CHAPTER 3
ULTIMATE PILE CAPACITY
3.1
Ultimate Capacity Of Driven Pile
In designing a pile, the depth of installation must be pre-determined. Then,
the pile is driven into the ground until have sufficient contact with a layer of rock or
hard stratum. Anyway, it is found that the requirement cannot always be satisfied
because soil profiles vary. A more rigorous assessment of the driving characteristic
of a pile may be achieved by means of a proper dynamic analysis of the pile soil
system. Among the several methods suggested, static analysis, pile driving formulas
and static load test are the three methods that most commonly used to determine the
ultimate load capacity of a pile.
3.2
Static Analysis
The ultimate load carrying of a pile is given by a simple equation as the sum
of the load carried at the pile point plus the total frictional resistance that derived
from the soil-pile interface:
28
Qu = Qb + Qs
……………….. Equation 3.1
where Qu = ultimate pile capacity
Qb = load carrying capacity of the pile point
Qs = frictional resistance
A pile subjected to load parallel to its axis will carry the load partly by shear
generated along the shaft, and partly by normal stresses generated at the base of the
pile. Therefore,
Qu = Abqb + As τs.
……………….. Equation 3.2
where Ab = nominal plan area of the pile base
As = nominal surface area of the pile in soil layer
qb = characteristic value per unit area of base
τs. = Characteristic value of the resistance per unit of the shaft in soil layer
The relative magnitude of the shaft and base capacity will depend on the
geometry of the pile ad the soil profile. Numerous published studies cover the
determination of the values of Qb and Qs, a few of them to be reviewed in the
following part.
3.2.1
Static Analysis For Estimating Pile Capacity In Cohesiveless Soil
3.2.1.1 Method Based On Standard Penetration Test
Base Resistance
Qb = σo’ Nq Ab
……………….. Equation 3.3
29
where σo’ = effective overburden pressure at the pile base
Nq = bearing capacity factor, which can obtained from Figure 3.1 below.
Figure 3.1: Bearing capacity factor, Nq (Berezantsev, 1961)
Due to the critical depth limitation and to the problem of obtaining values of the
required parameters, the above equations are sometimes difficult to apply in practice.
Therefore, Meyerhof had proposed the following empirical correlation to estimate
the values of qf and fs based on the results of pile loading tests and dynamic or static
penetration tests.
qf = 40N (Db/B) ≤ 400N
……………….. Equation 3.4
where Db = length of pile embedded in the sand
B = diameter of pile
N = value of standard penetration resistance in the vicinity of the pile base
And for the case of small-displacement piles such as spun and steel H piles, the
value of fs should be given by the following equation:
30
Fs = 2 N
……………….. Equation 3.5
where N = average value of standard penetration resistance over the embedded
length of pile within the sand stratum
Skin Friction
Qs = Ks σvo’ tan δ As
where
……………….. Equation 3.6
Ks = coefficient of horizontal soil stress
σvo’ = average effective overburden pressure over the length of the soil layer
δ = angle of wall friction
3.2.1.2 Method Based On Static Cone Penetration
Base Resistance
Qb = CKD Ab
……………….. Equation 3.7
where CKD = point resistance of cone which taken average from 4D above the pile
head until D distance below the pile base (KN/m2)
Skin Friction
Qs = As CKDave /200
……………….. Equation 3.8
where CKDave = average point resistance of cone per unit of the pile shaft (KN/m2)
Take the safety factor as 2.5
31
3.2.2
Static Analysis For Estimating Pile Capacity In Cohesive Soil
3.2.2.1 End Bearing Capacity, Qb
The long term, drained, end-bearing capacity of a pile in clay will be
considered larger than the undrained capacity, but the settlements required to
mobilize the drained capacity will be far too large to be tolerated by most structures.
In addition, the pile must have sufficient immediate load-carrying capacity to prevent
a short-term failure. That's why it is customary to calculate the base capacity of pile
in clay in terms of undrained shear strength of the clay, Cu and a bearing capacity
factor, Nc. Thus, the end-bearing pressure is
qb = Nc Cu .
