Since K =K,= 1 when = o, the passive earth pressure on the left side of the piling isgiven by:Pp =e(Z - H) + quand the active pressure onthe right side of the piling is given byPa=eZ -quwhereZ = depth below the original ground surface, ft.qu = 2c = unconfined compressive strength, Ibs-per sq. ft.Ye = effective unit soil weight (moist unit weight above thewater level and submerged unit weight below the waterlevel),Ibs-per cubic ft.The negative earth pressure or tension zone,as shown by thedotted line,is ignoredbecause the soil may develop tension cracks in the upper portion. Since the slopes of theactive and passive pressure lines are equal (Ka = K,), the net resistance on the left side ofthe wall is constant below the dredge line and is given by:Pp-Pa=2qu-eHNote that,theoretically,therewill be no net pressure and the wall will fail feHisgreater than 2qu.The height, Hc=2qu/e, is often called the critical wall height.For the lower portion, where the piling moves to the right, the net resistance is givenby:Pp-Pa=2qu +eHwhich is illustrated in Figure 19 (b).The resulting net pressure distribution on the wall isas shown in Figure 19 (a), and the method of solution is the same as that presented forthe design of cantilevered sheet pile walls in granular soils. The point d and the depth ofpenetration D are chosen so as to satisfy the conditions of static equilibrium; i.e., the sumof the horizontal forces equal to zero-and the sum of the moments about any point equalto zero.Similar to the simplified method for granular soils, the design may be made using thepressure diagram shown in Figure 19 (c): i.e., by assuming the passive pressure on theright side of thepilingis replacedbytheconcentrated reaction,C.The depth,Do,shouldbe increased by 20 to 40 percent to obtain the total design depth of penetration usingthis method.Wall inCohesive Soil Below DredgeLine-Granular Backill Above Dredgeline-Theabovemethods mayalsobe extendedtothe case where sheet piling isdriven in clay andbackfilled with granular soil as shown in Figure 20.The only difference is the activepressure above the dredge line is equal toKaez for a granular backill. The simplifiedmethod is shown in Figure 20 (b). The methods of design are exactly the same as dis-cussed previously24
Since Ka = Kp = 1 when = 0, the passive earth pressure on the left side of the piling is given by: and the active pressure on the right side of the piling is given by: where = depth below the original ground surface, ft. = 2c = unconfined compressive strength, Ibs-per sq. ft. = effective unit soil weight (moist unit weight above the water level and submerged unit weight below the water level), Ibs-per cubic ft. The negative earth pressure or tension zone, as shown by the dotted line, is ignored because the soil may develop tension cracks in the upper portion. Since the slopes of the active and passive pressure lines are equal (Ka = Kp ), the net resistance on the left side of the wall is constant below the dredge line and is given by: Note that, theoretically, there will be no net pressure and the wall will fail if is greater than 2qu . The height, is often called the critical wall height. For the lower portion, where the piling moves to the right, the net resistance is given by: which is illustrated in Figure 19 (b). The resulting net pressure distribution on the wall is as shown in Figure 19 (a), and the method of solution is the same as that presented for the design of cantilevered sheet pile walls in granular soils. The point d and the depth of penetration D are chosen so as to satisfy the conditions of static equilibrium; i.e., the sum of the horizontal forces equal to zero-and the sum of the moments about any point equal to zero. Similar to the simplified method for granular soils, the design may be made using the pressure diagram shown in Figure 19 (c); i.e., by assuming the passive pressure on the right side of the piling is replaced by the concentrated reaction, C. The depth, Do, should be increased by 20 to 40 percent to obtain the total design depth of penetration using this method. Wall in Cohesive Soil Below Dredge Line - Granular Backfill Above Dredgeline - The above methods may also be extended to the case where sheet piling is driven in clay and backfilled with granular soil as shown in Figure 20. The only difference is the active pressure above the dredge line is equal to for a granular backfill. The simplified method is shown in Figure 20 (b). The methods of design are exactly the same as discussed previously. 24
WateSand backfillPa(2q7eH)linTeH.-eH= Vertical pressure ofdredge level due tobackti, (submergecwt. below water lev(2qu-OH[(2qu+eH)(a)(b)Conventional MethodSimplified'MethodFig. 