50240455-18-pilef

Piled Foundations for Vertical Loads -- GEOTECHNICAL ENGINEERING-1997 -- by G.P. Raymond© 163

Figure 1. Comparison of stressed zone beneath(a) single pile; (b) pile group.

Figure 2. Comparison of single pile and group behaviour ofpiles and bearing.

Figure 3. Illustration of (a) friction and (b) end-bearing piles.

PILED FOUNDATIONS FOR VERTICAL LOADS

SYMBOLS

Notation Dimensional Analysis

A = Area L2

B = Breadth or diameter Lc = cohesive component of shear strength M L-1 T-2

D = depth Ld = depth factor -E = modulus M L-1 T-2

f = skin friction per unit area M L-1 T-2

F = Force M L T-2

H = Height of layer or socket LK = coefficient -N = blow count -Nc

* = bearing capacity coefficient (cohesion) -Nq

* = bearing capacity coefficient (surcharge) -PR = limit pressure from penetration test M L-1 T-2

q = stress or pressure M L-1 T-2

qp-cone = cone tip resistance per unit area M L-1 T-2

qu-cone = unconfined strength of rock core M L-1 T-2

Q = load M L T-2

S = settlement LSp = pile spacing Lα = coefficient -γ = unit weight M L-2 T-2

δ = friction angle between two different materials Angleρ = elastic deformation Lσ = stress M L-1 T-2

τ = shearing stress M L-1 T-2

φ = angle of internal friction Angle

Subscripts etc. where not identified above

a = adhesionc = coned = allowable design valuefp = failure of tipg = groupm = pressuremeter valuen = negative skin friction valueo = zero strain (i.e. at rest) or overburdenp = pile tips = shaft valueu = undrained´ = effective of intergranular value¯ = average value

INTRODUCTIONPiles may be used for a variety of reasons including resistance

to uplift and lateral loading. Herein comment is restricted to the supportof building foundations subject to vertical loading. For a morecomprehensive review of pile design and construction practice referencemay be made to the work of Tomlinson (1977). Some of the reasons forpiling a foundation are:(a) To transfer the load from the surface through poor strata to

underlying firmer material. In the majority of cases, where piles areused, they represent the only possible means of prohibiting ultimatefailure or excess settlement induced by the loading at the surface.

(b) For reasons of economics or speed; provided that a safe design isachieved, the ultimate cost is normally the criterion of engineeringdesign, and in difficult country, the use of piles may be a speedy andeconomical alternative to the construction of near ground surface

level foundations.(c) In sands to induce compaction.(d) In bridgework to transfer the load below the scour level.

As illustrated in Figures 1 and 2 a distinction has to be madebetween the ultimate bearing capacity of single piles and that of a groupin which the sum of individual pile capacities may be affected by "groupaction". In practice the design of piled foundations is also based, asillustrated in Figure 3, on the type of soil and strata forming thefoundation material. For construction, piles may be subdivided into fourbroad classification systems as:1. Displacement (or large-displacement) piles2. Small-displacement piles3. Non-displacement piles4. Composite piles


Figure 4. Typical socketed-in-rock pile.

Figure 5. Piles driven to rock (a) tightly closed joints; (b)clay filled joints; (c) inclined joints; (d) steeply inclined

joints.

Displacement (or large-displacement) piles: comprise solid-section piles or hollow-section piles with a closed end, which are drivenor jacked into the ground and thus displace the soil. All types of drivenand cast-in-situ piles come into this category.

Typical driven displacement piles are:1. Timber (round or square section, jointed or continuous).2. Precast concrete (solid or tubular section in continuous or jointed

units).3. Prestressed concrete (solid or tubular section).4. Steel tube (driven with closed end).5. Steel box (driven with closed end).6. Fluted and tapered steel tube.7. Jacked-down steel tube with closed end.

Typical driven and cast-in-place piles are:a. Steel tube driven and withdrawn after placing concrete.b. Precast concrete shell filled with concrete.c. Thin-walled steel shell driven by withdrawable mandrel and then

filled with concrete.

Small-displacement piles: are also driven or jacked into theground but have a relatively small cross-sectional area. Typical smalldisplacement piles are:1. Precast concrete (tubular section driven with open end, or cruciform

section).2. Prestressed concrete (tubular section driven with open end, or

cruciform section).3. Steel H-section.4. Steel tube section (driven with open end and soil removed as

required).5. Steel box section (driven with open end and soil removed as

required).6. Screw pile.7. Screw cylinder.

Non-displacement piles: are formed by first removing the soilby boring using a wide range of drilling techniques. Concrete may beplaced into an unlined or lined hole, or the lining may be withdrawn as theconcrete is placed. Preformed elements of timber, concrete, or steel maybe placed in drilled holes. Typical non-displacement piles are:1. Concrete placed in hole drilled by rotary auger, baling, grabbing,

airlift or reverse-circulation methods (bored and cast-in-situ).2. Tubes placed in hole drilled as above and filled with concrete as

necessary.3. Precast concrete units placed in drilled hole.4. Cement mortar injected into drilled hole.5. Steel sections placed in drilled hole.6. Steel tube drilled down.

Composite piles: In addition numerous types of compositeconstruction may be formed by combining units in each of the abovecategories, or by adopting combinations of piles in more than onecategory. Thus composite piles of a displacement type can be formed byjointing a timber section to a precast concrete section, or a precastconcrete pile can have an H-section jointed to its lower extremity. Theselection of the appropriate type of pile from any of the above categoriesdepends primarily on1. The location and type of structure.2. The ground conditions.3. Durability.

GEOTECHNICAL DESIGN OF DEEP FOUNDATIONS ON ROCKDeep foundations sitting on or socketed into rock normally

carry heavy loads. As shown in Figure 4 they may be bored or excavatedand cast-in-place. In this case the area of contact with rock is known andthe load capacity can be evaluated by design methods as outlined later.

Deep foundations may, as shown in Figure 5, also be driven torock. This includes steel H piles, pipe piles driven with a closed end or

precast concrete piles. The exact area of contact with the rock and thedepth of penetration into rock, as well as the quality of rock at thefoundation level, are largely unknown. Consequently, the determinationof the load capacity of such deep foundations can not be reliably made bydesign methods, and should be made on the basis of driving observations.Even when piles are test loaded, instability of piles groups may occur suchas where the piles are terminated on a sloping rock formation as shown inFigure 6.

LOAD CAPACITY OF DEEP FOUNDATIONS ON ROCKThe load capacity of deep foundations founded on or into rock

depend on a number of factors as given below.

1. Design AssumptionsIn most cases where cast-in place deep foundations are

socketed into rock (Figure 4) the depth of the socket is typically 1 to 3times the diameter of the foundation. The exact design of such deepfoundations varies from region to region. Three different designassumptions are in common use:(a) The load capacity is assumed to be derived from point resistance


Figure 6. Illustration of group failure for piles driven to asloping rock surface.

Figure 7. Bearing pressure coefficient Ksp

Spacing of Discontinuities Ksp

Very wideWideModerately close

> 3 metre1 - 3 m

0.3 - 1 m

0.4 0.250.1

only. This assumption can be considered as safe, since the bearingcapacity of the rock is available, irrespective of the constructionprocedure. However, if the bottom of the excavation is not properlycleaned, the bearing capacity may not be mobilized before largesettlements occur due to the compression of mud remaining in thebottom of the socket.

(b) The load capacity is assumed to be derived from the bond betweenconcrete and rock along the surface perimeter of the socket. Thisassumption is not necessarily safe. Theoretical considerationsindicate that a uniform mobilization of the bond is possible only ifthe modulus of elasticity of both concrete and surrounding rock areof the same order to magnitude (Coates, 1967). Furthermore theavailable bond strength is highly dependent on the quality of the rocksurface on the walls of the socket.

(c) The load capacity is assumed to be derived from both point resistanceand lateral bond. This assumption leads to high load capacities. Itshould not be used unless it can be proved applicable by means offull scale load tests or well-supported local experience.

2. Allowable Bearing Pressure from Properties of Rock Cores:Any design based on rock cores depends on the quality of the

rock. Rock may be considered as sound when the unconfinedcompression strength is in excess of 850 kPa and the spacing ofdiscontinuities is in excess of 1 metre. This includes rock of very lowstrength. Where rock is sound, and its discontinuities are closed and arefavourably oriented with respect to the applied forces, the strength of arock foundation is generally much in excess of design requirements. Anyinvestigation of a rock foundation should, therefore, be concentrated on:(a) The identification and mapping of all discontinuities in the rock mass

within the zone of influence of the foundation including thedetermination of the thickness of discontinuities.

