Chart for pile skin friction

CHARTS TO FACILITATE COMPUTATION OF SKIN FRICTION ON DRIVEN NON-TAPERED

PILES IN COHESIONLESS SOIL

GEOTECHNICAL ENGINEERING MANUAL

GEM-11 Revision #2

AUGUST 2015

EB 15-025 Page 1 of 19

GEOTECHNICAL ENGINEERING MANUAL:

CHARTS TO FACILITATE COMPUTATION OF SKIN FRICTION ON DRIVEN

NON-TAPERED PILES IN COHESIONLESS SOIL

GEM-11

Revision #2

STATE OF NEW YORK

DEPARTMENT OF TRANSPORTATION

GEOTECHNICAL ENGINEERING BUREAU

AUGUST 2015

EB 15-025 Page 2 of 19

TABLE OF CONTENTS

ABSTRACT .....................................................................................................................................3

DESIGN PROCEDURE ..................................................................................................................4

EXAMPLE PROBLEM ...................................................................................................................5

DESIGN CHARTS ..........................................................................................................................9

1 φ as a Function of NNY and Po ................................................................................10

2 Pile Type: CIP 10 in. Diameter ..............................................................................11


4 Pile Type: CIP 12 ¾ in. Diameter ..........................................................................13


6 Pile Type: HP 8x36 (48 ton Capacity) ...................................................................15

7 Pile Type: HP 10x42 (56 ton Capacity) .................................................................16



APPENDIX ....................................................................................................................................19

A. Derivation of Design Charts ............................................................................... A-1

B. "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 ....... B-1

C. "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 .....C-1

EB 15-025 Page 3 of 19

ABSTRACT

The Geotechnical Engineering Bureau currently uses the method developed by Nordlund (see

Appendices B and C) to determine the static capacity of a pile in cohesionless soil. This method has

been shown to accurately predict pile lengths and capacities for New York State soils, based on pile

driving records and dynamic load test results. However, the drawbacks to using Nordlund’s method

are that it is complex and time consuming.

The purpose of these charts is to permit a more rapid determination of the sin friction on driven

non-tapered piles in cohesionless soil. The charts in this manual were developed from Nordlund’s

method and results obtained using either Nordlund’s method or this manual should correspond. The

interested reader will find the development of these charts in Appendix A.

EB 15-025 Page 4 of 19

DESIGN PROCEDURE

1. Draw the plot of overburden pressure versus depth at the proposed pile location.

2. Break the soil in layers according to properties.

3. Calculate the average sampler blow count (NNY) for each layer, from the boring logs.

4. Calculate the average overburden pressure (Po) for each layer.

5. Use the values of Po and NNY calculated in Steps 3 and 4 to find θ from Figure 1.

6. Use Po and φ to find qs (side resistance per linear foot (meter) of pile) using the appropriate

chart from Figures 2 through 9 corresponding to the pile type being investigated.

7. Multiply the value of qs by the layer thickness to determine the side resistance for each

layer.

8. Sum the values of side resistance for each layer to determine the total side resistance, QS.

9. Calculate end bearing resistance, QP, as described in Appendices B and C.

10. Sum QS and QP to obtain the total static pile resistance, QT.

EB 15-025 Page 5 of 19

EXAMPLE PROBLEM

The purpose of this example problem is to illustrate the use of the design charts.

Problem: Find the length of a 12¾” diameter CIP pile required to support a design load of 35

tons.

Given: The soil is a Gravelly SAND. The water table is 10 ft. below the existing ground

surface, and the proposed bottom of footing elevation is 5 ft. above the water table

elevation. The sampler blow counts are tabulated below:

Depth Below Existing Ground Surface

(ft.)

NNY

(bpf)

1.5 4

6.5 5

11.5 9

16.5 11

21.5 13

26.5 13

31.5 16

36.5 18

41.5 15

Solution: Follow design procedure.

Draw the plot of overburden pressure (Po) versus depth at the proposed pile location.

Assume: γT = 0.120 kcf

EB 15-025 Page 6 of 19

EB 15-025 Page 7 of 19

EB 15-025 Page 8 of 19

Layer Average

NNY per

Layer

Po at

Midpoint

(ksf)

φ

qs

(kips/ft.)

Layer

Thickness

(ft.)

QS

(kips)

1 5.0 0.90 29° 0.80 5 4

2 11.5 1.78 31° 2.00 20 40

3 17.0 2.60 33° 3.50 10 35

QS = 79

Check point resistance:

Ap = π (d2/4) = 0.887 ft

2

Po = 2.9 ksf use NNY = 15

φ = 32°

From Appendix B, Fig. 1 Nq = 26

QP = (0.887 ft2) x (26) x (2.9 ksf) = 67 kips

QT = QS + QP = 79 + 67 = 146 kips = 73 tons

Since 70 ton of resistance are needed to provide a safety factor of two

against soil bearing capacity failure (2 x 35 ton = 70 tons), a pile length of

35 ft. is sufficient.

PxNxAQ oqPP

EB 15-025 Page 9 of 19

CHARTS TO FACILITATE COMPUTATION OF SKIN FRICTION ON

DRIVEN NON-TAPERED PILES IN COHESIONLESS SOIL

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APPENDIX A

APPENDIX A

EB 15-025 A-1

DERIVATION OF DESIGN CHARTS

The design charts contained in this manual were derived form the method developed by Nordlund

(see Appendices B and C). The development of these charts is shown in this Appendix.

The equation for side resistance of a pile in cohesionless soil is as follows:

Equation 1

Kδ’ depends on the displacement volume of the pile

Cd depends on the least pile perimeter

δ/φ is assumed to be a constant for each pile type

It follows, therefore, that since the factors Kδ’, sin δ, Cd depend on pile type, they may be combined

into one factor for each pile type, for various values of φ.

First, the value of Kδ (for δ=0) must be determined for each pile type. Kδ depends on w, the pile

taper, φ, the soil friction angle, and V, the volume displaced by a 1 ft. length of pile. Since tapered

piles are less frequently used, these charts were developed for non-tapered piles with w=0. A graph

of Kδ vs. V (for δ=0) equal to 25°, 30°, 35°, and 40° may be plotted from the information in Fig. 4

through Fig. 7 in Appendix C. This graph of Kδ vs. V is shown as Figure 10. Using this figure,

values of Kδ for each volume corresponding to a pile type may be found. These values of Kδ are

given in Table 1.

Using the values from Table 1, δ/φ and Cd, it is possible to determine sin δ and Kδ’ (for δ≠φ) for

each pile type. The product of Kδ’, sin δ, and Cd is shown for each pile type in Table 2. The values

of (Kδ’ sin δ Cd) are plotted versus θ in Figure 11 and Figure 12 so values for any friction angle

between 25° and 40° can be determined. The values of (Kδ’ sin δ Cd) and θ are shown for CIP and

H-Piles in Table 3.

If we assume that d=1 ft. in Equation 1, than the value of qs, side resistance per linear foot of depth,

can be defined as follows:

Equation 2

dCKPQ doS )sin( '

CKPq doS )sin( '

APPENDIX A

EB 15-025 A-2

The value of qs can be calculated for different values of Po, for each pile type. The relationship

between qs and Po for various pile types are shown on Figure 2 through Figure 9.

Note that the value of φ must be known to use Figures 2 through 9. Nordlund has correlated φ with

Nc. Nc is the standard sampler blow count for the last foot of driving, corrected for overburden

pressure. The value of Nc is defined as follows:

Equation 3

CN is the correction factor for overburden pressure;

NSTD is the blow count on a sampler for the last foot of driving

using a 140 lb. hammer falling 30 in.

NSTD can be defined in terms of NNY as follows:

Equation 4

NNY is the blow count on a sampler for the last foot of driving

using a 140 lb. hammer falling 30 in.

Substituting Equation 4 into Equation 3 and solving for Nc yields:

Equation 5

N’c is the New York sampler blow count for the last foot of

driving, corrected for overburden pressure.

NSTDc CxNN

NYSTD NxN 29.1

'29.129.1 cNYNc NxNxCxN

APPENDIX A

EB 15-025 A-3

According to Peck, Hanson and Thornburn, the correction factor CN is defined as:

Equation 6

The relationship between φ and NNY is shown on Figure 13. Please note that Figure 13 has been

developed by Nordlund for pile analysis only. This figure should not be used to correct blow counts

for settlement analysis.

If NNY is multiplied by CN, the product will equal the New York sampler blow count corrected for

overburden pressure. Using this relationship and Figure 13, values of φ corresponding to NNY and

Po can be determined. These are shown in Table 4, and plotted in Figure 1.

