urac信信:IKaYH?PP, (HORIZ.)=P, COSSACTIVEPASSIVEFig.3 (b)-Coulomb earth pressureForasmoothwall(zerowall friction)withlevelbackfillorif=β fora slopingbackfill,theRankineandCoulombTheories giveidentical results.Log-Spiralpressureassumesthatthesurfaceheonnartrofslidingsomewhatfromreality.FortheDallularactive caseerrorcan belargeanolowthe failuresurfacedeviatesconsiderablpassivepressuresforcearingwill increacurvedfailureleastdrivingresistalforcecoefficient.Kforincreasingaailure2waaCoulomtA Jo a5uvCoulombcorrcmant(a)Fig. 4 - Comparison of Coulomb and log-spiral failure surface (after Terzahgi?2)The method of computing earth pressures for a log-spiral failure surface is summarized inSoil Mechanics in Engineering Practice by Terzaghi and Peck. Table 1 lists values ofpassive lateral earth pressure coefficients for a curved surface of failure and level backfillforvariousrelative values of the angle of internal friction,,and the angle of wallfriction,8.The charts in Figure 5(a) give the active and passive coefficients for a log-spiralfailure surface for the case of wall friction and sloping backill.=10°2.5015°7.5920°35°140°16.=-01.89217.508=0/21.561.761.98510.388m±01.551.704.60.42800.640.61+/6805-0.52Table 1. Values of Passive Lateral-earth-pressureCoefficients Kp(Curved Surfaces of Failure)(after Caquot and Kerise12l)
ACTIVE Fig. 3 (b) - Coulomb earth pressure For a smooth wall (zero wall friction) with level backfill or if = for a sloping backfill, the Rankine and Coulomb Theories give identical results. Log-Spiral Theory - The Coulomb Theory of earth pressure assumes that the surface of sliding or failure is a plane. This assumption deviates somewhat from reality. For the active case the error introduced is small. However, for the passive case the error can be large and is always on the unsafe side. If the angle of wall friction, , is low the failure surface is almost plane. However, if is high, the passive failure plane deviates considerably from Coulomb’s assumption, which predicts unrealistically high passive pressures. Large angles of wall friction that cause a downward tangential shearing force will increase the vertical pressures in the soil close to the wall, thus causing a curved failure surface as shown in Figure 4(a). The soil fails on this curved surface of least resistance and not on the Coulomb plane, which would require a greater lateral driving force. Figure 4(b) shows the reduction in the passive earth pressure coefficient, Kp , for increasing values of wall friction for the actual curved surface of failure. (a) Fig. 4 - Comparison of Coulomb and log-spiral failure surface (after Terzahgi22) The method of computing earth pressures for a log-spiral failure surface is summarized in Soil Mechanics in Engineering Practice by Terzaghi and Peck. Table 1 lists values of passive lateral earth pressure coefficients for a curved surface of failure and level backfill for various relative values of the angle of internal friction, , and the angle of wall friction, The charts in Figure 5(a) give the active and passive coefficients for a log-spiral failure surface for the case of wall friction and sloping backfill. 1.65 1.89 2.19 2.55 3.01 4.29 6.42 10.20 17.50 1.56 1.76 1.98 2.25 2.59 3.46 4.78 6.88 10.38 1.42 1.55 1.70 1.85 2.04 2.46 3.00 3.70 4.60 0.73 0.68 0.64 0.61 0.58 0.55 0.53 0.53 0.52 Table 1. Values of Passive Lateral-earth-pressure Coefficients (Curved Surfaces of Failure) (after Caquot and Kerise121) 9
β/Φ = +.690.0REDUCTIONFACTOR(R)OFKpβ/d =+1 -80.0β/ = +,4FORVARIOUSRATIOSOF-8/d3/=+870.06/00.70.60.50.40.30.20.10.0460.010.978.962.946.929912.898.881.86450.0β/Φ = +.2-15.961.934.907.881854.830.803.77520.939.901.862.824.787.752.716.67840.025.759.912.860.808.711.666.620.574.68630.878.811.746.627.574.520.46730.0β/β = 035.674.603.536.475362836.752.41740.783.592.512439.682.375.316.26245.414.718.600.500339.276.22117420.0SAORYIYTRTOTAVTANIYPROβ/Φ - .2-2L+BFAILURE-SURFACE900IP-E10.0LOGARITHMICβ/μ=—.49.0PHSPIRALH/38.0SIA7.0Op"KOTH6.0PASSIVE PRESSUREAβ/@=-.65.0Pp-KpyH"/2;PH-Ppcos8,P,-Ppsin8NOTE:CURVES SHOWN ARE4.0FOR6/@=-1.0EXAMPLE:0-25*:β/O--.26/0=-33.0K,R(K FOR 8/b-=1)R= 711β/Φ =-.8(KpFOR 8/@--1.0)=3.62Kp-.711x3.62-2.502.0β/Φ=-.93NO1.0ISS2987β/Φ = -1-8=01β/Φ= +1EAS5=0.6ENO.5.4OR90-0FAILURE8=ΦB/0-+.8.36-0SURFACE5=0Bl6 s +,6PHLOGARITHMIC8-0P++5SPIRALB/0-+.4=0H3VPA2=0OgK,7HttB/0-0=06=0B1o--4ACTIVEPRESSURE-8=05=0B/g -_1.08-0PyoPgsino.102010304045ANGLE OFINTERNAL FRICTION ,DEGREESFig.5(a)-Activeandpassivecoefficientswithwall friction (slopingbackfill) (afterCaquotandKerisel21)10
