Determination of Pile Base Resistance in Sands

DETERMINATION OF PILE BASE RESISTANCE IN SANDS

By J. H. Lee1 and R. Salgado,2 Member, ASCE

ABSTRACT: Advances in the design of axially loaded piles are desirable because significant cost savings mayresult. Well-designed piles settle by amounts that are well tolerated by the superstructure and induce strainsaround the pile base that are far removed from failure. To investigate the development of base resistance for agiven soil condition and increasing settlements, piles embedded in sand are modeled using the finite-elementmethod with a nonlinear elastic-plastic model. Based on the load-settlement response obtained from the finite-element analysis and cone penetration resistance obtained from cavity expansion and stress rotation analyses,values of normalized base resistance, defined as base resistance divided by cone penetration resistance, areobtained. The relationship between base resistance and cone resistance is useful in the design of deep foundationusing cone penetration test results. The effect of the initial coefficient of earth pressure at rest K0 on normalizedbase resistance values is also investigated. Several case histories, including both nondisplacement and displace-ment piles, are used for comparison with the theoretical results.

INTRODUCTION

With the rapid growth of metropolitan areas, and fast in-dustrialization resulting from the fast-paced economic global-ization, there has been a need to build heavier and taller struc-tures on marginal sites, where surface soils are weak andshallow foundations are usually not the best design solution.At the same time, advances in piling technology permit theinstallation of several types of piles, particularly nondisplace-ment piles, at lower costs than was possible in the past. Ad-ditionally, there is a growing realization in the foundation en-gineering industry that certain types of deep foundations (suchas large-diameter drilled shafts) are conservatively designed(Harrop-Williams 1989; Hirany and Kulhawy 1989; De Melloand Aoki 1993). In this context, advances in pile design meth-ods can have significant economic impact and should be ac-tively pursued.

Based on the method of installation, pile foundations areclassified as either displacement or nondisplacement piles.Driven piles are the most common type of displacement piles,and drilled shafts (bored piles) are the most common type ofnondisplacement piles. The load-carrying capacity of both dis-placement and nondisplacement piles consists of two compo-nents: Base resistance and side resistance. The side resistanceof piles is in most cases fully mobilized well before the max-imum base resistance is reached (Franke 1993). After full mo-bilization of side resistance, any increment of axial load istransferred fully to the base. As the side resistance is mobilizedearly in the loading process, the determination of base resis-tance is a key element in pile design.

Although friction piles are sometimes used, it is usually de-sirable to avoid relying solely on side resistance to developthe needed pile load capacity. This is done by placing the pilebase in a bearing layer. Physically, what keeps a well-designedpile from plunging when acted on by an axial load is the baseresistance developed in this layer, because the side resistanceis fully mobilized early in the loading process. Plunging willtake place only when the base unit load overcomes the limitbase resistance qbL, which is dependent not only on the densitybut also on the lateral confinement imposed by the surroundingsoil immediately beneath the pile base.

1PhD Candidate, School of Civ. Engrg., Purdue Univ., West Lafayette,IN 47907-1284.

2Assoc. Prof., School of Civ. Engrg., Purdue Univ., West Lafayette,IN. E-mail: [email protected]

Note: Discussion open until January 1, 2000. To extend the closingdate one month, a written request must be filed with the ASCE Managerof Journals. The manuscript for this paper was submitted for review andpossible publication on July 8, 1998. This paper is part of the Journalof Geotechnical and Geoenvironmental Engineering, Vol. 125, No. 8,August, 1999. qASCE, ISSN 1090-0241/99/0008-0673–0683/$8.00 1$.50 per page. Paper No. 18739.

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Pile design methods using in situ test results have beenmainly based on the standard penetration test (SPT) and thecone penetration test (CPT) (Bandini and Salgado 1998). SPTblow counts result from dynamically driving a standard sam-pler 1 ft into the ground. Such a process is not well related tothe quasi-static pile loading process. Static cone penetration,on the other hand, is better related to the pile loading process.The test is performed quasi-statically and resembles a scaled-down pile load test. Cone penetration resistance may be usedas a proxy for limit base resistance in piles with small error,according to many authors (De Beer 1984; Jamiolkowski andLancellotta 1988; Franke 1989, 1993; Ghionna et al. 1993,1994; Fioravante et al. 1995).

In the present study, the base load-settlement curves of ax-ially loaded piles bearing in sand are obtained for differentstresses and densities using the finite-element analysis with anonlinear elastic-plastic constitutive model. The calculatedload-settlement curves are then used to determine the pile baseresistance qb corresponding to certain settlement levels. Coneresistance qc is determined for the same soil conditions fromthe penetration resistance analysis of Salgado et al. (1997b)using the program CONPOINT (Salgado 1993; Salgado et al.1997a,b; Salgado et al. 1998). The calculated load-settlementcurves are normalized as follows: qb with respect to qc, andsettlement s with respect to pile diameter B. The fully devel-oped load-settlement curves in terms of qb/qc versus relativesettlement s/B can be used to determine the normalized pilebase resistance qb/qc for any settlement-based design criterion.The results obtained from this analysis are compared with ex-perimental results from case histories.

LOAD-SETTLEMENT RESPONSE OF PILES IN SAND

Methods for Investigating Load-Settlement Response

If a pile were continuously pushed down into a homoge-neous granular soil mass, it would reach a condition of pen-etration at a constant load in the same way a cone penetrom-eter does in a CPT. This is a condition of limited interest inpile design, and in most cases impossible to establish withconventional load test procedures and equipment; unless thepile is relatively small in diameter and length. Typical load-settlement curves for piles embedded in sand show graduallyincreasing curvature rather than a clear peak load. Three ap-proaches are possible to obtain the vertical load-settlement re-lationship for a pile: Full-scale pile load tests, calibrationchamber tests, and numerical modeling. Full-scale pile loadtests are the best option to investigate a load-settlement rela-tionship for a specific site and pile, but these tests cannot typ-ically be used to obtain an accurate correlation between base

ICAL AND GEOENVIRONMENTAL ENGINEERING / AUGUST 1999 / 673

resistance and the soil state. Only fully instrumented load testswith significant efforts to characterize the soil around the pilecould potentially be used for that purpose. Difficulties thatwould still need to be addressed include the fact that relativedensity and lateral stress are not known in the field, and thattypical natural granular deposits tend to be variable.

