Lateral Earth Pressure on Lagging in Soldier Pile Wall Systems

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1 Lterl Erth Pressure on Lgging in Soldier Pile Wll Systems Howrd A. Perko, Ph.D, P.E., CTL Thompson, Fort Collins, CO, USA John J Boulden, SGM, Inc., Grnd Junction, CO Soldier pile nd lgging is conventionl mens of temporry excvtion shoring. Timber lgging design hs trditionlly been bsed upon the designer s experience or empiricl rules. One such method is the Goldberg Zoino chrt used by the Federl Highwy Administrtion. Most of these methods restrict the designer to consistent soil profile, certin pile spcing, construction grde timber lgging, nd limited depth. The methods do not tke into ccount surchrge lods or vriety of other fctors tht could rise. A designer working outside of ordinry circumstnces with unusul lods, vrying soil conditions, or lternte lgging mterils hs difficulty estimting lterl erth pressures. In rigid erth retention systems, lterl erth pressure is generlly ssumed to be constnt long the length of the wll. In soldier pile nd lgging systems, the lgging is often considerbly less stiff thn the steel soldier piles. As the lgging deflects, the soil tends to bridge between the stiffer elements resulting in lower pressure on the lgging. Severl previously published methods by others for determining this reduced pressure re summrized nd discussed. These methods typiclly consist of using portion of the ctive erth pressure in severl different pressure distributions. A simple theoreticl model is presented for determintion of lterl erth pressures on wood lgging. The model is bsed on three-dimensionl silo shped sliding wedge nlysis. Results of the model re compred with other published methods. The model compres well with these methods which cover the norml spectrum of design situtions. In ddition, the model cn be used to estimte lterl erth pressures outside typicl situtions. INTRODUCTION Soldier pile nd lgging wlls re commonly used systems for supporting excvtions in urbn environments where property lines, rods, nd utilities prohibit sloped or benched excvtions. Soldier pile nd lgging wlls cn be more economicl nd fster to construct thn mny other erth shoring systems. Excvtions in excess of 30 m (100 ft) in depth hve been successfully completed using soldier pile nd lgging systems with tie-bcks or brcing. The min components of soldier pile nd lgging excvtion support systems re steel H-piles plced verticlly t 1.22 m to 3.05 m (4 to 10 ft) on center with lgging plced between the piling to retin the soil. An exmple of portion of soldier pile nd lgging wll is shown in Fig. 1. The lgging my consist of rough swn timber, metl decking, or even precst concrete plnks. H-piles cn be instlled by driving, vibrting, or by drilling hole nd wetsetting the pile in grout column t the bottom of the excvtion. Soldier piles re plced prior to excvtion. As the excvtion is dvnced, lgging is plced between the soldier piles. In soils with some stnd-up time, lgging cn be drug from the top nd pulled downwrd. In other soils, lgging is sometimes instlled continuously on the outside of the piles. If sloughing or slight cving occurs, soil is pcked behind the lgging. [Fig. 1] Portion of Soldier Pile nd Lgging Wll System (US Nvy, 1988) Soldier pile nd lgging systems re usully employed in competent soils nd re not effective in soft clys or below the groundwter tble where experience hs shown tht the soils cnnot rch between piles. TRADITIONAL DESIGN METHODS It is well-known tht soil rches between soldier piling creting silo effect s shown in Fig. 2. Friction nd cohesion long the sides of the silo resist sliding of the soil mss nd thereby [46] DFI JOURNAL Vol. 2 No. 1 November 2008