)(

2077.0

tonsPLogC

o

N

APPENDIX A

EB 15-025 A-4

APPENDIX A

EB 15-025 A-5

Table 1 – Values of Kδ

Pile Type

V

Volume

(ft3/ft)

δ = φ

25° 30° 35° 40°

HP 8x36 0.074 0.68 0.81 1.07 1.53

HP 10x42 0.086 0.69 0.83 1.11 1.61

HP 12x53 0.108 0.71 0.86 1.17 1.75

HP 14x73 0.148 0.73 0.90 1.25 1.93

10 in. CIP 0.545 0.81 1.07 1.60 2.66

12 in. CIP 0.785 0.84 1.12 1.69 2.86

12 ¾ in. CIP 0.887 0.85 1.14 1.73 2.94

14 in. CIP 1.070 0.86 1.16 1.78 3.05

APPENDIX A

EB 15-025 A-6

Table 2

Pile δ/φ Cd (ft.) δ=φ Kδ δ sin δ Kδ

Corr.

Factor

Kδ’ (Kδ’ sin δ Cd)

HP 8x36 0.73 2.67 25° 0.68 18.25 0.313 0.94 0.639 0.53

30° 0.81 21.90 0.373 0.90 0.729 0.73

35° 1.07 25.55 0.431 0.86 0.920 1.06

40° 1.53 29.20 0.488 0.84 1.285 1.67

HP 10x42 0.74 3.33 25° 0.69 18.5 0.317 0.95 0.656 0.69

30° 0.83 22.2 0.378 0.91 0.755 0.95

35° 1.11 25.9 0.437 0.87 0.966 1.41

40° 1.61 29.6 0.494 0.84 1.352 2.22

HP 12x53 0.76 4.00 25° 0.71 19.0 0.326 0.96 0.677 0.88

30° 0.86 22.8 0.388 0.92 0.791 1.23

35° 1.17 26.6 0.448 0.89 1.041 1.87

40° 1.75 30.4 0.506 0.86 1.505 3.05

HP 14x73 0.78 4.67 25° 0.73 19.50 0.334 0.96 0.701 1.09

30° 0.90 23.40 0.397 0.93 0.837 1.55

35° 1.25 27.30 0.459 0.90 1.125 2.41

40° 1.93 31.20 0.518 0.87 1.679 4.06

10 in. CIP 0.50 2.62 25° 0.81 12.50 0.216 0.81 0.656 0.37

30° 1.07 15.00 0.259 0.75 0.803 0.54

35° 1.60 17.50 0.300 0.68 1.088 0.86

40° 2.66 20.00 0.342 0.62 1.649 1.48

12 in. CIP 0.59 3.14 25° 0.84 14.8 0.255 0.86 0.722 0.58

30° 1.12 17.7 0.304 0.82 0.918 0.88

35° 1.69 20.7 0.353 0.76 1.284 1.42

40° 2.86 23.6 0.400 0.70 2.002 2.52

12 ¾ in. CIP 0.62 3.34 25° 0.85 15.5 0.267 0.87 0.735 0.66

30° 1.14 18.6 0.319 0.83 0.946 1.01

35° 1.73 21.7 0.370 0.77 1.332 1.65

40° 2.94 24.8 0.419 0.71 2.087 2.92

14 in. CIP 0.67 3.67 25° 0.86 16.75 0.288 0.90 0.774 0.82

30° 1.16 20.10 0.344 0.85 0.986 1.24

35° 1.78 23.45 0.398 0.82 1.460 2.13

40° 3.05 26.80 0.451 0.76 2.318 3.84

APPENDIX A

EB 15-025 A-7

APPENDIX A

EB 15-025 A-8

APPENDIX A

EB 15-025 A-9

Table 3 – Values of (Kδ’ sin δ Cd) for Various Pile Types

φ HP 8x36 HP 10x42 HP 12x53 HP 14x73 10 in. CIP 12 in. CIP 12 ¾ in. CIP 14 in. CIP

