Lateral Load Capacity of Piles

Transcription

1 Lateral Load Capacity of Piles M. T. DAVSSON, Department of Civil Engineering, University of llinois, Urbana Pile fondations sally find resistance to lateral loads from (a) passive soil resistance on the face of the cap, (b) shear on the base of the cap, and (c) passive soil resistance against the pile shafts. The latter sorce is sally the only reliable one. Analysis of the problem yields deflections, rotations, moments, shears, and soil reactions as reqired for strctral design. Beam-on-elastic-fondation theory is adeqate for analysis of the problem. Most piles are relatively flexible and may be analyzed as thogh infinitely long. Only short rigid piles are likely to reqire consideration of the loer bondary conditions in analysis. Nondimensional soltions are available for both constant and linearly increasing modls-depth relationships; soltions are also available for a stepped variation of modls, k. Sfficient experimental data are no available to allo selection of the appropriate variation of k ith depth. Typical vales for k are available and have been related to readily observable soil characteristics. Simple lateral load tests also allo experimental determinations of the magnitde of k if greater accracy is reqired. PLES are often reqired to resist lateral loads and moments in addition to their primary se as axially loaded members. The goals of designers are to determine deflections and stresses in the selected soil-pile system in order that they may be controlled ithin tolerable limits. Techniqes for analyzing this problem in soil-pile interaction ill be given in this paper. A schematic representation of the loads acting on a pile fondation is shon in Figre 1. The pile cap may be sbjected to moment, M, and shear, Q, loads in addition to the sal gravity load, W. Axial loads are resisted by the axial capacity of the piles and ill not be discssed frther here. The applied moment and shear are resisted to varying degrees by (a) passive soil resistance on the face of the cap, (b) shear along the base of the cap, and (c) moment and shear resistance of the piles at the jnction to the cap. Clearly the moment and shear resistance of the piles are fnctions of the strength and stiffness of both the soil and the pile. Passive soil resistance can be very effective in resisting lateral loads, bt consideration mst be given to the fact that it may not be permanent. Repairs, alterations, or other projects may be case for removal of the soil; therefore, passive resistance is sally disconted or ignored. Shear along the base of the cap also can be very effective in resisting lateral loads. Hoever, a slight settlement of the soil beneath the cap can essentially eliminate this resistance, and it is sally ignored for design prposes. The moment and shear resistances of the piles are sally the only factors considered sfficiently permanent for se in design. This discssion is aimed primarily at the resistance offered by the piles. ANALYSS The deflected shapes of both a short and a long pile sbjected to moment and shear loads are shon in Figre 2. A rotation a can be sed to define the deflected shape of a rigid member (Fig. 2a), hereas the flexral deflections become important for a Paper sponsored by Committee on Fondations of Bridges and Other Strctres and presented at the 49th Annal Meeting. 14

2 15 t o ~ '- Shear On Cop Pile or Pier Figre 1. Sorces of lateral resistance. flexible member (Fig. 2b). Frthermore, the moment and shear at the loer end of a rigid member are qite important to a proper analysis, bt they sally can be ignored for long flexible members (!). Q Q "- Deflected Shape ~ - Flellral Deflection mportant mportant --- Shear J Moment ' l ' Shear Moment '-V Negll<jlble a) Rigid b) Flexible Figre 2. Rigid verss flexible pile or pier.

3 16 A practical procedre for the analysis of a soil-srronded flexral member is needed so that a proper design can be made. The qantities needed are the deflections, moments, shears, and soil pressres. Deflection (and rotation) is important becase of practical limitations on deformations of strctres, and perhaps for determining the natral freqency for dynamic analyses. Moments and shears are needed for the sal strctral design prposes, hereas soil pressres are reqired for checking (a) El "8 _J (b) Figre 3. Sbgrade modls. Deformation against the alloable lateral soil pressres along the embedded portion of the piles. At present, the analytical techniqes involving the theory of a beam on an elastic fondation are the most sefl. The theory considers a continos flexral member ith stiffness El (Fig. 3a) spported by infinitely closely spaced independent springs ith stiffness k. Hoever, the load-deformation characteristics of soils are not linear as shon in Figre 3b. t is necessary, therefore, to develop information on the secant modls compatible ith the deflection of the flexral member before proper se can Depth, x D = Embedded length of pile or pier, k = Sbgrade Modls, k k = consfant modls, fo rce nit lengthnit deflection Actal a) bl R = DR < 2, Rigid DR Modls, k T = 2-4, ntermediate DR < 4, Flexible DT < 2' Rigid DT = 2-4 ntermediate Depth, x DT > 4, Flexible be made of beam-on-elasticfondation theory. A frther complicating factor is that the soil stiffness is variable along the length of the pile. Therefore, beam-on-elastic-fondation theory mst be modified to accont for variations in the spring stiffness k. For example, preloaded clay actally has a variation of stiffness ith respect to depth as shon in Figre 4a. A constant stiffness is sally assned for analysis, bt the errors may be 5 to 1 percent in both deflections and moment (2) becase the analysis is nsalfy sensitive to soil stiffness variations in the zone adjacent to the grond srface. Granlar soils and normally loaded cohesive soils, on the other hand, exhibit stiffness increasing almost directly ith depth as shon in Figre 4b (3). Beam-on-elastic-fondation theory involves the ell-knon eqation El~+ kxy = Figre 4. Relative stiffness factors. here El is the flexral stiffness of the pile, x is the depth in the soil, y is the deflection, and kx