(b) An evaluation of the mechanical properties of these discontinuities;frictional resistance, compressibility and strength of infillingmaterial; and

(c) The identification and evaluation of the strength of the rock material.Such investigations should be carried out by a person competent in thisfield of work.

The final determination of the bearing pressure of rock resultsfrom the analysis of the influence of the discontinuities on the behaviourof the foundation. As a guideline, in the case of a rock mass withfavourable characteristics (i.e., the rock surface is perpendicular to thefoundation, the load has no tangential component, the rock mass has noopen discontinuities), the allowable bearing pressure may be estimated fora non-embedded load (pile tip resting on the rock surface elevation) from

qa ' Ksp qu&core (1)

whereqa = the allowable design bearing pressure of surface rockqu-core = the average unconfined compressive strength of rock cores, as

determined from ASTM D2938-71, and

Ksp = an empirical coefficient that depends on the spacing of thediscontinuities as given below but also includes a factor ofsafety of 3.

NOTE: The factors influencing the magnitude of coefficient Ksp areshown graphically in Figure 7 to provide additional understanding of theeffects of discontinuities. The relationship given in Figure 7 is valid fora rock mass with spacing of discontinuities greater than 300 mm,thickness of discontinuities less than 5 mm (or less than 25 mm if filledwith soil or rock debris) and for a foundation width greater than 300 mm.For sedimentary or foliated rocks, the strata must be level or nearly so.

Conditions are frequently encountered where the rock is ofvery low strength, has discontinuities at a very close spacing, or isweathered or fragmented. It is common practice in such cases to considerthe rock as a granular mass and to design the foundation on the basis ofconventional soil mechanics. However, the strength parameters necessaryfor such a design are difficult to evaluate.

If the rock meets the requirements of having favourablecharacteristics the estimation of the allowable design bearing pressure ofa deep foundation embedded in rock may be obtained from the propertiesof rock as follows:

qa ' qu&core Ksp d (2)

whered = depth factor = [1.0 + (0.4 Hs/B)] # 3.0 (3) Hs = depth of the socket in rock having a strength qu-coreB = diameter (breadth) of the socket

This method is generally not applicable to soft stratified rocks


Depth of SocketPile Diameter

0 1 2 3 5 7

Kb 0.8 2.8 3.6 4.2 4.9 5.2

Spacing ofDiscontinuities

< 3 m

1-3 m

0.3-1m

80-300mm

αm 1 0.75 0.5 0.25

such as shales or limestones. For these rocks the values of the basicparameter qu-core are generally not representative of the actual mechanicalproperties of the rock mass due to the effect of sampling disturbance andthe absence of discontinuities in the test specimens.

The allowable bearing pressure as obtained from this methodshould be checked against the range of values shown in Table 1.

3. Allowable Bearing Pressure from Pressuremeter Test Results:In situ pressuremeter tests permit the determination of the

strength of the rock mass, including the effect of joints and weathering.Where performed properly the pressuremeter test gives a strength indexof the rock mass called the limit pressure, PR. The test and thecorresponding design methods are best applied to weathered or closelyjointed rocks and for soft rocks in general.

The allowable design bearing pressure is given by:

qa '13

[Kb (pR & po) % σo] (4)

whereqa = the allowable design bearing pressureσo = overburden stress (effective if appicable)po = the at rest horizontal stress in the rock at the elevation of the

pile tippR = the limit pressure as determined from the pressuremeter tests

in the zone extending 2 pile diameters above and below thepile tip, and

Kb = an empirical bearing capacity coefficient as follows:

4. Load Capacity from Bond Between Concrete and Rock:For a pile socketed into rock (Figure 5) it is sometimes

assumed that the entire load from a pile is transferred to the rock byadhesion between the concrete of the socket and the surrounding rock.The allowable load capacity is given by:

Qa ' π B Hs τa (5)

whereQa = the allowable design load on the pileB = the pile diameter or breadthHs = the depth of the socket in sound rock, andτa = the allowable design bond strength between the concrete and

the rock.

The available bond strength τa is a function of the strength ofthe concrete and the rock as well as the quality of the contact arearesulting from the excavation process. τa is generally higher than the bondstrength normally considered in concrete design due to the Poisson's Ratioeffect in the confined concrete socket.

Design values of 650 to 2000 kPa are applicable to goodconstruction methods and sound unshattered rock. Much lower values,however, are likely on actual sockets where the construction process hasproduced a poor contact area.

This design method is based on the assumption that the wallsof the socket are of sound rock, unshattered by the excavation process andare clean from any drilling mud or smear. This may in fact be difficult to

achieve particularly in sedimentary rocks although rotary drilling methodsminimize this problem. The design method should therefore be used withgreat caution and a careful visual inspection of the rock socket beforeconcreting is mandatory. To ensure the safety of the design it is commonpractice to limit the load capacity Qd determined by this method to themaximum value resulting from the smaller of methods (2) or (3) if bothrock cores and pressuremeter tests have been performed.

SETTLEMENTS OF DEEP FOUNDATIONS ON ROCKSettlement analysis of piles sitting on or socketed in rock is

very difficult and frequently unreliable because of the discontinuousnature of rock masses.

In general, in sound rock, settlements are minute and can beneglected. Important rock settlements are generally associated with thepresence of open joints in the rock mass and, in sedimentary rocks, withthe occurrence of seams of compressible material. Where such conditionsare expected to exist special investigations and analysis by a personcompetent in this field of work is generally necessary.

Settlements may also result from the presence of debrisbetween the bottom of the concrete shaft and the rock surface. Carefulinspection of the bottom of each excavation is necessary to eliminate thisproblem especially in the case where the deep foundation has beendesigned according to the previous sections.

In some cases, such as for deep foundations of largedimensions or those carrying high loads, a settlement analysis may bedesirable. Three methods are available.

1. Settlements from Tests on Rock Cores: Elastic moduli measured on rock core samples have little

relation in the actual settlement behaviour of rock masses, since theinfluence of joints and other rock discontinuities is neglected. Asettlement analysis based on such moduli must include arbitraryassumptions on the influence of joints, and is therefore of limited practicalvalue.

2. Settlements from Pressuremeter Tests: Settlements can be estimated on the basis of in-situ

pressuremeter tests. To do so, a large number of tests must be performedto allow for an assessment of the variability of elastic moduli of the rockmass, including some measure of the influence of joints and otherdiscontinuities.As a first approximation the settlement is given by:

S 'qa B

9 αm E(6)

whereS = the settlementqa = the design pressureB = the tip diameter (breadth) of the pileE = the average pressuremeter modulus in the zone extending 3

diameters below the pile tipαm = a coefficient which is a function of the structure of the rock

mass as follows

This method is applicable to homogeneous as well as tostratified rock masses. In the latter case the modulus to be used in theformula is taken as a weighted average of the moduli measured in the


Figure 8. Illustration of build up of resistance with depth ofpiles driven into cohesionless soil.

different strata, provided the moduli do not differ by more than a factor of10. The effect of thin horizontal joints or compressible seams cannot betaken into account in this method and the results may be misleading ifsuch joints or seams occur.

3. Settlements from Plate Load Tests: In situ plate load tests may be used to assess the settlement

behaviour of a rock mass under a deep foundation. The importance of sizeeffects on the results of such tests should be recognized. Ideally the plateshould be of the same diameter as the deep foundation. For practicalreasons, however, this is seldom possible and smaller plates are generallyused. The results obtained from loading smaller plates may generally beconsidered representative of the actual foundation behaviour provided thediameter of the plate is not less than half the diameter of the foundation,and is always in excess of 300 mm.

Plate load tests are difficult to carry out properly and results arefrequently variable. To obtain a reliable evaluation of the foundationbehaviour a series of tests have to be carried out. The cost of such testsis high. In general the tests are only justified by projects of a very largesize or when the structure to be supported is very sensitive to settlements.

The performance and interpretation of such plate load testsshould be carried out be a person competent in this field of work.

GENERAL COMMENTS ON PILES IN GRANULAR SOILSThe following sections cover the design of all kinds of piles

embedded in granular soils,i.e., gravels, sands, and non-cohesive silts.The design methods described are applicable only to unstratified depositswhere granular soils extend to a significant depth beneath the lowest partof the deep foundation or to layered deposits where granular soils areunderlain by more competent materials such as tills or rock.

In cases of layered deposits where granular soils are underlainby compressible materials the design methods described under the sectiondealing with piles in layered deposits should be used.

Piles in granular soils derive their load carrying capacity fromboth (Figure 3) point resistance and shaft friction. The relativecontributions of point resistance and shaft friction to the total capacity ofthe pile depend essentially on the density and shear strength of the soil andon the characteristics of the pile. A typical graph of the separatecomponents for a driven pile at various depths of penetration is shown inFigure 8.

