Formula Sheet

Foundation Engineering-II

Static Pile Capacity Equations

bfult QQQ .

Piles in sand

bqvsv

bsult

ANAK

AqAfQ

tan

Values of After US Army Corps of Engineers)

Pile material

Steel 0.67 to 0.83

Concrete 0.90 to 1.0

Timber 0.80 to 1.0

Values of K After US Army Corps of Engineers)

Soil Type Values of K

In compression (Kc) In Tension (Kt)

Sand 1.00 to 2.00 0.50 to 0.70

D/B = 20

D/B = 5

D/B = 70

26 28 30 32 34 36 38 40

175

150

125

100

75

50

25

0

Angle of shearing resistance, o

(Af ter Tomlinson)

Bea

ring

capa

city

fac

tor,

Nq

Silt 1.0 0.50 to 0.70

Clay 1.0 0.70 to 1.00

Note: The above values do not apply to piles that are prebored, jetted or

installed with a vibratory hammer. Picking K values at the upper end of

the above ranges should be based on local experience.

AMERICAN PETROLEUM INSTITUTE 1993 DESIGN RECOMMENDATIONS* FOR PILES IN

COHESIONLESS SILICEOUS SOILS

Density Soil

description

Soil/pile

friction

angle ()

Limiting skin

friction

values (kPa)

Nq Limiting unit end-

bearing values

(MN/m2)

Very loose

Loose

Medium

Sand

Sand-silt**

Silt

15 47.8 8 1.9

Loose

Medium

Dense

Sand

Sand-silt**

Silt

20 67 13 2.9

Medium

Dense

Sand

Sand-silt

25 81.3 20 4.8

Dense

Very dense

Sand

Sand-silt**

30 95.7 40 9.6

Dense

Very dense

Gravel

Sand

35 114.8 50 12.0

*The parameters listed in this table are intended as guidelines only. Where detailed information such as in-situ cone

tests, strength tests on high quality samples, model tests, or pile driving performance is available, other values may

be justified.

**Sand-silt includes those soils with significant fractions of both sand and silt. Strength values generally increase with

increasing sand fractions and decrease with increasing silt fractions.

Piles in Clay

2

4dcNdLcs

AqAfQ

c

bsult

Recommended Values of and f for Estimation of Drilled Shaft Side Resistance in

Cohesive Soil (Reese and O’Neill, 1988)

Location along drilled shaft Value of Limiting value of load

transfer, f (ksf)

From ground surface to depth along

drilled shaft of 5 ft *

0 -

Bottom 1 diameter of the drilled shaft or

1 stem diameter above the top of the

bell (if skin friction is being used)

0 -

All other points along the sides of the

drilled shaft

0.55 5.5 (263 kPa)

The depth of 5 ft may need adjustment if the drilled shaft is installed in expansive clay, or if there is

substantial groundline deflection from lateral loading.

Limiting Values of Unit End Bearing and Side Resistance

Cohesive Soil Non-Cohesive Soil

Unit Side Resistance (ksf). 5.5 (263 kPa) 4 (192 kPa)

Unit End Bearing (ksf) 80 (3830 kPa) 1.2N or 90 for N 75

2

bs

a

QQQ

0.35.1

bs

a

QQQ

Group in Strong Soil Overlying Weaker Soil

qE = qLo + (H/10B1)(qUP – qLo) qUP

where

qLo = Ultimate unit tip capacity of an equivalent shaft bearing in weaker underlying soil layer (ksf)

qUP = Ultimate unit tip capacity of an equivalent shaft bearing in stronger upper soil layer (ksf)

B1 = Least width of shaft group (ft)

H = Distance from shaft tip to top of weak soil layer (ft)

Recommended Factor of Safety on Ultimate Geotechnical Capacity Based on Specified Construction

Control. (Ref: AASHTO Specification for Highway Bridges)

Increasing Construction Control

Subsurface exploration X(1)

X X X X

Static Calculation X X X X X

Dynamic Formula X

Wave equation X X X X

Dynamic measurement and analysis X X

Static load test X X

Factor of safety 3.50 2.75 2.25 2.00(2)

1.90

X(1)

= Construction control specified on Contract Plans

X(2)

= For any combination of construction control that includes an approved static load test, a factor of

safety of 2.0 may be used.

NAVFAC DM-7.2 METHOD

BEARING CAPACITY FACTORS – Nq

* (deg) 26 28 30 31 32 33 34 35 36 37 38 39 40

Nq

(Driven Pile

10 15 21 24 29 35 42 50 62 77 86 120 145

Nq**

(Drilled Piers)

5 8 10 12 14 17 21 25 30 38 43 60 72

EARTH PRESSURE COEFFICIENTS KHC AND KHT

PILE TYPE KHC KHT

Driven single H-Pile 0.5 – 1.0 0.3 – 0.5

Driven single Displacement Pile 1.0 – 1.5 0.6 – 1.0

Driven single Displacement Tapered Pile

1.5 – 2.0 1.0 – 1.3

Driven Jetted Pile 0.4 – 0.9 0.3 – 0.6

Drilled Pile (Less than 24 Diameter)

0.7 0.4

FRICTION ANGLE –

PILE TYPE

Steel 20

Concrete 3/4

Timber 3/4

*Limit to 28 if jetting is used

**(a) In case a bailer or grab bucket is used below ground water table, calculate end bearing

based on not exceeding 28.

(b) For piers greater than 24-inch diameter, settlement rather than bearing capacity usually

controls the design. For estimating settlement, take 50% of the settlement for an

equivalent footing resting on the surface of comparable granular soils.

RECOMMENDED VALUES OF ADHESION (NAVFAC DM-7.2)

PILE TYPE CONSISTENCY

OF SOIL

COHESION, C,

PSF

ADHESION, CA

(= C), PSF

TIMBER AND

CONCRETE

Very Soft 0 – 250 0 – 250

Soft 250 – 500 250 – 480

Medium Stiff 500 – 1000 480 – 750

Stiff 1000 – 2000 750 – 950

Very Stiff 2000 – 4000 950 – 1300

STEEL

Very Soft 0 – 250 0 – 250

Soft 250 – 500 250 – 460

Medium Stiff 500 – 1000 460 – 700

Stiff 1000 – 2000 700 – 720

Very Stiff 2000 – 4000 720 – 750

Berezantzev et al. (1961) Theory: Relationship between and Nq

deg 28 30 32 34 36 38 40

Nq

L/B = 25 12 17 25 40 58 89 137

L/B = 50 9 14 22 37 56 88 136

The Engineering News Formula

cs

WhR

The Hiley formula

WhcsR

2

1

STANDARD PENETRATION TEST (SPT)

st DANnmNAR

m = 400103 for driven piles

120 103 for bored piles

N = SPT index at the pile toe obtained by averaging blows over length 6 - 10B above and 2 - 4B

below the base.

At = Pile toe area

n = 2103 for driven piles

1103 for bored piles

N = Average SPT index along the pile

D = Pile embedment length

Alternate Form of Meyerhof (1976) method for driven piles

Ultimate bearing capacity at base NB

DNq b

b 40040 (kN/m2)

N = SPT resistance in the vicinity of the pile base

Db = Length of pile embedded in the sand

Average Skin Friction over the length of pile is determined as

Nqs 2 (kN/m2)

Where N is the average value of SPT resistance over the embedded length of the pile within the

sand stratum.

For bored piles, the values of qb and qs are approximately 1/3 and 1/2, respectively, of the

corresponding values for driven piles.

AXIAL CAPACITY BASED ON STATIC CONE-PENETRATION TESTS

Canadian Foundation Engineering Manual

DAfAqR sstc

qc = point resistance from the cone-penetration test. (It is recommended that for piles with B > 500

mm, a design value of qc smaller than the measured average qc, or even equal to the

minimum measured value be used). (Ref: Canadian Foundation Engg. Manual).

fs = average unit side shear measured by the static cone-penetrometer test.

Tomlinson (2001)

Plot all relevant qc/depth profiles together and draw an average line for the section around the pile

base. A load factor of 2.0 – 2.5 is then applied to the base resistance (Abqb) depending on the

scatter of the profile.

Practice in Netherlands

For end bearing capacity, use mean of two averages qc1 and qc2, for single profile, determined:

(1) between 0.7B and 4B below the pile base (qc1). If qc increases steadily below the pile, the

average is determined only to depth 0.7B. If a pronounced decrease in qc occurs between

0.7B and 4B, the lowest value within that range is taken as qc1.

(2) 8B above the base (qc2). The average value of qc2 above the base should be determined,

working upward from the base, using only values, which decrease from or equal to that at the

base.

The value of end bearing capacity (qb) should be restricted to15 MPa.

Shaft resistance per unit area (qs) can be determined from values of local sleeve resistance (fs).

However, fs must be multiplied by a factor to allow for the effect of pile installation on the density of

the sand. The factor depends on the material and end shape of the pile; suggested values being

1.1 for a concrete pile with a pointed end and 0.7 for a steel H pile.

Shaft resistance can also be determined from direct correlations with cone resistance, e.g. qs =

0.012qc for timber, precast concrete and steel displacement piles.

The value of qs should be restricted to 0.12 MPa.

