( ψ ) = C( ψ ) y t ψ () ( ) ( ) ( ), functions of pemeability depending y on of the poe wate pessue (). he specific moistue capacity: ( ψ ) θ = C () z θ - volumetic wate content. Fo the definition pemeability functions ae numeous examples in the scientific liteatue Childs and Colins [6]; Budine [5]; Mualem and Dagan [6]; Kosugi [6]. Fo the estimation of pemeability function is used the Budine model : l ( / m k S S ) e [ m e ] = (3) whee: k - elative pemeability; S e - the effective satuation: θ θ S e = (4) θs θ θ s is the satuated moistue content and θ is the esidual moistue content of the soil. ISBN:

2 he elationship between pessue head and effective satuation deived fom the van Genuchten model [7] : S e = [ + ( αψ ) ] n m (5) Fo van Genuchten model the equation of specific moistue capacity becomes: C = n m [ ] n ( θ ) mn( αψ ) + ( αψ ) θ (6) s Appling the method of weighted esiduals, focing the weighted esiduals to be equal to zeo in each Gauss node and consideing weighted function to be the same as intepolating functions a system of odinay diffeential equations is obtained [3]: t n t ψ ψ n [ C( ψ )] + [ K( ψ )] = { } (7) [ K( ψ )] - conductance matix; [ ( )] C ψ capacitance matix. System of equations can be solved using backwad diffeence method [3] : [ C( ψ )] + ω t[ K( ψ )] ψ t + t = ([ C ψ ] ( ω) t[ K( ψ )]){ ψ } t ( 8) ( ){ } ( ) III. INIIAL CONDIIONS In ode to stat calculations some initial conditions ae specified on the bounday fo all types of dams, fo all types of exploitation egimes. Fo the initial conditions defined steady state of seepage was taken in consideation. he Diichlet bounday condition specifies the pessue head on some pat of the bounday, wheeas the Neuman condition specifies the flux on othe pat of the bounday. Neuman conditions wee not specified, no nodal fluxes wee consideed. On the upsteam wetted wee assigned with pessue heads, downsteam toe was consideed dy and pessue heads wee defined as zeo. he initial condition consists in obtaining distibution of the pessue head and the satuation thoughout the solution domain at the stat of the solution histoy. IV. BOUNDARY CONDIIONS In all the undelying assumptions that we have consideed the wate level downsteam is equal to nil, wate level in the lake will linealy o suddenly vay. Fo the dam with m height is consideed an incease in the total time of 6 hous, 5 m fo the hous and the dam with a height of m fom the calculation of the total 4 hous. Fo each height thee wee consideed two types of opeating:. he dam is consideed with nonpemanent stoage and wate level vaiation occus fom to the maximum height of the wate in the lake, while the vaiation peiod is listed above.. he dam with pemanent stoage, the wate level vaiation is linea, fom to a nomal etention level consideed /3 of the height of the dam, up to the maximum. V. BOUNDARY CONDIIONS We studied in detail the homogeneous dams with, 5 and metes height. hee have been poposed to study cosssections with the following chaacteistics: able. Slopes of the embankments Soil Upsteam slope Downsteam slope Sandy clay 3: : he cest width was consideed as poposed by Lewis [5] the foundation soil is the same type of mateial used in the dam s body and its thickness equal to the height of the dam. able. Paametes of dams with slopes of :3 and : Dams height m Dams height 5 m Dams height m Cest width B=m Cest width B=3.5 m Cest width B=4. m o solve the poblem of unsteady seepage was necessay to choose a model fo the pemeability and wate etention functions. In ode to solve unsteady unsatuated seepage, fo the wate etention functions was chosen the model poposed by van Genuchten and fo the pemeability functions the model poposed by Budine [5]. Paametes fo the soil wee obtained using REC softwae [8]. able 3. Paametes chaacteizing seepage fo the unsatuated zone CL sandy clay θ R =.67; θ S =.3963 α=.4; n=.3348; m=.58 K S =.46x -6 m/s VI. RESULS AND DISCUSSION he models wee composed in the gmsh.exe pogam, meshing is unifom thoughout the aea, the size of the elements as the esult of a sensitivity analysis aound.5 squae metes, the elements used to mesh ae tiangula and linea. In ode to veify how the type of the wate level change in the lake (linea o suddenly) influences the esults, one of the hypotheses consides at time t >, t wate level suddenly inceases to maximum height. o solve the poblem of unsteady seepage though unsatuated soils was used a vaiation of MNPNS.exe pogam []. Systems of nonlinea equations ae solved by the substitution method, fo the solution to be acceptable; the equied toleance fo two successive iteations is.5%. A. Sandy clay dam with height of metes Consideing dam with height of two metes may seem a little unfotunate, but the esults obtained may pove wong. Fo ISBN:

3 diffeent type of dam exploitation ules, with pemanent o non pemanent stoage we obtained diffeent final esult fo the end of time peiod consideed. Results ae pesented in Fig. and Fig.. Fig.. Linea wate level ise fom to.5 m pesented in Fig. 5. Fist is the wate level in the piezomete obtained consideing linea aise of the wate level fo nonpemanent lake, second fo a sudden aise of wate in the lake fo the same type of stoage. he middle column is the benchmak, in ou case the esult fo the steady seepage fo the maximum level. Last two columns ae epesenting the esults fo the pemanent lake, fist one fo the linea vaiation of the level and last one fo the sudden aise of bounday conditions. % % 8% Fig.. Linea wate level ise fom.6 to.5 m he evolution of satuated aea inside the embankment fo diffeent positions is shown in the Fig. 3 and Fig. 4. 6% 4% % % 38.% 35.85% 55.93% 56.5% 6.% 3.3% 47.6% 46.9% 8.9% 6.9% 4.7% 4.8% 3.3%.5% 39.8% 38.5%.% 8.7% 37.7% 36.5% 9.% 6.3% 36.57% 35.9% Piezomete position [m] Poly. (6) Poly. (7) Poly. (8) Poly. (9) Fig. 5. Compaison of the piezometic suface in diffeent scenaio compaed with steady seepage B. Sandy clay dam with height of 5 metes Fo the five metes height dam esults of poe pessue distibution and the position of the vitual piezometes ae pesented in Fig. 6 and Fig. 7. Fig. 3. Evolution of pessue head fo diffeent piezomete positions fo dams with non pemanent stoage Fig. 6. Linea wate level ise fom to 4.5 m Poly. (6) Poly. (7) Poly. (8) Poly. (9) Fig. 4. Evolution of pessue head fo diffeent piezomete positions fo dams with pemanent stoage Fo a bette undestanding of the impotance of unsteady seepage analysis the esults ae shown fo the same positions of vitual piezometes, compaed to the steady seepage analysis esults. Fo the steady seepage analysis the wate level in the lake was consideed at the maximum. Consideing the esults in mates of pecentage, allows us to undestand, that the unsteady seepage analysis is impotant to be conducted even fo small dams. Fo the each piezomete position five diffeent esults ae Fig. 7. Linea wate level ise fom.6 to 4.5 m Evolution of the satuated zone in the embankment shown in Fig. 8 and Fig. 9 fo the diffeent exploitation scenaios ae exposing the fact that impotant changes occu in case of dams with nonpemanent stoage afte fist half of the inteval, but only in the upsteam pat of the dam. ISBN:

4 pe. Mov. Avg. (5) 4 pe. Mov. Avg. (7) 4 pe. Mov. Avg. (9) 4 pe. Mov. Avg. () 4 pe. Mov. Avg. (5) 4 pe. Mov. Avg. (3) metes height in ode to be in the categoy of small dams need to have a volume smalle than 4 millions cubic metes. his means that total gowth times fo the hydogaphs can not be moe than 4 hous. he model consides that as the gowth time; the final and the evolution of esults ae pesented in Fig. and Fig.. Fig. 8. Evolution of pessue head fo diffeent piezomete positions fo dams with non pemanent stoage Fig.. Linea wate level ise fom to 9.5 m pe. Mov. Avg. (5) 4 pe. Mov. Avg. (7) 4 pe. Mov. Avg. (9) 4 pe. Mov. Avg. () 4 pe. Mov. Avg. (5) 4 pe. Mov. Avg. (3) Fig. 9. Evolution of pessue head fo diffeent piezomete positions fo dams with pemanent stoage Like the esults obtained in the othe cases, diffeences obtained fo diffeent types of loading in the lake (fo the chosen time inteval) ae showing negligible diffeences fo the final esults. Fig.. Linea wate level ise fom 3.3 to 9.5 m Pesue heads pe. Mov. Avg. (3) 4 pe. Mov. Avg. (35) 3 pe. Mov. Avg. (4) pe. Mov. Avg. (45) pe. Mov. Avg. (5) Fig. 3. Evolution of pessue fo diffeent piezomete positions fo dams with non pemanent stoage % Pesue heads % 4.5 8% 6% 4% % % 38.% 34.43% 5.73% 5.% 5.9%.36% 4.8% 39.% 8.8% 3.37% 37.6% 34.5% 4.% 9.4% 34.4% 3.6%.4% 6.89% 3.37% 9.8% 9.7% 5.38% 3.3% 8.7% Piezomete position [m] pe. Mov. Avg. (3) 4 pe. Mov. Avg. (35) 3 pe. Mov. Avg. (4) pe. Mov. Avg. (45) pe. Mov. Avg. (5) Fig.. Compaison of the piezometic suface in diffeent scenaio compaed with steady seepage Fig. 4. Evolution of pessue heads fo diffeent piezomete positions fo dams with pemanent stoage he esults obtained by modeling unsteady seepage though unsatuated soils eveal significant diffeences in medium and small dams ( to 5 m), whee the wate level in the dained dams with nonpemanent esevois is between 38% and % of the level achieved the steady seepage and between 56% and 3% fo the dams with pemanent esevoi. C. Sandy clay dam with height of metes Chaacteized by a bigge volume to be satuated, dams with ISBN:

5 % % 8% 6% 4% % % 3.7% 5.7% 5.57% 46.9% 8.9% 5.6% 36.94% 3.8%.8% 8.58% 3.6% 9.%.% 5.3% 3.5% 7.6% 7.6% 3.75% 8.57% 6.% 7.7% 3.68% 9.57% 6.8% Piezomete position [m] Fig. 5. Compaison of the piezometic suface in diffeent scenaio compaed with steady seepage he way the wate level vaiation in lake is consideed (linealy o suddenly ove the analyzed peiod) eveals that the diffeences fo dams with the height of metes ae 7% fo the upsteam aea of the dam and unde 4-5% towad downsteam. Regadless of the height of the dam, the esults obtained show a significant diffeence compaed to those obtained by classical methods. he esults pesented in this pape ae only a pat of the study conducted on the infiltation fo majoity types of soils used fo dams in homogeneous solution: silty sand, clayey sand, silty clay and fat cay. he main aspect that influences the way the satuated zone evolves is the cosssectional dimensions. he pecentage values epoted to the steady state seepage emain close in value fo each height, vaying within 5%. Fo dams with non pemanent stoage: heights of metes between 39% fo the upsteam piezometes to % fo the downsteam piezometes, 5 metes heights between 37% and 8% and fo metes dam between 8% and 6%. Fo dams with pemanent stoage: metes height between 59% and 37%, 5 metes 53% and 33%, and fo metes values between 45 and 6%. VII. CONCLUSION Compaison of wate levels in piezometes in elation to the esults obtained if the seepage is consideed steady at maximum levels duing floods can not povide the eal behavio of the dam and gives a false sense of safety. he way wate flow is calculated though eath fill dams, influences the stability safety facto of downsteam slope of embankment. If the model is consideing the seepage in steady conditions, the eadings at specific inspection equipment will indicate significantly diffeent values. Costly investments can be made in ode to eplace the inspection equipment with no esult. Confusion intevenes and excessive caution can be imposed in the exploitation ules, caution that may lead to a decease in the degee of flood attenuation and unnecessay damages downsteam. his pudence can lead to the initiation of expensive investments such watepoofing o ovesized daining elements. REFERENCES [] Botos M.L. Solving steady and unsteady seepage poblems using custom pogams, C6 Intenational Confeence, Cluj-Napoca, 3 [] Botos M.L. Small dams with non-pemanent esevois in Romania, C6 Intenational Confeence, Cluj-Napoca, 3. [3] Books R.H, Coey A.. Hydaulic popeties of poous media Hydology Pape 3, Coloado State Univesity, Fot Collins, Coloado 964. [4] Butsaet W. Some methods of calculating unsatuated pemeability ansactions of the Ameican Society of Agicultual Enginees,, 966, pp [5] Budine, N.. Relative pemeability calculations fom poe-size distibution data. ans. Am. Inst. Min. Metall. Pet. Eng. 98: [6] Childs, E.C., and N. Collis-Geoge. he pemeability of poous mateials. Poc. R. Soc. London, Se. A. : [7] Fedlund D.G, A. Xing Equations fo the soil wate chaacteistic cuve Canadian Geotechnical Jounal, 3 (4), 994, pp [8] Fedlund D.G., A. Xing, S. Huang Pedicting the pemeability function fo unsatuated soil using the soil wate chaacteistic cuve Canadian Geotechnical Jounal, 3 (3), 994, pp [9] Fedlund D.G., D. Sheng, J. Zhao Estimation of soil suction fom the soil wate chaacteistic cuve Canadian Geotechnical Jounal, 48,, pp [] Gadne W.R. Some steady state solutions of the unsatuated moistue flow equation with application to evapoation fom a wate table Soil Science, 85 (4), 958, pp. 8 3 [] Geen R.E., J.C. CoeyCalculation of hydaulic conductivity: a futhe evaluation of some pedictive methods Soil Science Society of Ameica Poceedings, 35, 97, pp. 3 8 [] ICOLD. SMALL DAMS Design, Suveillance and Rehabilitation, [3] Istok J. D., Goundwate Modelling by the Finite Element Method, Wate Resouces Monogaph Seies, Volume 3, 989. [4] Kosugi, K.. Geneal model fo unsatuated hydaulic conductivity fo soils with lognomal poesize distibution. Soil Sci. Soc. Am. J., 999. [5] Lewis B. Fam Dams Planning, Constuction and Maintenance, National Libay of Austalia Cataloguing;. [6] Mualem, Y., and G. Dagan. Hydaulic conductivity of soils: Unified appoach to the statistical models. Soil Sci. Soc. Am.978. [7] van Genuchten M. A closed-fom equation fo pedicting the hydaulic conductivity of unsatuated soils Soil Science Society of Ameica Jounal, 44, 98,pp [8] Yates, S.R., M.h. van Genuchten, A.W.Waick, and F.J. Leij. Analysis of measued, pedicted, and estimated hydaulic conductivity using the REC compute pogam. Soil Sci. Soc. Am.99. ISBN: