DESIGN OF AXIALLY LOADED COMPRESSION PILES ACCORDING TO EUROCODE 7
Bauduin C. Besix, Brussels; V.U.B. University of Brussels, Belgium
The Eurocode 7 “Geotechnical Design” is based on “Limit State Design”, tackling the
uncertainties as much as possible at their source through:
selection of characteristic values of variables (loads, soil properties, pile resistance, …);
partial factors applied on the characteristic values;
model factors to account explicitly for uncertainties of the calculation rule if necessary.
Eurocode 7 will propose three “design approaches”. The selection of one of them will be by
National Determination. For pile design, the approaches are:
approach 1 is a “material factoring approach” at load side and a “resistance factoring
approach” at resistance side. The structural and geotechnical design are checked for both
of two separate sets of partial factors.
approach 2 is a “load and resistance factoring approach” and is in several aspects close to
a deterministic approach. The design is checked for one set of partial factors.
approach 3 is a material factoring approach, at load as well as at resistance side. The
design is checked for one set of factors.
The aim of this paper is to introduce to the design of pile foundations based on pile load tests
and on ground test results (semi-empirical and analytical methods) in the frame-work of the
three design approaches.
Detailed attention is devoted to:
the selection of the characteristic value of the pile resistance, accounting for spatial
variability and stiffness of the structure;
the reliability of the prediction of the pile resistance using analytical or semi-empirical
methods which may be accounted for through a “model factor”.
The results of a large test campaign on screw piles in OC Clay and a calculation example
illustrate the proposed procedure when calculation rules using CPT results are used.
MAIN FEATURES OF THE EUROCODE
Safety framework according to the
system and application to Eurocode 7
Eurocode
Eurocode 0 “Basis of Design” establishes principles and
requirements for safety, serviceability and durability of
structures. It deals with the “action” values of loads and
their partial factors, etc. Eurocode 7 gives additional
basis rules for geotechnical design and rules for
checking common geotechnical structures.
The Eurocode requires a semi-probabilistic safety
framework: the rules for checking the design show much
resemblance with deterministic methods but the
variables are introduced in the calculation rules as
design values. The idea behind semi-probabilistic safety
systems is that the uncertainties are treated right at
sources by introducing the “characteristic value” and the
“design value” of the variables. The characteristic and
design values have a statistical background.
Such a safety system is different of the classical
deterministic systems which treats all sources of
uncertainties through a single (global) safety factor.
In a semi-probabilistic framework, the design fulfils the
ultimate limit states requirements if the calculated design
value of the action (or action effect) Ed is lower than the
calculated design value of the resistance Rd:
Ed < Rd
Due to the novelty of Limit State Design in most of the
European Countries, and the wide variety of soil
conditions, soil testing and design methods, Eurocode 7
allows for three different design approaches when
assessing Rd and Ed. The choice of the approach and
the value of the partial factors is left to national
determination and will have to be indicated in the
National Document accompanying Eurocode 7.
Approach 1
The design shall be checked against failure in the soil
and in the structure for two sets of partial factors. The
partial factors are mainly applied at the source as load
and material factors. Table 1 indicates typical values as
proposed in Annex A of prEN 1997-1: 2001(E). They
may be modified by national determination. Ultimate limit
states are usually checked by applying partial factors to
the shear resistance parameters c’ and ϕ’ (or cu).
Design value of pile and anchor resistances are
obtained by applying the partial factors on their
(measured or calculated) resistance. When load factors
applied at the source lead to physically impossible
situations, they may be applied to the effects of the
actions. Where it is obvious that one set governs the
design, it is not necessary to perform full calculations for
the other set. Often the geotechnical “sizing” is governed
by set 2 and the structural design is governed by set 1.
Table 1: Partial factors in approach 1according to Annex
A of prEN 1997-1: 2001(E)
Set 2
Set 1
Actions or action effects
permanent
permanent variabel
unfavourable
favourable
1.0
1.0
1.3
1.35
1.0
1.5
Ground parameters
c’
cu
Tan ϕ’
1.25
1.25
1.4
1.0
1.0
1.0
Piles
Resistance
1.3-1.6
( tanϕ’ &
c’:1.0)
1.0
Approach 2
The design shall be checked against failure in the soil
and in the structure for one sets of partial factors. The
partial factors are applied as load and resistance factors:
the design value of the actions is obtained by multiplying
their effects by the load factors and the design value of
the resistance offered by the soil is obtained by applying
the partial factors to the resistance assessed using
characteristic values for the shear strength of the soil.
Approach 2 is thus fully a load and resistance factoring
approach. Table 2 indicates typical values as proposed
in prEN 1997-1:2001(E). They may be modified by
national determination.
Table 2: Partial factors in approach 2 according to
Annex A of prEN 1997-1: 2001(E)
Effect of actions
permanent
permanent
unfavourable
unfavourable
1.35
1.00
Ground parameters
variabel tan ϕ’
c’
cu
1.50
1.00
1.00
Resistance
1.00
Factor >1.0
Approach 3
The design shall be checked against failure in the soil
and in the structure for one sets of partial factors. The
effects of loads coming from the structure are multiplied
by the load factors 1.35 and 1.50 to assess their design
values. Design values of actions arising from the soil or
transferred trough it are assessed using design values of
soil strength parameters. Design values of the soil
resistance are obtained by applying the partial factors on
the shear strength parameters. This approach is fully a
material factoring approach. Table 3 indicates typical
values as proposed in Annex A of prEN 1997-1:
2001(E). They may be modified by national
determination.
Table 3: Partial factors in approach 3 according to
Annex A of prEN 1997-1: 2001(E)
Actions or action effects
Action from
The structure
From or through
the ground
permanent permanent
unfavourable favourable
1.35
1.00
1.0
1.00
Ground
parameters
variable tan ϕ’
1.50
1.30
c’
Resistance
cu
1.0
1.25 1.25 1.4 (tan ϕ’,c’:1.25 ;
cu : 1.40)
In some cases the effects of uncertainties in the models
used in the calculations should be considered explicitly.
This may lead to the application of a coefficient of model
uncertainty which modifies the results from the
calculation model to ensure that the design calculation is
either accurate or errs on the side of safety:
- at the load side: γSd applied either to the actions or to
the actions effects;
- at the resistance side: γRd applied to the resistance.
The characteristic value of material properties is the
value having a prescribed probability of not being
attained. For geotechnical design, prEN1997 defines
the characteristic value of a ground property or of a
resistance as “a cautious estimate of the value affecting
the occurrence of a limit state” and recommends: “If
statistical methods are used, the characteristic value
should be derived such that the calculated probability of
a worse value governing the occurrence of a limit state
is not greater than 5%” A nominal value may be used as
the characteristic value in some circumstances.