AXIAL CAPACITY BASED ON PRESSUREMETER TEST

vhlmep pkAQ /

A = pile base area

plme = equivalent limit pressure

h = horizontal pressure at the base level

v = total vertical pressure at the base level

k = bearing capacity factor hlm

vu

p

q

Bearing Capacity Factor, k for Axially Loaded Piles (After LCPC-SETRA, 1985)

Ground type plm (kPa) Category Bored piles and small

displacement piles

Full displacement

piles

Clay 0 – 1200

I

1.2

1.8 Silt 0 – 700

Firm clay or marl 1800 – 4000

II

1.1

3.2 – 4.2

Compact silt 1200 – 3000

Compressible sand 400 – 800

Soft or weathered rock

1000 – 3000

Sand and gravel 1000 – 2000

III

1.8

2.6 Rock 4000 – 10000

Very compact sand and gravel

3000 – 6000 IV 1.1 – 1.8* 1.8 – 3.2

* 3.2 for dense sand or gravel; 4.2 for loose sand or gravel limited data base

The equivalent limit pressure, plme is taken as the average limit pressure within a distance a below

and a distance d above the pile base level, that is

ilmilme zpda

p1

where plmi is the limit pressure over depth zi, which is the thickness of a layer at which plm is

measured such that

z1+ …. +zn = a+d

a and d are distances depending on the pile diameter and embedment length. d is equal to a or the

distance between the pile base and the top of the bearing layer which ever is smallest. a is given

by:

a = 0.5 if Be < 1 m

= Be/2 if Be > 1 m

Where

Be= 4base area of pile / base perimeter of pile

It is assumed that the pile penetrates the bearing layer such that the equivalent embedment depth,

de, is greater than 5B, where de is given by:

ilmi

lme

e zpp

d1

k is reduced to ke if de < 5B, where ke is given by

B

d

B

dkk ee

e

10

25

8.08.0

The ultimate friction capacity, Qf, is given by:

isif zqQ

where

qsi = unit skin friction for soil layer i and zi is the thickness of soil layer i. The unit friction is obtained

from Table below read in conjunction with Figure below.

The selection of design curves for unit friction (after LCPC SETRA, 1985)

Soil type plm (MPa)

Bored concrete

Bored and lined Driven Grouted

Concrete Steel Concrete Steel Low pressure

High pressure

Soft clay 0-0.7 A A A A A B

Stiff clay 1.2-2 A, (B) A, (B) A A, (B) A B E*

Very stiff clay >2 A, (B) A, (B) A A, (B) A, B E*

Loose sand 0-0.7 A A A A A B

Medium dense sand 1-2 B, (C) A, (B) A B, (C) B C E

Very dense sand >2.5 C, (D) B, (C) B C, (D) C D E

Completely weathered chalk 0-0.7 A A A A A B

Partially weathered chalk >1 C, (D) B, (C) B C, (D) C E E

Marl 1.5-4 D, (F) C, (D) C F F F G

Stiff marl >4.5 F G G

Weathered rock 2.5-4 G G G G G G

Fractured rock >4.5 G G G

Curves in parentheses only apply for well-constructed piles

* If plm < 1.5 MPa

Pier Capacity in Compression

As given by Reese et al. (1976) the pier capacity in clay is

For piers in sand Reese et al. (1976)

(1)

Settlement due to axial deformation of pile shaft; Sa

p

sspaAE

LQQS

Qp = point load transmitted to the pile tip in the working stress range

Qs = shaft friction load transmitted by the pile in the working stress range (in force units)

s = 0.5 for parabolic or uniform distribution of shaft friction

= 0.67 for triangular distribution of shaft friction starting from zero friction at pile head to a

maximum value at pile point

= 0.33 for triangular distribution of shaft friction starting from maximum at pile head to zero at

the pile point.

(2) Settlement of pile point caused by load transmitted at the point

o

pp

ppBq

QCS

where

Cp = empirical coefficient depending on soil type and method of construction (see Table below)

B = pile diameter

qo = ultimate end bearing capacity

Table: Typical Values* of Coefficient Cp for Estimating Settlement of a Single Pile

Soil Type Driven Pile Bored Pile

Sand (dense to loose) 0.02 to 0.04 0.09 to 0.18

Clay (stiff to soft) 0.02 to 0.03 0.03 to 0.06

Silt (Dense to loose) 0.03 to 0.05 0.09 to 0.12

* Bearing stratum under pile tip assumed to extend at least 10-pile diameter below tip and soil

below tip is of comparable or higher stiffness.

(3) Settlement of pile points caused by load transmitted along the pile shaft,

o

ss

psDq

QCS

where Cs = (0.93 + 0.16 D/B) Cp

D = embedded length

Settlement of Pile Group in Granular Soils

BBSS og

Converse-Labarre equation:

mn

nmmnEg

90

111

Where,

Eg = pile group efficiency

= arctan (d/s), deg.

n = number of piles in a row

m = number of rows of piles

d = diameter of a pile

s = spacing of piles, centre to centre, in same unit as pile diameter.

Lateral loads on piles

Single piles in cohesive soils

Single piles in granular soils