CHARTS TO FACILITATE COMPUTATION OF SKIN FRICTION ON DRIVEN NON-TAPERED PILES IN COHESIONLESS SOIL
GEOTECHNICAL ENGINEERING MANUAL GEM-11 Revision #2
AUGUST 2015
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 1 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 3 Pile Type: CIP 12 in. Diameter ...... 12 4 Pile Type: CIP 12 ¾ in. Diameter ...... 13 5 Pile Type: CIP 14 in. Diameter ...... 14 6 Pile Type: HP 8x36 (48 ton Capacity) ...... 15 7 Pile Type: HP 10x42 (56 ton Capacity) ...... 16 8 Pile Type: HP 12x53 (70 ton Capacity) ...... 17 9 Pile Type: HP 14x73 (96 ton Capacity) ...... 18
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 2 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 3 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 4 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 NNY (ft.) (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 5 of 19
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Layer Average Po at qs Layer QS NNY per Midpoint φ (kips/ft.) Thickness (kips) Layer (ksf) (ft.) 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:
QP AP xNq xPo
2 2 Ap = π (d /4) = 0.887 ft Po = 2.9 ksf use NNY = 15 φ = 32°
From Appendix B, Fig. 1 Nq = 26
2 QP = (0.887 ft ) 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.
EB 15-025 Page 8 of 19
CHARTS TO FACILITATE COMPUTATION OF SKIN FRICTION ON DRIVEN NON-TAPERED PILES IN COHESIONLESS SOIL
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APPENDIX A
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APPENDIX A
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
Q P (K ' sin C )d S o d
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
q P (K ' sin C ) S o d
EB 15-025 A-1 APPENDIX A
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
Nc N STD xCN
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
NSTD 1.29 xN NY
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
' Nc 1.29 xCN xN NY 1.29 xNc
N’c is the New York sampler blow count for the last foot of driving, corrected for overburden pressure.
EB 15-025 A-2 APPENDIX A
According to Peck, Hanson and Thornburn, the correction factor CN is defined as: Equation 6
20 CN 0.77 Log Po (tons)
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.
EB 15-025 A-3 APPENDIX A
EB 15-025 A-4 APPENDIX A
Table 1 – Values of Kδ
V δ = φ Pile Type Volume 25° 30° 35° 40° (ft3/ft) 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
EB 15-025 A-5 APPENDIX A
Table 2
Pile δ/φ Cd (ft.) δ=φ Kδ δ sin δ Kδ Kδ’ (Kδ’ sin δ Cd) Corr. Factor 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
EB 15-025 A-6 APPENDIX A
EB 15-025 A-7 APPENDIX A
EB 15-025 A-8 APPENDIX A
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
EB 15-025 A-9 APPENDIX A
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 CN NNY (ksf) 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 NY xCN ) N NY CN
EB 15-025 A-10 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
EB 15-025 B-2 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-3 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-4 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-5 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-6 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-7 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-8 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-9 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-10 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-11 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-12 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-13 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-14 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-15 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-16 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-17 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-18 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-19 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-20 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-21 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-22 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-23 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-24 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-25 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-26 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-27 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-28 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-29 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-30 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-31 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-32 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-33 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-34 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963 APPENDIX B
EB 15-025 B-35 Ref: "Bearing Capacity of Piles in Cohesionless Soils" by R.L. Nordlund, 1963
APPENDIX C
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.
EB 15-025 C-1 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 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
QP Nq Ap D
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.
EB 15-025 C-2 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 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
dD QS d0 K sin pd Cd d
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
EB 15-025 C-3 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 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
EB 15-025 C-4 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 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.
EB 15-025 C-5 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 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.
EB 15-025 C-6 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
Figure 1 – Bearing Capacity Factor Nq (after Berezantzev et. al.)
EB 15-025 C-7 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
Figure 2 – Maximum Unit Bearing Capacity vs. φ (after Meyerhof)
EB 15-025 C-8 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
Figure 3 – General Equation for Ultimate Bearing Capacity
EB 15-025 C-9 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
Figure 4 – Design Curves for Evaluating Kδ for Piles when φ=δ=25°
EB 15-025 C-10 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
Figure 5 – Design Curves for Evaluating Kδ for Piles when φ=δ=30°
EB 15-025 C-11 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
Figure 6 – Design Curves for Evaluating Kδ for Piles when φ=δ=35°
EB 15-025 C-12 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
Figure 7 – Design Curves for Evaluating Kδ for Piles when φ=δ=40°
EB 15-025 C-13 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
Figure 8 – Correction Factor for Kδ when δ≠φ
EB 15-025 C-14 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
Figure 9 – Relation of δ/φ and Pile Displacement, V, for Various Types of Piles
EB 15-025 C-15 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
Figure 10 – Relationship Between Standard Penetration Test Values and φ or Relative Density Descriptions (re-plotted after Peck, Hanson, and Thornburn)
EB 15-025 C-16 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
Figure 11 – Chart for Correction of N-Values in Sand for Influence of Effective Overburden Pressure
EB 15-025 C-17 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
Test Shaft Point Total Computed Computed Computed Computed Computed Computed Computed No. Load- ton Load Load Shaft Load Shaft Load Point Load Total Shaft Load Point Load Total (1) (2) (3) (4) (5) (6) (7) (8) (9) (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. Test No. 25 – Pipe Pile (2) Difference between (3) and (1). Test No. 26 – Monotube Pile (3) From Load Tests Test No. 27 – Pipe Pile (4) According to Cutter and Warder using Nordlund’s 1963 Test No. 28 – Raymond Pile method. Test No. 38 – Square Tapered Precast Concrete Piles (5) According to Nordlund using his 1963 method. Test No. 39 – Square Tapered Precast Concrete Piles (6) According to Nordlund using his 1963 method. Test No. 41 – Pipe Pile (7) According to Nordlund using his 1963 method. Test No. 42 – Raymond Pile (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)
* Computed ignoring taper. Figure 12- Comparison of Observed and Computed Ultimate Bearing Capacity for Some Tests Reported by Cutter and Warder (Ref. 8)
EB 15-025 C-18 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
Figure 13 – Pile Load Test Results (Data Reproduced from Cutter and Warder, Ref. 8)
EB 15-025 C-19 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 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 ft3/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)
From 31 ft. to 57 ft.: 1. Effective overburden pressure for N-value correction is: (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.
EB 15-025 C-20 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 APPENDIX C
From 57 ft. to 70 ft.: 1. Effective overburden pressure for N-value correction is: (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: 1. Effective overburden pressure for N-value correction is: (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
EB 15-025 C-21 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 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.
EB 15-025 C-22 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979 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
EB 15-025 C-23 Ref: "Point Bearing and Shaft Friction of Piles in Sand" by R.L. Nordlund, 1979