第38卷增刊上海交通大學(xué)學(xué)報Vol.38 sup.2004年6月JOURNAL OF SHANGHAI JIAOTONG UNIVERSITYJun. 2004文章編號: 1006-2467(2004)S1-0217-06The Influence of Water Level Change in Slope Stability of Earth DamXiao Zheng-hua 12, Han Bo1'b, Liao Hong-jian1'c and Gao Xiao-yu1,d'Department of Civil Engineering, Xi'an Jiaotong University, Xi'an 710049, ChinaCollege of Architectural Engineering, Xinjiang University, Urumqi 830008, Chinaxzh-70@ 163.com, "han_ _bo961 @ 163.com, hjliao@ mail.xjtu.edu.cn, dycgao@ mail.xjtu.edu.cnAbstract: The analysis of seepage flow and slope stability to earth dam in water level change isperformed. FEM is used to analyzing the influence of percolation and the results including the porewater head of any point, seepage discharge and so on are obtained. The method of slices isintroduced to calculating the slope stability of the earth dam. Through an example it is separatelydiscussed the influence of seepage flow when water level is changed in earth dam slope and theeffects of percolation in the stability of the earth dam slope. Some helpful conclusions are gained.This can be making the best of the tow methods and the results can be used in engineering forreference.Key word: seepage flow; stability factor; FEM; the method of Bishop1 IntroductionEarth dam is a rapidly development type of dam and be widely used in internal and overseas.Because it can be constructed by a rolling compaction local earth materials and the constructiontechnique is simple and shortcut, so it is adopted broadly. This type of dam can be foundeverywhere in our hydraulic engineering. But most of them had been constructed in 1950s and thestandard of flood protection was low level in that time and its quality was poor. The current states ofthese dams are in maintenance, overhaul and reinforcement. After the standards of flood control towater-storage are established, the main tasks of the reinforced earth dam projects are the analysis ofseepage flow and slope stability. Before the earth dam had happened catastrophic events, majorityof them belong to infiltration flow and seepage deformation problems, so the approach of theregularities of leak through liquid field distribution is an important means to analyze the reasonswhy dangerous condition happened and evaluate secure states of dam body and design and optimizethe dam. But the acting head, the dam body section, property of the earth fll, geologic conditions,soil structure and feature, terrain condition and so forth of practicable projects are myriads ofchanges, to reflect the general rule, this paper aims at the mentioned above factors, generalizes thetypical conditions and studies the slope stability when water level of the dam is changed dam.The analysis of infiltration flow and slope stability to homogeneous earth dam in water leveldepression is performed by an example in the paper. FEM'I is used to calculating the efects ofseepage flow and we can achieve the hydraulic head of any point in the dam body and the otherelement factors concermed. The method of Bishop2] is中國煤化工pe stability on thebasis of pore water pressure field gained by the FENYHCNMHGbest of the towmethods and the results may be helpful in actual engine_218上海交通大學(xué)學(xué)報第38卷2 FEM Fundament of Calculating the Action of Seepage FlowThe mathematic model of infiltration flow numerical computation is divided two classes, i.e.thetwo-dimensional plane and the-dimensional space seepage flow. Because the length of dykebuilding is far greater than its widh, the two-dimensional plane seepage flow model is used. Theinfiltration flow caused by water level is depression in dam body is unsteady seepage.Unsteady seepage flow differential equation. Isotropic soil differential equation appliedtwo-dimensional unsteady seepage model isdH_耿aH+8H、(1)可μax2+ayz)Boundary condition. Boundary condition of groundwater movement is divided three classesin response to flow mathematic model:(a) head boundary is that in the borderthe position and head are specified and thenormal stream speed is unknown, e.g. inhyFig.1 the border ae and cd.Ie(b) discharge boundary is that in thedTborder the normal lead number of headFig.1 Boundary condition of groundwater movementfunction is known and the head is unknown,e.g. in Fig.1 the border ed.