In some cases, when deviation in the geometrical data
have significant effect on the reliability of the structure,
the geometrical design values are defined by:
ad = anom + Δa
where Δa takes account of the possibility of unfavourable
deviations from the characteristic (nominal) value. Δa is
only introduced when the influence of deviations is
critical; otherwise they are covered by the partial factors.
APPLICATION OF THE PRINCIPLES OF THE
EUROCODE TO THE DESIGN OF AXIALLY LOADED
PILES
The Eurocode 7 allows the design of pile foundations
using the following methods:
- The results of static pile load tests;
- From ground test results using semi-empirical or
analytical methods;
- Dynamic pile load test and wave equation analysis
(not further discussed in this paper).
When assessing the validity of a calculation method
(semi-empirical model or analytical), the following items
should be considered:
- Soil type;
- Method of installation of the pile, including the method
of boring or driving;
- Length, diameter, material and shape of the shaft and
the base of the pile;
- Method of ground testing…
A model factor may be needed to ensure that the
predicted resistance is sufficiently safe.
The table 4 below summarises the main factors affecting
the reliability of the design of the pile foundation and the
way the uncertainties are covered in the semiprobabilistic framework according to Eurocode 7.
When designing foundations, advantage should be
taken for the effect of stiffness of the structure carried by
the pile and the ability of the foundation to transfer loads
from “weaker” to “stronger” piles.
Table 4: Overview of main sources of uncertainty in
ultimate limit state design of pile foundations and
corresponding partial factors
Source of
Aspect to consider
uncertainty
Loads and effects - Unfavourable
deviation
of loads
from representative values
of load
- Simplifications in models for
effect of loads
Geometrical data Base and shaft diameter
Base level
Spatial variability Soil investigation: the more
of pile resistance extensive, the better the
over the site due variability is known
to variability of soil
Reliability of the
predicted bearing
capacity
- Pile load test: effect may be
neglected
- Semi-empirical
rule:
calibration of the rule by
static tests
- Dynamic test
“partial factor”
-
Load factors γF γQ
Partial factors γm on soil
shear strength parameters
(when relevant)
Small deviations to be
included in calculation rule
through γcal
Small
and
unexpected
deviations through γb and γs
Large deviations: Δa
Characteristic value of pile
resistance
depending
amongst other of the number
of tests (number of static
tests, in situ tested profiles,
dynamic tests) (through ξ
factor)
Calibration factor γcal
Calibration of the results
Larger deviations
than expected in
previous steps
- Effect of installation is
different than expected
- Deviations of calculation
model and of real value of
characteristic
value
of
bearing
capacity
from
calculated value
Partial factor on
resistance and on
resistance γb, γs or γt
base
shaft
ULTIMATE COMPRESSIVE RESISTANCE FROM
STATIC PILE LOAD TESTS
Design of pile foundations based on static load tests
may be unusual in some countries. However, the
procedure according to prEN1997 (2001) is explained in
this section as design procedures based on calculations
always need to be related to the results of pile load
tests. The procedure for design of piles from the results
of static pile load tests is according to following scheme:
Figure 1: Procedure for the design of piles from static
pile load tests and partial factors
Assessment of the characteristic value of the pile
resistance
The N pile load tests deliver N values Rci (or Rbi and Rsi)
of ultimate bearing capacity, (being recommended by
prEN1997-1:2001 as the value at a settlement of 10% of
the pile diameter) out of which the characteristic value of
the pile compressive resistance Rck (or Rbk and Rsk) has
to be selected. It should account for:
1. The number of tests: as more test become available
the uncertainty of the variation of the bearing capacity
at the site considered reduces;
2. The variability of the measured bearing capacity:
when a large variability is observed, lowest value of
the measured values which should govern the
foundation design; when the variability is small (small
variation coefficient), than a value close to the mean
value should govern the design;
3. The stiffness of the structure and its ability to transfer
loads from “weak” to “strong” piles.
The characteristic value of the pile compressive
resistance Rc,k is assessed using the equation:
Rc,k = min{(Rc;m)mean/ξ1, (Rc;m)min/ξ2}
Where:
(Rc;m)mean: the mean value of the measured pile
resistances;
(Rc;m)min: the lowest measured pile compressive
resistance;
ξ1 and ξ2: correlation factors relating the mean and the
lowest value to the characteristic value of the
pile compressive resistance.
Table 5 indicates values of ξ1 and ξ2 proposed in prEN
1997-1: 2001(E); they may be modified by national
determination (values in prEN 1997 are slightly different
from the values quoted in ENV 1997).
Table 5: values of ξ1 and ξ2 for pile load test, piles under
structure allowing no load transfer.
Number of pile load tests
ξ1 applied to the mean of the
measured compressive resistances
ξ2, applied to the lowest of the
measured compressive resistances
1
1.4
2
1.3
3
1.2
4
1.1
≥5
1.0
1.4
1.2
1.05
1.0
1.0
The favourable effect of the stiffness of the structure
(which is independent of the variability of the pile
resistance over the site considered, but allows to a
certain extent to transfer loads from “weaker” piles to
“stronger” piles) is introduced by dividing the values ξ1
and ξ2 by a factor 1.1.
Some more theoretical considerations on the values of ξ
are given in section ”Ultimate compressive resistance
from ground test results”.
Assessment of the design value of the pile
resistance
The design value of the pile compressive resistance is
deduced from the characteristic value using the
following equation:
- When the characteristic values of the base and shaft
resistance are known separately:
Rc,d = Rbk/γb + Rsk/γs
- When the characteristic values of the base and shaft
resistance are not known separately, but the
characteristic value of total resistance is known:
Rc,d = Rck/γt
Typical values for the partial factors as proposed in
prENV 1997-1:2001(E) are indicated in table 7.
Clearly, approach three is not suited for establishing
design values of the pile resistance on base of the
results of pile load tests.
Remarks:
1. Usually only the total load acting on the pile is
measured (and not the shaft and base resistance
separately). In this case, one may apply the partial
factor γt on the total resistance or one may distinguish
between base and shaft resistance, eg by calculations
based on the results of the ground investigation. Of
course, the values of base and shaft resistance
assessed in this way will not be exact, but the effect of
the error on the design value of the pile resistance is
rather small.
2. The difference of the values of the partial factors
between driven, CFA and bored piles is mainly related
to the increasing probability of unexpected effects
during pile installation affecting adversely the pile
bearing capacity. These adverse effects are
considered to be more likely to affect pile base than
the shaft bearing capacity. It might be considered as
strange that prEN 1997-1 is not consistent in this
respect between approaches 1 and 2.