20 -Initial earth pressure for design of cantilever sheet pilingin cohesive soil backfilled with granular soil (after Teng)The long-term condition for sheet piling in clays must also be considered, as mentionedpreviously:due to timedependentchangesand c.The analysis should becarried outusing effective stress parametersobtained from consolidated-drained tests,orOfrom consolidated-undrainedtestswhichpressuremeasurementsaremadeLimitedexperimental data indicates-term valueof c is quite small,and thatthatihe0fordesignpurposescmaybeas zero.Thefinal value of @is usuallyconservativeltakenbetween20and30degrees.Thelateralpressures in the clay over a long period of timeapproach those for a granular soil.Therefore.the long-term condition is analyzed asdescribed in the preceding section for granular soils.Figure 22, page 26 provides design curves for cantilever sheet piling in cohesive soilwithgranularsoil backfill baseduponthesimplifiedmethod of analysis.Thischartallowsthe designer to obtain directly the depth ratio, D/H, and the maximum moment ratio,Mmax/'KaH3 as a function of the net passive resistance, 2qu - eH, divided by theexpression 'Ka.The chart is,therefore,independent of the method of obtaining K.and was developed for a wet unit weight.,equal to twice the submerged unit weight,'.To use Figure 22, the values for qu and emay be obtained from Table 3. For the sandbackill, may be found in Table 4 and K, from Figure 3(a). A design example is givenattheendofProblemNo.2(pages91-94)ANCHOREDWALLSGeneral-Anchored sheetpilewalls derivetheir supportbytwomeans:passivepressureon the front of the embedded portion of the wall and anchor tie rods near thetop of thepiling.This method is suitablefor heights up to about 35 feet,depending on the soilconditions. For higher walls the use of high-strength steel piling, reinforced sheet piling.relieving platforms or additional tiers of tie rods may be necessary.The overall stabilityofanchoredsheetpilewallsandthestressesinthemembersdependsontheinteractionofa number of factors, such as the relative stiffness of the piling, the depth of piling pene-tration,the relative compressibilityand strength of the soil,the amount of anchoryieldetc. In general, the greater the depth of penetration the lower the resultant flexuralstresses.Figure 21 shows the general relationship between depth of penetration, lateral pressuredistribution and elastic line or deflection shape.OWDredgeA(a)(b)(c)Fig.21.Affect of depth of penetration on pressure distribution and deflected shape25
Water level (a) Conventional Method (b) Simplified Method Fig. 20 - Initial earth pressure for design of cantilever sheet piling: in cohesive soil backfilled with granular soil (after Teng1 ) The long-term condition for sheet piling in clays must also be considered, as mentioned previously, due to time dependent changes in and c. The analysis should be carried out using effective stress parameters c' and obtained from consolidated-drained tests, or from consolidated-undrained tests in which pore pressure measurements are made. Limited experimental data indicates that the long-term value of c is quite small, and that for design purposes c may be conservatively taken as zero. The final value of is usually between 20 and 30 degrees. The lateral pressures in the clay over a long period of time approach those for a granular soil. Therefore, the long-term condition is analyzed as described in the preceding section for granular soils. Figure 22, page 26 provides design curves for cantilever sheet piling in cohesive soil with granular soil backfill based upon the simplified method of analysis. This chart allows the designer to obtain directly the depth ratio, D/H, and the maximum moment ratio, as a function of the net passive resistance, 2qu - divided by the expression . The chart is, therefore, independent of the method of obtaining Ka and was developed for a wet unit weight, , equal to twice the submerged unit weight, To use Figure 22, the values for qu and may be obtained from Table 3. For the sand backfill, may be found in Table 4 and Ka from Figure 3(a). A design example is given at the end of Problem No. 2 (pages 91-94). ANCHORED WALLS General - Anchored sheet pile walls derive their support by two means: passive pressure on the front of the embedded portion of the wall and anchor tie rods near the top of the piling. This method is suitable for heights up to about 35 feet, depending on the soil conditions. For higher walls the use high-strength steel piling, reinforced sheet piling, relieving platforms or additional tiers of tie rods may be necessary. The overall stability of anchored sheet pile walls and the stresses in the members depends on the interaction of a number of factors, such as the relative stiffness of the piling, the depth of piling penetration, the relative compressibility and strength of the soil, the amount of anchor yield, etc. In general, the greater the depth of penetration the lower the resultant flexural stresses. Figure 21 shows the general relationship between depth of penetration, lateral pressure distribution and elastic line or deflection shape. C (a) (b) (c) (d) Fig. 21 - Affect of depth of penetration on pressure distribution and deflected shape 25
MOMENTRATIOPERFT.WIDTH,M"KaH3aX02009'0001110OgS100106080MINGTMAI-LHlNESNNIOSNOL0'92TIOS0'S中-OSEH0t08工D0H'yE6OES(H-z)0/b00d01608L'000.b9'0S0bA9'07b0006to.b3Z0o9'89'0225O1DEPTHRATIO,D/H(INCREASEBY20%TO40%FORS.F.)26
MOMENT RATIO PER FT. WIDTH, DEPTH RATIO, D/H (INCREASE BY 20% TO 40% FOR S.F.) 26