2 reduce lterl pressure. It is lso well known by prctitioners tht the pressure on lgging pproches constnt t some depth for most soil conditions. Lgging hs trditionlly been designed bsed upon experience or empiricl methods. One method is chrt of recommended timber lgging thickness for different soil types, pile spcing, nd wll heights. This chrt ws developed by Goldberg-Zoino nd Assocites to be used by the Federl Highwy Administrtion for designing timber lgging. It is lso referenced by the US Nvy (1988). The chrt is shown in Fig. 3. [Fig. 2] Silo Effect for Soil Lgging (US Nvy, 1988) In the Goldberg-Zoino chrt, soils re clssified into three ctegories bsed upon their degree of competency. Timber lgging thickness is then selected from two or three depth ctegories nd the lgging cler spn. The imum depth vilble on the chrt is 60 feet. Determintion of soil ctegory is left to the judgment of the designer. The Goldberg-Zoino chrt does not ddress different species or grdes of timber lgging. The chrt provides no ssistnce for other types of lgging mterils. Surchrge lods t the ground surfce re not tken into ccount. Another populr method of estimting the pressure on timber lgging hs become known in prctice s Terzghi s trp door nlogy. Terzghi (1943) explined tht when n opening is creted in structure contining soil, sher zone is creted bove the opening. Soil bove the sher zone is held in plce by rching. Therefore, the lod cting on the door of the opening is equl to the weight of soil below the sher zone. This soil weight is independent of the height of soil bove the opening. Rther it depends only on the density nd sher strength of the soil which defines the geometry of the sher zone. In n unpublished document, Spencer, White nd Prentis, Inc. (1986), stted tht Terzghi s trp door nlogy could be extended to explin horizontl rching between soldier piles. They showed tht mixed hrdwood with 76 mm (3-inch) thickness nd n llowble bending strength of 11 MP (1600 psi) could spn n unsupported distnce of 2.9 m (9-6 ) in snd soils with friction ngle of 30 deg. The pressure on the lgging did not depend on the height of retined erth. The Terzghi trp door nlogy is useful becuse it tkes cohesion into ccount. It gives vlue of pressure on the lgging which cn be used in design of different mterils. The method hs been used successfully for mny yers. However, its simple derivtion cuses some structurl engineers to question its vlidity. It is difficult for some to mke the lep from verticl pressure s derived by Terzghi to horizontl pressure s suggested by Spencer, White nd Prentis, Inc. Also, the method ws not published in open literture to the uthor s knowledge. A more rigorous mthemticl model subject to the scrutiny of professionl publiction my be beneficil to the industry. Severl other mthemticl methods hve been used to estimte the reduced soil pressure on the lgging. These methods typiclly consist of using portion of the ctive erth pressure in different distributions. Two pressure distributions re shown in Fig. 4. The pressure distribution on the left side of the figure is bsed on theory tht the ctive erth pressure is imum t the soldier piles nd minimum midwy between the piles. The pressure distribution on the right side of the DFI JOURNAL Vol. 2 No. 1 November 2008 [47]

3 [Fig. 3] Goldberg-Zoino nd Assocites Chrt (Goldberg, et l. 1976) [48] DFI JOURNAL Vol. 2 No. 1 November 2008

4 [Fig. 4] Reduced Soil Pressure Digrms on Lgging (McNb, 2002) figure is bsed on theory tht the pressure on the lgging is equl to hlf the ctive erth pressure. According to both methods the pressure exerted on the lgging increses proportionlly with depth without limit, which is contrry to experience. DEVELOPMENT OF MATHEMATICAL MODEL Mechnics of the soil semi-silo pictured in Fig. 2 cnnot be nlyzed using conventionl grin silo theory s described in Bowles (1988). Sttic grin silo theories ignore friction long the sides of the silo. Dynmic theories re bsed on flow of grin down the center of the silo nd resulting conicl wedge tht dds to hoop stresses. The erth pressure cting on timber lgging cn be modeled using sliding wedge nlysis. A number of ssumptions cn be mde to simplify the model. First, it is ssumed tht the soil bridges between the piles creting silo of soil behind the lgging with semi-circulr cross section s shown below in Fig. 5. It is further ssumed tht the bottom of the silo hs wedge shpe opening towrd the lgging. The shpe shown in Fig. 5 is chosen becuse it is simple combintion of surchrge over smll ctive erth wedge. The verticl surchrge pressure, Fv, cting on the smll wedge t depth D is the weight of the column of soil, W, nd ny uniform surchrge cting upon it minus the friction long the sides of the silo. The friction of surrounding soil cn be integrted over the surfce re of the cylinder. Friction long the front of the silo ginst the lgging is ignored to be conservtive nd lso becuse the lgging often cn slide with respect to the pile. The verticl surchrge force of the columnr silo is given by (1) where W = weight of soil silo = D w = uniform distributed surchrge lod = cross-sectionl re of silo = 1/8 πl 2 D = height of silo T = sher strength of soil = zk tn( ) l = lgging cler spn K = coefficient of ctive erth pressure = unit weight of soil = internl ngle of friction [Fig. 5] Soil Wedge Geometry The ngle of the bottom of the wedge reltive to horizontl would be 45+( /2) ccording to Rnkine. The slope of the bottom wedge cn be DFI JOURNAL Vol. 2 No. 1 November 2008 [49]