Calibration chamber testing and numerical analysis are moreflexible than pile load testing. A variety of stress states, den-sities, and boundary conditions can be considered. Calibrationchamber plate load tests have been used to investigate theload-settlement response of nondisplacement piles (Ghionna etal. 1994; Lee 1999; Lee and Salgado 1999). A number ofnumerical techniques have been identified for the same pur-pose (Desai and Christian 1977; Lee et al. 1989; Poulos 1989).The finite-element method is among the most popular, as itallows modeling of complicated nonlinear soil behavior andvarious interface conditions, with different geometries and soilconditions. A key element in a finite-element analysis is theuse of a relevant constitutive model, which should model thestrongly nonlinear soil behavior. In the present study, a non-linear elastic-plastic constitutive model is used in a finite-el-ement analysis to determine the load-settlement response ofvertically loaded piles.

Stress-Strain Relationship

The hyperbolic family of soil models has often been usedto describe the nonlinear soil behavior observed from the earlystages of loading (Kondner 1963; Duncan and Chang 1970;Hardin and Drnevich 1972; Tatsuoka et al. 1993). Fahey andCarter (1993) proposed a modification of the original hyper-bolic equation as follows:

gG t

= 1 2 f (1)S DG to max

where G = secant shear modulus; Go = initial shear modulus;t, tmax = current and maximum shear stress, respectively; andf, g = material parameters. Eq. (1) represents the degradationof shear modulus from its initial maximum value Go accordingto the stress level t/tmax. In numerical analyses using nonlinearelastic models, a tangent modulus rather than a secant modulusis often used with successive incremental analysis (Desai andChristian 1977). Differentiating (1) with respect to shear strain,the tangent modulus Gt can be obtained as

2G (G/G )t o= (2)gG [1 2 f (1 2 g)(t/t ) ]o max

Sand usually behaves as a linear elastic material with shearmodulus Go for shear strains up to ;1025, after which thestress-strain relationship is strongly nonlinear. In this study,the following empirical equation, based on the work of Hardinand Black (1966), was used to estimate the initial maximumshear modulus of sand

2(e 2 e )g o (12n ) ng gG = C P (s9) (3)o g a m1 1 eo

where Cg, ng, and eg = intrinsic material variables; eo = initialvoid ratio; Pa = reference pressure = 100 kPa; and = initials9mmean effective stress in the same unit as Pa. Considering aninitial anisotropic stress state, (1) may be rewritten as

gG t 2 to= 1 2 f (4)S DG t 2 to max o

where to = shear stress due to the initial K0 condition. Usingthe stress tensor invariants, the nonlinear elastic stress-strainrelationship given by (4) can be written for 3D stress condi-tions as follows:

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gG J 2 JÏ Ï2 2o= 1 2 f (5)S DG J 2 Jo Ï Ï2max 2o

where J2 = second invariant of the deviatoric stress tensor; andand = 3D equivalents of t, to, and tmax inJ , J , J2 2o 2maxÏ Ï Ï

(4), respectively. The shear modulus, however, may also in-crease due to the increase of confinement. To account for theinfluence of confinement on shear modulus during loading, thefollowing relationship is used instead of (5):

g ngG J 2 J IÏ Ï2 2o 1= 1 2 f (6)F S D G S DG IJ 2 Jo 1oÏ Ï2max 2o

where I1 and I1o are the first variants of the stress tensor at thecurrent and initial states, respectively. The parameter ng is thesame as that in (3): In both equations, ng represents the de-pendence of the shear modulus on confinement. The tangentmodulus Gt corresponding to (2) is given by

ng2G (G/G ) It o 1= (7)g S DG Io 1oJ 2 JÏ Ï2 2o1 2 f (1 2 g)F S D GJ 2 JÏ Ï2max 2o

The elastic stress-strain relationship may be expressed bytwo constants: The bulk modulus K and the shear modulus Gare often used. In a nonlinear elastic model, as the stress statechanges, the elastic parameters K and G also change. Hence,the full description of nonlinear elastic response requiresproper representation of the variation of K and G with changesin stress state. The variation of shear modulus as a functionof current stress state has been discussed earlier. The bulkmodulus depends mainly on the amount of confining stress(Naylor et al. 1981). Based on the discussion of the K-G modelby Naylor et al. (1981), the tangent bulk modulus Kt can berepresented by the following equation:

n (12n )k kK = D ? (s9) (P ) (8)t s m a

where Pa = reference pressure = 100 kPa; = mean effectives9mstress in the same unit as Pa; Ds = material constant that canbe calculated from the initial values of bulk modulus and con-fining stress; and nk can be taken as 0.5. The values of initialbulk modulus may be obtained from the initial shear modulusGo and the initial Poisson’s ratio no, which takes a value in the0.1–0.15 range.

A nonlinear form of the Drucker-Prager failure criterion wasadopted to describe failure and postfailure soil response. TheDrucker-Prager failure criterion is given by

F = J 2 (aI 1 k) = 0 (9)Ï 2 1

where

2 sin fa = (10)

3(3 2 sin f)Ï

6c ?cos fk = (11)

3(3 2 sin f)Ï

in which c = cohesion; and f = internal friction angle. It hasbeen recognized that the original Drucker-Prager plastic modelwith an associated flow rule causes a large negative volumetricstrain, i.e., excessive dilational behavior (Desai and Siriwarden1984; Chen and Baladi 1985). To suppress unrealistic dilation,a nonassociated flow rule with the von Mises plastic potentialfunction was used. The details of the use of a von Mises plasticpotential can be found in Borja et al. (1989). The a parameterin the Drucker-Prager failure criterion can be obtained fromthe peak friction angle as a function of relative density andconfining stress. The peak friction angle in sands can be ex-pressed in terms of the friction angle at the critical state and

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TABLE 1. Basic Soil Properties at Georgia Tech Sitea

Layernumber

(1)

Depth(m)(2)

f9(&)(3)

K0

(4)

s9v o

(kPa)(5)

eo

(6)

Go

(kPa)(7)