4 is the spring stiffness or sbgrade modls. The sbscript x indicates that k may be variable ith depth x. As defined here, k has nits of force per nit of length per nit of deflection (lbin. 2 ); the idth of the flexral member has already been considered. Soltions to the differential eqation are readily available for the cases here k eqals a constant and k = nhx; nh is the eoefficient of horizontal sbgrade reaction (1) The latter is a linearly increasing modls ;i.th respect to depth as shon in Figre 4b. Soltions can readily be obtained for other desired variations of k by hand methods or ith the aid of electronic compters (5). The selection of appropriate vales fork ill be presented later. - NOND ENSONAL SOLUTONS Soltions for the aforementioned differential eqation are readily available in nondimensional form. For constant vales of k, the relative stiffness factor is defined as R here R =.ftm and has nits of length. f the embedded length D is divided by R, the reslt is a dimensionless nnber indicative of the flexibility of the flexral member relative to the soil. Soltions for DR vales in excess of 4 are essentially eqal to that for DR eqal to 17 DEFLECTON 8 MOMENT COEFFCENT, C z > Q 2 1--~~--t ~--~-,...,,-1-~~~-1- " " Momeni = G A :i:: >- Deflection = OR :1 1 ~ 31--~~11~1--1'1-~~-1-~~~+-~~~ (al > z ii: " Deflection= CM R 2 E ~ 3 i--~; ~~t-t~~~~-r-~~~-i-~~~-1-~~~~ (b) Figre 5. Deflection and moment verss depth.

5 18 infinity; almost all piles are in this category. This fortnate occrrence simplifies analysis becase only one set of soltions is reqired and it is applicable to almost all problems. Soltions for deflection and moment for constant vales of k, and also for a stepped variation ink, are available (2). The case here the soil to a depth of.4r has a modls eqal to.5k (Fig. 4a) is a better approximation for preloaded cohesive soils than the case here k is constant; sch soltions are shon in Figre 5. For the case here k = nhx the relative stiffness factor T is defined as 5 T =JE!Tnh and has nits of length. f the embedded length Dis divided by T, the reslt is a dimensionless nmber indicative of the flexibility of the system (Fig. 4b). n Figre 6 the nondimensional deflection coefficient has been plotted verss the nondimensional depth coefficient xt here xis the depth belo the grond srface; this plot has been made for a shear load Q for varios vales of DT. Note that the deformations for DT = 2 are essentially de to rotation (relatively rigid member), hereas deformations for D T = 4 are essentially the same as for DT = 5 and DT = 1 and are dependent on the flexral detlections. n most practical cases DT exceeds 4 and only one set of soltions is needed; sch soltions are readily available (5, 6). Fixity at the top of the flexral member strongly inflences both deflection and moment. This is shon in Figre 7 (7), here the nondimensional moment coefficient has been plotted verss nondimensionil depth xt. A fixity factor F (Fig. 7) has been sed to describe the degree of restraint at the top of the flexral member; 1- z Li:... z j::...j ~ ' ~ 2. 1, -1. ~ ~ ~ '_ '-..,..._ D T 2,, -... r3' DEPTH COEFFCENT, f y = OT3 x Coe!. E Figre 6. Deflection verss depth. 4 ca 1 5. ths, the inflence of both moment and shear loads has been combined in one diagram. An F-vale of zero corres sponds to a free-head case, and the maximm moment occrs at a depth of 1.35 T. An F-vale of -.93 corresponds to fll fixity, and the maximm moment occrs at the top. As a practical matter the degree of fixity that can sally be developed is, in the riter's experience, approximately -.4 to -.5; note that in this case the positive and negative moments are approximately eqal, perhaps an aid to efficient se of flexral resistance. Nondimensional deflections verss depth are shon in Figre 8 in a similar manner. For relatively flexible flexral members embedded in a relatively rigid concrete cap, an estimate of fixity at the pilehead can be obtained by considering the problem as a beam on an elastic fondation herein an analysis is made of the pile embedded in concrete. n this case, the concrete controls the modls of sbgrade reaction. Note that axial loads aid fixity and that conditions at the pile top are likely to exert considerable inflence on behavior. This occrs ith short embedments here the beam cannot be considered infinitely