5 pproximted s 45 degrees in the model for simplicity of integrtion. As long s the erth pressure is still computed bsed on Rnkine, the only effect of this geometric simplifiction is slight chnge in depth of the silo. The horizontl pressure, P, on the lgging t depth D+ l/2 is the ctive erth pressure on the smll bottom wedge nd the verticl surchrge pressure, F v /, times the ctive erth pressure coefficient, K. K l Fv K P = + 2 (2) After inserting Eqn. (1) nd integrting the sher strength term, the lterl pressure t depth, D+l/2, is lγ 2γ 2 P = K + w + γd ( K tn( ϕ) D ) 2 l (3) A smple plot of lterl pressure distribution (Eqn. 3) shows tht the pressure increses with depth to imum vlue where friction on the soil overcomes the driving force. In ctulity, tension crck will develop due to bridging nd the pressure will remin constnt with incresing depth. depth [Fig. 6] Smple Results The depth t which the imum pressure on the lgging occurs cn be found by tking the prtil derivtive of horizontl pressure (Eqn. 3) with respect to depth nd setting the result equl to zero s shown below. P 4K = K γ 1 D pressure tension crck develops model tn( ϕ) D l = ctul 0 (4) The ctive erth pressure coefficient nd tngent term re both functions of ngle of internl friction,. If new prmeter is introduced,, such tht then Eqn. (5) cn be re-written s the product of this new prmeter nd the free spn of the lgging given by D = χl (7) If Eqn. (7) is substituted for D in Eqn. (3), the imum pressure on the lgging, P, cn be found. 1 P = K w + lγ (1 + χ) 2 (8) Further simplifictions cn be mde by exmining the prmeter,. A grph showing vlues of for vrious ngles of internl friction,, is shown below. At very low vlues of friction indicting wek soils, cn be s high s 5 to 7 or even higher. This (Eqn. 7) indictes the depth to imum pressure is 5 to 7 or more times greter thn the cler spn of the lgging, l. Pressure on the lgging is lso high. For most common grnulr mterils, the ngle of internl friction commonly lies between 15 deg nd 45 deg. The vlue of is firly constnt over this rnge s shown in Fig. 7. In fct, is within pproximtely +/- 5% of constnt vlue of 1.4 over the rnge of most grnulr soils. If =1.4 is substituted into Eqn. (7) nd Eqn. (8), one obtins the following very simple equtions for imum pressure on lgging nd the depth t which this pressure occurs nd then remins constnt. D = 1. 4l (9) P = K ( w + 1.2lγ ) (6) (10) If there is no surchrge, then the imum pressure is even simpler. Solving for the silo height t which the imum pressure occurs, D, yields l D = 4K tn( ϕ) (5) [50] DFI JOURNAL Vol. 2 No. 1 November 2008 P =1.2K lγ (11)