1 0–1.82 34 0.44 18.2 0.70 23,6422 1.82–3.93 34 0.44 53.8 0.70 43,8383 3.93–5.93 37 0.40 87.6 0.73 54,0564 5.93–7.93 33 0.46 119.9 0.73 67,0815 7.93–9.93 32 0.47 151.8 0.74 76,0516 9.93–11.93 32 0.47 185.6 0.72 87,8497 11.83–13.93 36 0.41 219.9 0.70 96,1028 13.93–14.93 38 0.38 244.8 0.67 100,4729 14.93–16.76 36 0.41 268.6 0.67 112,540

10 16.76–18.28 36 0.41 296.8 0.67 119,145aAfter Mayne and Harris (1993).

the dilatancy angle. The critical-state friction angle for a givensoil is independent of stress state and density. The dilatancyangle is a function of density and confinement, increasing withincreases in density and decreasing with increases in confine-ment. Consequently, the envelope of the failure surface is non-linear. Bolton (1986) proposed the following equation to es-timate the peak friction angle in sand:

f = f 1 0.8 ?c (12)p c p

where fp = peak friction angle; fc = critical state friction an-gle; and cp = peak dilatancy angle given by

6.25I for plane-strain conditionsRc = (13)p H3.75I for triaxial conditionsR

The dilatancy index IR that appears in (13) is given by

PaI = I Q 1 ln 2 1 (14)R D F S DG100P9p

where ID = relative density (as a number between 0 and 1); Pa

= reference pressure = 100 kPa; = mean effective stress atP9ppeak strength in the same unit as Pa; and Q = intrinsic soilvariable, '10 for silica sands. Eqs. (12)–(14) were used todefine the nonlinear Drucker-Prager failure surface.

Numerical Analysis: Details and Validation

The commercial finite-element program ABAQUS was usedto model vertically loaded piles. The program ABAQUS hasbeen used to analyze many engineering problems. It providesa set of material models available for geotechnical problems,and several types of elements. The analysis procedure is di-vided in two parts: Interpretation of model information andimplementation of history data. Model information includeselement types, material definitions, and boundary conditions.History data define analysis type and any control parameternecessary for a nonlinear solution procedure. In most geo-technical problems, the first step consists of defining the initialgeostatic equilibrium condition.

Instead of using one of the material models available in theprogram, a subroutine was written for the nonlinear elastic-

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FIG. 1. Load-Settlement Curves for Pile Load Test at GeorgiaTech

plastic model described previously. Because the pile stiffnessis very large compared with soil stiffness, the pile was as-sumed to be made of linear elastic material. Eight-noded ax-isymmetric elements were used to model both the soil and thepile. Thin layer interface elements with zero initial thickness,allowing slippage, were used between the pile and the soil.The interface elements follow a Coulomb friction mechanism,for which slippage takes place when the tangential stress ex-ceeds a critical shear stress defined by a friction angle andnormal stress acting on the surface between the pile and soil.The necessity of interface elements in the analysis of axiallyloaded piles is discussed in Trochanis et al. (1991).

To assess the validity of the proposed finite-element analysisof pile base load-settlement response in sand, Lee (1999) andLee and Salgado (1999) analyzed 30 calibration chamber plateload tests performed under carefully controlled conditions:Comparison between predicted and measured loads at severallevels of relative settlement were very good. To further assessthe performance of the proposed analysis, a pile load test per-formed by the Georgia Institute of Technology (Mayne andHarris 1993) was modeled, and the numerical and experi-mental results were compared.

The test site has a layer of residual, silty silica sand ex-tending down to 15.8–19.5 m, underlain by partially weath-ered rock down to 20–24.8 m and then sound bedrock. Grainsize distribution analysis showed the soil to be composed of;70% sand, with the clay fraction <10%. A series of labora-tory tests on the soil samples collected at several depths wereperformed to obtain basic soil properties. Table 1 shows thesoil property profile with depth and layers used in the analysis.The bottom boundary of the finite-element mesh was locatedat a depth of 21.93 m from the surface, at which the bedrockwas encountered. The last layer of the mesh from 18.28 to21.93 m was the partially weathered rock layer, which wasassumed to behave as an elastic material. Initial shear modulusGo for each soil layer was calculated based on Hardin andBlack’s equation for angular sand. According to the Hardin

TABLE 2. Basic Properties of Ticino Sanda

D10

(mm)(1)

D50

(mm)(2)

Gsb

(3)U c

(4)

fc

(&)(5)

emax

(6)emin

(7)

gmax

(kN/m3)(8)

gmin

(kN/m3)(9)

Cg

(10)ng

(11)eg

(12)

0.36 0.54 2.623 1.5 34.8 0.922 0.573 16.68 13.65 647 0.44 2.27aAfter Ghionna et al. (1994).bGs = specific gravity.cU = coefficient of uniformity.


and Black’s equation and the observation made by Salgado etal. (1999), regarding changes in stiffness as a function of finescontent, the values adopted for Cg, eg, and ng were Cg = 214,eg = 2.97, and ng = 0.5, respectively. The model parameters fand g required in nonlinear elastic plastic model were used as0.98 and 0.05, respectively, based on the observed nonlinearelastic properties of silty sand (Salgado et al. 1999). The test-drilled shaft had a diameter equal to 76 cm and a length equalto 16.8 m. Measured and predicted base load-settlement curveswere plotted together in Fig. 1. Overall, agreement is observedto be reasonable.

Analysis of Axially Loaded Piles in Sand

The pile base load-settlement response for various soil andstress conditions can be obtained by analyzing axially loadedpiles with different pile lengths and relative densities. Threepile lengths of 5, 10, and 20 m with a diameter equal to 60cm were used. Different pile lengths imply different confiningstress levels at the pile base. For an assumed unit weight = 20kN/m3, initial vertical stresses at the pile base level (corre-sponding to 5, 10, and 20 m) are = 100, 200, and 400 kPa,s9vo

respectively. All of the piles were positioned within a granularsoil deposit assumed as normally consolidated Ticino sandwith K0 = 0.43. A K0 value of 0.43 was selected because it isnear the center of the typical range of 0.39–0.47 observed for

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TABLE 3. Pile Geometry and Soil Conditions Used in Finite-Element Analyses

Pilelength

(m)(1)

Relativedensity

(%)(2)

Type ofsand(3)

as9v o

(kPa)(4)

as9ho

(kPa)(5)

5 30 Ticino 100 4350 Ticino 100 4370 Ticino 100 4390 Ticino 100 43



aInitial stresses at the pile base level.