It is usual to distinguish between a displacement pile and anon-displacement pile.

ALLOWABLE LOAD ON A SINGLE PILE IN GRANULAR SOILAllowable loads for piles should be determined from field

tests. These tests are generally not performed until construction of thefinal structure. For preliminary design some method is needed to obtainapproximate allowable loads. Such empirical methods are based onstandard site investigation tests.

1. Method Based on the Standard Penetration Test: The ultimate bearing capacity of a single pile in granular soils

may be estimated from the results of the Standard Penetration Test assuggested by Meyerhof (1956).

Qf ' 400 N Ap % 2 N As (7)

whereQf = the ultimate pile load, kNN = the average standard penetration index at the pile tip elevation,

blows/300 mmAp = the cross-sectional area of the pile tip, m2

N̄ = the average standard penetration index along the pile shaftblows/300 mm with a maximum value of 50, and

As = the surface area of the pile shaft, m2.Note the equation is empirical so the correct dimensional units must beused.

The Standard penetration Test is subject to many errors and muchcare must be exercised when using the test results. For this reason aminimum factor of safety of 4 should be applied to Qf. The allowable loadcapacity of a pile is therefore:

Qd #Qf4

(8)

2. Method Based on the Theory of Plasticity: The allowable load on a single pile in a granular soil may be

estimated from the friction angle of the soil by use of the theory ofplasticity (or ultimate bearing capacity theory).

The ultimate bearing pressure of a pile in a granular soil ofconstant density increases in a linear manner with increase in effectiveoverburden pressure only down to a certain depth called the critical depth(Figure 8). Investigations up to the present time indicate that there is verylittle increase in end bearing pressure or shaft friction below this criticalvalue. The ratio of the critical depth Dc to the pile diameter B increaseswith increase in the angle of shearing resistance, φ, and in the density ofthe soil. For most pile applications where the breadth of the pile is smallin comparison with the buried depth of the tip Dc/B ranges between avalue of 7 at φ = 30E to 22 at φ = 45E. For shallow foundations therelationships given in the chapter on ultimate bearing capacity should beconsulted. Since the density of most granular soils increase with depthand since many other factors influence the validity of theoretical estimatesof pile capacity in granular soil, reference should be made to Meyerhof(1975) before finalising pre-design estimates. In addition, in the absenceof a load test, a factor of safety or at least three should be applied to anytheoretical computation.

For piles with a length in granular soil less than Dc the ultimate


point resistance is given by:

qfp ' γ) Dp N(

q (9)

whereqfp = ultimate point resistanceγ' = effective unit weight of the soilDp = length (depth) of the pile tip embedmentNq

* = a bearing capacity coefficient for piles as derived fromBerezantsev (1961). Nq

* is given as a function of the angle ofshearing resistance φ of the soil as follows:

φ = 25E 30E 35E 40ENq

* = 15 30 75 150

Considering the exponential increase of Nq* with φ the selection of adesign value of φ should be made with caution.

For lengths of piles in excess of Dc, the ultimate pointresistance is constant and equal to:

qfp ' γ) Dc N(

q (10)

The ultimate unit skin friction at any given value ofoverburden, fs, in homogeneous sand may be expressed by:

fs ' Ks σ)

o tanδ # fc (11)

whereKs = the coefficient of earth pressure on the pile shaftσ/

o = the given effective overburdenδ = the angle of friction at the sand-pile contactfc = the maximum value of F at and below the critical depth

The value of Ks tan δ is influenced by (a) the angle of shearingresistance of the soil, (b) the method of pile installation (c) thecompressibility of the soil, (d) the original horizontal stress in the ground,and (e) the pile size and shape. It increases with increases in the in situdensity and angle of shearing resistance of the soil and with the amountof displacement experienced. It is higher for large displacement piles thanfor H piles. The value of Ks tan δ is a minimum for bored piles whichdevelop about one quarter of the resistance generated around largedisplacement piles. Reliable values for Ks tan δ can only be obtained fromload tests.

The factor of safety to apply to qfp and fs should be at leastequal to three.

The resulting allowable load on a single pile with a diameter(breadth) B and a length (depth in soil) Dp, is computed as follows:for Dp < Dc

Qa '13qfp π B

2

4%

π B Dp fs2

(12)

where qfp and fs are computed at depth = Dp.for Dp > Dc

Qa'13qfpπB

2

4%fsπBDc

2% fsπB(Dp&Dc) (13)

where qfp and fs are computed at depth Dc.

3. Method Based on Static Penetration Tests: The allowable load on a pile in granular soil can be computed

from the results of static cone penetration tests (Dutch cone). The test isbest suited for silts and sands that are loose to dense. The test is difficult

to carry out in coarse gravels and in sands that are very dense.

The ultimate load capacity of a single pile in granular soil maybe determined from:

Qf ' qp&cone Ap % fcone As (14)

whereQf = ultimate pile loadqp-cone = point resistance per unit area from cone tests. (It is

recommended that for piles with B > 500mm the design valueof qp-cone should be between the limits of the minimummeasured qp-cone and the measured average qp-cone.)

Ap = cross-sectional area of the pile tipfcone= average skin friction measured by cone tests. (The use of a

cone equipped with a friction sleeve is recommended.)As = surface area of the pile shaft.

The results of static cone penetration tests are morereproducible than those of the Standard Penetration Test and a greaterconfidence can be put in the design method basad upon them.

The factor of safety to apply to Qf should be between 2.5 and3 depending on the number of cone tests performed and on the observedvariability of the test results; the lower value of factor of safety shouldonly be used when a large number of results with a variability of less than± 10% of the average have been obtained.

4. Method Basad on Load Tests: The design of piles on the basis of theoretical or empirical

methods, as previously described, are the subject of some uncertaintiesdue to:(a) the soil properties can not be measured with great accuracy and are

always variable within a building site.(b) the correlation between the soil parameters and the bearing capacity

of a pile include a margin of error;(c) the actual driving or placing conditions vary from pile to pile and can

not be properly taken into account.Therefore, the best method of assessing the bearing capacity

of piles is to load test typical units.

5. Compacted Concrete Piles: Compacted concrete piles in granular soils derive their bearing

capacity from the densification of the soil around the base. The bearingcapacity of such piles is therefore entirely dependent on the constructionmethod and can only be assessed from load tests and from welldocumented local experience.

6. Resistance to Pile Penetration: In some granular soils the ultimate capacity of driven piles is

subjected to change with time during or following driving. In densesaturated fine grained soils such as non-cohesive silts and fine sands, theultimate capacity may decrease after initial driving. This is known asrelaxation. The driving process is believed to cause the soil below the piletip to dilate thereby generating negative pore pressures and a temporaryhigher strength. When these pressures dissipate the resistance reduces.On the other hand temporary liquefaction and consequent failure, ordropping resistance to pile penetration, may also occur in saturated finegrained sands or silts. The probability of liquefaction is greater in loosethan in dense sand, but even in dense material liquefaction can occur ifthere are a sufficient number of stress cycles, or if the magnitude of thestress cycle is large enough, or if the confining pressure is low. After thetemporary pore pressures dissipate the indication of true capacity is given,in initial redriving, by the return to a higher resistance to pile penetration.Because the resistance to pile penetration may increase (freeze) ordecrease (relaxation) after final set, it is essential that retapping be carriedout once equilibrium conditions in the soil have been re-established. Thetime for the return of equilibrium conditions can be determined only bytrial. The resistance developed in the first five blows of retap are


Figure 9. Results of loading a compressive pile to failure.

generally indicative of the equilibrium resistance. However, even withretapping, load testing may be required to appraise the final working load.The effects of freeze should be treated with great caution in large pilegroups because of the effects of group action.

7. Driving Resistance: The penetration per blow decreases rapidly after a set of 5

blows per 25 mm for friction piles and 10 blows per 25 mm for end-bearing piles. There is little justification in requiring sets higher than 10blows per 25 mm with friction piles and a final set of 20 blows per 25mmfor an end-bearing pile may only be warranted if driving is easy in the soilabove the bearing stratum.

ALLOWABLE LOAD ON A PILE GROUP IN GRANULAR SOILIt is common practice to define the allowable load on a pile

group in granular soil as the sum of the allowable loads of the individualpiles in the group. However, it is known that piles in groups in granularsoils develop a larger load capacity than isolated piles: their groupefficiency, defined as the ratio of the ultimate load capacity of a pile in agroup to that of the same pile when isolated, is greater than 100%. Whereit would be necessary to take this effect into account in design, theinfluence of pile spacing and pile cap should be considered. The effect ofspacing is such that:(a) piles at a spacing greater than seven times the average pile diameter

act individually(b) piles act as a group at spacings varying from 2.5 to 7 times the

average pile diameter(c) piles should not be installed at spacing less than 2.5 times the average

pile diameter.