6 [Fig. 7] Firly Constnt Prmeter COMPARISON OF RESULTS Experience hs shown tht soil pressure on lgging is generlly constnt with depth. Deeper excvtions typiclly do not hve thicker lgging; rther the supporting piles hve to be lrger to resist the greter lterl erth pressures. The model confirms this phenomenon. The model cn be compred with Terzghi s trp door nlogy given by Spencer, White nd Prentis, Inc. (1986). According to this nlogy, the imum pressure on lgging is given by P = K 2c l γ l 2 tn (12) which for cohesionless soils reduces to P K lγ = (13) 2 tn When Eqn. 13 is compred with the new model, Eqn. 11, one observes tht there re mny similrities. In fct, both equtions result in the sme pressure t n ngle of internl friction of pproximtely π/8 (22.5 deg). The trp door nlogy predicts much higher pressure (bout 155%) t smller ngles of friction. The new model is not influenced s much by friction ngle but is becomes more conservtive t higher ngles of friction. Using the model, timber lgging thicknesses were clculted for three theoreticl soils nd compred to the thicknesses recommended in the chrt by Goldberg-Zoino nd Assocites. The competent soil ws ssumed to hve n internl ngle of friction of 38 degrees nd unit weight of 1,920 kg/m3 (120 pcf). The difficult soil ws ssumed to hve n ngle of internl friction of 28 degrees nd unit weight of 1,760 kg/m3 (110 pcf). The potentilly dngerous soil ws ssumed to hve n ngle of internl friction of 18 degrees nd unit weight of 1,600 kg/m3 (100 pcf). For the purpose of this comprison, lgging ws ssumed to hve imum bending stress of 69 MP (1,000 psi) which is consistent with the lowest reported vlues in the FHWA report. NDS (2005) fctors for short durtion use, wet service, repetitive member, nd flt use were incorported into the design. When combined, these fctors increse bending strength by fctor of pproximtely 1.6. Shown in Tble 1 is comprison of the recommended thickness from Goldberg- Zoino nd the clculted thickness bsed on the model for the three different soils. It is importnt to note tht the cler spn of the lgging shown on the tble is defined s the distnce between the outermost extents of the H-Pile flnges, not the center-to-center spcing of the piles. The clculted vlues bsed on the model re not s conservtive s the vlues shown on the Goldberg-Zoino chrt for short free spns nd lmost exctly the sme for longer spns. This seems to mtch common prctice firly well. DISCUSSION The model cn be used to determine required lgging thickness for mny soil conditions nd lod cses outside those considered in the Goldberg-Zoino chrt. The lower portion of Tble 1 shows the required lgging thickness for the sme three different soil conditions nd lgging spns of 1.52 to 3.05 m (5 to 10 ft) with 9.58 kp (200 psf) uniform surchrge t the ground surfce. This is n importnt cpbility when the soldier pile nd lgging wll system borders rods, sidewlks, or other structures. The model lso llows for determintion of lterl erth pressures on other lgging mterils. For comprison, the model ws used to clculte required lgging thicknesses for utility grde lumber. Utility grde lumber is rted t only ¼ times the llowble bending strength of construction grde lumber ccording to NDS (2005). It is very pprent the effect tht timber strength hs on the required lgging thickness. On verge, utility grde lumber needs to be lmost twice s thick s construction grde lumber. The model lso could be used to size other mterils such s flexible steel decking DFI JOURNAL Vol. 2 No. 1 November 2008 [51]

7 [Tble 1] Comprison of Results spnning between soldier piles. One cution is tht the derivtion of the model is bsed on the ssumption tht lgging mteril tht is considerbly less rigid thn the soldier piles. Rigid pre-cst concrete plnk my be required to crry full ctive erth pressures. Recently, the model ws tested successfully on project in New York City for n unusul shoring condition. The model ws used to estimte the erth pressure on n existing 6-wyth brick foundtion wll tht ws brced with soldier piles. A photogrph of the wll system is shown in Fig. 8. The brick wll in the photogrph existed directly djcent gs sttion with onestory block structure, severl buried tnks, nd cnopy. The developer did not hve permission to plce shoring outside of the brick wll. The shoring contrctor determined tht there ws too much risk of movement of the djcent structures to remove the brick wll. It ws decided to ttempt to use the brick wll s lgging between the soldier piles. Mortr in the brick wll ws severely degrded such tht it ws essentilly held together by friction. The soils were silty snds nd high plstic silts with some ground wter. The punching nd flexurl strength of the brick wll ws estimted bsed on dry stck pproch using friction only. Lterl erth pressures bsed on the model indicted tht the brick wll would bridge between the soldier piles with sufficient fctor of sfety. The excvtion ws mde without excess movement or ny dmge to the nerby structures. The brick wll ws pproximtely ten feet deep. The excvtion extended to depth of pproximtely 5 m (16 ft) below existing grdes. Wood lgging ws used below the brick wll. A wler with cross brces ws positioned ner the top of the soldier piles. The wler ws removed fter construction of the structurl mt foundtion. On nother recent project, the Convention Center Hotel project in Denver, soil cving occurred during plcement of timber lgging. The soil conditions consisted of firly clen, poorly grded, corse snd overlying clystone bedrock. The soil which flowed out from beneth the lgging formed nerly perfect silo shpe s shown in Fig. 9. This imge gives credence to the ssumptions used in development of the model for snd soils. Although this cving occurred, the soil successfully rched between the solder [52] DFI JOURNAL Vol. 2 No. 1 November 2008