6 19 embedded. n other strctral schemes, the strctral connection at the top of the piles can be considered to sit on springs ith axial, lateral, and rotational s tiffnesses that are a fnction of both the pile and the strctral characteristics of the connection. The analysis also allos a calclation of the soil reactions ky. These reactions can be checked against the alloable lateral pressres determined from theory and soil s trength MOMENT COEFFCENT-C 1. 4 o e SOL MODULUS Typical vales for k are available for a ide variety of soils. For a given soil, k increases as density increases, as old be expected. The vales for k given in Table 1 are based on both the literatre and the riter's experience. On the basis of simple soil tests, sch as the standard penetration test or the nconfined compression strength, reasonable vales can be selected for k. There are 2 phenomena that have a marked effect on k, namely, grop action and repeated loading. With respect to grop action, the spacing in the direction of the load is of primary importance. At a spacing center to center of 8d or more M = C Q T k:: "ti. Figre 7. Moment verss depth. DEFLECTON COEPFCENT,C Q.r -1--t--Q~ p c ~ t k = "", Figre 8. Deflection verss depth.

7 11 TABLE 1 ESTMATED VALUES FOR k Soil Type Granlar soils Normally loaded organic silt Peat Cohesive soils Vale nh ranges from 1.5 to 2 lbin.', ls J:eneral,ly in the range from 1 to 1 lb in.', and is ajlpro>dmately vrvrlial L relallve density nh ranges from.4 to 3. lb in.' nh is approximately.2 lb ln. 3 k is approximately 67 C, here C ls the ndrained shear strength of the soil Note: The effects of grop action and repeated loading are not inclded in these estimates. (dis the pile diameter), there is essentially no inflence of one pile on another providing the spacing normal to the direction of loading is at least 2.5d (Fig. 9). When the spacing parallel to loading is less _than Bd, the effective vale of k (keff) is less than that for an isolated pile. At a spacing of 3d, keff is approximately.25k. For other spacings, k eff can be determined by interpolation beteen 3d and 8d. This information is based on a model stdy on piles in sand (7). Repeated loading cases some deterioration Of the soil resistance, effectively redcing the modls k. The net effect is that the deflection observed nder first application of a load is essentially dobled if the load is cycled 5 times or more (1, 7, 9). Moments are also increased and occr over an increased depth of embedment. -Repeated loading has the effect of redcing k to approximately 3 percent of the applicable to initial loading. f both grop effects and repeated load effects mst be considered, k~ff can be as lo as 1 percent of that applicable to initial loading of an isolated pile l7). t is the riter's experience that for most problems an analytical investigation based on reasonable vales for k, determined ith the aid of rotine soil tests and jdgment based on data given in Table 1, ill lead to the decision that an adeqate design can be developed ithot frther information. For the remaining problems, it is relatively easy to make in sit tests to get more accrate des~gn information if the potential benefits oteigh significantly the additional cost of an acceptable design based on available data. A simple lateral load test on a pile ill provide accrate design information. For simplicity the loads shold be applied and the deformations measred at the grond or more 2.5 d a ~.. al Bd, keff = 1 %k 1 al 3d, k.11 = 25% k ~1 Figre 9. Effect of grop action.