The effect of the pile cap is such that if the pile cap is incontact with granular soil then experience has shown that the soil developsa bearing capacity which increases the apparent group efficiency. Thisadditional bearing capacity should not be relied on.

SETTLEMENT OF A SINGLE PILE IN GRANULAR SOILMany factors that can not be included in theoretical analysis

influence the actual settlement of piles, with the result that estimates basedonly upon considerations of the elastic properties of the soil and pilematerial are generally so inaccurate as to be of no practical value. Instead,estimates of settlements of piles are based upon empirical relationships.

1. Empirical Methods: For normal load levels, the settlement of a single pile in

granular soils is a function of the ratio of applied load to ultimate loadcapacity and of the diameter of the pile.

For normal load levels, the settlement of a displacement pilemay be estimated from the empirical formula (approximated from Vesic,1977):

S 'Qactual α B

Qa% ρ *(15)

* The Canadian Foundation Engineering Manual assumes Qactual = Qa andα = 0.01. For a load tested pile S for a single pile will be known. whereS = settlement of pile headQ = applied pile loadQa = maximum allowable design loadα = a coefficient approximately

0.01 to 0.01 for driven piles in sand and 0.045 to 0.09 for bored piles in sand

B = pile diameter or breadthρ = elastic deformation of pile shaft.For the purpose of this analysis it is common practice to assume

ρ 'Qactual DpA E

(16)

whereQ = applied pile loadA = average cross-sectional area of the pileDp = length of the pileE = modulus of elasticity of the pile materialThe ultimate or failure load would produce a settlement approximately 3time as great.

2. Settlement from Load Tests: Since time effects are usually negligible in granular soils, the

settlements observed during load tests can be considered as representativeof the long behaviour of the pile.

SETTLEMENT OF A PILE GROUP IN GRANULAR SOILThe settlement of a pile group in granular soil is evaluated on

empirical experience and the methods are less reliable than those used forsingle piles because of the limited data that are available. It isrecommended that the settlement of a pile group be evaluated on the basisproposed by Skempton et al (1953).

The settlement of a pile groups Sgroup is always larger than thatof the individual piles forming the group.

Sgroup ' αg S (17)

whereS = settlement of a single pile under its allowable loadαg = group settlement ratio; a function of the dimension of the

group and of the pile spacing, or of the ratio Bg/B (i.e. thewidth of the pile group to the diameter of the individual pilesas follows:

Bg/B = 1 5 10 20 40 60αg = 1 3.5 5 7.5 10 12

PILES IN COHESIVE SOILSFor practical design of piles in clay engineers generally must

base their calculations of the working and failure loads on conditions ata relatively short time after installation. The reliability of thesecalculations is generally assessed by loading tests also made a relativelyshort time after installation although time effects may be appreciable.


Figure 10. Friction pile force distribution (a) at point 'A' inFig. 9; (b) at point 'B' in Fig. 9; (c) at point 'D' in Fig. 9.

Figure 11. Typical design factors for adhesion based on soilshear strength for different penetrations into stiff clay

(e.g. Tomlinson, 1970)

When a pile driven in cohesive soil is subject to an increasingcompressive load (over a period of days) the resulting load settlementrelationship is as shown in Figure 9. Up to point A the curve is relativelyelastic. At point B when full skin friction is developed, some slippageoccurs between A and B but this is small and if unloading occurs to pointC only a small permanent set occurs. Generally movements of about1/2% of the diameter are required to mobilize full skin friction whilemovement of about 10% of the diameter would be required to mobilize thefull base resistance (shown by point D). Further load then causes the pileto plunge downwards producing large settlements.

The mobilization of resistance of a pile in cohesive soil occursfirst along the shaft as given by Figure 10(a) corresponding to point A inFigure 9. Then at the point B in Figure 9 full skin friction is mobilizedalong with partial end resistance as shown in Figure 10(b). At point D inFigure 9 maximum end resistance is also mobilized as shown in Figure10(c). In fact in some clays some loss of skin friction may have occurredat this point, however, this is generally neglected so that the concept ofseparate evaluation of shaft and base resistance forms the basic of ̀ static'calculations of the pile carrying capacity.

1. Limitations of Design Methods: Design methods for piles in cohesive soils are in some cases

of doubtful reliability. This is particularly so for the bearing capacity offriction piles in clays of medium to high shear strength. Therefore, thedesign methods described in later sections must be used with caution andessentially only for:(a) the preliminary design of large foundations. In this case in situ full

scale load tests should be performed as part of the final design or atthe beginning of construction.

(b) the design of small foundations, provided adequate safety factors areused.

Settlements of groups of friction piles in clay are estimated bymeans of the methods normally used for shallow foundations with anadditional empirical assumption concerning the transfer of load from thepiles to the soil. Consequently, settlement estimates will be reliable onlyin terms of an order of magnitude. Differential settlements are difficult topredict.

2. Disturbance Caused by Driving:Piles driven into cohesive soils induce some disturbance which

is a function of:(a) the soil properties, particularly sensitivity,(b) the geometry of the pile foundation (diameter of piles, number and

spacing of piles in the groups), and(c) the driving method and sequence.

This disturbance results in a temporary loss of strength in somesoils and a corresponding reduction of support provided by the piles. Insome cases such as in soft sensitive clays, complete remoulding of the claymay occur with the result that further construction becomes impossible.The effect of disturbance diminishes with time following driving as thesoil adjacent to the pile consolidates. This results in an increase in the

bearing capacity of the pile. This increase in capacity occurs at a slowerrate around a dense concrete or a steel pile than around a timber pile.Load testing of a pile in clay should not be carried out without anawareness of these processes. It is advisable to delay load testing for atleast two weeks after driving and preferably for a longer period.

3. Pore Water Pressures Induced by Driving:Driving piles in clay generates high pore water pressures, the

effect of which is to:(a) temporarily reduce the bearing capacity of the piles,(b) affect the process of reconsolidation of the clay around the pile

thereby making it necessary to delay the application of the load,(c) alter the natural stability condition in sloping ground. (Examples

exist of landslides triggered by pile driving operations.)As demonstrated by Lo and Stermac (1985), pore water

pressures at the end of driving can, in a first approximation, be assumedequal to the effective initial overburden pressure along the full length ofthe pile within a ring equal in width to the pile diameter. Asreconsolidation of clay around the pile occurs the high pore waterpressures are diminished by gradual redistribution of stresses to the lessdisturbed soil further from the pile.

ALLOWABLE LOAD ON A SINGLE PILE IN COHESIVE SOILSPiles in cohesive soils generally derive their load capacity from

shaft adhesion or friction. However, in very stiff clays or in cohesive tills,a substantial point resistance may be mobilized which, for large diameterbored piles, may represent the total bearing capacity of the pile.


1. Total Stress vs Effective Stress Approach:Until recent times, it was the general practice to evaluate the

bearing capacity of piles in clay from a total stress approach (i.e., on thebasis of the undrained shear strength cu of the clay). Empiricalcorrelations between cu and the point resistance and skin friction on a pilehave been developed, but these have not proved entirely reliable,particularly for cu in excess of 25 kPa and analysis in terms of effectivestresses appear more rational.

2. Driven Piles in Clays where cu < 100 kPa:A pile driven in clay with an undrained shear strength of less

than 100 kPa derives its load capacity almost entirely from shaft adhesionor friction.

For estimating the ultimate capacity in terms of total stresses, it iscommon practice to determine the ultimate load capacity of a single pilefrom the formula:

Qf ' α cu As (18)

whereQf = the ultimate load capacityα = the adhesion factor, derived from Figure 11cu = the undrained shear strengthAs = the surface area of the pile shaft.The values of α are empirical and actual adhesion may differ significantlyfrom these values depending on the geometry of the foundation, thedriving method and sequence, the properties of the clay and time effects.The ultimate capacity of piles resulting from the above formula should beconfirmed by load tests.

In estimating the ultimate capacity in terms of effective stressesrecent investigations suggest that the ultimate load capacity of a singlepile in clay may be derived from:

Qf ' As τs (19)

whereQf = ultimate load capacityAs = surface area of pile shaftτs = average effective shaft frictionτs is normally computed at various depths along the pile shaft and the totalintegrated over the embedment depth.