……………….. Equation 3.9
Meyerhof's Method
The bearing capacity factors increase with the embedment ratio, Lb/D and reach the
maximum value of Lb/D critical embedment ratio, 0.5 (Lb/D)cr (Meyerhof , 1976).
The maximum value of Nc* and Nq* will apply for calculation of qp for all pile
variation of Nc* and Nq* with friction angle, ø is show in Figure 3.2. Therefore, for
piles in saturated clays in undrained conditions ( ø = 0),
Qp = Nc* Cu Ap = 9 Cu Ap
……………….. Equation 3.10
where, Cu = undrained cohesion of the soil below the pile tip
Lb = length of the pile embedded in the sand
32
Figure 3.2: Variation of the maximum values of Nc* and Nq* with friction
angle, ø (after Meyerhof, 1976)
Janbu's Method
Janbu (1976) proposed calculating Qb as Qb = Ap(CNc* + q*Nq*). Where Nc* and
Nq* are the bearing capacity factor that calculated by assuming a failure surface in
soil at the pile tip as shown in Figure 3.3. The bearing capacity relationship then
become
Nq* = (tanø + √1 + tan2ø )2 ( e2ηtanø) for non cohesive soil, and
Nc* = (Nq* - 1) cotø for cohesive soil.
Therefore, for analysis in cohesive soil, equation 3.11 become
33
Qb = CNc*Ap
………Equation 3.11
where c = cohesion of soil that supporting the pile
Figure 3.3: Janbu's bearing capacity factors (Janbu, 1976)
Terzaghi's Method
According to Terzaghi’s equation, the point bearing of piles is
Qp = Ap qp = Ap (cNc* + q’Nq*)
……………….. Equation 3.12
34
where
Ap = area of pile tip
c = cohesion of the soil supporting the pile tip
qp = unit point resistance
q’ = effective vertical stress at the level of the pile tip
Nc*, Nq* = the bearing capacity factors
3.2.2.2 Frictional Resistance In Clay, Qs
Several methods for obtaining unit frictional resistance of pile is presently
available in the literature. Anyway, only three of the presently accepted procedures
are described.
The α Total Stress Method (Meyerhof’s Method)
The α total stress method is the most widely used method in estimating the ultimate
capacity of a driven pile in cohesive soil. This formula take accounts for installation
effects when driving piles and presented in:
fs = α Cu
…………………..Equation 3.13
where, α = empirical adhesion factor
Cu = mean undrained shear strength (ø = 0 concept)
In the absence of any specific data, typical values for the undrained shear
strength of cohesive soils can be referred to Table 3.1 while the value of α may be
estimated from the Figure 3.4 below. For the normal consolidated clays with Cu ≤
50 KN/m2, α = 1, thus,
Qs = Σ ƒp
L
…………………..Equation 3.14
35
where, ƒ = unit friction resistance at any depth z
p = perimeter of pile section
L = incremental pile length over which p and ƒ are taken constant
Table 3.1: Typical value for the undrained shear strength of cohesive soils
(Bridge Design Code, 1992).
Consistency of Cohesive Soil
Characteristic Undrained Shear Strength (kPa)
Very soft
Soft
Firm
Stiff
Very Stiff
Hard
0 - 10
10 – 25
25 – 50
50 – 100
100 – 200
> 200
Figure 3.4: Variation of α with undrained cohesive of clay (Das, B.M., 1995).
36
λ Method
This method was proposed by Vijayvergiya and Focht (1972), based on the
assumption that the displacement of soil caused by pile driving results in a passive
lateral pressure at any depth and that the average unit skin resistance is
ƒav = λ ( σ'v + 2 Cu)
…………………..Equation 3.15
where, σ'v = mean effective vertical stress for the entire embedment length
Cu = mean undrained shear strength (ø = 0 concept)
The value of λ changes with the depth of pile penetration as shown in
Figure 3.5. Thus, the total frictional resistance may be calculated as
Qs = pL ƒav .