ULTIMATE
COMPRESSIVE
FROM
GROUND
TEST
APPROACHES 1 AND 2
RESISTANCE
RESULTS,
This section is devoted to the assessment of the design
value of the pile compressive resistance according to
prEN 1997-1:2001, clauses 7.6.2.3 (1) to (9). They are
the core of the design of piles using ground test results
in approaches 1 and 2. An alternative method, starting
directly from global characteristic values of base and
shaft resistance (indicated in clause (10)) will be
explained later on this paper. Approach 3 requires a
slightly different procedure.
The proposed procedure is similar to the procedure used
when pile load tests are available, excepted that the pile
resistance is calculated at each test location. The
characteristic and design values have to be deduced
from all these calculated values, in a similar way as
done for static load tests (see fig. 2). Due to this
similarity, the method will be referred to as “model pile
procedure”. As the bearing capacity of a “model pile” is
derived at each tested profile, clearly the design value of
the bearing capacity is obtained by dividing the
characteristic resistance by a partial factor: it is a
resistance factoring approach and is thus restricted to
approaches 1 and 2. The procedure is very well suited
when the design is based on the results of in-situ tests
combined with calculation rules allowing to derive the
pile resistance from any measured “resistance” (CPT,
PMT… methods), although it might be as well applied to
analytical methods for pile design.
The design procedure involves three main steps:
1) assess the compressive resistance of an hypothetic
pile at each test location by using a calculation rule
and by calibrating the result if necessary;
2) select the characteristic value of the pile resistance
from the assessed compressive resistances;
3) calculate the design value of the pile compressive
resistance from the characteristic value.
Figure 2: design procedure using semi-empirical
methods and the “model pile procedure”
The different sources of uncertainty will be treated at
their source in the relevant step.
Calculation rule and calibration factor
Calculation rule
The calculation rule aims to predict as accurately as
possible the ultimate pile compressive resistance, taking
account of:
- The ground conditions
- The effects of pile installation
- The dimensions and the shape of the pile (base and
shaft)
- Effects which may affect the results of the test and the
compressive resistance of the pile in different ways
Lot of calculation rules were developed parallel to the
corresponding in situ testing method in the past. De
Cock et al, 1997 provide a detailed review of the
calculation rules most widely used in Europe.
When ground tests are used, the compressive Rc
resistance is obtained as the sum of the base resistance
Rb and the shaft resistance Rs:
Rci = Rbi + Rsi
The calculation rule (for base as well as for shaft
compressive resistance) always involves some account
for the effects of pile installation. This may be done
either directly in the calculation (eg charts for base and
shaft resistance for PMT or through bearing capacity
factors when using analytical methods) or in two steps
using explicit “installation factors” (eg when using CPT
method according to De Beer 1971-1972 or prEN1997-3
annex B4):
A first step starts from the measured in-situ cone
resistance and translates it into unit base and shaft
resistances for a cylindrical full displacement
(driven) pile
A second step corrects the results for obtained in
the first one by taking account for the shape, the
installation method… of the real pile though “shape”
and “installation factors
Calibration of the calculation rule: model factor
Calculation rules and installation factors shall have been
validated by static pile load tests. Of course, no
calculation rule is perfect: no calculation rule exists
which give for each prediction, whatever the soil
conditions etc a 100% exact prediction of the pile
bearing capacity. To cover the uncertainty of the
prediction, the Eurocode allows to introduce “model
factors” or “calibration factors”. The need of a
“calibration” arises from the inaccuracy and the
variability of the predicted bearing capacity. When
checking the reliability a calculation rule with pile load
tests consideration is to be given to:
- The mean value of the predictions compared to the
mean value of the predictions
- The variability of the prediction
The value of calibration factor is thus related to the
calculation rule and is obtained by comparing load tests
results and corresponding predictions performed in the
past (eg to validate the calculation rule). The calibration
factors may aim to provide a required reliability to the
prediction: for instance, one may wish to make such
predictions that if load tests are performed, 95 % of the
measured bearing capacities will be higher than the
predictions (a 95% reliable prediction is consistent with
the partial factors of approach 1). Eurocode 7 gives no
procedure to assess the value of a calibration factor.
The procedure proposed below is in line with the semiprobabilistic safety approach and is borrowed from
Eurocode 0.
The calibration or model factor may be determined by
establishing a histogram of the ratio Rc,predicted /
Rc,measured. On basis of this histogram, one makes an
assumption about the distribution, eg normal or lognormal. Assuming that enough representative test
results are available so that complementary test will not
affect the distribution, one establishes the fractile
corresponding to the required reliability of the prediction:
if one wishes that only 5% of the measurements will be
lower than the predicted value, one establishes the 5%
fractile of the distribution (Rc,measured / Rc,predicted)5% in
accordance to the following statistical formula:
(Rc,measured / Rc,predicted)5% = (Rc,measured / Rc,predicted)mean
⎡
* ⎢1 −
⎢⎣
V.tn5%−1
⎤
1
+ 1⎥
n
⎥⎦
Where:
V: coefficient of variation of the ratio Rc,measured /
Rcpredicted
n: number of tests considered to calibrate the
calculation rule
t n5%−1 : student factor for 5% fractile, n-1 degrees of
freedom
The value of the calibration factor is:
γcal = 1/ (Rc,measured / Rc,predicted)5%
6
5
n
4
3
2
1
0
0.800.85
0.850.90
0.950.95
0.951.001.051.00
1.05
1.10
Rc;measured / Rc;predicted
1.101.15
1.151.20
1.201.25
Figure 3: Example of histogram (Rc,measured / Rc,predicted)
The “calibrated pile compressive resistance” is the
product of predicted compressive resistance as
calculated using the semi-empirical rule by the
calibration factor. If the histogram is representative,
each later prediction will be somewhere on it, but on an
unknown place (ie the ratio Rmeasured/Rpredicted if any load
test should be performed); the only what is achieved by
the calibration factor is that there is 95 % chance that
the real value of the compressive resistance will be
higher than the predicted and calibrated value.
The calibration factor (or model) has to be introduced in
the calculations together with the further the partial
factors.
Discussion
Three main “philosophies” may be compared when
selecting a method for calibrating the calculation rule
(and especially the values of the installation factors):
- The first one is to work at a very high level of details;
the extreme of this being that each type of pile (or
even each way of performing a pile) is calibrated for
the main relevant types of soil conditions (normally
consolidated and overconsolidated sand; normally
consolidated and overconsolidated clay; loam; sandclay mixes…). This approach allows the highly
detailed values of installation factors (in fact, for each
type of pile in each type of soil). However it needs an
enormous amount of pile load test: a significant
number for each type of pile, in each type of soil (for
realistic statistical approaches, let’s say five pile load
tests up to failure).
- The second approach is to work at a lower level of
details by bringing “similar” piles in similar main soil
categories together. This lead to larger statistical
samples, but the resolution between slightly differing
piles is diminished: the same installation and model
factors are then attributed to a family of piles which
were assembled for that purpose. The main
advantage of this system is the much larger sample,
which may turn out in lower calibration factors.