τs ' σ)o Ko tanδ (20)

whereσo' = effective overburden pressure at the considered depthKo = at rest earth pressure coefficientδ = effective angle of friction between the clay and the pile shaft.

This method requires that Ko and δ be known. Both parameters aredifficult to measure. However, available test results indicate that, forclays with cu less than 100 kPa, which are not heavily over consolidated,the factor (Ko tan δ) varies only from 0.25 to 0.40. For design purposesa typical value of 0.3 may be used, so that:

τs ' 0.3σ)o (21)

It is recommended that the calculated ultimate pile capacity beconfirmed by load tests.

To obtain the allowable load capacity of the pile, from the ultimatecapacities given by Equations (18) and (19), it is recommended that afactor of safety of at least 2.5 be applied and that load tests also be carriedout during construction of the foundation. In cases where no load tests areperformed, a factor of safety of at least 3.0 should be applied.

3. Driven Piles in Clays where cu > 100 kPa:A pile driven in clay with an undrained shear strength in excess of

100 kPa derives its bearing capacity from both shaft adhesion or frictionand point resistance.

The shaft friction of such a pile however, cannot be predictedwith any degree of reliability because little is known of the effect ofdriving on the adhesion and on the final effective contact area betweenclay and pile. For preliminary design, however, the relationship shown inFigure 11 can be used.

For final design purposes it is suggested that the ultimatebearing capacity be determined by pile loading tests. Tapered piles havebeen suggested as a means for developing closer contact. However, theeffective stress analysis above suggests that more shaft and end bearingarea should be provided at lower levels to take advantage of the higherfriction and end bearing resistance available.

4. Bored Piles in Clays where cu > 100 kPa:Large diameter bored piles with or without enlarged or belled

bases are successfully used in clays or cohesive tills where cu > 100 kPa.They derive their load carrying capacity from both shaft adhesion orfriction and point resistance. Present design methods have been derivedfrom extensive studies on bored piles in London clays. Considering theunusual properties of these soils, the generalization of empirical designparameters to other types of cohesive soils should be made with caution.

In estimating the shaft adhesion in terms of total stresses theultimate load may be obtained from:

Qfs ' ca As (22)

whereQfs = ultimate shaft resistanceAs = surface area of pile shaftca = ultimate adhesion.Experience shows that:

ca ' 0.3 to 0.4 cu (23)

The actual value of ca is greatly affected by the excavationprocess which may cause remoulding or softening of the clay, and by thestructure of the clay such as its degree of fissuring. it is recommended thatca be determined from the minimum undrained shear strength cu, and thatit be limited to a maximum of 100 kPa.

In estimating the shaft adhesion in terms of effective stressesthe same approach and formula as given for driven piles may be applied.However, the earth pressure coefficient Ko is highly dependent upon thegeological history of a particular clay. It is therefore impossible to givetypical values of (Ko tan δ), and the method may be applied only where Kohas been determined by appropriate methods or evaluated from load tests.

Qfp ' N(

c cu Ap (24)

whereQfp = ultimate point loadAp = cross-sectional area of pile pointcu = minimum undrained shear strength of the clay at pile point

levelNc

* = a bearing capacity coefficient which is a function of the pilepoint diameter as follows:

Point Diameter Nc*

Less than 0.5 m 90.5 to 1 m 7Greater than 1 m 6

In very stiff clays and tills were samples are difficult to retrieveand cu is not easily measured, the pressuremeter method of estimating theallowable bearing pressure may be used.


Figure 12. Block foundation behaviour of pile group in adeep soft soil deposit.

The allowable loads on bored piles are determined from acombination of shaft adhesion and point resistance, after the applicationof appropriate factors of safety. The relative contribution of the shaftadhesion and the point resistance is a function of the rigidity of the pileand the compressibility of the clay around the shaft and below the base ofthe pile.

If the soil below the base has the same or greatercompressibility than the soil around the shaft, the allowable design loadon the pile may be taken as

Qd '1

2.5(Qfs % Qfp) (25)

If the soil below the base has the same or less compressibilitythan the soil around the shaft, the allowable design load on the pile maybe taken as:

Qd '12Qfp (26)

While the above formulas may be considered as limiting cases,the decision to consider shaft adhesion in addition to base resistance mustbe made with care and only after properly designed and interpreted loadtests are carried out. Such tests should indicate whether or not theresistance available is commensurate with strain both around the shaft andat the base, and any possibility of reduction in that resistance with time.The selection of the allowable load should be based upon permissible pilemovement, as determined from these tests.

5. Pile Capacity from Load Tests:The ultimate load capacity of piles in clays should be

determined or confirmed by means of full scale load tests.

Load tests cannot be performed slowly enough for anevaluation of the time-settlement behaviour of piles in clays; only theultimate load capacity may be determined. Under such conditions it isrecommended that the method, known as the constant rate of penetrationmethod, is best suited for a rapid and accurate evaluation of the ultimatepile capacity in clays.

To obtain the allowable pile capacity a factor of safety of 2.5

should be applied to the ultimate pile capacity.

ALLOWABLE LOAD ON A PILE GROUP IN COHESIVE SOILIf piles in groups are driven through soft clay, loose sand, or

fill, to terminate in a stiff clay, there is no risk of general shear failure ofthe group provided that there is an adequate safety factor against failureof the single pile. However, the settlement of the group must becalculated as described later.

If it is necessary to terminate a group of piles entirely withina soft clay (this is not desirable practice) then the safety factor against'block failure' of the group must be calculated. The ultimate bearingcapacity of the block of soil encompassed by the group shown in Figure12 is calculated as though the group was a footing of depth Dp, width Band length L. Because the side of such a footing is ideally the cohesiveshearing strength cu of the clay. If the piles are large displacement pilesand considerable remoulding has occurred the cu would have been reducedto a value close to its remoulded value along the block sides. In all casesthe possibility of block failure should be checked as well as the possibilityof failure by individual action. Terzaghi and Peck (1967) recommend afactor of safety of 3 against block failure.

1. Piles in Clays where cu < 100 kPa:When a group of driven friction piles are formed in clays with

undrained shear strengths of less than 100 kPa and block failure does notgovern, then the ultimate load capacity of the group is usually less than thesum of the ultimate load capacities of the individual piles in the group.For spacings of 2.5 to 4 times the average pile diameter, the groupefficiency can be taken to be equal to 70% of the sum of the capacities ofthe individual piles.

2. Piles in Clay where cu > 100 kPa:It is common practice to neglect group effects in the

determination of the load capacity of pile groups in clays with cu in excessof 100 kPa. Thus the capacity of the group is given by the lesser of a blockfailure or the sum of the capacity of the individual piles.

SETTLEMENT OF A SINGLE PILE IN COHESIVE SOIL1. Piles in Clays where cu < 100 kPa:

Piles in clays where cu is less than 100 kPa are seldom used assingle piles but they act as single piles in groups where the spacing is inexcess of 7 times the pile diameter and where the pile cap is not in contactwith the soil. In this case limited field observations indicate that thesettlement is due to local shear deformations along the pile shaft ratherthan to consolidation settlements, and is therefore very limited. If suchcases occur it is recommended that special analyses, based on load testsbe performed.

2. Piles in Clays where cu > 100 kPa:Because of their high load capacity, bored piles in stiff clays

are often used as single piles.

The analysis of settlement of single piles in stiff clays isdifficult at the present time because little data is available on the actualbehaviour of such piles. Discussions on the validity of available methodsof analysis are found in the reference list at the end of these notes.

Where it is important to evaluate settlements the use of loadtests, designed, carried out and interpreted by a person competent in thisfield is recommended.

SETTLEMENT OF A PILE GROUP IN COHESIVE SOIL1. Introduction:

Settlements of groups of piles in clay are estimated by meansof methods normally used for shallow foundations, after application of anadditional empirical assumption concerning the transfer of load from thepile group of the soil. Total and differential settlement predictions willtherefore be less reliable for pile groups than for footings.


Figure 13. Stress distribution beneath pile group in clayusing theoretical footing concept.

2. Suggested Method:The following method, proposed by Terzaghi and Peck (1948),

and confirmed by limited field observations, is suggested for theevaluation of the settlement of pile groups in clay. The load carried by thepile group is assumed to be transferred to the soil through a theoreticalfooting located at 1/3 the pile length up from the pile point (Figure 13).The load is assumed to spread within the frustum of a pyramid of sideslopes at 30E and to cause uniform additional vertical pressure at lowerlevels, the pressure at any level being equal to the load carried by thegroup divided by the cross-sectional area of the pyramid at that level. Thesettlement calculation then follows the method used for shallowfoundations.