(c) free face boundary is that in the border the head is equal to the height, e.g. in Fig.1 theborder ab.Initial condition. The general initial condition is the head boundary, i.e. the head distributionin flow field and it has dominant action to whole flow field at zero hour t=0. When we do unsteadyseepage flow computation or experiment, we first gain the head distribution in seepage flow field atzero hour and specify it as initial condition (generally, the seepage flow field is steady seepage flowfield at zero hour); or we can use the infilration flow state at any time as initial condition. Only inparticular cases the initial condition is the discharge or free face boundary.Finite element method. The key task to calculate the action of seepage flow used FEM issolving the head function to determine the free face and seepage discharge in seepage flow field.The main thought is transforming the seepage flow differential equation (eq. 1), boundary conditionand initial condition into computing functional and extremeness according to variation principle.First, the seepage flow field is diverged to finite unit body, then unit seepage flow matrix is formedand total seepage flow matrix is assembled by it, finally the unknown node head values are gainedby derivation the linear system of equation through computer. The head values in unit body can becomputed by difference equation and the head function at any point in the seepage flow field isachieved. FEM can be expressed by following matrix to total seepage flow field:[K]{H}={F} .(2)中國煤化工[K] expresses total seepage flow matrix, {H} expresses.MYHCN M H Gumn vetor, {F}presents free term column vector.增刊Xiao Zheng-hua.et al: The Influence ofWater Level Change in ..2193 The Method of BishopBishop defined stability factor is the ratio of soil shear strength along the whole slip surfacer, divided by actual produced shear stress t,e.g.F, =Tg/r. The acting forces on any soil unitflank are considered. In Fig.2(a), the slip surface is assumed as a circle arc that its radius is R andthe center of circle is 0 and any soilunit is selected as a free bodyb(Fig.2(b)). The acting forces in the free1x0body are:↓E(a) the tangential force T; andXi+1Rnormal force N; which action spot is inWthe center of the bottom surface arecaused by the soil unit deadweight W.V;(b) the normal force E, E+1 and(a(b)tangential force Xi; Xi+1 are acting onfig.2 The method of Bishop force diagramthe soil unit flank(c) pore water pressure Ui which action spot is also in the center of the bottom surface.On the basis of limiting equilibrium condition, the stability factor of Bishop method gained byeffective stress analysis and the tangential forces are ignored.21 [cil cosa, +(W, -U, cosa)]tanq;]p.=旨ma(3)Zw; sina,from which,sin a;ma =cosa; +F.(4)Because F: is appeared in two side of the equality, iterative method is used to calculate it. First,F, =1 is assumed to calculate ma. Thenanew F is obtained by eq.(3). If the new F, is notequal to 1, the new mo and F。 will be computed using the new Ff. The process is repeated tillfore and after F, is very approach. This generally needs 3~4 frequency iteration to get the solutionmet the accuracy standard and the iteration always is convergence.4 ExampleConsider the case of a homogeneousisotropic embankment dam that its heightis 15m on an impermeable foundation andthe pyramidal drainage structure is in thedownstream, as shown in Fig3. The中國煤化工upstream ratio of slope is 1:2 and theTYHCNMH Gdownstream ratio of slope is l:1.15. The upstream water height is 12.0m and downstream waterheight is 1.0m. The upstream water level will fall down to 4.0m. The soil layer property parameters220上海交通大學(xué)學(xué)報第38卷of the earth dam are shown in table 1.Tab.1 The soil layer property parameters of the earth damzoneSoilNode number-KJ(md7) K/(md')c/kPa中/°)numbertype(kN:m3)_ ( kN.m-ing areaclay0.0090018.519.020.022.8-1,0,1,2,3.2coarse20.00025.0 2.1,4,-30.00019.521.022.024.0__ 0,3.4.5,6.-4.1First, use FEM to calculate the seepage flow action. In the process of water level fllig down,consider the seepage flow isunsteady flow andchoosetriangular unit that its breadth is1m. Mesh the whole earth dambody and get 726 nodes and 1330units, as shown in Fig.4. Obtainthe seepage lines at different hourFig.4 Meshing the whole carth dam body(Fig. 5), the pore water pressurefield values and other results.Then use the above results tocalculate the dam slope stabilityfactor. In the calculating processwe respectively discuss theinfluence on the seepage flowand slope stability using differentFig.5 Phreatic lines at different hourhead, permeability velocity andpermeabilitycoefficient whenwater level is depression, theresults are shown in Fig. 6 to0.045steady seepage flow 11m*◆-11m0.04Fig.11.When upstream water level0.030. 