- The third approach is to analyse all available ratios
Rmeasured/Rcalculated as one single sample. This leads to
one single value of the calibration factor for all piles in
all soils (but different installation factors). Depending
of the variability of the predictions of certain types of
piles compared to the global variability, some types of
piles might then benefit of a too “favourable”
calibration factor (in fact, this means that the
calibration factor valid for the whole sample is too low
for some sub-families in this sampling; as an example,
it might be expected that the variability of the ratio
Rmeasured/Rcalculated of bored piles in sand is larger than
the variability of the ratio Rmeasured/Rcalculated for all piles
together). This too favourable calibration factor can be
“corrected” by differentiating the values of the partial
safety factors.
From a theoretical point of view, one might try to
calibrate separately the base and the shaft resistance.
However, this needs very careful and expensive static
load test allowing separate measurement of base and
shaft resistance. Further on, often a negative correlation
between shaft and base resistance is observed,
justifying the simplification of a global calibration.
It is important to note that:
- the assessment of the value of the calibration factors
on base of statistical methods alone may not be
always sufficient: the calculated value, combined with
the value of partial safety factors, should not lead to
“trend break” with existing successful proven design
practice;
- the value of the model factor is related to the value of
the partial factor on the loads and on the pile
resistance, as their product provides the required
safety level. Thus, the required reliability of the
calculation rule and hence the value of the model
factor may be somewhat different according to the
design approach 1, 2 or 3 chosen.
Characteristic value of the pile compressive
resistance
The second step in the design procedure is to select the
characteristic value of the pile compressive resistance.
The characteristic value is obtained from the N
calculated (and calibrated) pile compressive resistances
Rci (i ranging from 1 to the number N of test locations) at
each test location (remember the analogy of “model
pile” with pile load test). This characteristic value should
take account of:
1 The variability of the compressive resistance of the
piles over the site. This variability will be estimated by
comparing the calculated values of the pile
compressive resistance for each test location for the
presumed pile length. When the variability of the
calculated compressive resistances is small, the
characteristic value of the pile compressive resistance
should be selected emphasizing the mean value of the
calculated pile resistances; when the variability is
large, the characteristic value should focus on the
smallest calculated resistance. This has been
introduced in the future EN through he following
considerations:
− When the coefficient of variation of the pile bearing
capacity is smaller than about 10%, the
characteristic value of the pile resistance is selected
through the mean value of the calculated and
calibrated pile bearing capacities.
− When the coefficient of variation of the pile bearing
capacity is larger than about 10%, the characteristic
value of the pile resistance is selected from the
lowest value of the calculated and calibrated pile
bearing capacities.
2 The number of tests: the larger the number of test, the
smaller becomes the uncertainty of the variation of the
bearing capacity in the site considered is reduced.
3 The stiffness of the structure and its ability to transfer
loads from weak to strong spots: Under a stiff
structure where loads can be redistributed, the
characteristic value will be a cautious estimate of the
mean value of the pile resistance in the
“homogeneous group” considered; under a structure
where no loads can be redistributed, the characteristic
value will be a cautious estimate of the lower
resistance in the “homogeneous group” considered.
The characteristic value of the pile compressive
resistance Rc,k is obtained from the calculated pile
compressive resistance at each test location (ie CPT or
PMT profiles, boring providing vertical profiles of shear
strength parameters etc) according to the following
equation:
Rc,k = min{(Rc,cal)mean/ξ3, (Rc, cal)min/ξ4}
Where ξ3 and ξ4 are correlation factors that depend of
the number of tested profiles N (eg number of CPT,
number of PMT …) and are applied respectively:
To the mean value:
As: (Rc;cal)mean = (Rb;cal + Rs;cal)mean = 1/N*Σi (Rb;cal;i
+Rs;cal;i) = 1/N*Σi Rb;cal;i +1/N*ΣiRs;cal;i
= (Rb;cal) mean + (Rs;cal)mean, it follows that:
Rc,k = (Rc;cal)mean/ξ3 = (Rb;cal + Rs;cal)mean/ξ3 =
(Rb;cal)mean /ξ3 + (Rs;cal)mean/ξ3
To the lowest value:
(Rc;cal)min = (Rb;cal + Rs;cal)min :
the lowest of the calculated compressive
resistances at all the tested profiles, thus:
Rc,k =(Rb;cal + Rs;cal)min/ξ4 ≠(Rb;cal) min /ξ4+ (Rs;cal)min /ξ4
It is important to note that the “lowest value” is the
lowest of the total compressive resistance, and not a
combination of the lowest base compressive resistance
deduced from one test with the lowest shaft friction
deduced from another test.
Values of ξ3 and ξ4 are proposed by prEN 19971:2001(E) in the table below; they may be modified by
national determination.
Table 6: values of ξ3 and ξ4 when ground test results are
used, piles under structure allowing no load transfer
Number of tested profiles
1
2
3
4
5
7
10
20
ξ3 applied to the mean
ξ4, applied to the lowest
1.40
1.40
1.35
1.27
1.33
1.23
1.31
1.20
1.29
1.15
1.27
1.12
1.25
1.08
1.20
1.00
The values quoted in table 6 are based on the following
assumptions:
- When the coefficient of variation of the pile bearing
capacity is smaller than 10%, the characteristic value
of the pile resistance is governed by the mean value
of the calculated pile compressive resistances.
- When the coefficient of variation of the pile bearing
capacity is larger than 10%, the characteristic value of
the pile resistance is governed by the lowest value of
the calculated pile compressive resistances.
- The structure is not strong and stiff to transfer load
from a “weak” spot to a strong spot. If the structure is
able to do so, the ξ values may be divided by 1.10
When different areas can be identified in a global site,
where in each of these areas the tests indicate a small
variability, the global side may be subdivided into
several “homogeneous areas” which may be treated
separately according to the formulas above. The
number of tested profiles to be considered in such an
area is the number of test in the “homogeneous” area
considered (not the total number of tests over the whole
site).
The choice of a “boundary” for the coefficient of variation
of about 10% provides the ratio between ξ1 and ξ2.
Clearly this ratio increases with the number of tests as
the statistical population increases. The value of ξ3 and
ξ4 decrease with increasing number of tests because as
the number of tests increases, the uncertainty about the
soil decreases. Some theoretical backgrounds to the
values of ξ3 and ξ4 are given in (Bauduin, 2001).
The values of ξ3 relating the characteristic value to the
mean value of the calculated resistances (structure
without load transfer) corresponds fairly good to a 5%
fractile of calculated compressive resistances from the N
test, V being considered as known and slightly higher
than 10%.
The favourable effect of the stiffness of the structure
(which is independent of the variability of the pile
resistance over the site considered, but allows to a
certain extent to transfer loads from “weaker” piles to
“stronger” piles under the foundation) is introduced
through the reduction by 1.1 of the values ξ3 and ξ4.
