Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 42 Topic 3: Permeability and seepage of soil 3.1 Flow through fully saturated soil Sincesoilsconsistofdiscreteparticles,theporespacesbetweenparticlesareall interconnectedsothatwaterisfreetoflowwithinthesoilmass.Insuchaporousmedia, water will flow from zones of higher to lower pore pressure. When considering problems of water flow, it is usual to express a pressure as a pressure head or head, measured in metres of water. Bernoulli's equation states three head components, the sum of which provide the total head (h) causing a water flow: Thelastcomponent,thevelocityhead,isusuallyignoredinproblemsofgroundwaterflow, since u is quite small owing to the high resistance to flow offered by the granular structure of the soil. The first two terms, therefore, represent the head tending to cause the flow of water through a mass of soil. In saturated conditions, one-dimensional flow is governed by Darcy's law, which states that the flow velocity is proportional to the hydraulic gradient: Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 43 Figure 3.1: One-dimensional flow of soil The quantity flowing is therefore given by: 3.2 Darcys Law and coefficient of permeability (Laboratory and I n situ methods) Coefficient of permeability Thecapacityofasoiltoallowwatertopassthroughitistermeditspermeability(or hydraulicconductivity).Thecoefficientofpermeability(k)maybedefinedastheflow velocity produced by a hydraulic gradient of unity (see eqn [5.2]). The value of ft is used as a measure of the resistance to flow offered by the soil, and it is affected by several factors: (a) The porosity of the soil. (b) The particle-size distribution. (c) The shape and orientation of soil particles. (d) The degree of saturation/presence of air. (e)Thetypeofcationandthicknessofadsorbedlayersassociatedwithclayminerals(if present). (f) The viscosity of the soil water, which varies with temperature. Therangeofvaluesforkisextremelylarge,extendingfrom100m/sinthecaseofvery coarse-grainedgravelstoalmostnothinginthecaseofclay.Ingranularmaterialskvaries approximately inversely with the specific surface, but in fine soils the relationships are more Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 44 complex. In clay soils, such factors as water content and temperature are significant, as also is the presence of fissures when considering the permeability of large masses. Table3.1 shows therangeofaveragevaluesforkforvarioussoilsandalsoindicatespotentialdrainage conditions. Table 3.1: Range of values of k (m/s) Effect of temperature Since the viscosity and density of water both vary markedly with temperature, it follows that the value of the coefficient of permeability will be affected by changes in temperature. A correction for the effect of temperature may, therefore, be obtained as follows: Table3.2givesvaluesoft,whichwillhaveavalueof1.0at20Csinceitisatthis temperature that most laboratory graduations are standardised. Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 45 Table 3.2:Values of temperature correction coefficient t Determination of k in the laboratory Thecoefficientofpermeabilitykcanbemeasuredusingfieldtests,ortestsconductedina laboratory. The main categories of problems associated with the reliability of laboratory tests are:(a)thoseconcernedwithobtaininggoodrepresentativesamples,(b)thoseconcerned withthereproducibilityoflaboratorymeasurements,and(c)thoseconcernedwith reproducing field conditions. (i) Reliability of sample Thepermeabilityofasoilmassisdependentonbothitsmicrostructure(i.e.particlesize, shape,arrangement,etc.)anditsmacrostructure(i.e.whetherornotstratified,presenceof fissures,pipes,lenses,etc.).Forobviouspracticalreasonsthesizeofsamplestakenfor laboratorytestsisquitesmall,andthereforeunlikelytobesatisfactorilyrepresentativein soilswithsignificantmacrostructurecharacteristics.Tosomeextentthisdeficiencymaybe overcome by obtaining carefully selected groups of samples. (ii) Reliability of laboratory measurements Theaiminanylaboratoryprocedureshouldbetoreproducesimilarresultsusingthesame procedureandforthesetocomparefavourablywithresultsusingdifferentprocedures.In laboratory permeability tests disparities may occur due to: (a)The presence of air bubbles in the permeant (water) (b)Variations