NEGATIVE SKIN FRICTION OF PILES IN COHESIVE SOIL1. Introduction:

When a clay deposit, in which or through which piles havebeen installed, is subject to consolidation, the resulting downwardmovement of the clay around the piles induces downdrag forces on thepiles. This force, which tends to reduce the usable pile capacity, is callednegative skin friction.

Negative skin friction develops in cases where piles are placedin soil that is consolidating under an applied load, or where a fill is placedaround an existing pile foundation. It develops in clay deposits subject togeneral subsidence resulting from lowering of the ground water table orother causes. It may also be generated by reconsolidation of theremoulded clay layer around any driven pile. The magnitude andsignificance of negative skin friction in the design of piles in clays differswidely from case to case.

Negative skin friction is a pile capacity problem only in thecase of a true bearing pile on rock, where the pile capacity is generallycontrolled by its structural strength and where settlements of the pile arenegligible. In all other cases of piles bearing in compressible soils, wherethe pile capacity is controlled by point resistance and shaft adhesion orfriction, the problem of negative skin friction may be regarded as asettlement problem (see Fellenius, 1972).

2. Magnitude of Negative Skin Friction:The most common method of computing negative skin friction

τn is to assume

τn ' α cu (27)

whereα = the adhesion factor given in Figure 11cu = the undrained shear strength

For an isolated pile the total force Fn due to negative skinfriction is therefore:

Fn ' τn As (28)

whereAs = the area of pile in contact with the settling clay layer.

For pile groups the maximum force Fn on a pile is limited bythe weight of clay between the piles so that:

Fn ' τn As # S2p H γ (29)

whereSp = the pile spacingH = the thickness of the clay layerγ = the unit weight of clay

Field observations on instrumented piles have shown that themagnitude of negative skin friction is a function of the effective stressacting on the pile and may be expressed as:

τn ' σ)o K tan γ (30)

whereσ/

o = the effective overburden pressure including the stress from theconsolidated portion of the fill

K = the coefficient of earth pressure equal to or greater than Koδ = the effective angle of friction between the clay and the pile

material.For all practical purposes it may be assumed that:

τn ' 0.3 σ)o (31)

3. Means for Reducing the Negative Skin Friction:For piles driven to rock the occurrence of negative skin friction

means that a considerable increase of structural strength and bearingcapacity above that needed to carry the building load will be required.Negative skin friction acting on driven piles may be reduced by theapplication of bituminous or other viscous coatings to the pile surfaces orin the case of steel piles by using the electro-osmosis technique. For cast-in-place piles floating sleeves have been used successfully. The choice ofthe appropriate method and the evaluation of its effectiveness, in anyparticular case, should be left to a person competent in this field of work.

SPECIAL PROBLEMS: PILES IN COHESIVE SOILS1. Piles Driven Near Slopes:

As discussed earlier driving piles in clay generates pore waterpressures in clay. After driving, these pore water pressures are distributedin the clay mass over a considerable distance from the piles. If piles aredriven in the vicinity of a slope, the increase in pore pressure produced bydriving may cause failure of the slope. This phenomenon must be takeninto account in design, particularly in sensitive clays by:(a) analysis of the stability of the slope before and after driving, and(b) instrumentation of the clay layer for pore water pressure

measurements during driving.

If necessary, pore water pressures can be reduced by:(a) the use of proper driving techniques and sequences (preboring is an


Figure 14. Safety of pile group against punching failure.

efficient way of reducing pore water pressures), and(b) the use of drain strips attached to the surface of the piles.

2. Heave Due to Pile Driving:When piles are driven in clays, the volume of soil displaced by

the pile generally causes a heave of the soil surface. The heave ofadjacent piles may also occur, possibly resulting in a reduction in thecapacity of these piles. This problem is of particular significance whenlarge pile groups are driven.

Experience has shown that the heaved volume at the groundsurface is generally of the order of 40% to 60% of the pile volume. Ifsuch heave is unacceptable, preboring is the method usually applied toreduce it.

3. Piles in Swelling Clays:Piles driven in swelling clays may be subjected to uplift forces

in the upper active layer as the result of the swelling process. The effectof these forces on the structural integrity of the piles or on thedeformations of the foundation must be taken into account in design by:(a) neglecting the contribution to the bearing capacity of that part of the

pile embedded in than active layer of swelling clay,(b) ensuring that the uplift resistance of that portion of the pile located

below the active layer of swelling clay is sufficient to withstanduplift forces generated in the swelling clay layer, and

(c) ensuring that the structural resistance of the pile is sufficient towithstand the uplift forces.

If necessary, uplift forces may be eliminated by isolating thepiles from the swelling clay in the active layer. This can be achieved by

the use of floating sleeves or by the application of bituminous or otherviscous coatings applied to the pile surface.

PILES IN LAYERED DEPOSITSPiles are commonly driven through a layer of soft soil to a

competent stratum or through alternating layers of competent and non-competent soils. In such cases the pile foundation is generally designedin accordance with the methods already described but with modificationcontingent upon the prevailing subsoil conditions. In designing such pilesparticular attention should be paid to:(a) the relative stiffness and strengths of the different layers penetrated

by the piles. (This will lead to an evaluation of the probable relativecontribution of these layers to the pile capacity), and

(b) the stratigraphy immediately below the pile tip which influences thestability and the settlement of the pile groups.

ALLOWABLE PILE CAPACITY OF PILES IN LAYERED SOILThe relative contribution of the various strata penetrated by a

pile to the capacity of that pile is primarily a function of the relativestiffness of these layers and of the type of pile.

(1) End Bearing Piles:Piles extending through layers of weaker soils to a very

competent stratum such as bedrock or very dense till or gravel should beassumed to derive their bearing capacities only from the resistancemobilized in this supporting stratum. Because of the comparatively highstiffness of the supporting stratum and the pile, the relative displacementsof pile and soil in the upper layers are generally insufficient to mobilizeany significant shaft friction.

Similarly for compacted concrete piles it should not be assumed thatany other resistance will be mobilized other than that obtained at thecompacted base.

(2) Piles in a Two-layer Deposit:For piles extending through a layer of soft soil of some depth into a

deep deposit of competent soil, such as sand, it is generally assumed thattheir bearing capacities are derived from only the point resistance and skinfriction developed in the lower layer. The upper layer is considered tocontribute to the pile capacity only by increasing the overburden pressureused in the computation.

In cases where the bearing stratum is granular soil the critical depthis taken from the upper surface of that stratum.

(3) Piles in a Multi-layer Deposit:Piles driven through a multi-layer deposit may derive their load

capacities from both skin friction and point resistance. However, theevaluation of the relative importance of skin friction and point resistanceare difficult and may need to be confirmed by load tests. Wheneverpossible, piles in multi-layer deposits should be driven to a layer ofsufficient strength and thickness that it may be assumed that they derivetheir load capacity entirely from that layer. In such a case, the loadcapacity may be determined according to the methods previously given.It is essential to check that the bearing layer extends below the proposedpile tip elevation to a depth sufficient to ensure safety against a punchingfailure of the bearing layer into a lower weaker material. Safety againsta punching failure may be evaluated by the following empirical method.The total load Q on the pile group is assumed to be transferred to the soilthrough a theoretical footing located at the base of the pile group. Theload is assumed to be spread within the frustum of a pyramid with sideslopes at 30E. The resulting stress q' at the upper limit of the lowerweaker layer may then be calculated as shown in Figure 14. In the generalcase where this layer is of cohesive soil with an undrained shear strengthcu the margin of safety against a punching failure will be sufficient if:

qe ' # 3 cu (32)


SETTLEMENT OF PILE GROUPS IN LAYERED SOILSThe methods of evaluating settlements of pile groups previously

given are applicable to groups in layered deposits provided the layer inwhich the pile tips are located extends to a depth at least equal to 3 timesthe width of the pile group below the base of the group.

Where alternating layers of compressible and non-compressible soilsare present below the pile tips, the settlement is assumed to originate in thecompressible layers only. The total load Q on the pile group is assumedto be transferred to and distributed in the soil as indicated in Figure 14.The stresses acting on the compressible layers below the pile tips arecomputed and the corresponding settlements are determined according tostandard settlement analysis. This analysis usually leads to anoverestimate of the settlements.

REFERENCES

Canadian Foundation Engineering Manual, 1978, Canadian GeotechnicalSociety, Montreal

Chellis, R.D., 1961. Pile Foundation, 2nd Ed., McGraw Hill, New York.

Tomlinson, J.J., 1977. Pile Design and Construction Practice, GardenCity Press Ltd., Letchworth.

Deep Foundations on Rock

Coates, D.F., 1967. Rock Mechanics Principles, Mines BranchMonograph 874, Queen's Printer, Ottawa, p. 358.