Then the value of ξ3 is close to the theoretical value for
a 95 % reliable guess of the mean value of calculated
compressive resistances from the N tests, V being
considered as known and slightly higher than 10%.
Care should be taken if taking advantage of the
reduction the ξ values by 1.1 for stiff structures in
following situations:
- Brittle soil, tensile piles: failure of the pile may be
followed by a drastic (post peak) reduction of the
compressive resistance; in such cases, it is doubtful if
there is enough strength left in the “non failed” piles to
allow redistribution of loads, even for stiff structures
- When the possibility of redistribution of loads have
been considered explicitely in an earlier stage of the
design, eg by performing a soil-structure interaction
analysis, specially modelling non-linear (e.g. elastoplastic) pile behaviour
-
Note: alternative procedure
As an alternative to the “model pile” procedure above,
prEN 1997-1 allows to assess the characteristic values
by: Rb,k = Ab . qb,k and Rs,k = Σ As;j . qs,k;j
Where qb,k and qs,k;j are characteristic values of base
resistance and shaft friction in the various strata derived
from values of ground parameters. These characteristic
are derived for the whole layer considered, according to
the principles for the selection of characteristic values of
ground parameters: this method abandons the idea of
“model pile”. The alternative procedure may be
appropriate when:
Using tables or charts indicating qb,k and qs,k values
as a function of any measured soil parameter for
determining the characteristic resistance from any
given soil parameter;
Using (analytical) formulas to calculate the pile
bearing capacity using characteristic values of soil
shear strength parameters (ck’ and ϕk’ or cu;k) valid
over the site considered.
Variability, # of tests
Stiffness of structure
Tables;
charts
"characteristic
value" of
parameter
Measured
soil
parameter
Shear strength
parameters ϕ,
c;cu
Characteristic
value ϕk, ck; cu;k
Variability, # of tests
Stiffness of structure
Rck = Rb,k + Rs,k
= Ab * qb,k +
Σ As;j . qs,k;j
Calculation
rule
(
l ti l)
Calibrated value
of the
characteristic
pile resistance
Reliability of
prediction; model
f t
Design value
Rc,d = Rb,k/γb +
Rs,k/γs
Uncertainties:
partial factors
b d
Figure 4: Design procedure using semi-empirical
methods alternative to the “model pile procedure”.
The value of qb,k and qs,k;j (tabulated or chart values or
derived from characteristic values of the shear strength
parameters ck’ and ϕk’ or cu;k) should readily account for
the variability of the ground parameters, the volume of
soil involved in the failure mechanism considered, the
spatial variability of the pile resistance and the stiffness
of the structure. As a consequence of this, the factor ξ
should not be used explicitly in this alternative method.
When charts or tabulated values are established, they
should be at the side of safety as they directly provide
characteristic values of resistances which should include
the effects of variability of the resistance, of the
installation effects etc…Some hints for the selection of
characteristic shear strength parameters are given in the
section dealing with approach 3.
It is the author’s opinion that this alternative method is
less appropriate than the “model pile” approach,
because it does not allow for proper consideration of
spatial variability of the pile compression resistance and
the stiffness of the structure:
On one hand, the “characteristic value” of qb,k and
qs,k;j is selected for the soil layer as a homogeneous
volume, and do not necessarily reflect the variability
-
of the bearing capacities of the piles over the site:
weak spots in terms of bearing capacity may be not
discovered: this may lead to an overestimate of the
characteristic value of the pile resistance;
On the other hand, reduction of variance (i.e. the
variability of the pile resistance may be much
smaller than the variability of the shear strength
parameters) is difficult to treat: this may lead to an
overestimate of the variability of the pile resistance
There is no or a poor relationship between the
statistical confidence which can be gained from the
number of tests and the way it affects the
characteristic value of the pile resistance: having
twelve triaxial test on samples from one single
boring gives poor information about the variability of
the pile resistance over a site; Four borings with
three triaxial test delivers much more information,
although from standard statistical methods, both
samples will give the same characteristic value.
It is much more complicated to treat local variability
of the pile resistance over the site considered when
using charts or tables established from a data-bank
having a regional character.
Design value of the pile compressive resistance
The design value of the pile compressive resistance is
deduced from the characteristic value using the
following equation:
Rc,d = Rbk/γb + Rsk/γs
The values of the partial factors are given in the table
below (same values as for static load tests); these
values may be modified by national determination.
Table 7: Partial factors for approaches 1 and 2 for
different types of piles according to prEN 19971:2001(E)
Type of pile
Driven piles
Bored piles
Continuous flight
auger
Approach 1,
γb
γs
1.3
1.30
1.3
1.60
1.3
1.45
set 2
γt
1.30
1.45
1.35
Appr. 1, set 1
γb
γs
γt
1.0
1.0
1.0
1.25
1.0
1.15
1.10
1.0
1.10
Approach 2
γb =γs=γt
1.10
1.10
1.10
Combining the equation for characteristic value and the
equation above delivers (“model pile procedure”):
- When the mean value governs the characteristic
value:
Rc,d = Rbk/γb + Rsk/γs =
(Rb;cal) mean /(ξ3. γb) + (Rs;cal)mean/(ξ3. γs)
- When the lowest value governs the characteristic
value:
Rc,d = Rbk/γb + Rsk/γs = (Rb;cal /γb + Rs;cal/γs) min /ξ4
where (Rb;cal + Rs;cal)min is the lowest of the
calculated compressive resistances.
The Eurocode proposal is to determine a single value of
the calibration factor for all piles in all soil and to deal
with probable larger variation coefficient of the ratio
Rmeasured/ Rcalculated for CFA and bored piles trough the
higher value of their partial safety factor (see third
philosophy for assessing the value of the calibration
factor). However, if different values of calibration factors
are introduced for different main types of piles (all based
on the same reliability criterion of the prediction and
taking into account its variability), it seems more
appropriate to apply the same value of the partial factors
to all types of piles. Such a system is allowed to be
applied by national determination.
The margin between the predicted compressive
resistance and the design value is (for a given ξ-value)
fully determined by the product Γ = γcal . γb and γcal . γs
One might argue that the split of Γ is an unnecessary
complication and that a single factor should be given.
The advantage of the distinction between a “calibration”
factor and a “safety” factor, is that for different
calculation rules, the same level of reliability of the pile
compressive resistance (in a probabilistic sense) can be
obtained when the same reliability criterion is required
for the calibration factor. So, different calculation rules X,
Y or Z (when calibrated on the same requirements) will
have their own value of the calibration factor and, when
these will be combined with the same values of the
partial safety factors, will lead to almost equal reliability
of the design resistance.