K0 in sands. Ticino sand was selected because it has beenstudied extensively (Salgado 1993; Bellotti et al. 1996) andhas been used in hundreds of calibration chamber plate loadand cone penetration tests (Ghionna et al. 1994; Salgado et al.1997b). These sand properties are shown in Table 2. Valuesof relative density DR used in calculations were 30, 50, 70,

FIG. 2. Finite-Element Meshes: (a) 5-m; (b) 10-m; (c) 20-m Piles

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FIG. 3. Base Load-Settlement Curves: (a) 5-m; (b) 10-m;(c) 20-m Piles

and 90% for each of the pile lengths assumed. To determinethe parameters f and g for the nonlinear elastic-plastic model,triaxial tests performed by Giuseppe (1991) and Vecchia(1991) were analyzed. Because the triaxial tests were per-formed for only two relative densities, medium dense (DR '

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50%) and dense (DR ' 90%), the values of f and g for DR =30% and DR = 70% were extrapolated and interpolated fromthe measured values, respectively. The basic pile geometry andsoil conditions are illustrated in Table 3.

The finite-element meshes for these pile lengths are shownin Fig. 2. The bottom boundaries of the meshes were locatedat a depth larger than two times the corresponding pile lengthsmeasured from the ground surface. The widths of the mesheswere equal to or larger than the pile lengths. Finite-elementanalyses performed separately with infinite elements at the lat-eral boundary showed that the mesh dimensions used in thisstudy are large enough to eliminate geometric boundary ef-fects. Fig. 3 shows a set of pile base load-settlement curvesobtained from finite-element analyses done for the differentpile lengths and relative densities. The curves in Fig. 3 extendup to a base settlement equal to 12 cm, corresponding to arelative settlement s/B of 20%.

DETERMINATION OF BASE RESISTANCE OFNONDISPLACEMENT PILES

Normalized Base Resistance qb /qc

To determine the pile base resistance in terms of cone pen-etration resistance, the load-settlement curves obtained previ-ously were normalized as follows: The base resistance qb at agiven DR and stress state was divided by the cone resistanceqc for the same soil conditions, and the settlement was dividedby the pile diameter B. The cone resistance qc was determinedusing the penetration resistance analysis of Salgado et al.(1997b). For clean, noncemented sands, it is generally possibleto write

q = q (D , s9, s9) (15)c c R v h

where qc = function containing intrinsic variables; DR = rela-tive density of sand before penetration; and and = ver-s9 s9v h

tical and lateral initial effective stresses. The theoretical de-velopment and evaluation of the function represented by (15)are available in Salgado et al. (1997b). The analysis is con-tained in the program CONPOINT (Salgado 1993; Salgado etal. 1997a,b; Salgado et al. 1998), which can be used to com-pute qc for sands.

Fig. 4 shows the fully developed load-settlement curves interms of qb/qc and s/B for each of the pile lengths and relativedensities. A common design approach for nondisplacementpiles is to stipulate that so long as the load is less than theload required for the pile settlement to reach a certain per-centage of the shaft diameter B, serviceability and ultimatelimit states are not reached. Franke (1993), for example, pro-posed that the critical load corresponds to s/B = 0.1, whereasReese and O’Neill (1988) implicitly define a critical load ascorresponding to s/B = 0.05. The British code for pile designis based on the s/B = 0.1 criterion. It may be stipulated in agiven project, based on structural or architectural require-ments, that some other values of s/B should not be exceeded.Several authors [e.g., Jamiolkowski and Lancellotta (1988),Franke (1989), Ghionna et al. (1994), and Salgado (1995)]have recommended values of qb/qc corresponding to differentlevels of s/B (see Table 4).

Table 5 shows the values of qb/qc at s/B = 5 and 10% fordifferent relative densities and pile lengths obtained using thefinite-element and penetration resistance analyses. Values ofqb/qc fall within the 0.07–0.13 range for s/B = 5% and withinthe 0.12–0.21 range for s/B = 10%, respectively. Fig. 5 illus-trates the influence of pile length (i.e., confinement at pile baselevel) and relative density on the normalized base resistanceqb/qc. The effect of pile length on qb/qc is small because qb

and qc depend on initial confining stress in a similar way. Only

CAL AND GEOENVIRONMENTAL ENGINEERING / AUGUST 1999 / 677

FIG. 4. Normalized Base Load-Settlement Curves in Terms ofqb /qc and s /B: (a) 5-m; (b) 10-m; (c) 20-m Piles

a slight decrease of qb/qc can be observed [Fig. 5(a)] for loosesand as the pile length increases. For dense sand, pile lengthhas essentially no influence on qb/qc. As can be seen in Fig.5(b), the influence of relative density on the normalized baseresistance is substantial. The normalized base resistance qb/qc

decreases as the relative density increases. The value of qb/qc

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TABLE 4. Values of qb /qc According to Several Authors

Authors(1)

qb/qc

(s/B = 5%)(2)

qb/qc

(s/B = 10%)(3)

German specification[DIN 4014, Franke (1993)] — 0.2

Franke (1989) — 0.2Jamiolkowski and Lancellotta

(1988)0.2

(for B < 60 cm) —Ghionna et al. (1994) 0.09 6 0.02 0.13 6 0.02Salgado (1995) — 0.15

TABLE 5. Values of qb /qc at s /B = 5 and 10%

Pilelength

(m)(1)

DR

(%)(2)

qb

(s/B = 5%)(kPa)

(3)

qb

(s/B = 10%)(kPa)

(4)

qc

(kPa)(5)

qb/qc

(s/B = 5%)(6)

qb/qc

(s/B = 10%)(7)

5 30 939 1,517 7,157 0.13 0.2150 1,303 2,062 12,052 0.10 0.1770 1,726 2,789 19,562 0.09 0.1490 2,238 3,630 30,121 0.07 0.12

10 30 1,343 2,158 10,922 0.12 0.2050 1,817 2,915 17,544 0.10 0.1670 2,409 3,871 26,644 0.09 0.1490 3,054 4,970 38,816 0.08 0.13