…………………..Equation 3.16
In layered soil, the values of σ'v and Cu can be calculated as
σ'v = [(A1 + A2 + A3 +…)/L]
…………………..Equation
16
…………………..Equation
3.17
Cu = [(Cu1L1 + Cu2L2 + Cu3L3 + …)/L]
…………………..Equation 3.18
where, A1, A2 , A3 ……. = areas of the vertical effective stress diagram
37
Figure 3.5: Variation of λ with pile embedment length (redrawn after
McClelland, 1974)
β Method
β Method determine that the unit frictional resistance for the pile can be determined
on the basis of the effective stress parameters of the clay in a remolded state (c = 0).
Thus at any depth
ƒ = β σ'v
…………………..Equation 3.19
where, σ'v = vertical effective stresses
β = K tan ØR
ØR = drained friction angle of remolded clay
K = earth pressure coefficient at rest or
= 1 – sin ØR (for normally consolidated clays) and
= 1 – sin ØR √ OCR (for normally consolidated clays) and
38
Therefore, with the value of ƒ determined, the total frictional resistance may be
evaluated as
Qs = Σ ƒp L
3.2.3
…………………..Equation 3.20
Negative Skin Friction
If driven or bored piles are installed in compressible fill or any soil showing
appreciable consolidation under its own weight, a load additional to the working load
on the head of the pile is transmitted in skin friction, i.e. ‘negative skin friction’ as
shown in Figure 3.6, to the pile surface. Negative friction or down drag of piles may
occur wherever piles are driven through, or adjacent to, recently placed fill. Such fill
may merely be to raise the existing ground level, or may be part of an embankment,
for a bridge approach. The problem is normally associated with soft, lightly over
consolidated deposits of clay. In some sensitive clay, remolding of the soil during
driving may lead to down drag of the piles, even where no fill is placed (Fellenius,
1972). The unit negative skin friction at any depth can be calculated from empirical
methods below.
3.2.3.1 Total Overburden Pressure Method
This method using undrained shear strength in analysis the maximum skin
friction that apply to the pile. The negative skin friction could be calculated by
ƒs neg = α Cu
where α is a empirical factor and
Cu is undrained shear strength
…………………..Equation 3.21
39
For practical purposes, it is common to assume that the positive or negative
value of skin friction generated at pile shaft which caused by any relative movement
between the pile and earth interaction are the same but in opposite direction. Hence,
the α value in the above equation can be obtained from the relation between α and
undrained shear strength for pile under axis load action.
However, attention should be given while using this method due to increase
in undrained shear strength proportionately with the consolidation process.
3.2.3.1 Effective Overburden Pressure Method
ƒs neg = β ρo
…………………..Equation 3.22
where ρo is the effective overburden pressure and β is a reduction factor shown by
Meyerhof to be equal to 0.3 for piles up to 15m long, decreasing to 0.2 and 0.1 for
40m and 60m long piles respectively. If the fill has been in place for a very long
period of years or has otherwise been well consolidated, the negative skin friction
can be ignored in estimating the total working load on the pile.
For cases intermediate between recently placed and old fill the safety factor,
given by
Ultimate carrying capacity
S.F. = working load + negative skin friction
…………………..Equation 3.23
and may be reduced below the value that normally adopted for working loads alone.
40
Figure 3.6: Pile subjected to negative friction (W.G.K. Fleming)
3.3
Pile Driving Formulas
The most widespread method of estimating the dynamic capacity of piles is
by using pile driving formulas, relating the measured permanent displacement of the
pile at each blow of the hammer to the pile capacity. These formulas are useful in
the field to determine whether the pile has reached satisfactory bearing value at the
pre-determined depth.
41
3.3.1
Concept Of Pile Driving Formulas
Pile driving formulas are based on the theory that the energy balance
between the (dynamic) input energy of the hammer and the (static) work required to
install the pile permanently in a small distance (A simplified picture of the driving
process, and variation of piles resistance with displacement is shown in the Figure
3.7 below). Means, the concept assumes that the soil resistance remains constant
during and after driving operations.