in sample density and porosity (c)Variations in temperature and therefore viscosity of the permeant (iii) Reproduction of field conditions Itisgenerallydifficulttoobtaintrulyundisturbedsamplesandparticularlydifficultto simulate in the laboratory the true field conditions of flow and stress. In the main, disparities between laboratory and field conditions will be: (a) Variations in density and porosity (b) Variation in flow direction with respect to bedding (c) Limited ability of a small sample to simulate anisotropic conditions (d) Variation in pore pressure and effective stress condition Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 46 Forthesereasonslaboratorytestsshould,whereverpossibleandappropriate,beaugmented with field tests. Since the range of values of k is so large the choice of method and equipment varies with the type of soil. The most common types of test in present use are: (a)Constant head test: suitable for gravels and sands with values of k > l0-5 m/s. (b)Falling head test: suitable for fine sands, silts and clayr wlth vrluor of & between l0-5 and l0-7 m/s. (a)The constant head test Theconstantheadtestisusedtodeterminethecoefficientsofpermeability(k)ofcoarse-grained soils such as gravels and sands having values of k above l0-4 m/s. The apparatus used is called a constant head permeameter and is shown diagrammatically in Figure 3.2. The soil sample is contained in a perspex cylinder with wire mesh and gravel filters above and below. In the side of the cylinder a number of manometer connection points areprovided to enable pairs of pressure head readings to be taken (only one pair is shown in the diagram). Water is allowed to flow through the sample from a tank or reservoir designed to maintain a constant head and the quantity of water measured by weighing a collecting vessel. Since the presence of air bubbles can seriously affect the results, it is imperative to ensure as little air as possible in the system. This may be effected by first of all supplying only de-aired watertotheconstant-headtankandsecondlybyapplyingavacuumtothesamplepriorto commencementofthetest.ThetestisthenstartedwithvalvesAandBopenandvalveC closed, with the valve A being used to control the rate of flow.Flow is allowed to continue untilasteadystatehasbeenestablished,i.e.thelevelsinthemanometertubesremain constant.Onceasteadystatehasbeenreached,thequantityflowingduringagiventime intervalismeasured,andthetwomanometerlevelsnoted.Theflowrateisthenvariedand theprocedurerepeated.Severaltestsatvaryingflowratesandheadsshouldbecarriedout andtheaveragevalueofkestablishedwhichisthencorrectedfortemperature(Table3.2). The dry density and void ratio should also be reported. Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 47 Figure 3.2: Constant head test apparatus Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 48 Worked Example 3.1 During a test using a constant-head permeameter, the following data were collected. Determine the average value of k. (b) The falling head test The falling head test is used to determine the coefficient of permeability of fine soils, such as fine sands, silts and clays. For these soils, the rate of flow of water through them is too small toenableaccuratemeasurementsusingtheconstantheadpermeameter.Thefallinghead permeameter is shown diagrammatically in Figure 3.3. An undisturbed soil sample is obtained in a 100 mm diameter (usually) cylinder, which may be a Ul00 sample tube or a core-cutter tube as used in field density tests. Samples can also be prepared by compaction in a standard mould. A wire mesh and gravel filter is provided at the top and bottom of the sample. The base of the cylinder is stood in a water reservoir fitted with a constant-level overflow and the top connected to a glass standpipe of known diameter. Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 49 Thetestisconductedbyfillingthestandpipewithde-airedwaterandallowingseepageto takeplacethroughthesample.Theheightofwaterinthestandpipeisrecordedatseveral timeintervalsduringthetest,andthetestrepeatedusingstandpipesofdifferentdiameter. Following computation of the results, the average value for k is determined. It is usual also to report the initial and final unit weights and water contents of the sample. Commencing with Darcy's law (eqn [5.3]): q = kAi But, referring to Figure 3.3, if the level in the standpipe falls dh in a time of dt then Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 50 Figure 3.3 Falling head test apparatus Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 51 Worked Example 3.2 During a test using falling head permeameter the following data were recorded. Determine the average value of k. Field permeability tests Becauseoftheproblemsassociatedwiththereliabilityoflaboratorytests,as,fieldmethods shouldbeusedwhenpermeabilityvaluesareofsignificantimportance.Comprehensive multiple-well pumping tests can be expensive to carry out, but offer i high level of reliability owingtotheinclusionofawiderangeofmacro-structuralcharacteristics.Theuseofsite investigationboreholescanbeeconomicallyadvantageous,providingthepumping/ observation sequences are carefully planned and controlled. Steady state pumping tests In a confined aquifer, the pumping rate must not be high to reduce the level in the pumping well Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 52 Pumpingtestinvolvesthemeasurementofapumpedquantityfromawell,togetherwith observationsinotherwellsoftheresultingdrawdownofthegroundwaterlevel.Asteady stateisachievedwhen,ataconstantpumpingrate,thelevelsintheobservationwellsalso remain constant. The pumping rate and the levels in two or more observation wells are then noted. The analysis of the results depends on whether the aquifer is confined or unconfined. (a) Pumping test in a confined aquifer In a confined aquifer, the pumping rate must not be high to reduce the level in the pumping wellbelowthetopoftheaquifer.Theinterfacebetweenthetopoftheaquiferandthe overlying impermeable stratum therefore forms the top stream line. AnarrangementofapumpingwellandtwoobservationwellsisshowninFigure3.4.The piezometric surface is assumed to be above the upper surface of the aquifer and the hydraulic gradient is assumed to be constant at a given radius. Then, in steady state conditions, the flow is considered through an elemental cylinder having radius r, thickness dr and height h. Whenonlyoneobservationwellisavailable,thepumpingwellmaybeutilisedasan observationwell.Becauseofsoildisturbancearoundthewellaneffectiveradiusof1.2 actual radius should be used. The observed pumping well drawdown must also be corrected, sincethepiezometriclevelatthewellwillgenerallybehigherduringpumpingthanthe actual level in the well. Stepped drawdown tests may be used to evaluate the pumping level loss,oralossassumedwhichisbasedonexperience(e.g.20percent).Thefollowing substitutions may then be made in eqn [5.13]: Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 53 Figure 3.4: Pumping test in a confined aquifer Another, albeit more crude, approximation may be derived from a consideration of the radius ofinfluence(r0)ofthepumping.Itmaybeassumedthatnodrawdownofthepiezometric headtakesplaceoutsidetheradiusofinfluence,i.e.whenr=r0.Thus,eqn[5.13]maybe used with the following substitutions: r2 = r0 and h2 = h0 Worked Example 3.3 A permeability pumping test was carried out from a well sunk into a confined stratum of dense sand. Figure 3.5 shows the arrangement of the pumping well and observationwells,togetherwithrelevantdimensions.Initially,thepiezometricsurfacewas locatedatadepthof2.5m.Whenasteadystatewasachievedatapumpingrateof77.4 m3/hr, the following drawdowns were observed: Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 54 Figure 3.5 (b) Pumping test in an unconfined aquifer Anunconfinedaquiferisafree-drainingsurfacelayerunderlainbyanimperviousbase. Under conditions of steady state pumping the hydraulic gradient at a given radius is assumed tobeconstantinahomogeneousmedium.Anarrangementofapumpingwellandtwo observation wells is shown in Figure 3.6. Consider the inflow through an elemental cylinder of radius r, thickness dr and height h. Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 55 Figure 3.6: Pumping test in an unconfined aquifer Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 56 WorkedExample3.4Apermeabilitytestwascarriedoutfromawellsunkthrougha surface layer of medium dense sand. Figure 5.10 shows the arrangement of the pumping well andobservationwells,togetherwithrelevantdimensions.Initially,thewatertablewas located at a depth of 2.5 m. When a steady state was achieved at a pumping rate of 23.4 m3/hr, the following drawdowns were observed: Figure 3.7 Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 57 3.3 Seepage Theory: Laplaces Equation of Continuity Theseepagetakingplacearoundsheet-piling,dams,underotherwater-retainingstructures and through embankments and earth dams is two-dimensional. That is to say, the vertical and horizontalvelocitycomponentsvaryfrompointtopolntwithinthecross-sectionofthesoil mass(Figure3.8).Tobeginwith,thegeneralcasewillbeconsideredoftwo-dimensional flowinahomogeneousandisotropic(i.e.kH=kV)soilmass,andthenthegraphical representation known as a flow net will be introduced. Figure 3.8: Two-dimensional flow Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 58 General flow equation InFigure3.9anelementofsaturatedsoilhavingdimensionsdx,dyanddzisshownwith flowtakingplaceinthexzplaneonly.Thevelocitygradientsinthex-andz-directionsare du"ldz and du,ldx respectively. Assuming water to be incompressible and no volume change in the soil skeleton: Quantity flowing into element = quantity flowing out of element Figure 3.9: General two-dimensional flow condition Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 59 Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 60 Figure 3.10: Graphical interpretation of flow Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 61 3.4 Flow nets Properties of a flow net Flow nets - construction rules and boundary conditions In the previous section, flow nets were introduced as diagrammatic constructions representing two-dimensionalflowconditions.Onceaflownethasbeendrawn,quantitiessuchasthe amount of seepage and pressure distribution may be evaluated. In order to produce a correctly constructed flow net a number of 'rules' must be observed (see Figure 3.11). Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 62 Figure 3.11: Flow net boundaries To construct a flow net, first of all a scaled cross-section is drawn defining all the boundaries due to the site, structure, etc. Then, following the rules given above, a few trial flow lines and equipotentialsaredrawninpencil.Asfurthersquare'fieldsareaddedtheflownettakes shape.Aseriesofsuccessivetrialsisnecessary,involvingthejudicioususeofpenciland eraser, with the ultimate aim of drawing a flow net in which all parts comply with the rules. A gooddealofpracticewillberequired,sothat studentsshouldattemptasmanyflownetsas possible to gain proficiency in the sketching process. Theoretically, any number of flow lines may be drawn and the greater the number, the more accurate should be thecalculations that follow.However, froma practical point of view the task is simplified by drawing only a few flow lines; it is not often that more than five or six will be necessary. Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 63 Worked Example 3.5 Figure 3.5( a) shows the cross-section of a line of sheet-piling driven toadepthof7mintoastratumofhomogeneoussandysoilwhichhasathicknessof12m and is underlain by an impermeable stratum. From an original depth of 5.5 m the water level on one side of the piles is reduced by pumping to a depth of 0.5 m. Draw a flow net for the seepageconditionsandfromitdetermine:(a)thequantityofseepageunderthepilesper metre run, and (b) the pore pressure in the soil at points P and Q. The coefficient of permeability k = 7.2 x l0-3 mm/s Figure 3.12 Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 64 Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 65 WorkedExample3.6Figure3.13showsthecross-sectionofalongcofferdamformedby driving two parallel rows of sheet piles into a stratum of sand. Within the coffer dam the sand isexcavateddowntothelevelshownandthewatermaintainedatthislevelbypumping. Draw a suitable flow net and use it to determine the pumping rate required per metre run (k= 4.5 x 10-5 m/s). Figure 3.13 Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 66 Worked Example 3.7 Figure 3.14 shows the cross-section of a dam founded on a permeable stratum, which in turn is underlain by an impermeable stratum. A row of sheet piles has been inserted near the upstream face of the dam in order to reduce the quantity of seepage. Draw a flow net to represent the seepage conditions and from it:(a) determine the seepage quantitypermetrerun(k=5.2xI0-5m/s),and(b)plotthedistributionofupliftpressure acting on the base of the dam. Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 67 Figure 3.14 I nstability due to seepage The term piping is used to describe the unstable condition which can occur when the vertical component of seepage pressure acting in an upward direction exceeds the downward weight ofthesoil.Whentheupwardseepageforcebecomesequaltothesubmergedweightofthe soil,nofrictionalresistancecanbedevelopedbetweentheparticles.Thesoil/watermixture therefore has no shear strength and acts as a liquid. Iftheupwardseepageforcesexceedthesubmergedweight,theparticlesmaybecarried upwardstobedepositedatthegroundsurface.Thusa'pipe'isformedinthesoilnearthe surface. Piping failure can lead to the complete failure of a foundation or to the collapse of a supportingstructure,suchasthetoeofadam,orpartofacofferdam.Itisnecessary, therefore,tocheckthispotentialinstabilityconditionduringthedesignofwater-retaining structures. Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 68 Where a flow net has been drawn to represent the seepage conditions, a simple rule-of-thumb method may be used to determine a factor of safety against the occurrence of piping. This is donebyconsideringaprismofsoiladjacenttothedownstreamfaceofthestructure. ConsiderthecaseofasheetpilewallasshowninFigure3.15.Theeffectiveweightofthe prism of soil ABCD will be Thefactorofsafetyagainstpipingmaybeincreasedinanumberofways.Forexample,in the case of a coffer dam the depth of penetration of the piles could be increased, or a layer of coarse filter material could be laid on the downstream side before pumping down to the final level. In the case of dams, both an increase in the factor of safety against piping and a reduction in the quantity of seepagecan be obtained by increasing the length of theflow path. This may be done by driving a row of sheet piles, preferably at or near the upstream face, or by laying anapronofimpermeablepavinginfrontoftheupstreamface.Alayerofcoarsefilter material laid on the downstream side is another possibility (see Figure 3.16). Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 69 Figure 3.15: Factor of safety against piping Figure3.16:Methodsofimprovingseepageconditions(a)Cofferdam(b)Concreteor masonry dam Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 70 Exercises 3.1 The following data were recorded during a constant-head permeability test: Internal diameter of permeameter = 75 mm Head lost over a sample length of 180 mm = 241 mm Quantity of water collected in 60 s = 626 ml Calculate the coefficient of permeability for the soil. 3.2 A constant head permeameter has an internal diameter of 62.5 mm and is fitted in the side with three manometer tappings at points A, B and C. During tests on a specimen of sand the following data were recorded: Determine the coefficient of permeability of the soil (average of six values). 3.3 In a falling-head permeability test the following data were recorded: Internal diameter of permeameter = 75.2 mm Length of sample = 122.0 mm Internal diameter of standpipe = 6.25 mm Initial level in standpipe = 750.0 mm Level in standpipe after 15 min. = 247.0 mm Calculate the permeability of the soil. Semester 1, Session 2014/ 2015CEGB233 (Soil Mechanics) 71 3.4Afalling-headpermeameterhasaninternaldiameterof75mmandisconnectedtoa standpipe of diameter 12.5 mm. A specimen of fine soil of length 80 mm is to be tested and is heldinplacebetweentwodiscsoffinewiremesh.Theheadofwaterinthestandpipeis allowed to fall from 950 mm to 150 mm and the times noted as follows: Time taken when mesh discs only are in place = 4.4 s Time taken when soil specimen is in place = 114.8 s Calculatethecoefficientofpermeabilityofthesoil,makingdueallowanceforthe permeability of the wire mesh discs. 3.5 For a field pumping test a well was sunk through a horizontal layer of sand which proved to be 14.4 m thick and to be underlain by a stratum of clay. Two observation wells were sunk, respectively18mand64mfromthepumpingwell.Thewatertablewasinitially2.2m below ground level. At a steady state pumping rate of 328 litres/min., the drawdowns in the observation wells were found to be 1.92 and 1.16 m respectively. Calculate the coefficient of permeability of the sand.