20 30 1,933 3,106 16,716 0.11 0.1950 2,590 4,158 25,694 0.10 0.1670 3,357 5,401 36,718 0.09 0.1590 4,289 6,845 50,524 0.08 0.13

at s/B = 10% is 0.19–0.2 for DR = 30%, whereas it is 0.12–0.13 for DR = 90%. These results indicate that larger settle-ments are required for soils with higher relative densities toreach a base resistance equal to a set percentage of cone re-sistance qc. The results also offer some insight into why mostpile design methods that calculate qb by multiplying qc by acertain constant [e.g., 0.2 for 10% relative settlement, accord-ing to Franke (1989)] also place an upper limit (usually in the4.5–5 MPa range) on possible values of qb. When piles areembedded in very dense sand layers, the results of the presentanalysis indicate that, as an example, qb = 0.2qc [the valueproposed by Franke (1989) irrespective of relative density]would be too high for s/B = 10% (qb = 0.12qc would be moreappropriate). Placing a limit on qb (e.g., 5 MPa) serves a pur-pose in that case. On the other hand, if the qb/qc values ofTable 5 and Fig. 4 are used, there may not be a need for settingan upper limit on qb.

Effect of Initial Stress Ratio K0

Normally consolidated sand deposits have initial values ofthe coefficient of lateral earth pressure at rest (K0) in the 0.39–0.5 range. Overconsolidated sand deposits have K0 values typ-ically higher than that of normally consolidated deposits. Toinvestigate the effects of K0 on normalized base resistanceqb/qc, three K0 values (0.4, 0.7, and 1.0) were assumed in aseries of finite-element analyses. The value of K0 = 1.0, cor-responding to an isotropic stress condition, may be regarded,for practical purposes, as the upper limit on K0, observed forhighly overconsolidated sand deposits.

Fig. 6 represents the effects of K0 on the normalized baseresistance qb/qc at s/B = 10%. The curves in Figs. 6(a and b)were plotted for different relative densities (DR = 30, 50, 70,and 90%) and two pile lengths (L = 5 and 20 m). It is observedthat qb/qc tends to decrease as the initial K0 increases, althougha deviation from this trend can be seen in one case of Fig.6(b). This trend was most obvious for the lowest relative den-sity: For DR = 30% and L = 5 m [Fig. 6(a)], the differencebetween the normalized base resistance qb/qc at K0 = 0.4 andat K0 = 1.0 was equal to ;0.05. No difference in the normal-ized base resistance qb/qc was found at DR = 90% for K0 =

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FIG. 5. Normalized Base Resistance qb /qc versus: (a) MeanEffective Stress at Pile Base Level; (b) Relative Density DRs9m

0.4–1.0. Comparing Figs. 6(a and b), it can also be observedthat the confinement at the pile base level, which is determinedby the pile length, does not have as much influence as therelative density on the relationship between qb/qc and K0.

Considerations for Displacement Piles

Values and analyses presented previously were developedfor nondisplacement piles. The limit base resistance qbL, asmentioned earlier, is mobilized at very large settlement levelsand is theoretically identical for both nondisplacement and dis-placement piles (De Beer 1984, 1988; Ghionna et al. 1993;Salgado et al. 1997b). The normalized base resistance valuesof Fig. 4 for nondisplacement piles, however, cannot be di-rectly applied to displacement piles because of the very dif-ferent load-settlement response of displacement and nondis-placement piles for low-to-moderate settlement levels. De Beer(1984, 1988) has shown that, under the same conditions, theloads carried by a displacement pile and a geometrically iden-tical nondisplacement pile differ significantly for values of rel-ative settlement s/B of interest in pile design. Nondisplacementpiles settle more than displacement piles for the same appliedload. This is mainly due to the different installation processesfor these two types of piles. The installation of displacementpiles causes considerable densification of the soil around thepile. In terms of base resistance, this process could be seen asa preloading of the soil in the immediate neighborhood of the

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FIG. 6. Effect of Coefficient of Lateral Earth Pressure at RestK 0 for Several Values of Relative Densities: (a) 5-m; (b) 20-mPiles

TABLE 6. Base Resistance Ratio for Displacement and Non-displacement Piles

Relativesettlement

(s /B )(1)

qb,NDa/qb,D

b

De Beer(1988)

(2)

Ghionna et al.(1993)

(3)

2.5% 0.482 —5% 0.517 0.15–0.21

10% 0.587 0.3–0.525% 0.715 0.3–0.7→` →1.0 →1.0

aqb,ND = base resistance for nondisplacement pile.bqb,D = base resistance for displacement pile.

pile base; hence the stiffer response when compared with non-displacement piles. The difference between the loads carriedby the two types of piles for the same settlement level becomesless pronounced as the load approaches the limit base load ata theoretically infinite settlement. De Beer’s observations havebeen later confirmed by other authors [e.g., Jamiolkowski andLancellotta (1988) and Ghionna et al. (1993)].

Table 6 shows the ratio of base resistance between displace-ment and nondisplacement piles for different values of relativesettlement. As can be seen in Table 6, the ratio of qb of anondisplacement pile to qb of a geometrically identical dis-placement pile is much smaller than 1 at small relative settle-


TABLE 7. Values of qb /qc for Displacement Piles

Pile length(m)(1)

DR

(%)(2)

qb/qc

(s/B = 5%)(3)

qb/qc

(s/B = 10%)(4)

5 30 0.25 0.3550 0.19 0.2970 0.17 0.2490 0.14 0.20

10 30 0.23 0.3450 0.19 0.2770 0.17 0.2490 0.15 0.22

20 30 0.21 0.3250 0.19 0.2770 0.17 0.2690 0.15 0.22

ments, but approaches 1 as the settlement approaches infinity.A simple approach that may be used to determine qb/qc valuesas a function of s/B for displacement piles is the applicationof the ratios of Table 6 to the results of Table 5 for nondis-placement piles. Such an approach can provide useful designcriteria, but is naturally subject to more uncertainties than thevalues proposed for nondisplacement piles in Table 5. Table 7provides the normalized base resistance qb/qc for displacementpiles obtained using this approach.