Figure 3.7: Schematic diagram of pile driving (W.G.K. Fleming, et al)
42
3.3.2
Commonly Used Pile Driving Formulas
One of the earliest dynamic formulas, known as the Engineering News
Formula was developed in the late 1800 for timber piles that drives by a drop
hammer, which derived from the work-energy theory. It should only be used when
designing piles with a limited bearing capacity of 50 kips of less. Also, this formula
has been thoroughly discredited (Terzaghi, et al., 1996) as the statistical studies have
shown such poor correlation and poor precision. There is a variety of pile driving
formulas have been suggested, anyway only three of the most commonly used and
easy understand methods to be reviewed.
3.3.2.1 Modified Engineering News Record Formula.
This formula developed by Michigan Highway Department based on a series
of pile driving test that carried out in 1961, with the objective of evaluating the
accuracy of ENR formula.
Qu =
Where,
EWRh WR + n2WP
S+C
WR + WP
……………….. Equation 3.24
E = hammer efficiency
WR = Weight of ram
h = height of hammer drop
n = coefficient of restitution between the ram and the pile capacity
Wp = weight of the piles
C = 0.1 in if the units of S and h are in inches
In this equation, S equals the average penetration per hammer blow, which
can also be expressed as S = 1/N, where S in inches and N as the number of hammer
blows per inch of penetration. The Table 3.2 and Table 3.3 below show the typical
values for E and n respectively. Safety factor to be used is from 3 to 6.
43
Table 3.2: Typical values for the rated efficiency of the hammer, E
(B.M. Das, 1995)
Hammer Type
Single and double-acting hammers
Value E
0.7 – 0.85
Diesel Hammers
0.8 – 0.9
Drop Hammers
0.7 – 0.9
Table 3.3: Coefficient of restitution between the ram and the pile cap, n
(B.M. Das, 1995)
Pile Material
Coef. Of Restitution, n
Cast iron hammer and concrete piles (without cap)
0.4 – 0.5
Wood cushion on steel piles
0.3 – 0.4
Wooden piles
0.25 – 0.3
3.3.2.2 Hiley Formula
This formula was developed by Hiley, A. in 1925. The formula assumes the
energy of the falling hammer during pile driving is proportional resisted by the pile.
The method is widely considered to be one of the better formulas that intended to be
applied to cohesionless, well-drained soils or rock but comparison significant
differences are possible from the results of a static load test. The relationship is
presented by:
eh WRh
Qu = s + 1/2 (c + c + c )
1
2
3
WR + n2WP
WR + WP
eh = Hammer efficiency,
WR = Weight of ram,
h
= height of hammer drop
s
= Average penetration per hammer blow
Wp = Weight of the piles
……………….. Equation 3.25
44
n
= Coefficient of restitution between the ram and the pile capacity
c
= Temporary Compression in inches (refer Table 3.4 below)
Use a factor of safety of 3.
Table 3.4: Temporary Compression In Inches (Manufacturer Printed Manual)
Length of
Piles in feet
‘l’
Medium
Driving 0.006
‘l’
Hard
Driving
0.009 ‘l’
Very Hard
Driving 0.012
‘l’
20
30
40
50
60
70
80
90
100
0.12
0.18
0.24
0.30
0.36
0.42
0.48
0.54
0.60
0.18
0.27
0.36
0.45
0.54
0.63
0.72
0.81
0.90
0.24
0.36
0.48
0.60
0.72
0.84
0.96
1.08
1.20
Cap
Compression,
C1
-
0.10
0.15
0.20
Ground
Compression,
C3
-
0.15
0.20
0.10
Pile
Compression,
C2
3.3.2.3 Gates Method
This method was results of a research performed by Marvin Gates, J.M. in
1957. The basic assumption is that the resistance is directly proportional to the
squared root of the net hammer energy. The relationship is presented by:
Qu = a √(EHE ) (b – log S)
Where,
E = hammer efficiency
HE = rated hammer energy
……………….. Equation 3.26
45
s = average penetration per hammer blow
if Qu is in kips, then S is in inches,
a = 27, b = 1,
if Qu is in KN, then S is in mm,
a = 104.5, b = 2.4, and HE = is in KN-m,
E = 0.75 for drop hammer, E = 0.85 for all other hammers
Use a factor of safety of 3.