25° 0.53 0.69 0.88 1.09 0.37 0.58 0.66 0.82

26° 0.56 0.73 0.93 1.15 0.39 0.62 0.71 0.88

27° 0.60 0.78 1.00 1.23 0.42 0.68 0.77 0.95

28° 0.64 0.83 1.05 1.32 0.46 0.74 0.84 1.05

29° 0.68 0.88 1.14 1.43 0.49 0.80 0.92 1.16

30° 0.73 0.95 1.23 1.55 0.54 0.88 1.01 1.24

31° 0.78 1.02 1.31 1.68 0.59 0.96 1.12 1.37

32° 0.85 1.10 1.45 1.85 0.64 1.05 1.22 1.52

33° 0.92 1.20 1.56 2.00 0.70 1.15 1.35 1.70

34° 0.99 1.30 1.70 2.20 0.78 1.27 1.50 1.90

35° 1.06 1.41 1.87 2.41 0.86 1.42 1.65 2.13

36° 1.17 1.55 2.03 2.67 0.95 1.55 1.83 2.37

37° 1.28 1.70 2.26 2.96 1.06 1.75 2.05 2.67

38° 1.40 1.85 2.50 3.30 1.18 1.95 2.30 3.00

39° 1.53 2.00 2.76 3.63 1.32 2.20 2.59 3.40

40° 1.67 2.22 3.05 4.06 1.48 2.52 2.92 3.84

APPENDIX A

EB 15-025 A-10

Table 4 – Values of NNY

φ 27° 28° 29° 30° 31° 32° 33° 34° 35° 36° 37° 38° 39° 40°

NNY x CN 1.0 3.0 5.4 7.8 10.0 12.5 14.8 17.5 20.2 23.0 26.0 29.0 32.2 35.6

Po

(ksf)

CN NNY

0.5 1.47 0.7 2.0 3.7 5.3 6.8 8.5 10.1 11.9 13.7 15.6 17.7 19.7 21.9 24.2

1.0 1.23 0.8 2.4 4.4 6.3 8.1 10.2 12.0 14.2 16.4 18.7 21.1 23.6 26.2 28.9

1.5 1.10 0.9 2.7 4.9 7.1 9.1 11.4 13.5 15.9 18.4 20.9 23.6 26.4 29.3 32.4

2.0 1.00 1.0 3.0 5.4 7.8 10.0 12.5 14.8 17.5 20.2 23.0 26.4 29.0 32.2 35.6

2.5 0.93 1.1 3.2 5.8 8.4 10.8 13.4 15.9 18.8 21.7 24.7 28.0 31.2 34.6 38.3

3.0 0.87 1.1 3.4 6.2 9.0 11.5 14.4 17.0 20.1 23.2 26.4 30.0 33.3 37.0 40.9

3.5 0.81 1.2 3.7 6.7 9.6 12.3 15.4 18.3 21.6 24.9 28.4 32.1 35.8 39.8 44.0

4.0 0.77 1.3 3.9 7.0 10.1 13.0 16.2 19.2 22.7 26.2 29.9 33.8 37.7 41.8 46.2

N

NNY

NYC

CxNN

)(

APPENDIX A

EB 15-025 A-11

APPENDIX B

EB 15-025 B-1 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963

APPENDIX B


APPENDIX C

EB 15-025 C-1 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979

5th ANNUAL FUNDAMENTALS OF DEEP FOUNDATION DESIGN

November 12-16, 1979

St. Louis, Missouri

POINT BEARING AND SHAFT FRICTION OF PILES IN SAND

By R.L. Nordlund

I must confess to some alarm when I first saw the agenda for this meeting as it lists me as talking

about piles and piers. To me, pier mean those large, excavated , sheeted supports for bridges and

it was therefore with a great del of relief that I learned from Professor Schmidt that piers to him

meant pre-bored holes filled with concrete. I didn’t relish the idea of talking to you about

something I know next to nothing about.

What I would like to do this morning is present to you a rational practical way to predict the

ultimate bearing capacity of a single pile. Once we know the capacity of a single pile, it is

relatively easy to determine the capacity of a group of piles or at least to determine lower limits

of the capacity of a group of piles. It is important that an engineer be able to do this. Owners

want to know how much the foundation is going to cost before they commit themselves to the

project. The engineer there fore has to decide on pile length, pile load, and pile type. Later, the

contractor wants to know the pile length so he can order materials.

There are a myriad of types of piles. It seems to me that I hear about a new type of pile every few

months. It is in my opinion impossible to develop one set of design parameter that will allow us

to compute the bearing capacity of all types of piles. We must differentiate among piles in some

logical manner. Should it be by pile material? I think not, because obviously an H-Pile, for

example, driven into place versus the same pile jetted into place will behave differently. I think

we should divide piles into categories based on how they are installed. There are driven piles,

vibrated piles, augercast piles, jetted piles, and pre-bored piles. And combinations of these. We

can’t cover all of these categories today. However, some of these categories are not even

appropriate for our discussion. The subject is piles in sand. While it is possible to construct a pre-

bored pile in sand, I’ll bet you anything I can design the foundation more economically using

another type of pile. Of course, this comment only applies to situations where other alternatives

are available.

When a pile is jetted into place, the soil profile is completely destroyed, the friction angle of the

soil is altered, and there is no way that these changes can be predicted. So when it comes to jetted

piles, I believe we engineers will have to acknowledge defeat insofar as our ability to compute in

advance the ultimate bearing capacity of such a pile.

APPENDIX C


Vibrated piles are used in granular soils. I confess to having very little experience with this type

of construction. Professor Davidson has had a great deal of experience with vibrated piles and

perhaps he can tell us how to predict pile length and capacities when piles are going to be

vibrated into place.