0 10 20 30 40 45 ANGLE OF INTERNAL FRICTION , DEGREES Fig. 5(a) - Active and passive coefficients with wall friction (sloping backfill) (after Caquot and Kerisel21) 10
TrialConditions:Broken Slope BackillWedge ITrialIrregular SurchargeWedgel,P,.c,.o..Wall Friction IncludedSloping Ground Water LevelLayer?Lavered Soil0,-5,10,17T2PATrialWedgePAHVectorResultant Pa IsDiagramCamputed From AnalysesQf Trial FailureWedqesSFrorrWlWedge lPaP4OnLayerOOnLayerAVectorDiegramsU,AndUResultantWaterPressuretion Is Made EquivalentTHIendPAH2On Failure WedgeFig.5(b)- Generalized determination of active pressures (afterNavdock)45nLayer1Conditions:7..o.C..s.CenterOfArBroken Slope BackfilIrregular Surchargeayer2Wall Friction IncluderT..o.C.o.Sloping Ground Water Level45~4PALayered SoilStraightlaneadiW,W,W, Represent Total.WeightsTrial FailureCiretCenteVnF.VPpW(a)PPHOn LayerC, (ed)1o)Vector DiagramsJCircularAreStraightc,LM.(WedgePlane WedgeC.lcFig.5(c)-Generalized determination of passive pressures (after Navdock")Insummaryforthedeterminationoflateralearthpressuresonsheetpilewalls1.ActivepressuresshouldbecomputedusingtheCoulombTheoryorthelogarithmicspiralmethodasshowninFigure5(a)2PassivepressuresshouldbecomputedusingtheCoulombTheorywithanappropriate safety factor or the logarithmic spiral method as shown in Figure5(a).3.For‘complicatedcross sections involving irregular and stratified backfills,thereader should consult suchtexts asFundamentalsof Soil Mechanicsby Taylorand Soil Mechanics in Engineering Practice by Terzaghi and Peck. A graphicalanalysisforcomplicatedcrosssectionsisshownonFigures5(b)and5(c)11
Conditions: Broken Slope Backfill Irregular Surcharge Wall Friction Included Sloping Ground Water Level Layered Soil. Fig. 5(b) - Generalized determination of active pressures (after Navdock11) Fig. 5(c) - Generalized determination of passive pressures (after Navdock11) In summary for the determination of lateral earth pressures on sheet pile walls: 1. Active pressures should be computed using the Coulomb Theory or the logarithmic spiral method as shown in Figure 5(a). 2. Passive pressures should be computed using the Coulomb Theory with an appropriate safety factor or the logarithmic spiral method as shown in Figure 5(a). 3. For ‘complicated cross sections involving irregular and stratified backfills, the reader should consult such texts as Fundamentals of Soil Mechanics by Taylor and Soil Mechanics in Engineering Practice by Terzaghi and Peck. A graphical analysis for complicated cross sections is shown on Figures 5(b) and 5(c). 11
Soil Properties -Independent of the theory used to compute earth pressureeonretaining structures,theresults can be no more accurate thanthe soil properties used inthe calculations.Because of the wide variations of subsurface conditions at various sites,the soil constants should be determinedon the basis of an exploratory boring programand laboratory testsof representative samples. Only then can a safe and economicaldesignbe assured.However,forthe purpose of preliminarydesign itis oftennecessarytopresume appropriate soil properties.The followingtables and graphs are included forthispurposemerelyasaguide.Table 2 showsan approximaterelationship betweentherelativedensity.standardpenetration resistance,angle of internal friction, and unit weight of granular soils.CompactnessVery LooseLoose MediumDenseVery Dense15%35%65%85%100%Relative density D.03041050Standard penetra-0tion resistance,N-no.of blowsperfootΦ (degrees) *28303641Unit weight, pcf<100moist95-125110-140>130110-130< 6055-65> 75submerged60-7065-85"highly dependent on gradationTable 2-Granular soil (afterTeng')Table3shows an approximaterelationship between the unconfined compressivestrength, standard penetration resistance and the unit weight of cohesive soilsSoftMediumConsistencyVery SoftVeryStiffHardStiff00.250.501.002.004.00quunconfinedcompressionstrength, tonsper square ft2481632Standard penetra-tion resistance,N = no. of blowsper ft100-120110-130120-140130+Unit weight, pcf(saturated)ExudesIdentificationMoldedMoldedIndentedIndented Difficultfromby lightcharacteristicsby strong by thumbby thumb to indentbetweenfingerfingernailby thumbfingersnailpressurepressurewhensqueezedin handTable3--Cohesivesoil (afterTeng')12