025為一5respectively falls down from0. 0212m, 10m, 8m and 6m to 4m, i.e.0. 015。 0.01書the head difference is 0 h=0, 00511m, 9m， 7m and 5m， the50010001500permeability speed is 2m/d.Time/dUnsteady seepage flow isFig.6 Seepage discharge at various headconsidered, the number of timeincrement segment is 10, time increment is equal to 2" day (n=0, 1, ...9) and the initial head is theresult of steady seepage flow. From Fig. 6 and 7, the gn中國煤化工greater seepagedischarge, the smaller stability factor, the most unsafe staYHC N M H Gtime increasingthe seepage discharge and stability factor drive to equality.When upstream water level falls down from 12m to 4m, the permeability speed is 2m/d. Theseepage discharge and stability factor are calculated using various soil permeability cofficient, ie.增刊Xiao Zheng-hua.et al: The Influence of Water Level Change in ....221k=0.0009m/d,0.009m/dand0.09m/d. From Fig.8 and 9, to theearth dam slope with larger◆-ho11mpermeability coefficient the time一●h=9meffect of seepage flow is shorter, theseepage discharge is attenuated0 51015202530 35rapidly，the influence of slopeTime/dstability is disadvantage in shortterm; to the earth dam slope withFig.7 Stability factors at various headsmaller permeability coefficient thetime effect of seepage flow islonger, the seepage discharge is一一k=0. 0009attenuated slowly, the influence of-.-k=0.009slope stability is unfavorable in。k=0. 09long term and the most unsafe stateis also at initial time.When upstream water level2004006008001000Tine/dfalls down from 12m to 4m atvarious permeability speed, i.e.v=2m/d，3m/d， 4m/d and 8m/d,Fig.8 Seepage discharge at various permeability coefficientfrom Fig. 10 and 11, the fasterpermeability speed, the smallerstability factor, but the most unsafestate is at the third day, thisi 1.5峰李00illustrates the earth dam slope will-- k=0.009not failure at initial time and after0.5-★-k=0. 09some days the slope will failure.10203040The reason perhaps is that thepermeability speed is so rapid thatthe pore water can't be dischargedFig9 Slability factors at various permabiliy eoffcientin time, this leads to that theseepage surface is maintainedhigher after water level depressionand decreases the effective stressbetween soil particles and shearstrength, so the slope stability is in-8a/ddisadvantage.Consequently,elevation and subsidence of water0 200400600 800 1000 1200level will be slowly and at uniformTimeidspeed.Fig.10 Seepage discharee at various permeahility speedThe above results can be中國煤化工verified by the tests result31.YHCNMHG222上海交通大學(xué)學(xué)報第38卷5 ConclusionTo hydraulic structure, e.g. earth and masonrydam, when water level is change, in the analysis ofthe seepage flow and slope stability the stress in+mVdstress field will vary the soil permeability e C.8--tn/scoefficient and this will impact on the seepage flow其C2field; the seepage force in the seepage flow fieldwill change the stress in stress filed, so the coupling1u6Tine/daction must exist between them. In this paper thecoupling action is not considered, therefore, thecoupling action must be considered if we want toFig.11 Stability factors at varios permeability speedobtain the comprehensive and accurate analysis onslope stability concerned the seepage flow action, this will be discussed in another paper.Acknowledgement: The Natural Science Foundation of Xinjiang University in Chinasupports this paper. The authors express their gratitude to the persons who provided help for thestudy.Reference:[1]Gu Wei-ci: The Principle and Applicatio of Calculating Seepage Flow: The Industry of Building Material Press, Beijing, 2000[2] Qian Jia-huan: Soil Mechanics. Hehai University Press, Nanjin, 1988[3] Zou Xinjun: Theoretical Analysis and Model Test of Homogencous Embankment's Seepage in Consideration of Sress's Infuence.Hunan University, Changsha, 2001[4] Xiao Zheng-hua: the resarch in the infuence on water levet Variance in slope stability of eath dam and slope. Xi'an JiaoltongUniversity, Xi" an 2003中國煤化工MYHCNMHG