8 srface; hoever, this is not essential. Frther, the test pile need not be a prototype. t is only necessary that the pile be of sfficient depth to be considered infinitely long for theoretical evalation. t is necessary to make an assmption regarding the natre of the variation of k ith respect to depth; for example, constant, stepped, or trianglar. Then the appropriate nondimensional coefficients and expressions are sed to back-calclate k or nh. Corrections may then be applied, as described previosly, to accont for grop action and cyclic loading. L Fid Bosa Eqivolenl 111 ~ -a PARTALLY EMBEDDED PLES Often, ith partially embedded piles, the top of the pile is fixed to some degree and the strctre is then statically indeterminate. t is most convenient to the strctral engineer if the pile (Fig. loa) can be replaced (o) (b) for the prpose of analysis by an eqivalent free-standing pile (Fig. Figre 1. Partially embedded pile. lob) that is fixed at some depth, Lr, belo the grond srface. A theoretically correct soltion for determining the depth to fixity, Lf, for long piles, i.e., DT or DR > 4, is available (1). The soltion satisfies the conditions that the deflection and rotation at the top of the eqivalent pile as ell as the critical bckling load are the same as for the real pile. The depth to fixity is dependent on the stiffness of the pile and the magnitde and variation of the soil resistance bt is reasonably constant hen expressed in terms of the dimensionless parameters given previosly. Lf can be determined ith little approximation from the folloing: Real L f k = constant and f > 2, then Lr = 1.4 R L f k = nh X and T > 1, then Lr = 1. 8 T The eqivalent cantilever beam-colmn defined can be sed in conventional frame analyses for determining moments and loads at the top of the pile and for determining the bckling load for the pile. Hoever, the moment compted for the fixed end of the eqivalent pile ill be considerably larger than the actal moment in the real pile. Therefore, to analyze the embedded portion of the pile it is necessary to resort to the procedres previosly discssed, sing the moments and loads at the grondline. These can be determined from basic principles of statics once the conditions at the top of the pile have been determined from the frame analysis (1). SUMMARY Pile fondations sally find resistance to lateral loads from (a} passive soil resistance on the face of the cap, (b) shear on the base of the cap, and (c) passive soil resistance against the pile shafts. The latter sorce is sally the only reliable one. An analysis of the problem shold yield deflections, rotations, moments, shears, and

9 112 soil reactions as reqired for prposes of strctral design. Beam-on-elasticfondation theory is adeqate for analysis of the problem. A brief stdy indicates that most piles are relatively flexible and may be analyzed as thogh infinitely long. Only short rigid piles are likely to reqire consideration of the loer bondary conditions in analysis. Nondimemiinal sllins are available for both constant and linearly increasing modls-depth relationships; soltions are also available for a stepped variation of k. Sfficient experimental data are no available to allo selection of the appropriate variation of k ith depth. Typical vales for k are available and have been related to readily observable soil characteristics. The applicable nondimensional soltions copled ith simple lateral load tests also allo experimental determinations of the magnitde of k if reqired. Grop action can case a redction in effective modls to 25 percent of that applicable to an isolated pile. Frther, cyclic loading can case deflections to doble, approximately, compared to that for the first load cycle. This cases a frther redction in the effective modls. f both effects are present, the effective modls may be only 1 percent of that for first loading of an isolated pile. Fixity at the top of the pile is difficlt to attain ith the strctral details commonly sed. A fixity of 5 percent is sally attainable and has the advantage of approximately eqal positive and negative moments, ths maldng efficient strctral se of niform flexral members. f deflections mst be minimized, then increasing fixity is a very efficient ay of achieving stiffness. A techniqe is available for analyzing partially embedded piles tilizing the same nondimensional parameters presented for flly embedded piles. A depth to fixity is introdced based on both soil and pile stiffnesses, ths eliminating the objections to similar procedres involving arbitrary depths to fixity. Analyses based on conservative, assmed vales for k ill sally indicate that an acceptable design can be obtained economically. f, hoever, the analysis indicates that better design data may yield significant savings, it is relatively simple to generate a field test program that ill provide the data. REFERENCES 1. Davisson, M. T., and Salley, J. R. Model Stdy of Laterally Loaded Piles. Proc. ASCE, Vol. 96, No. SN5, Sept. 197, pp , 2. Davisson, M. T., and Gill, H. L. Laterally Loaded Piles in a Layered Soil System. Proc. ASCE, Vol. 89, No. SM3, May 1963, pp Terzaghi, K. Evalation of Coefficients of Sbgrade Reaction. Geotechniqe, Vol. 5, London, 1955, pp Hetenyi, M. Beams on Elastic Fondation. Univ. of Michigan Press, Ann Arbor, Reese, L. C., and Matlock, H. Non-Dimensional Soltions for Laterally Loaded Piles With Soil Modls Assmed Proportional to Depth. Proc. Eighth Texas Conf. on Soil Mechanics and Fondation Eng., Astin, Matlock, H., and Reese, L. C. Fondation Analysis of Off-Shore Pile Spported Strctres. Proc. Fifth nternat. Conf. on Soil Mechanics and Fondation Eng., Vol. 2, 1961, pp Prakash, S. Behavior of Pile Grops Sbjected to Lateral Load. University of llinois, PhD thesis, Hansen, J. B. The Ultimate Resistance of Rigid Poles Against Transversal Forces. Danish Geotechnical nstitte, Bll. 12, Alizadeh, M., and Davisson, M. T. Lateral Load Tests on Piles-Arkansas River Project. Proc. ASCE, Vol. 96, No. SM5, Sept. 197, pp Davisson, M. T., and Robinson, K. E. Bending and Bckling of Partially Embedded Piles. Proc. Sixth nternat. Conf. on Soil Mechanics and Fondation Eng., Vol. 2, 1965, pp