The Franki pile, which has a rammed-in-place concrete bulb at its tip, is a special unique type of

driven pile. I am going to discuss how to compute its bearing capacity in by 4 o’clock lecture

today.

That now leaves us with H-Piles, pipe piles, Raymond piles, Monotube piles, timber piles,

precast concrete piles, and augercast piles, which are the categories I will be discussing this

morning. If any of you are concerned that I have severely limited this discussion, pleas remember

that these piles along with the Franki pile constitute at least 90% of all piles installed in sand.

The augercast pile is not a driven pile. I am going to develop a method for computing the bearing

capacity of driven piles and then indicate how this method can be used for computing the

capacity of an augercast pile.

The total ultimate bearing capacity of a pile is the sum of its point resistance and its shaft friction.

Let us first consider the point resistance which is given by the formula

Equation 1

where Qp = ultimate total point resistance

Nq = a dimensionless bearing capacity factor

A = area of pile point

p = effective overburden pressure

D = length of pile below ground surface

There are at least half a dozen theoretical solutions for Nq. They are all a direct function of the

friction angle of the soil. The solution by Berezantzev et al. (Ref. 1) is shown in Figure 1. This

solution is more conservative than most other solutions and is the one around which I have

develop this design procedure. Considerable research has been done by Vesic (Ref. 2, 3) and

others on the point resistance of piles. There is some evidence that the point resistance reaches a

limiting value. This phenomenon can be attributed to arching in the soil and is quite complex. In

order to account for this phenomenon, I recommend that the effective overburden pressure be

limited to 3000 psf when calculating the point resistance.

DqP ApN Q

APPENDIX C


How good is this 3000 psf number? Meyerhof (Ref. 4) has presented a relationship between the

maximum allowable or limiting unit bearing capacity and the friction angle of the sand. This

relationship is shown in Figure 2. If I multiply 3000 psf by the Nq factors by Berezantzev, I get

good agreement with the limiting unit static resistance proposed by Meyerhof. Since the curve

given by Meyerhof was experimentally obtained (cone penetration tests), I feel very confident

about using a 3000 psf limit for effective overburden pressure when computing the point

resistance of a pile.

The shaft friction on a pile is an even more complicated quantity. If it weren’t for this subject,

soil mechanics literature would be reduced by half? However, it is complicated because there are

so many significant variables:

1. The friction angle of the soil, φ

2. The friction angle on surface of sliding, δ

3. The taper of the pile, ω

4. The effective unit weight of the soil, γ or γ’

5. The length of the pile, D

6. The minimum circumference encompassing the pile, C

7. The volume of displaced soil per unit length of pile, V

All of these variables are reflected in the following general equation for shaft friction:

Equation 2

The geometry and definition of these terms is shown in Figure 3. The formula has been

simplified from a form which includes ω directly, but for all tapered piles ω is so small that the

above equation is a very accurate approximation.

The influences of δ, φ, and ω are reflected by variations in Kδ. A function of δ also appears

directly in the equation. The effective unit weight of the soil and the length of the pile appear in

the factor pd. Since failure will always occur where least resistance is offered, the unit shear on

an area associated with least circumference will be the surface of failure. This occurs on the unit

area Cd x Δd which appears directly in the equation. Finally, the greater the volume of pile per

unit length, the greater is the compaction of the soil around the pile which will increase the

friction angle δ. Therefore, δ must be made a function of V. Moreover, as V increases the lateral

displacement of the soil increases and this increases Kδ so Kδ is also made a function of V.

Figures 4, 5, 6, and 7 give values of Kδ for various φ values with δ equal to φ. Figure 8 gives a

correction factor to be applied to Kδ when δ is not equal to φ. Figure 9 gives various values of

dCpK Q dd

Dd

dS

sin0

APPENDIX C


δ/φ for various pile materials and sizes (as measured by V). Knowing φ, δ can then be computed.

The derivations, justifications, and arguments supporting these design curves have all been

previously published by me (Ref. 5). Unfortunately there isn’t enough time today to review these

developments in detail, but if you are interested I suggest you read the original paper.

With these curves it is now possible to compute the ultimate bearing capacity of a pile in sand

assuming of course that we know the unit weight of the sand, the position of the water table, and

the friction angle φ of the sand. This latter assumption is really the nub of the problem because

we hardly ever, ever, know what φ is. It nearly always has to be estimated form N-values. Peck,

Hanson, and Thornburn (Ref. 6) give a relation between N and φ which is shown in Figure 10.