PrEN 1997-1:2001 stresses that when the alternative
method is used, the values of the partial factors γb and γs
as proposed in annex A may need to be corrected by
model factors as they were primarily established for the
design from static load test and from the “model pile”
procedure using both the ξ values to deal with variability
of pile resistance. In this respect, consideration should
be given to the following:
When standard tables or charts are used, the value
of the model factor depends (amongst other) on the
way the characteristic value of charts and tables
have been derived from the underlying data-base:
do they deliver a “cautious mean” value or a “low”
value ?…The reliability of the prediction using the
chart or tables should be known and, if necessary,
corrected by a calibration factor assessed similarly
as above
When analytical methods are used starting from
“characteristic values” of the shear strength
parameters, the value of the model factor depends
on the reliability of the analytical calculation rule and
correction factors for installation used. Usually,
analytical methods have large standard deviations
of the ratio Rc, measured/Rc, predicted (Jardine et al 1997).
The ξ values treat the variability of the pile
resistance in a slightly different way compared to
methods for the assessment of characteristic values
of soil parameters.
ULTIMATE
COMPRESSIVE
RESISTANCE
FROM GROUND TEST RESULTS, APPROACH 3
Approach 3 is fully in a material factoring approach: the
characteristic values of the strength parameters are
divided by the material factor γtanϕ γc or γcu before
entering the calculation rule. This provides design values
of the base and shaft resistance. The figure 5 illustrates
different steps of the procedure.
Calculation rule
(analytical)
N tested profiles
giving values of Step 1
shear strength
parameters
Design values of
Design value Rcd =
Characteristic
shear strength Step 3
Rb (ϕd, cd; cud)/γcal +
value ϕk, ck; Step 2
parameters ϕd, cd
cu;k
Rs(ϕd,cd;cud)/γcal
or cu;d
Variability, # of tests
Stiffness of structure
Uncertainties:
partial factors
γtanϕ γc or γcu
Reliability of
prediction;
model factor
Figure 5: Design procedure for approach 3.
Step 1: Selection of characteristic value
In a first step, the characteristic values of the soil
strength parameters have to be selected from the test
results and other relevant information accounting for the
variability of the ground parameters, the volume of soil
involved in the failure mechanism considered, the spatial
variability of the pile resistance and the stiffness of the
structure:
As usually the length of the pile is large compared to the
autocorrelation length of the variation parameter value,
the characteristic value of the shear strength parameters
to be used to assess the shaft resistance will be a
cautious estimate of the mean value. Not only the global
mean and standard deviation should be considered, but
also the variation of the mean values in the different
verticals tested: is the mean of the test results along a
vertical (e.g. the samples of a given boring) significantly
different of the others, then this boring indicates a weak
area which should be considered when assessing the
characteristic value. In fact, the variation of the mean
values of each tested vertical yields very valuable
information about the variability of the pile resistance
over the site.
Usually the soil volume involved in the failure
mechanism around the base is rather small (especially
for small diameter piles), so that the characteristic value
of the shear strength parameters to be used for the
assessment of the base resistance should be a cautious
estimate of the low (point) values or of the local mean
values of the shear strength parameters around the tip
level.
Step 2: Design value of the shear resistance
parameters
Once the characteristic value of the shear strength
parameters has been selected, the design value is
readily assessed by dividing them by the partial factors
indicated in table 3:
cd’= ck’/γc’ = c’/1.25 and tanϕd’ = tanϕk’ / γtanϕ =
tanϕk’ / 1.25; cud = cuk/ γcu = cu,k/1.4
Step 3: Design value of the pile resistance
The design value of the shear strength parameters are
entered into the analytical formulae to assess the design
value of shaft and base resistance:
Rc,d = Rb,d + Rs,d
Where: Rbd = Rb(cd’, ϕd’; cud) and Rsd = Rs(cd’, ϕd’ or cud)
If model (calibration) factors are needed, they should be
applied on the design value of the pile resistance.
EXAMPLE OF ASSESSMENT OF CALIBRATION
FACTOR FOR COMPRESSIVE PILES IN OC CLAY
USING CONE PENETRATION TEST RESULTS
This section illustrates the assessment of a “calibration
factor” for a semi-empirical calculation rule and
corresponding installation factors based on the results of
cone penetration tests when using the “model pile
method”. The required reliability (95 %) fits in an
approach 1 framework. Of course, the calibration of any
other calculation rule (semi-empirical, analytical or
charted values) for any other required reliability could be
done on a fully similar way.
The results of a large test campaign performed on screw
piles in O.C. Boom clay at Sint Katelijne Waver, reported
by Huybrechts (2001), complemented by other test on
similar piles in OC clay in Belgium will be used. The
calculation rule based on E1 CPT results as used in
Belgium (Holeyman et al, (1997) is applied:
- Base resistance:
Rb = αb .β .εb .Ab .qb
qb ultimate unit bearing resistance derived from the
E1 cone resistance according to the calculation
method of De Beer (1971-1972), which has been
established for cylindrical driven piles;
Ab nominal cross section of the base of the pile
deduced from the largest nominal diameter of the
base screw;
αb installation factor, taking into account the
difference between the pile as executed and the
cylindrical driven pile; proposed value for screw
piles in OC clay: 0.8, as proposed by Maertens et
al (2001);
β shape factor for non-circular or non square pile
base cross section; β = 1.0 as the pile is
cylindrical;
εb parameter referring to the scale dependency of
soil shear strength, taking into account the
different effect of fissures in the OC clay on the
cone resistance and the pile base resistance; εb =
1- 0.01(Db/dc – 1) where Db/dc is the ratio of the
largest pile base diameter to the diameter of the
CPT cone.
- Shaft resistance:
χs
Hi
Rs = χs .ΣHi ηpi. qci
nominal pile shaft perimeter, deduced from the
nominal shaft diameter: χs = π Ds
thickness of layer i
qci mean cone resistance in layer i
ηpi global empirical factor allowing to transform the
cone resistance to local shaft friction qsu; the
factor depends on the soil type, the pile
installation method and the roughness of the
shaft;: ηpi = 0.033 ( for qc between 1.5 and 3
MPa)
Remarks:
− calculation rules which account explicitly for each qc
value, e.g. every 0.2 m, have to be used in a “model
pile procedure” and cannot reasonably be used in the
“alternative method” or in approach 3.
− all consideration given in this section could easily be
translated to the calculation rule indicated in
prEN1997 annex B.4.
Analysis of the tests at Sint Katelijne Waver on screw
piles in OC Boom clay
The calculation rule is applied to the CPT performed at
the location of each pile tested to be tested. The
predicted base and shaft resistances and total pile
compressive resistances for each pile are summarised
in the table below. The value of the measured ultimate
compressive resistance at a relative settlement of 10%
of the nominal pile base diameter Db and the ratio of the
measured resistance to the calculated resistance are
also indicated.