Case (a)is commonly called the freeearth support method.The passive pressures in frontof the wall are insufficient to prevent lateral deflection and rotations at point C.Cases(b), (c) and (d) show the effect of increasing the depth of penetration. In cases (b) and (c)the passive pressure has increased enough to prevent lateral deflection at C;however,ro-tationstill occurs.Incase(d)passivepressureshavesufficientlydevelopedonbothsidesof the wall to prevent both lateral deflection and rotation at C. This case is commonlycalled the fixed earth supportmethod becausepointC is essentiallyfixed.Cases(a)and(d)representthetwoextremesindesignSomedifferentmethods incurrentusageforthedesignof anchoredsheetpilewallsaregrouped and discussedinthefollowing order:FreeEarthSupportMethodRowe'sMomentReduction MethodFixed Earth Support Method (Equivalent Beam)Graphical MethodsDanishRulesFree Earth Support Method - This method is based on the assumption that the soilinto which the lower end of the piling is driven is incapable of producing effectiverestraint frompassivepressureto theextentnecessarytoinduce negative bendingmoments. The piling is driven just deep enough to assure stability.assuming that themaximum possible passive resistance is fully mobilized.The sheet piling is assumed to beinflexible and that no pivot point exists below the dredge line i.e.,no passive resistancedevelops on the backside of the piling.Earth pressures may be computed by theCoulomb or log-spiral method.With these assumptions the design becomes a problem insimple statics.Procedures forthe design of anchored sheet piling in granular and cohesivesoilarediscussedseparatelybelow.Design in Granular Soil -Figure 23 shows the resulting pressure distributions for ananchored sheet pile wall in granular and cohesive soil. The following design procedure assuggested in Teng',may be used:In Granular SoilIin Cohesive SollH.LaverYKaLowtie rod pullKaHwatertie rod pullrkaHearthpressureabovepoinLHwHhorizontalforcesMhiti (except T)Pa = total horizYH20.7HEmforce(excepT) abovedredge lineHK,Dredge line(b)(Pp-Pa)D,(a) Fig.23-Design or anchored sheet piling by free-earth method (after Teng)1.Compute the active and passive lateral pressures using appropriate coefficients oflateral earthpressure.IftheCoulombmethodisused,it should beusedconservativelyforthepassivecase.Note:Figure 23 (a) shows the general case for an anchored wall in granular soilbackflled with granular material having different soil properties. Therefore, Yerefers to the equivalent soil unit weight,.either wet to submerged, for theAlso, Ka' refers to the active pressure coef-particular soil layer in question.ficient for the natural in-place granular soil.2.Calculate the weight of overburden and surcharge load at the dredge level, YeH.3.Locate the point of zero pressure given by=eHKa/(pp-Pa)27
Some different methods in current usage for the design of anchored sheet pile walls are grouped and discussed in the following order: Case (a) is commonly called the free earth support method. The passive pressures in front of the wall are insufficient to prevent lateral deflection and rotations at point C. Cases (b), (c) and (d) show the effect of increasing the depth of penetration. In cases (b) and (c) the passive pressure has increased enough to prevent lateral deflection at C; however, rotation still occurs. In case (d) passive pressures have sufficiently developed on both sides of the wall to prevent both lateral deflection and rotation at C. This case is commonly called the fixed earth support method because point C is essentially fixed. Cases (a) and (d) represent the two extremes in design. Free Earth Support Method Rowe’s Moment Reduction Method Fixed Earth Support Method (Equivalent Beam) Graphical Methods Danish Rules Free Earth Support Method - This method is based on the assumption that the soil into which the lower end of the piling is driven is incapable of producing effective restraint from passive pressure to the extent necessary to induce negative bending moments. The piling is driven just deep enough to assure stability, assuming that the maximum possible passive resistance is fully mobilized. The sheet piling is assumed to be inflexible and that no pivot point exists below the dredge line i.e., no passive resistance develops on the backside of the piling. Earth pressures may be computed by the Coulomb or log-spiral method. With these assumptions the design becomes a problem in simple statics. Procedures for the design of anchored sheet piling in granular and cohesive soil are discussed separately below. Design in Granular Soil - Figure 23 shows the resulting pressure distributions for an anchored sheet pile wall in granular and cohesive soil. The following design procedure as suggested in Teng1 , may be used: In Granular Soil tie rod pull earth pressure above point a + other horizontal forces (except T) (a) In Cohesive Soil tie rod pull total horiz. force (except T) above dredge line Fig. 23 - Design or anchored sheet piling by free-earth method (after Teng1 ) 1. Compute the active and passive lateral pressures using appropriate coefficients of lateral earth pressure. If the Coulomb method is used, it should be used conservatively for the passive case. Note: Figure 23 (a) shows the general case for an anchored wall in granular soil backfilled with granular material having different soil properties. Therefore, Ye refers to the equivalent soil unit weight, either wet to submerged, for the particular soil layer in question. Also, refers to the active pressure coefficient for the natural in-place granular soil. 3. Locate the point of zero pressure given by 2 . Calculate the weight of overburden and surcharge load at the dredge level, 27
MOMENTRATIOPER FT.WIDTHANCHOR PULL RATIO PER FT.WIDTHMx/KaHT/K,H?max9060080'0t09'09'0200:8a3-01IETT1.NGMHN-E.eE-.0SV.EE-18-V1!1Ho11M++1111+A11Ho-.11.2+.-1-HD→1-X11SL000A.18V0'010d106081T0L01b1o0'9WNb00OSA150'91OX601Yb210'ta0.0&1CON0'600bV050SLl0SL009000DEPTH RATIO,D/H (INCREASE BY 20% TO 40% FOR S.F.)28
MOMENT RATIO PER FT. WIDTH ANCHOR PULL RATIO PER FT. WIDTH DEPTH RATIO, D/H (INCREASE BY 20% TO 40% FOR S.F.) 2 8