The selection of the N-value from the boring log itself can be a tricky thing. Schertman (Ref. 7)

has pointed out all the pitfalls in the N-value. Since N-values are usually logged in 6 in.

increments, do you use the first two blow counts or the last two? If the soil contains gravel, I

discard all high values; such as in 7/8/20, I would use N of 15. Sometimes, the first value is very

low because of overwashing by the driller; such as in 4/10/12, I would use an N of 22.Small

variations in N cause variations in φ which significantly affect the computed value of shaft

friction.

In my 1963 paper (Ref. 5), I did not incorporate a correction factor for N because of the effect of

the effective overburden pressure. Because of subsequent research and data, however, I feel now

that the field N-value should be corrected accordingly. In Figure 11, a correction factor for field

N-values is shown. This curve has been plotted for a curve given by Peck, Hanson, and

Thornburn (Ref. 6). The corrected N-value should be used in conjunction with Figure 10.

The augercast pile is of course not driven, there is very little soil displacement, and there is

therefore no compaction of the sand. I recommend that for this type of pile, V be taken as 0.1

ft3/ft and δ be taken to equal φ.

On the basis of these graphs and Equations 1 and 2, it is now possible to compute the ultimate

bearing capacity of a pile. From the soil profile, select N-values for each stratum of sand. Apply

the correction factor of Figure 11. Determine φ from Figure 10. Determine Kδ from Figures 4, 5,

6, and 7 as is appropriate. Determine δ/φ form Figure 9 and compute δ. Determine a correction

factor for Kδ from Figure 8. Now you can compute the unit shaft friction at any depth and by

summing the unit skin friction and associate pile area, the total shaft friction is arrived at as per

Equation 2.

The point resistance is obtained by entering Figure 1 with a φ-value, determining Nq, and then

computing the total point resistance as per Equation 1, but restricting the effective overburden

pressure to 3000 psf maximum.

One point which is insufficiently appreciated is that there must be a relatively large amount of

movement of the pile before both ultimate shaft resistance and point resistance are mobilized. In

APPENDIX C


the vast majority of cases, load-tests are discontinued before this stage is reached. That this

consideration is not appreciated by may engineers is illustrated by a paper presented in 1978 by

Cutter and Warder at the Ohio River Valley Soils Seminar (Ref. 8). The paper was entitled

“Friction Piles in Sand – A Review of Static Design Procedures”. Of the 13 compression load-

tests discussed, five were not even close to bearing capacity failure. In order to have some idea of

the ultimate bearing capacity, the slope of the gross load-settlement curve should reach at least

0.05 in./ton.

The authors of the above mentioned 1978 paper estimated form the gross load-settlement curve

how much load was carried in friction – a very difficult feat! They then compared this quantity

with values computed by various static methods among which was the procedure in my 1963

paper. I have calculated the shaft and point resistance according to my 1963 paper and I am

unable to get the same calculated answers as Cutter and Warder. These results are shown in

Figure 12. The discrepancies between my calculated shaft resistance (1963 method) and Cutter

and Warder’s points up how sensitive φ is to the choice of N – I suspect this is where the source

of the discrepancy lies. I think it is wise to always use the N-values at the lower range for the

stratum being considered. Nevertheless there is good agreement for Tests 25, 26, 27, and 28.

However, there is no agreement whatsoever between the observed failure loads for Tests 38, 39,

40, and 41 and values computed by my 1963 procedure. Why is this? These four piles are fairly

long and have a large portion of their lengths extending into a dense sand layer. My 1963 data

had very few such cases. By now correcting the N-values for effective overburden pressure and

limiting the effective overburden pressure to 3000 psf when computing the point resistance, Tests

41 and 42 are brought into good agreement, all without destroying the correlations shown for test

data presented in my 1963 paper.

Tests 38 and 39 were made on square, tapered, precast concrete piles. No matter how I try I

cannot get these test results to fit. The only way they will fit is if I ignore the taper and then the

fit is quite good as shown in Figure 12. However, this solution offends my scientific nature! Why

should the taper for a circular section be considered and that for a square section ignored? I

suppose it is possible that when a square (or rectangular) tapered pile is driven into sand, there is

a concentration of soil stresses and displacements at the corners, arching tin effect, and this could

significantly reduce the pressure on the pile surface at points distant from the corners. In any

event, I do not have a well defined explanation for the behaviors of Tests 38 and 39. However, if

you are considering the use of such piles, the taper should be ignored. At least you will get

reasonable answers, even if for the wrong reasons.

For illustrative purposes, I have attached the computations for Test 41.