Table 8: summary of predicted and measured ultimate
compressive resistances for screw piles at Sint Katelijne
Waver
Pile
Db
Ds
εb
Ab . qb αb.εb.Ab πsDsΣHi χΣηpiqciHi
.qb
qci
[kN]
[kN]
Rc;predicted
Rc;
Ratio
= εb.αb.qb.Ab measured
+ χΣηpiqciHi
[m]
[m]
[kN]
[kN]
[kN]
[kN]
(measured/
A2 0.450 0.380 0.88 363.2 255.7 12038
397.3
653
786
1.204
A3 0.450 0.380 0.88 457.7 322.2 28442
938.6
1261
1216
0.964
B1 0.410 0.410 0.90 295.1 212.5 14923
predicted)
492.5
705
743
1.054
B2 0.410 0.410 0.90 305.0 219.6 30547 1008.1
1228
1258
1.024
B3 0.510 0.510 0.87 536.7 373.5 37485 1237.0
1611
1722
1.069
B4 0.510 0.510 0.87 482.5 335.8 19258
635.5
971
1134
1.168
C1 0.410 0.410 0.90 306.5 220.7 16683
550.5
771
719
0.933
C2 0.410 0.410 0.90 286.2 206.1 30423 1004.0
1210
1263
1.044
C3 0.510 0.510 0.87 527.0 366.8 39983 1319.4
1686
1637
0.971
C4 0.510 0.510 0.87 503.1 350.2 21776
1069
917
0.858
Mean
1.0289
Std.
0.104
718.6
deviation
The mean value of the ratio Rc,measured / Rc;predicted is
equal to 1.03 and the standard deviation is 0.10. This
allows to calculated the 5% fractile (n = 10) of the ratio
Rc,measured / Rc;predicted:(Rc,measured / Rc;predicted )5% =
1.03 . (1- 1.833 . 0.10 1 + 1 )
1.03
10
The value of the calibration factor is than equal to
1 / 0.83 = 1.20
Extension to other tests of screw piles and precast piles
in OC clay
To verify if the values of the installation factors and
calibration can be extended to other OC clays in
Belgium, a review of published data of static load tests in
OC clay has been performed. The same calculation rule
as applied to the results of Sint Katelijne Waver has
been applied. A much as possible, similar interpretation
as in Sint Katelijne Waver has been pursued: failure
defined as a relative settlement of 10% of nominal base
diameter, elimination of friction in soil layers which are
not the considered OC layers etc… Some
approximations have been needed to make all tests
comparable on the same base. They may have
introduced some error, which are however considered
as acceptable in the margins of the analyses. More
refined analyses may be appropriate. Two static tests in
on precast piles in Sint Katelijne Waver have also been
included. The values of their installation coefficients
were taken equal to: αb = 1.0 and ηpi = 0.036. All the
results are gathered in figure 6 below.
Summary of predicted and measured ultimate compressive resistance
2000
1800
1600
measured
1400
Precast pile
1200
Screw pile
1000
Screw pile, steel
shaft
Screw pile, St.
Katelijne Waver
Measurement =
prediction
Calibration
800
600
400
200
2000
1800
1600
1400
1200
800
1000
600
400
0
200
0
predicted
Figure 6: Predicted and measured compressive
resistances for screw piles in OC clay at Sint Katelijne
Waver and at other documented test sites (for
histogram: see fig 3)
The mean value of the ratios Rc,measured / Rc;predicted for the
supplementary tests on the screw piles does not deviate
significantly from the ratio found at Sint Katelijne Waver.
The variabilty of Rc,measured/Rc;predicted/ is also remarkably
low. It is more difficult to make a definite statement on
the expected mean value and standard deviation for the
two tests on precast piles. The proposed values of the
installation factors are at the side of safety and fit with
the experience.
Considering both conclusions above, the sample “Sint
Katlijne Waver” may be extended by the other tests and
all tests in O.C. tertiary clay may be analysed as one
“homogeneous” sample:
- The value of (Rc,measured / Rc;predicted)~mean is than equal
to 1.02;
- The coefficient of variation of Rc,measured / Rc;predicted is
than equal to 0.10;
- The calibration factor remains equal to 1.20
The
coefficient
of
variation
of
the
ratio
Rc,measured/Rc;predicted has been evaluated on starting from
the total compressive resistance. Making an analysis on
base and shaft separately indicate somewhat larger
variations. It appeared however in the tests analysed
that there was some “compensation” of smaller base
resistance by larger shaft resistance in the OC clay with
the piles tested. This has to be confirmed in other types
of soils, where the total resistance is mainly given by the
pile base.
The
coefficient
of
variation
of
the
ratio
Rc,measured/Rc;predicted for the screw piles in O.C. clay is
rather small compared to published data on other types
of piles in other soil. Dutch experience summarized in
van Tol [1994] indicate a coefficient of variation of the
ratio Rb,measured / Rb;predicted (base resistance) of about
30% in sand. French experience, reported by Frank
(1997), using PMT rules indicate a coefficient of
variation of the ratio Rc,measured / Rc;predicted of about 20%
(the mean value being equal to about 1.25).
VALIDATION
The values of partial factors and model factors need to
be validated in relation to the required safety level and
successful existing design practice. This can be done by
different manners as explained below.
Equivalent deterministic safety factor
Within a deterministic framework, the factors of safety
are globally applied to the components of the resistance:
F ≤ Σ Ri/si
Where:
F : effect of the actions (representative values)
Ri : representative value of component i to the
resistance
si : global safety factor applied to component i of
the resistance
In approaches 1 and 2 one can define an “equivalent
deterministic safety factor” seq as:
seq = γcal. γpile.ξ.γF
Where:
γcal : calibration factor
γpile : partial factors on the pile resistance ( γpile
weighted value of γb & γs if relevant)
γF : weighted load factor = P/(P + Q) γG +
Q/(P+Q).γQ)
In common design practice, the global safety factor is
constant. The value of seq will not be constant as γpile
may depend on the relative parts of shaft and base
resistance, as γF depends on the relative parts of
variable and permanent loads and as ξ depends on the
number of tests, the variability of the compressive
resistance and the stiffness of the structure.
When using analytical formulas in approach 3,
comparison with deterministic approaches is more
complicated due to the non-linear character of the
bearing capacity factors in drained conditions.
Parametric analyses are than needed for comparison.
Existing codes using partial factors
When validating the partial and model factors by
comparison with partial factors indicated in existing
codes, it is advised to compare the product of all factors
rather than comparing individual values of partial factors
as these may differ more than their products.
Probabilistic evaluation of the reliability of the pile
compressive resistance
Probabilistic methods may be used to evaluate the
reliability of the design when using the partial factors of
the Eurocode. The reliability of the prediction of the
bearing resistance and way the spatial variation is
covered through the ξ- factors are key elements in the
reliability obtained. These aspects are however out of
the scope of the present paper.