CASE HISTORIES

In this section we reexamine the values of normalized baseresistance qb/qc that were presented previously for nondis-placement and displacement piles. We do so in the context ofa few case histories involving actual pile load tests, calibrationchamber test data, and other numerical analyses. The case his-tories for nondisplacement piles include two instrumented pileload tests on drilled shafts, a series of calibration chamber tests(Ghionna et al. 1994), and the numerical results of Simonini(1996). A load test on a drilled shaft performed at a site onthe Georgia Tech campus in Atlanta (Mayne and Harris 1993;Harris and Mayne 1994) and another performed at the Uni-versity of Paulo (USP), Carlos, experimental field˜ ˜Sao Sao(Albiero et al. 1995) are analyzed. For displacement piles, theload test on a steel H-pile performed at the Purdue Universitycampus (Goble et al. 1972) and the load tests on the precastconcrete piles carried out by NGI (Gregersen et al. 1973) wereused. All of the load tests used in this section were instru-mented; thus base load-settlement responses were recordedseparately. The observed values of qb/qc for each case are sum-marized in Table 8.

Nondisplacement Piles

The Georgia Tech load test was described in the previoussection. The representative value of qc for base resistance cal-culation, an average value between the level of the pile baseand a level about one-and-a half to two pile diameters belowthe pile base, is 6.5 MPa. The measured base loads for theshaft at 5 and 10% relative settlement are 580 and 810 kN,respectively, corresponding to qb/qc values of 0.18 and 0.26,respectively. Because the relative density of the soil aroundthe pile base was not determined, the relationship between qc

and the relative density DR suggested by Salgado et al. (1997a)was used. The estimated relative density of the soil around thepile base with a K0 value of 0.41 was about 20–30%, repre-senting a loose state. Using Table 5, the corresponding valuesof qb/qc at s/B = 5 and 10% can be found as 0.12–0.13 and0.20–0.21, respectively. The difference between measured andpredicted values of qb in this example appears to be small (20–30% underprediction).


TABLE 8. Values of qb/qc from Load Tests on Nondisplace-ment and Displacement Piles

Pile type(1)

Test name(2)

qb/qc

(s/B = 5%)(3)

qb/qc

(s/B = 10%)(4)

Nondisplacement(drilled shafts)

Georgia Tech testUSP testSimonini’s analysis

0.180.09n/a

0.260.200.17

Displacement(driven piles)

Purdue testNGI Test ANGI Test BNGI Test CNGI Test D

0.270.320.320.300.43

0.320.360.360.390.47

The USP, Paulo, test site is located near downtown˜SaoCarlos, in the state of Paulo (Teixeria and Albiero˜ ˜Sao Sao

1994). The site geology consists of two clayey sand layersseparated by a thin layer of pebbles. The upper layer is areddish material of Cenozoic age, collapsible upon inundation(Vilar 1979), with void ratios close to 1. The lower layer is abrownish residual soil from a sandstone of the Bauru forma-tion. The water table oscillates, but is typically ;10 m deep.The base of the test shaft was placed at a depth of 10 m andthe shaft diameter was 50 cm. The measured base loads cor-responding to s/B = 5 and 10% are 50 and 114 kN, respec-tively. The load for 10% relative settlement was obtained froma quick maintained load test performed after a slow maintainedload test up to 5% relative settlement. The value of qc wasobtained from the CPT sounding provided in Albiero et al.(1995) as 2.8 MPa. This yields qb/qc values of 0.09 and 0.20for s/B = 5 and 10%, respectively. Considering the void ratio(;0.7) at the pile base level, the measured qb/qc values forthis case were also favorably compared with the results inTable 5, namely, qb/qc = 0.09–0.10 for s/B = 5%, and qb/qc =0.14–0.17 for s/B = 10% for medium dense sand.

Simonini (1996) carried out finite-element analyses to ob-tain the base resistance of nondisplacement piles in sands. Thepile was modeled with a diameter equal to 1 m and a lengthequal to 30 m in dry sand with fc = 337, DR = 90%, and soilunit weight gm = 16.5 kN/m3. The value of the base resistanceqb corresponding to s/B = 10% was found to be 8.6 MPa.Combining this result with qc from the penetration resistanceanalysis of Salgado et al. (1997a,b), the value of qb/qc can beobtained as 0.17.

A series of 30 calibration chamber load tests were carriedout by Ghionna et al. (1994) in sand samples with two differ-ent relative densities, dense (DR ' 90%) and medium dense(DR ' 50%). These tests simulate the installation and loadingof the base of drilled shafts. Calibration chamber size effectson the values of qb were shown by Lee (1999) and Lee andSalgado (1999) to be small. Fig. 7 shows the values of qb/qc

in the calibration chamber tests corresponding to s/B = 5 and10%. The cone resistance qc in Fig. 7 was obtained from thepenetration resistance analysis of Salgado et al. (1997a,b). Ascan be seen in Fig. 7, the values of qb/qc are in the 0.09–0.14range for DR ' 50% and 0.07–0.10 range for DR ' 90% ats/B = 5%, and in the 0.11–0.19 range for DR ' 50% and0.10–0.14 range for DR ' 90% at s/B = 10%. Although theresults for DR ' 50% show more scatter than those for DR '90%, the average values of qb/qc for both relative densities arein reasonable agreement with the proposed results given inTable 5.

Displacement Piles

The Purdue University load test was performed on the west-ern side of Purdue University campus in West Lafayette, Ind.(Goble et al. 1972). This site is located on the edge of a largeterrace along the Wabash river with a variable depth of weath-ered loess covering stratified sand and gravel layers. A 15-m-


FIG. 7. Values of qb /qc in Calibration Chamber Tests: (a) s/B =5%; (b) s/B = 10%

long steel H-pile (10HBP57) was driven using a DELMAGD-12 diesel hammer and load-tested. H-piles are sometimesreferred to as small displacement piles because their relativelysmall cross section does not cause as much disturbance anddensification of the surrounding soil during the installationprocess as concrete or pipe piles would.