Soil Properties - Independent of the theory used to compute earth pressure on retaining structures, the results can be no more accurate than the soil properties used in the calculations. Because of the wide variations of subsurface conditions at various sites, the soil constants should be determined on the basis of an exploratory boring program and laboratory tests of representative samples. Only then can a safe and economical design be assured. However, for the purpose of preliminary design it is often necessary to presume appropriate soil properties. The following tables and graphs are included for this purpose merely as a guide. Table 2 shows an approximate relationship between the relative density, standard penetration resistance, angle of internal friction, and unit weight of granular soils. Compactness Very Loose Loose Medium Dense Very Dense Relative density Dd Standard penetration resistance, N = no. of blows per foot (degrees) * Unit weight, pcf moist submerged *highly dependent on gradation Table 2 - Granular soil (after Teng1 ) Table 3 shows an approximate relationship between the unconfined compressive strength, standard penetration resistance and the unit weight of cohesive soils. Consistency Very Soft Soft Medium Stiff Very Stiff Hard = unconfined compression strength, tons per square ft Standard penetration resistance, N = no. of blows per ft Unit weight, pcf (saturated) Identification characteristics Exudes Molded Molded Indented Indented Difficult from by light by strong by thumb by thumb to indent between finger finger nail by thumb fingers pressure pressure nail when squeezed in hand Table 3 - Cohesive soil (after Teng1 ) 12
Figure6shows the approximate relationship between the angle of internalfriction andthe dry unit weight for various relative densities and types of granular soils.The porosityn, and the void ratio, e, are also shown for coarse grained soils that have a specific gravity,G, equal to 2.68.ANGLE OF INTERNAL FRICTIONVS.DRY UNIT WEIGHT(FOR COARSE GRAINED SOILS)40RELATIVEOENSIIYATERIALTYPEGpSW35MLINTHISRAOBTAINEDFROM30EFFECTIVESTRESSFAILURE ENVELOPESAPPROXIMATE CORRELATIONISFOR COHESIONLESSMATERIALS WITHOUTPLASTICFINES25POROSITY,n (FOR G2.68)545215.5525.352VOID RATIO e (FOR G = 2.68)1.08.75.7A353.25.2151.29656555451.120LL901301401507580100110120DRY UNIT WEIGHT, Yd PCFFig. 6 -Granular soils (after Navdocks")Table 4 shows friction angles for various soils against steel sheet piles.tand$ (degree)Steel sheet piles against the following soils:220.40Clean gravel, gravel-sand mixtures, well-graded rock fil with spalls17Clean sand, silty sand-gravel mixture, single size hard rock fll0.300.2514Silty sand, gravel or sand mixed with silt or clayFine sandy silt, non-plastic silt0.2011Table 4.Wall friction (afterNavdocks")As mentionedpreviously,earthpressure is time-dependent in nature.This is particularlytrue in clay and clayey soils where the values of cohesion, c, and internal friction, , tendto change with time.Sheet pile structures inclayey soils should be designed for both theperiod immediately after construction and long term conditions.Limited informationindicates that due to creep effects the long term value of c approaches zero and that of somewherebetween20and30degrees.Thelongtermcasethusapproachesthatforsheetpiling in granular soils.13
Figure 6 shows the approximate relationship between the angle of internal friction and the dry unit weight for various relative densities and types of granular soils. The porosity, n, and the void ratio, e, are also shown for coarse grained soils that have a specific gravity, G, equal to 2.68. ANGLE OF INTERNAL FRICTION VS. DRY UNIT WEIGHT APPROXIMATE CORRELATION IS FOR COHESIONLESS MATERIALS WITHOUT OBTAINED FROM EFFECTIVE STRESS FAILURE ENVELOPES. PLASTIC FINES. (FOR COARSE GRAINED SOILS) DRY UNIT WEIGHT, PCF Fig. 6 - Granular soils (after Navdocks11) Table 4 shows friction angles for various soils against steel sheet piles. Steel sheet piles against the following soils: Clean gravel, gravel-sand mixtures, well-graded rock fill with spalls . Clean sand, silty sand-gravel mixture, single size hard rock fill . Silty sand, gravel or sand mixed with silt or clay . Fine sandy silt, non-plastic silt . 0.40 0.30 0.25 0.20 Table 4 - Wall friction (after Navdocks11) 22 17 14 11 As mentioned previously, earth pressure is time-dependent in nature. This is particularly true in clay and clayey soils where the values of cohesion, c, and internal friction, , tend to change with time. Sheet pile structures in clayey soils should be designed for both the period immediately after construction and long term conditions. Limited information indicates that due to creep effects the long term value of c approaches zero and that of somewhere between 20 and 30 degrees. The long term case thus approaches that for sheet piling in granular soils. 13