8 [Fig. 8] Existing Brick Wll Used s Lgging piles with no detriment to the shoring system. (Hrt, 2008) Some ttempt ws mde to include cohesion in the derivtion of the model so tht it could be extended to fine grin soils. It ws found during tht exercise tht smll mount of cohesion significntly reduced the computed pressure on the lgging. In fct, the predicted pressure on the lgging becme negligible t cohesion, c, given by lγ c = 2 (14) This indictes tht soil cohesion of only bout 14.4 kp (300 psf) would reduce pressure to zero for lgging with cler spn of 1.52 m (5 ft). Interestingly, this is exctly the sme result tht would be determined from Terzghi s trp door nlogy given by Eqn. 12. Those who hve worked round soldier pile nd lgging systems for some time hve long recognized tht cohesive soil behind lgging seldom comes into contct with the lgging. The photogrph shown in Fig. 10 tken from nother project in Colordo is demonstrtion of this. The gp between the cohesive soils nd the lgging t the top of the wll system is very pprent. In ddition, the lck of ny discernble deflection of the lgging is clerly shown despite the fct tht the wll is in excess of 5.5 m (18 ft) tll. (Hrt, 2008) Mny fine grin soils nd some well-grded corse grin soils exhibit some cohesion. In some cses, this cohesion is pprent mening tht it cn dissipte over time nd with the introduction of moisture. The use of cohesion [Fig. 9] Soil Silo Formed by Cving (Courtesy of Coggins nd Sons, Inc.) [Fig. 10] Seprtion Between Lgging nd Cohesive Soils (Courtesy of Coggins nd Sons, Inc.) DFI JOURNAL Vol. 2 No. 1 November 2008 [53]

9 in the design of temporry shoring systems should be pproched with cution nd is the decision of the experienced designer. It ws commented by one of the reviewers of this pper tht tie-bck post tensioning often governs the lterl pressure on lgging for tll wlls. This is n excellent observtion. It is suggested tht the upper limit of lgging pressure in this cse could be computed by substituting the pssive erth pressure coefficient, K p, for the ctive erth pressure coefficient in Eqns. 8 nd 11. CONCLUSIONS A mthemticl model bsed on silo shped sliding wedge nlysis ws presented. The results of the mthemticl model compre well with the recommended lgging thicknesses shown in the chrt prepred by Goldberg-Zoino nd Assocites in the 1976 FHWA report. Using the mthemticl model produces results which re slightly more conservtive thn the chrted vlues t lrger lgging spns, but the model llows the designer the freedom of designing outside of the norml situtions. The model predicts constnt lterl erth pressure beginning t depth of roughly 1.4 times the spcing between the soldier piles. Reduced ctive pressure digrms suggested previously by others were not compred with the model. The reson is becuse the reduced ctive pressure digrms suggest lterl pressure tht increses without limit, nd the new model gives constnt vlue of pressure beyond certin depth. Any comprison between the reduced ctive pressure digrms nd new model would show one vlue tht mtches exctly t some depth. Therefter, the reduced ctive pressure digrms would be more conservtive for deeper excvtions. A constnt pressure model is better representtion of conditions observed in prctice. 4. Americn Forest nd Pper Assocition, (2005) Ntionl Design Specifiction, Design Vlues for Wood Construction, pp US Nvy (1988) Militry Hndbook: Sewlls, Bulkheds, nd Quywlls MIL- HDBK-1025/4, Sept Terzghi, K. (1943) Theoreticl Soil Mechnics, Wiley, New York 7. Spencer, White nd Prentis, Inc. (1986) Lgging Design, Smple Clcultions provided by Tom Tuozzolo, Moretrench Geotec, Rockwy, NJ (unpublished) 8. Bowles (1988) Foundtion Anlysis nd Design, 4th Edition, McGrw-Hill, Inc., New York REFERENCES 1. Mcnb, A. (2002) Erth Retention Systems Hndbook, McGrw-Hill, New York, pp Goldberg, D.T., Jworski, W.E. nd Gordon, M.D. (1976) Lterl Support Systems nd Underpinning, FHWA-RD , pp Hrt, J. (2008) Coggins nd Sons, Inc., Denver, CO (Personl Communiction) [54] DFI JOURNAL Vol. 2 No. 1 November 2008

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