Menard, L., 1965. "Regles pour le calcul de la force portante et dutassement des foundation en fonction des resultats Pressiometriques".Proceedings of the Sixth Conference on Soil Mechanics and FoundationEngineering,Paris, Volume 2, pp. 11-15.

DeBeer, E.E., 1963. "The scale effect in the transportation of the resultsof deep sounding tests on the ultimate bearing capacity of piles andcaisson foundations". Geotechnique, Volume 13, pp. 39-75.

Ireland, H.O., 1957. "Pulling tests on piles in sand". Proceedings of theFourth International Conference on Soil Mechanics and FoundationEngineering, London, Volume 2, pp. 42-45.

Kishida, H., and Meyerhof, G.F., 1965. "Bearing capacity of pile groupsunder eccentric loads in sand". Proceedings of the Sixth InternationalConference on Soil Mechanics and Foundation Engineering, Montreal,Volume 2, pp. 270-274.

Lee, K.S. and Seed, H.B., 1967. "Cyclic stress conditions causingliquefaction of sand". Journal of the Soil Mechanics and FoundationDivision, Proceedings American Society of Civil Engineers. Volume 93,No. SM1, pp. 47-70.

Meyerhof, G.C., 1956. "Penetration tests and bearing capacity ofcohesionless soils". Journal of the Geotechnical Engineering Division,Proceedings American Society of Civil Engineers, Volume 102, No GT3,pp 195 - 228.

Robinsky, E.I. and Cragg, C.G.B., 1973. "Volume displacement effectson pile capacity in coarse sand". Canadian Geotechnical Journal, Volume10, No. 4, pp.

Selby, K.G., 1970. "Pile tests of Beach River". Canadian GeotechnicalJournal, Volume 7, No. 4, pp. 470-471.

Skempton, A.W., Vassin, A.A. and Gibson, R.E., 1953. "Theorie de la

force portante des pieux dans le sable". Ann. Inst. Tech. Bati, TravauxPubs, 63-64, 285-290.

Van Der Veen, C., and Boersma, L, 1957. "The bearing capacity of a pilepredetermined by a cone penetration test". Proceedings of the FourthInternational Conference on Soil Mechanics and Foundation Engineering,London, Volume 2, pp. 72-75.

Vesic, A.S., 1969. "Experiments with Instrumented Pile Groups in Sand".Conference on Performance of Deep Foundations, American Society forTesting Materials, Special Technical Publications 444, pp. 177-222.

Vesic, A.S., 1970. "Tests on instrumented piles, Ogeechee River site".Journal of the Soil Mechanics and Foundation Division, ProceedingsAmerican Society of Civil Engineers, Volume 96, No. SM2, pp. 561-584.

Vesic, A.S., 1977. "Design of pile foundations". National CooperativeHighway Research Program, Synthesis of highway Practice No. 42,Transportation Research Board, Washington, D.C., p. 68.

Yang, N.C., 1970. "Relaxation of pile in sand and inorganic silt". Journalof the Soil Mechanics and Foundation Division, Proceedings AmericanSociety of Civil Engineers, Volume 96, No. SM2, pp. 395-410.

Piles in Cohesive Soils

Barnard, R., 1956. Pipe piles for bridges and buildings. Armco Bulletin561, Armco Drainage and Metal Products Inc., Middleton, Ohio.

Bjerrum, L. and Johannessen, I., 1961. "Pore pressures resulting fromdriving piles in soft clay". Proceedings of the Conference on PorePressures and Suction in Soils, London, Butterworths, pp

Bjerrun, L., Johannessen, I.J. and Eide,O., 1968. "Reduction of negativeskin friction on steel piles to rock". Proceedings of the SeventhInternational Conference on Soil Mechanics and Foundation Engineering,Mexico, Volume 2, pp. 27-34.

Bozozuk, M., 1972. "Downdrag measurements on a 160 ft. floating pipetest pile in marine clay". Canadian Geotechnical Journal, Volume 9, pp127-136.

Brezinski, L.S., 1969. "Behaviour of an overpass carried on footings andfriction piles". Canadian Geotechnical Journal, Volume 6, pp. 369-382.

Burland, J.B., 1973. "Shaft friction of piles in clay - a simple fundamentalapproach". Ground Engineering, Volume 6, No. 3, pp. 30-42.

Clark, J.I., and Meyerhof, G.G., 1972. "The behaviour of piles driven inclay. I. An investigation of soil stress and pore water pressure as relatedto soil properties". Canadian Geotechnical Journal, Volume 9, pp. 351-373.

Clark, J.I. and Meyerhof, G.G.,1973. "The behaviour of piles driven inclay. II. Investigation of the bearing capacity of using total and effectivestrength parameters". Canadian Geotechnical Journal, Volume 10, pp. 86-102.

Cummings, A.E. Kerkhoff, G.O. and Peck, R.B., 1950. "Effect of drivingpiles into soft clays". Transactions of the American Society of CivilEngineers, Volume 115, pp. 275-285.

Eide, P., Hutchingson, J.N. and Landva, A., 1961. "Short and long termloading of a friction pile in clay". Proceedings of the Fifth InternationalConference on Soil Mechanics and Foundation Engineering, Paris,Volume 2, pp. 45-53.


Flaate, K., 1972. "Effects of pile driving in clay". Canadian GeotechnicalJournal, Volume 9, pp. 81-88.

Fellenius, B.H., 1972. "Downdrag n piles in clay due to negative skinfriction". Canadian Geotechnical Journal, Volume 9, pp. 323-337.

Lo, K.Y. and Stermac, A.G., 1965. "Induced pore pressures during piledriving operations". Proceedings of the Sixth International Conference onSoil Mechanics and Foundation Engineering, Montreal, Volume 2, pp.285-289.

Orrje, P., and Broms, B., 1967. "Effects of pile driving on soilproperties". Journal of the Soil Mechanics and Foundation Division,Proceedings American Society of Civil Engineers, Volume 93, No. SM5,pp. 59-74.

Skempton, A.W., 1959. Cast-oil-place bored piles in London clay.Geotechnique, Volume 9, pp. 153-173.

Stermac, A.G., Selby, K.G., and Devata, M., 1969. "Behaviour of varioustypes of piles in stiff clay". Proceedings of the Seventh Internationalconference on Soil Mechanics and Foundation Engineering, Mexico,Volume 2, pp 239-246.

Terzaghi, K., and Peck. R.B., 1948, 1967. Soil Mechanics in EngineeringPractice, J. Wiley and Sons, N.Y.

Tomlinson, M.J., 1971. "Some effects of pile driving on skin friction".Proceedings of the Conference on the Behaviour of Piles, The Institute ofCivil Engineers, London,pp. 107-113 (see reply to Discussion).

Trow, W. and Bradstock, J., 1972. "Instrumented foundations for two 42-storey buildings on till, Metropolitan Toronto:. Canadian GeotechnicalJournal, Volume 9, pp 290-303.

Whitaker, T., 1970. The design of piles foundations. Pergamon Press,London.

Whitaker, T., and Cooke, R.W., 1966. An investigation of the shaft andbase resistance of large bored piles in London clay. Proceedings of theSymposium on Large Bored Piles, Institution of Civil Engineers,London,pp. 7-49.


EXAMPLE 1 Illustrative Example of Why Pile Driving Formulae based on

Energy Input Don't Work_________________________________________________________

ENERGY OF IMPACT' W H W HVELOCITY OF WEIGHT ON IMPACT' 2gH 2g 2H '

MOMENTUM OF IMPACT

'Wg

º ' W 2gH W2g

2 gH

To solve problem momentum of impact needs to be equated tomomentum dissipation after impact. Presently only the "WaveEquation" method of analysis attempts to do this with any degree ofexactness and even so it cannot account for pile freeze or relaxation.

Since momentum of impact is driving force and note energy itbecomes obvious why Pile driving Formulae based on energyconsiderations don't give good results.