I wish to point out that curves a and b of Figure 9 are located differently than shown on the

corresponding figure in my 1963 paper. This change has been necessary to compensate for now

taking into account correction to the N-values and limiting the effective overburden stress to

3000 psf maximum for point resistance.

APPENDIX C


So far I have talked about the bearing capacity of a single pile. But what about a group of piles?

A group of piles can be analyzed in two ways: first as a block whose depth is the depth of the

piles and whose point bearing area is equal to the area within the circumference o the group; and,

second, as the sum of the individual pile capacities. Model studies, computations, and experience

show that in sands, the bearing capacity of the block is always greater than the sum of the

individual pile capacities provided that the pile spacing is greater than about 2 pile diameters. I

do not recall ever having seen a cluster of piles whose spacing was less than 2 pile diameters. In

any event, in sands it would not be possible to drive piles as close together as 2 pile diameters

because of the compaction effect. Therefore, you can safely assume that the minimum bearing

capacity of a group of piles in sand is the sum of the individual pile capacities.

APPENDIX C


Figure 1 – Bearing Capacity Factor Nq (after Berezantzev et. al.)

APPENDIX C


Figure 2 – Maximum Unit Bearing Capacity vs. φ (after Meyerhof)

APPENDIX C


Figure 3 – General Equation for Ultimate Bearing Capacity

APPENDIX C


Figure 4 – Design Curves for Evaluating Kδ for Piles when φ=δ=25°

APPENDIX C



APPENDIX C


Figure 8 – Correction Factor for Kδ when δ≠φ

APPENDIX C


Figure 9 – Relation of δ/φ and Pile Displacement, V, for Various Types of Piles

APPENDIX C


Figure 10 – Relationship Between Standard Penetration Test Values and φ or Relative Density

Descriptions (re-plotted after Peck, Hanson, and Thornburn)

APPENDIX C


Figure 11 – Chart for Correction of N-Values in Sand for Influence of Effective Overburden Pressure

APPENDIX C


Test

No.

Shaft

Load- ton

(1)

Point

Load

(2)

Total

Load

(3)

Computed

Shaft Load

(4)

Computed

Shaft Load

(5)

Computed

Point Load

(6)

Computed

Total

(7)

Computed

Shaft Load

(8)

Computed

Point Load

(9)

Computed

Total

(10)

25 42 5 47 29 25 10 35 30 10 40

26 45 15 60 62 54 5 59 56 5 61

27 30 10 40 29 25 10 35 30 10 40

28 72 33 105 97 84 6 90 84 6 90

38 122 63 185 891 559 137 696 149* 44 193

39 122 63 185 813 680 137 817 158* 37 195

41 72 73 145 190 130 133 263 124 26 150

42 105 60 165 561 395 79 474 172 27 199

(1) According to Cutter and Warder.

(2) Difference between (3) and (1).

(3) From Load Tests

(4) According to Cutter and Warder using Nordlund’s 1963

method.

(5) According to Nordlund using his 1963 method.



(8) According to Nordlund using revised 1963 method (1979).

(9) According to Nordlund using revised 1963 method (1979).

(10) According to Nordlund using revised 1963 method (1979)

Test No. 25 – Pipe Pile

Test No. 26 – Monotube Pile


Test No. 28 – Raymond Pile

Test No. 38 – Square Tapered Precast Concrete Piles

Test No. 39 – Square Tapered Precast Concrete Piles


Test No. 42 – Raymond Pile

* Computed ignoring taper.

Figure 12- Comparison of Observed and Computed Ultimate Bearing Capacity for Some Tests

Reported by Cutter and Warder (Ref. 8)

APPENDIX C


Figure 13 – Pile Load Test Results (Data Reproduced from Cutter and Warder, Ref. 8)

APPENDIX C


Test No. 41 (see Figure 13)

From 0 to 13 ft.:

1. Effective overburden pressure at mid-depth when borings were made is:

20.5 x 110 = 2255 psf ≈ 1 tsf

Therefore no correction of N is required.