The base resistance qb and relative settlement s/B were cal-culated based on the equivalent circular base area transformedfrom the half-perimeter area of the H-pile. The obtained qb

values for s/B = 5 and 10% were 2.43 and 3.37 MPa, respec-tively. Because the SPT was used instead of the CPT, the coneresistance qc was estimated from the SPT blow count at thepile base level based on the SPT-CPT correlation of Robertsonand Campanella (1983). The estimated qc value at the pile baselevel was ;9.0 MPa. The values of qb/qc corresponding tos/B = 5 and 10% were 0.27 and 0.37, respectively. These re-sults appear to be near the upper range of the values of qb/qc

for displacement piles shown in Table 7.The NGI load tests were performed on precast concrete piles

driven into a very loose deposit of quite homogeneous sandysoil. The site is located in a small island, Holmen, in the mid-dle of the Drammen river near the city of Drammen, Norway.The soil layer consists of a uniform, loose upper sand layerdown to 30 m, underlain by a clay layer, and finally bedrock.From the geological history of this area, the subsoil conditionis believed to be normally consolidated (Gregersen et al.1973). Four instrumented piles with two lengths, 8 and 16 m,were tested. The four piles are referred to by the letters A, B,

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C, and D in Table 8. Piles A and C had the same length (8m); Pile A had a diameter of 28 cm, while Pile C was a taperedpile with diameter varying from 28 cm at the pile top to 20cm at the pile base. Piles B and D had the same length (16m); Pile B had a diameter of 28 cm, while Pile D was madeby connecting Piles A and C, resulting in a pile with a diameterof 28 cm from the top to half the pile length, and then taperedwith a diameter of 20 cm at the pile base. The cone resistancescorresponding to the depths of 8 and 16 m from the surfacewere 3.1 and 5.0 MPa, respectively. The values of qb/qc foreach pile are given in Table 8. Although Pile D shows excep-tionally high values of qb/qc, most of the qb/qc values fallwithin the 0.29–0.32 range for s/B = 5% and the 0.36–0.39range for s/B = 10%. Considering that the soil is in a loosestate, these measured values agree well with the values pro-posed for displacement piles in Table 7.

SUMMARY AND CONCLUSIONS

The determination of base resistance is a key element in thedesign of piles bearing in sands because the side resistance isfully mobilized well before the maximum base resistance isreached. The CPT resembles the vertical loading process in apile; thus, it is regarded as one of the most effective toolsavailable for pile design. In the present study, to take advan-tage of the CPT for pile design, load-settlement curves interms of normalized base resistance qb/qc versus relative set-tlement s/B were developed. Although the limit state designconcept for pile design has been used mostly with respect toeither s/B = 5% or s/B = 10%, the normalized load-settlementcurves obtained in this study allow determination of pile baseresistance at any relative settlement level within the 0–20%range. This is important because it permits the considerationof specific project features that are related to the superstructureor other components of the facility by selecting an appropriatedesign value of s/B.

To obtain the pile base load-settlement relationship, finite-element analyses were performed with a nonlinear elastic-plas-tic constitutive model. Three 60-cm-diameter piles withlengths of 5, 10, and 20 m were used in the analyses. Thepiles were positioned within a granular soil deposit with DR =30, 50, 70, and 90%. Because the soil conditions around thepiles were assumed to be the same as those existing beforepile installation, the results obtained represent those corre-sponding to nondisplacement piles. The cone resistance qc wascalculated from the penetration resistance analysis of Salgadoet al. (1997b) and used to normalize the load-settlement curvesto express them in terms of qb/qc and s/B.

Most qb/qc values obtained from the finite-element and pen-etration resistance analyses fall within the 0.07–0.13 range fors/B = 5% and the 0.10–0.20 range for s/B = 10%. The effectof relative density on the normalized base resistance was sig-nificant, whereas that of the confining stress at the pile baselevel was small. At higher relative densities, the value of qb/qc was smaller (qb/qc = 0.12–0.13 for DR = 90%) than at lowerrelative densities (qb/qc = 0.19–0.2 for DR = 30%). The effectof the coefficient of lateral earth pressure at rest K0 was alsoinvestigated. The value of qb/qc tends to decrease as the valueof K0 increases. This trend was more pronounced at lowerrelative densities, and negligible for very dense sand.

Based on the results by De Beer (1984, 1988), the valuesof qb/qc for displacement piles were obtained as well. The val-ues of qb/qc were typically in the 0.15–0.25 range for s/B =5% and in the 0.22–0.35 range for s/B = 10%. The analysisof some case histories involving both nondisplacement anddisplacement piles showed that the values of qb/qc from thefinite-element and penetration resistance analyses agreed wellwith measured values.


ACKNOWLEDGMENTS

The research presented in this paper was funded by the Indiana De-partment of Transportation and the Federal Highway Administrationthrough the Joint Transportation Research Program.

APPENDIX I. REFERENCES

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Bandini, P., and Salgado, R. (1998). ‘‘Methods of pile design based onCPT and SPT results.’’ Proc., 1st Int. Conf. on Site Characterization,P. Robertson and P. Mayne, eds., Balkema, Rotterdam, The Nether-lands, 967–976.

Bellotti, R., Jamiolkowski, M., Lo Presti, D. C. F., and O’Neill, D. A.(1996). ‘‘Anisotropy of small strain stiffness in Ticino sand.’’ Geo-technique, London, 46(1), 115–131.

Bolton, M. D. (1986). ‘‘The strength and dilatancy of sands.’’ Geotech-nique, London, 36(1), 65–78.

Borja, R. I., Lee, S. R., and Seed, R. B. (1989). ‘‘Numerical simulationof excavation in elastoplastic soils.’’ Int. J. Numer. and AnalyticalMethods in Geomech., 13(3), 231–249.

Chen, W. F., and Baladi, G. Y. (1985). Soil plasticity: Theory and imple-mentation. Elsevier Science, New York.

De Beer, E. (1984). ‘‘Different behavior of bored and driven piles.’’Proc., 6th Conf. on Soil Mech. and Found. Engrg., G. Petrasovits, ed.,Budapest, 307–318.

De Beer, E. (1988). ‘‘Different behavior of bored and drivenpiles.’’ Proc., Deep Found. on Bored and Auger Piles, Van Impe, ed.,Balkema, Rotterdam, 47–82.

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Fioravante, V., Ghionna, V. N., Jamiolkowski, M., and Pedroni, S. (1995).‘‘Load carrying capacity of large-diameter bored piles in sand andgravel.’’ Proc., 10th Asian Regional Conf. in Soil Mech. and Found.Engrg., 1–13.

Franke, E. (1989). ‘‘Co-report to discussion, session 13, on large diameterpiles.’’ Proc., 12th Int. Conf. on Soil Mech. and Found. Engrg.