EXAMPLE 2Calculate the allowable bearing capacity load of a pile cast-in-placeand socketed into rock. The socket/pile diameter is 300 mm and thesocket depth is 500 mm. Site investigations established the rockdiscontinuities as having a thickness of 3 mm spaced at 500 mm. Therock strength was measured as 4000 kPa.

qallowable ' qu&core Ksp d&&&&&&&&&&&&&

qu&core ' 4000 kPa&&&&&&&&&&&&&

Ksp [Fs OF 3] '3 %

Discontinuity SpacingSocket Diaameter

10 1 % 300 Discontinuity ThichnessDiscontinuity Spacing

'

3 %500300

10 1 % 300 3500

' 0.279 OR FROM FIGURE&&&&&&&&&&&&&

d ' 1.0 % 0.4HsB

' 1.0 % 0.4 500300

' 1.67 # 3.0

&&&&&&&&&&&&&

qa ' 4000 0.279 1.67 ' 1860 kPa

Qa ' qaπ B 2

4' 131 kN


Depth of SocketPile Diameter

0 1 2 3 5 7

Kb 0.8 2.8 3.6 4.2 4.9 5.2

EXAMPLE 3Calculate the allowable bearing capacity load of a cast-in-place andsocketed pile into rock. The socket/pile diameter is 300 mm and thesocket =depth is 500 mm. Tests established the allowable shaft bondshearing strength as 550 kPa.

Qallowable ' π B Hs τa' 3.14 0.3 0.5 550' 259 kN

EXAMPLE 4Calculate the failure bearing capacity load of a cast-in-place socketedpile into rock. The socket/pile diameter is 300 mm diameter and thesocket depth is 500 mm. Pressuremeter tests gave a limit pressureof 6000 kPa and an at rest lateral pressure in rock of 1000 kPa. Theeffective overburden on the tip of the 20 m length pile 200 kPa.

FAILURE CAPACITY OF PILE ' Qfqf ' Kb (pR & po) % σo

/

&&&&&&&&&&&&&

Kb ' FROM TABLEHsB

' 1.67

GIVES approx 3.3&&&&&&&&&&&&&&&

qf ' 3.3 (6000 & 1000) % 200' 16.7 kPa

Qf ' π 0.152 × 16.7 ' 1.18 kN


Spacing ofDiscontinuities

< 3 m

1-3 m

0.3-1m

80-300mm

αm 1 0.75 0.5 0.25

EXAMPLE 5Estimate the settlement of a pile socketed in rock on the basis of thefollowing in-situ pressuremeter test data:Design tip contact pressure = 4 MPa.;Socket dia. = 0.4 m.;Average pressuremeter modulus over 3 diameters below the tip = 40 kPa.;Discontinuity spacing in rock = 0.5 m.;

Settlement is approximated by:

S 'qd B

9 αm E'

4 0.49 0.5 40

' 0.0089 m ' 8.9 mm

whereS = the settlement,qd = the design pressure,B = the tip diameter (breadth) of the pile,E = the average pressuremeter modulus in the zone extending

3 diameters below the pile tip,αm = a coefficient which is a function of the structure of the rock

mass as follows

EXAMPLE 6Calculate for a 400 mm pile driven 20 m into sand the (a) failure shaftresistance; (b) failure base resistance (c) allowable bearing capacityload. Standard Penetration blow counts gave an average over theshaft length of 10 blows/300 mm and a count at the tip elevation of 30blows/300 mm. Neglect pile weight.

(a) Qshaft ' 2 N Ashaft' 2 10 π 0.4 20' 502 kN

(b) Qbase ' 400 N Atip

' 400 30 π 0.42

4' 1508 kN

(c) Qallow 'Qf4

'Qs % Qb

4

'502 % 1508

4' 502 kN


EXAMPLE 7Calculate the bearing capacity of a 12 m long pile driven into

sand having a water table at the ground surface. The diameter of thepile is 0.3 m. The soil unit weight is 19 kN/m3 and friction angle 30E.Neglect the self weight of the pile and assume the coefficient of earthpressure = 1 - sinφ and δ = 2φ/3. (A) Neglect depth limitations (B)Assuming critical depth Dc = 7B. Compare the bearing capacity of a6 x 6 pile block having a spacing of 1.2 m using the above pile datawith the piles (a) as a block (b) singularly._________________________________________________________

NO LIMITATION ON Dc

QB ' Ab γ) Df N

(

q where N (

q ' 30Note Nγ term is small (Df > > B) and neglected

'π4

0.32 (18 & 9.81) 12 (30) ' 208 kN

Qs ' mDf

oπ Dia (γ & γw ) (1&sinφ) z (tanδ) dz

' π 0.3 (18 & 9.81) (1 & sin30) z2

2tan20

12

0' 101 kN

QT ' QB % Qs ' 208 % 101 ' 309kN

LIMITATION ON Dc = 7B

QB ' Ab γ) Dc N

(

q 'π4

0.32 (18 & 9.81) (7×0.3) 30

' 36.4 kN

Qs ' m (perimeter distance) (side friction) dzNOTE:& side friction constant below Dc

' mDc

0

π Dia [(γ & γw) (1 & sinφ) z tanδ] dz

% mDp

Dc

π Dia [(γ & γw) (1 & sinφ) Dc tanδ] dz

' π 0.3 (18&9.81) (1&sin30) z2

2tan20

7×0.3

0

% π 0.3 (18&9.81) (1&sin30) (7×0.3) tan20 (z) 127×0.3

' 3.1 % 29.2 ' 32.3 kN

QT ' 36.4 % 32.3 ' 68.7 kN

BLOCK ACTIONPerimeter distance of block = 4 sides of (5 x spacing + Dia)

= 4 x 6.3 = 25.2 m.

Dc max of block ' 6.3 x 7 > 12m

Qs ' 25.2 mDf

o(γ&γw ) (1&sinφ) z (tanφ) dz

NOTE: φ rather than δ is used since in a block failure thefoundation side is made of soil. Thus a soil to soil failure is occurring

' 25.2 m12

o(18 & 9.81) (1 & sin30) tan30 z dz

' 25.2 (8.19) 0.5 (0.577) 122

2' 4.28 MN

QB ' Ab (γ) Df Nq dq sq % 0.5 γ) B Nγ dγ sγ ) % water uplift

From bearing capacity chart for φ = 30E; Nq = 18; Nγ = 17

dq ' dγ ' 1Df

10 Btan (45 %

φ2

) # 10

sq ' 1

sγ ' 1 &B

2.5 Ldq ' dγ ' 1.33si ' 1sγ ' 0.6

QB ' 6.32 [ (18&9.81) 12 (18) 1.33 × 1% 0.5 (18&9.81) 6.3 (17) 1.33 × 0.6 ]

' 6.32 [ 2.34 % 0.35 ] ' 107 MN % Water Uplift

QT ' QB (including water uplift) % Qs & Ab D γ

' QB (excluding water uplift) % QS & Ab D (γ & γw)

' 107 % 4.28 & 6.32 x 12 x 8.19 x 10&3 ' 106 MN

SINGULARLY

Neglecting Dc limitation = 36 x 309 = 11.1 MN

With Dc limitation = 36 x 68.7 = 2.47 MN


EXAMPLE 8A storage tank 14 metres in diameter when full and including its

foundation results in a pressure of 200 kPa on its base. This tank isbuild on a foundation of 100 piles each 385 mm in diameter driven ina deep bed of clay.

The clay's properties are

φu ' 0;cuσ)o

' 0.25; γ ' 19.81kN/m 3

The water table is at the surface. The contact requires a factorof safety of 2 against failure of each individual pile based on shaftresistance only. Calculate the required length of pile roundedupwards to the nearest metre assuming the adhesion between clayand pile is 0.67 cu. Calculate the factor of safety against block failureof the required pile depth. Assume Nc for a circle increases linearlyfrom 6 at the surface to 9 at a depth 3 times the diameter of the circleand remains constant at this value for greater depths._________________________________________________________SHAFT RESISTANCE OF SINGLE PILE

Shearing strength' cu ' 0.25 σ)o ' 0.25 (γ & γw ) z ' 2.5 z kPa

Adhesion ' 0.67 cu ' 1.675 z kPa

Shaft adhesion'

π DiamDf

oca dz ' 2.02 z 2

2

Df

o

' 1.01D 2f kN

Load per pile 'π4tankDia

2 qNo of piles

'π4

142 200100

' 308kN

F of S ' 2 ' 1.01D 2f

308ˆ Df ' 24.7 ' 25 m ( to nearest metre rounded up )

BLOCK FAILURE OF GROUP

Base resistance ' (cu Nc % γ Df ) (Area of base ) ' 151 MNSelf Wt. of block ' γ Df (Area of base ) ' 76 MN

Base res. & Self Wt. ' cu Ncπ4

( tank dia. )2

' 0.25 (10) 25 6 %3 (25)

42π4

142 ' 75 MN

Adehsion ' π 14 mDf

0

2.5 z ' 35 MN

Note full shear strength is used in block failure since foundation ismade of soil (ie soil to soil failure)

Failure resistance ' Base resistance & SelfWt. % Adhesion' 75 % 35 ' 109 MN

Tank load 'π4

142 2001000

' 31 MN

Block faiulre F of s ' 10931

' 3.5


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