2. For N=8, φ= 29.5° (Fig. 10)

V= 0.785(1)2 = 0.785 ft

3/ft

δ/φ = 0.58 (Fig. 9)

δ = 0.58 x 29.5 = 17.1°

Kδ = 0.84 + 0.9 (1.07 – 0.84) (Fig.’s 4 & 5)

= 1.05

Kδ (corrected) = 0.784 x 1.05 (Fig. 8)

= 0.82

3. Shaft Resistance = 0.8 sin 17.1° x 110 x 6.5 x π x 1 x 13 = 6900 lbs.

From 13 ft. to 31 ft.:

1. Effective overburden pressure for N-value correction is:

26 x 110 = 2860 psf or 1.43 tsf

Corrected N = 0.9 x 18 = 16 (Fig. 11)

2. For N=16, φ = 32° (Fig. 10)

V= 0.785 ft3/ft

δ/φ = 0.58 (Fig. 9)

δ = 0.58 x 32 = 18.5°

Kδ = 1.07 + 0.4 ( 1.67 – 1.07) = 1.31 (Fig.’s 5 & 6)

Kδ (corrected) = 1.31 x 0.74 (Fig. 8)

= 0.97

3. Shaft Resistance = 0.97 sin 18.5° x 105 x 22 x π x 1 x 18 = 40200 lbs.

(used 105 instead of 110 to compensate for 2 ft. of submerged soil)



(43 x 110) + (15 x 50) = 5480 psf or 2.74 tsf

Corrected N = 0.65 x 38 = 25 (Fig. 11)

2. For N=25, φ = 35°

δ/φ = 0.58

δ = 0.58 x 35 = 20.3°

Kδ = 1.67

Kδ (corrected) = 1.67 x 0.71

= 1.19

3. Shaft Resistance = 1.19 sin 20.3° x ((29 x 110) + (15 x 50)) x π x 1 x 26 = 132900 lbs.

APPENDIX C




(43 x 110) + (34.5 x 50) = 6455 psf or 3.23 tsf

Corrected N = 0.6 x 32 = 19

2. For N=19, φ = 33°

δ/φ = 0.58

δ = 0.58 x 33 = 19.1°

Kδ = 1.07 + 0.6 ( 1.67 – 1.07) = 1.43

Kδ (corrected) = 1.43 x 0.72

= 1.03

3. Shaft Resistance = 1.03 sin 19.1° x ((29 x 110) + (34.5 x 50)) x π x 1 x 13 = 67600 lbs.

Point Resistance:


(43 x 110) + (39 x 50) = 6680 psf or 3.34 tsf

Corrected N = 0.6 x 32 = 19

φ = 32°

Nq = 22

2. Point Resistance = 22 x 3000 x 0.785 = 51800 lbs.

Total Ultimate Bearing Capacity = 6900

+ 40200

+132,900

+ 67600

247600 = Shaft Friction

+ 51800

299400 or 150 ton

APPENDIX C


REFERENCES

1. “Load Bearing Capacity and Deformation of Piled Foundations”, by V. Berezantzev, V.

Khristoforov, and V. Golubkov, Proceedings, 5th

International Conference on Soil

Mechanics and foundations Engineering, Paris, 1961.

2. “Bearing Capacity of Deep Foundations in Sand”, National Academy of Sciences, Highway

Research Record 39, 1963, by A. Vesic.

3. “A Study of Bearing Capacity of Pile Foundations, Final Report”, Georgia Institute of

Technology, Atlanta GA, 1966, by A. Vesic.

4. “Bearing Capacity and Settlement of Pile Foundations”, Journal of the Geotechnical

Division, ASCE, 1976, by G. Meyerhof.

5. “Bearing Capacity of Piles in Cohesionless Soils”, Journal of Soil Mechanics and

Foundation Division, ASCE, 1963, by R.L. Nordlund.

6. “Foundation Engineering”, Wiley, Second Edition, by Peck, Hanson, and Thornburn.

7. “Statics of STP”, Journal of the Geotechnical Division, ASCE, 1979, by John H.

Schmertman.

8. “Friction Piles in Sand – A Review of static Design Procedures”, Ohio River Valley Soils

Seminar, 1978, by William A. Cutter and David L. Warder.

APPENDIX C


Symbols

A = Area of Pile Point

B = Diameter of the Point of a Pile

C = Minimum Perimeter Encompassing a Pile

D = Depth from Ground Surface to Pile Tip

Kδ = A Dimensionless Factor Expressing the Ratio of the

Resultant of the Effective Normal and Shear Stresses on an

Incipient Failure Plane Passing Through a Point and the

Effective Overburden Pressure at that Point

N = Standard Penetration Test

Nq = Dimensionless Bearing Capacity Factor

PU = Total Ultimate Bearing Capacity of the Pile

p = Effective Overburden Pressure

QP = Total Ultimate Point Resistance of Pile

V = Volume of Displaced Soil per Unit Length of Pile

δ = Friction Angle on Surface of Sliding Around Pile Shaft

φ = Friction Angle of Soil

ω = Taper of Pile Expressed as an Angle

γ, γ’ = Effective Unit Weight of Soil

Chart for pile skin friction

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Transcript of Chart for pile skin friction