Franke, E. (1993). ‘‘Design of bored piles, including negative skin frictionand horizontal loading.’’Proc., 2nd Int. Geotech. Seminar on DeepFound. on Bored and Auger Piles, Van Impe, ed., Balkema, Rotterdam,The Netherlands, 43–57.

Ghionna, V. N., Jamiolkowsi, M., Lancellotta, R. and Pedroni, S. (1993).‘‘Base capacity of bored piles in sands from in-situ tests.’’ Proc., 2ndInt. Geotech. Seminar on Deep Found. on Bored and Auger Piles, VanImpe, ed., Balkema, Rotterdam, The Netherlands, 67–74.

Ghionna, V. N., Jamiolkowsi, M., Pedroni, S., and Salgado, R. (1994).‘‘The tip displacement of drilled shafts in sands.’’ Proc., Settlement’94, A. Yeung and T. Felio, eds., Vol. 2, Geotech. Engrg. Div., ASCE,Reston, Va., 1039–1057.

Giuseppe, B. (1991). ‘‘Modellazione numerica delle prove pressiome-triche in camera di calibrazione per la sabbia del ticino,’’ MS thesis,Dipartimento Di Ingegneria Strutturale, Politecnico Di Torino, Italy.

Goble, G. G., Kovacs, A. M., and Rausche, F. (1972). ‘‘Field demonstra-tion: Response of instrumented piles to driving and load testing.’’Proc., Specialty Conf. on Perf. of Earth and Earth-Supported Struct.,Vol. 3, ASCE, Reston, Va., 3–38.

Gregersen, O. S., Aas, G., and Dibiagio, E. (1973). ‘‘Load tests on frictionpiles in loose sand.’’ Proc., 8th Int. Conf. on Soil Mech. and Found.Engrg., Vol. 2, 109–117.

Hardin, B. O., and Black, W. L. (1966). ‘‘Sand stiffness under varioustriaxial stresses.’’ J. Soil Mech. and Found. Div., ASCE, 92(2), 27–42.

Hardin, B. O., and Drnevich, V. P. (1972). ‘‘Shear modulus and dampingin soils; design equations and curves.’’ J. Soil Mech. and Found. Div.,ASCE, 98(7), 667–692.


Harris, D. E., and Mayne, P. W. (1994). ‘‘Axial compression behavior oftwo drilled shafts in Piedmont residual soils.’’ Proc., Int. Conf. Des.and Constr. of Deep Found., Vol. 2, 352–367.

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Hirany, A., and Kulhawy, F. H. (1989). ‘‘Interpretation of load tests ondrilled shafts part 1: Axial compression.’’ Proc., Congr. on Found.Engrg., H. Kulhawy, ed., Vol. 2, ASCE, Reston, Va., 1132–1149.

Jamiolkowski, M., and Lancellotta, R. (1988). ‘‘Relevance of in-situ testresults for evaluation of allowable base resistance of bored piles insands.’’ Proc., 1st Int. Geotech. Seminar on Deep Found. on Boredand Auger Piles, Van Impe, ed., Balkema, Rotterdam, 107–120.

Kondner, R. L. (1963). ‘‘Hyperbolic stress-strain response: Cohesivesoil.’’ J. Soil Mech. and Found. Div., ASCE, 189(1), 115–143.

Lee, C. Y., Allman, M. A., and Poulos, H. G. (1989). ‘‘Static behavior ofpiles in cemented calcareous sands.’’ Proc., 1989 Found. Engrg.Congr., Vol. 1, ASCE, Reston, Va., 485–499.

Lee, J. H. (1999). ‘‘Design of foundations bearing in sand based on CPTresults,’’ PhD thesis, School of Civil Engrg., Purdue University, WestLafayette, Ind.

Lee, J. H., and Salgado, R. (1999). ‘‘Analysis of calibration chamber plateload tests.’’ Can. Geotech. J., Ottawa, December.

Mayne, P. W., and Harris, D. E. (1993). ‘‘Axial load-displacement be-havior of drilled shaft foundation in Piedmont residium.’’ Tech. Rep.No. 41-30-2175, Federal Highway Administration, Washington, D.C.

Naylor, D. J., Pande, G. N., Simpson, B., and Tabb, R. (1981). Finiteelements in geotechnical engineering. Pineridge, Swansea, U.K.

Poulos, H. G. (1989). ‘‘Developments in the analysis of static and cycliclateral response of piles.’’ Proc., 4th Int. Conf. on Numer. Methods inGeomechanics, Vol. 3, Rotterdam, Balkema, The Netherlands, 1117–1135.

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APPENDIX II. NOTATION

The following symbols are used in this paper:

B = pile diameter;Cg = small-strain shear modulus number;


c = cohesion;DR = relative density (%);Ds = confining stress constant in expression for tangent bulk

modulus;eg = small-strain shear modulus void ratio number;

emax = maximum void ratio;emin = minimum void ratio;

eo = initial void ratio;F = Drucker-Prager failure criterion;f = material parameter in modified hyperbolic equation;

G = secant shear modulus;Go = initial shear modulus;Gt = tangent shear modulus;g = material parameter in modified hyperbolic equation;

ID = relative density as number between 0 and 1;IR = dilatancy index;I1 = first invariant of stress tensor;

I1o = initial first invariant of stress tensor;J2 = second invariant of deviatoric stress tensor;

J2max = maximum invariant of deviatoric stress tensor;J2o = initial invariant of deviatoric stress tensor;K = bulk modulus;Kt = tangent bulk modulus;K0 = coefficient of lateral Earth pressure at rest;

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L = pile length;ng = small-strain shear modulus exponent;nk = exponent in expression for tangent bulk modulus;Pa = atmospheric pressure;P 9p = mean effective stress at peak strength;Q = dilatancy-related parameter in correlation for peak fric-

tion angle;qb = base resistance;

qbL = limit base resistance;qc = cone tip resistance;s = base settlement;a = friction angle parameter in Drucker-Prager failure crite-

rion;k = cohesion parameter in Drucker-Prager failure criterion;no = initial Poisson’s ratio;s9h = horizontal effective stress;s9m = mean effective stress;s9v = vertical effective stress;t = shear stress;

tmax = maximum shear stress;to = initial shear stress;f = friction angle;fc = friction angle at critical state; andfp = peak friction angle.


Determination of Pile Base Resistance in Sands

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