3.3.2.4 Danish Formula.
One of the few formulas considered to have a reasonable precision, based on
statically study of pile load test, is Danish formula (Olson and Flaate, 1967).
Qu =
Where,
EHE
S + √(EHEL/2ApEp)
……………….. Equation 3.27
E = hammer efficiency
HE = rated hammer energy
Ep = modulus of elasticity of the pile materials (refer Figure 3.8 below)
L = length of piles
Ap = area of the pile cross section
Qu/Ap (kip/in.2)
46
Figure 3.8: Modulus of elasticity of the pile materials, Ep (B.M. Das, 1995)
3.4
Estimation Of Ultimate Capacity From Pile Load Test
The ultimate load of a pile is usually not well defined in design stage. In
practice, an exact definition of the ultimate load is not all that important provided an
adequate factor of safety is clearly demonstrated. Tests on piles are usually
performed to check that their structural integrity is satisfactory and real capacity with
the forecast load-settlement curve of the anticipated working load. For the engineer,
the load test is considered satisfactory when it has been possible to determine:
The ultimate resistance, Qu
The pile settlement under working load, Qw
The shaft Qs and toe Qb resistance under Qu
There are a number of methods of estimating the pile ultimate capacity from
the load test result. Many authors including Van der Veen (1953), Brinch Hansen
(1963), Chin (1970), Davisson (1972), Mazurklewicz (1972), fuller & Hoy (1977)
and others have proposed their methods to define the ultimate resistance, Qu and
47
possibly the shaft resistance, Qs. Unfortunately, many of the proposed techniques
are either empirical or based on set deformation criteria.
3.4.1
Chin’s Method
The after Chin’s method (1970) derived the ultimate resistance, Qu as
asymptotic ultimate load. This method of estimating the ultimate capacity assumes
the form of the load/deformation curve is hyperbolic and is an empirical method.
The Professor Chin’s method is recognized as one of the simplest methods and has
been adopted by engineers in many countries. It is primarily developed for footings
and precast floating piles. However, at a later time, Chin observed that in many case,
the plot of the settlement, s, versus the ratio s/Q gives a linear relationship when the
pile approaches failure. Also, it is useful in that if the results are plotted at the time
of the test, deviations from the expected curve are easily seen and the test procedure
can be checked. It may in some case also be used to obtain an estimate of shaft or
base load separately.
In a system of hyperbolic coordinates s versus s/Q, a given typical
relationship s-Q obtained from a routine pile test as shown in Figure 3.9(a), system
becomes generally:
In most cases and according to the evidence presented by Chin (1970), a
single straight as shown in Figure 3.9(b).
For other cases, two straight lines plot with an A and B part as illustrated
in Figure 3.9(c).
48
(a)
(b)
(c)
Figure 3.9: (a) Typical routine load settlement curve, s vs. Q; (b) Single
straight line relationship, s vs. s/Q; (c) Bilinear relationship, s vs. s/Q For Piles.
(B. Serge, et al., 2004)
Behavior of a pile that supporting the load purely through shaft friction or end
bearing, could be modeled as Figure 3.9(b). While the plot with its two lines
intersects in Figure 3.9 (b) is supposed to correspond to piles supported by combined
shaft friction and end bearing. Figure 3.10 shows the Chin's method for estimate of
ultimate load while Figure 3.11 shows the stability plot, which consists initially of a
straight line PQ and RS. The inverse slope of line PQ gives the ultimate value of the
skin friction in compression and the second straight line RS with a higher value of
inverse slope, gives the ultimate load bearing capacity.
49
Figure 3.10 : The Chin's method for estimation of ultimate load
(Chin, 1970).
Figure 3.11: Stability plot – the bearing capacity of pile is skin friction plus end
bearing (Chin, 1978).