As an example, the CPT method with the calibration
factor γcal = 1.20, combined with the partial factors of
approach 1 and the ξ-factors as proposed in table 6
yields values of reliability index β for screw piles in OC
clay of 3 to 3.5.
Settlement
The values of the global safety factors as used in the
current design practice are often considered to cover
serviceability limit states for piles in sand and stiff clays.
As the equivalent deterministic factor of safety may be
somewhat lower than the values in the current practice,
it may be necessary to check if serviceability limit states
are likely to occur when using the partial factors γcal, γpile,
ξ, and γF.
Reference to load-settlement curves of pile load tests is
needed. The figure 7 (Bauduin, 2001) illustrates a
possible procedure on the base of the pile load test
results obtained in Sint Katelijne Waver for piles in OC
clay: the figure shows the relative settlement as a
function of the mobilised resistance Rmobilised/Rultimate
(thus considering the values αb = 0.8 and η= 0.033; γcal
= 1.0). The range of the equivalent deterministic safety
factors using the load and the resistance factors of
approaches 1 and 2 is also indicated. The relative
settlement is about 0.3% to 0.7% of the largest pile base
diameter Db. Such relative settlements are in line with
the SLS requirements often used in Belgium (for a
summary, see e.g. Holeyman et al. 1997).
0.8
0.7
Rmobilised/Rultimate (-)
0.6
seq = 1.8
Design of Axially Loaded Piles : European Practice.
Rotterdam: Balkema. pp. 39-46.
HUYBRECHTS, N., 2001. Test campaign at Sint
Katelijne Waver and installation techniques of screw
piles. Proceedings of the symposium on Screw Piles.
Installation and design in stiff clay. Rotterdam, Balkema.
th
March 15 2001, Brussels. pp. 151-204.
MAERTENS, J., HUYBRECHTS, N. 2001. Results of the
static load tests. Proceedings of the symposium on
Screw Piles: Installation and design in stiff clay.
th
Rotterdam, Balkema. March 15 2001, Brussels. pp.
205 - 246.
HOLEYMAN, A., BAUDUIN, C., BOTTIAU, M.,
DEBACKER, P., DE COCK, F., DUPONT, E., HILDE,
J.L., LEGRAND, C., HUYBRECHTS, N., MENGÉ, P.,
MILLER, J.P.& SIMON,G. 1997. Design of Axially
Loaded Piles. In De Cock & Legrand (eds). Rotterdam,
Balkema. pp. 57-82.
PrEN 1997-1 final draft doc 355 version h.
2001. Eurocode 7 – Geotechnical design,
General
rules
(working
document
transformation of ENV 1997-1 to EN 1997-1),
250/SC7/PT 1.
0.5
seq = 2.2
0.4
October
part 1:
towards
CEN/TC
0.3
TOL, A.F., 1994. Hoe betrouwbaar is de paalfundering?
Intreerede, Technische Universiteit Delft, Faculteit der
Civiele Techniek.
0.2
Screw piles
0.1
Precast concrete
piles
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
s0/Db (%)
Figure 7: Rmobilised/Rultimate as a function of relative pile
settlement so/Db.
REFERENCES
ENV 1997-1, 1994. Eurocode 7 – Geotechnical design,
part 1: General rules. CEN/TC 250/SC7. Bruxelles:
Comité Européen de Normalisation.
BAUDUIN, C., 2001. Design procedure according to
Eurocode 7 and analysis of the test results. Proceedings
of the symposium Screw Piles : Installation and design
in stiff clay. Rotterdam, Balkema pp. 275-303.
CALLE, E., 1987. Toepassing van statistiek en
stochastiek
in
de
grondmechanica,
Stichting
postdoctoraal onderwijs in de civiele techniek. Cursus
nieuwe ontwikkelingen in de geotechniek.
DE BEER, E., 1971-1972. Méthodes de déduction de la
capacité portante d'un pieu à partir des résultants des
essais de pénétration. Annales des Travaux Publics de
Belgique, No 4 (p. 191-268), 5 (p. 321-353) & 6 (p. 351405), Brussels.
DE COCK, F., LEGRAND C., 1997 (editors). Design of
axially loaded piles. European Practice. Rotterdam,
Balkema.
FRANK, R., 1997. Some comparisons of safety for
axially loaded piles. In De Cock & Legrand, (eds),
ANNEX: CALCULATION EXAMPLE:
APPROACH 1 AND 2, SEMI-EMPIRICAL
CALCULATION RULE ON CPT APPLYING THE
“MODEL PILE” PROCEDURE
A pile foundation in overconsolidated clay supports a
stiff structure. The piles are supposed to be screw piles,
with Db = 400mm, Ds = 360 mm (these sections are
hypothetical); length 11m below soil level. Four CPT
tests have been performed: A2, A3, B4 and C4.
WORKED EXAMPLE FOR APPROACH 1
The loads to be carried by the foundation are permanent
load qk = 3900 kN, variable load Qk = 800 kN. The
design values become:
Approach 1, set 2: 390 * 1 + 800 * 1.3 = 4940 kN
Approach 1, set 1: 390 * 1.35 + 800 * 1.5 = 6450 kN
Step 1: calculation of the compressive resistance at
each of the CPT locations
Using De Beer's method, one calculates qb for piles with
base diameter of 400 mm. The base compressive
resistance is obtained as Rb = qbu. Ab. αb . εb in which :
- αb = 0.8 (value hereabove suggested for screw piles
in OC clay)
- εb = 1-0.01(Db/dc – 1) = 1 – 0.01(400/37 – 1) = 0.9
- Ab = 0.42 π/4 = 0.125 m²
The shaft compressive resistance is calculated using:
Rs = ηpi . qci . χ where:
- ηpi = 0.033
- χ = π . Ds = π . (0.360) = 1.13 m²/m’
The value of the calibration factor γcal is assumed to be
1.20 (see previously).
The calculation results are summarised in the table
below.
Table 9: Calculation results of predicted and calibrated
compressive resistance at each CPT
CPT
A2
A3
B4
C4
qb
αb. εb.Abqb
(MPa)
(kN)
1.8
160
2.9
263
2.3
211
2.4
216
Rc
Σχ . ηpi.hI . qc
(kN)
(kN)
828
988 = 160 + 828
925
1188 = 263 + 925
887
1098 = 211 + 887
945
1161 = 216 + 945
Rc / γcal
(kN)
823 = 133+ 690
990 = 219 + 771
915 = 176 + 739
968 = 180 + 788
Step 2 : selection of the characteristic value of the
compressive resistance
The mean value of the (calibrated) pile compressive
resistance out of the 4 tests is 924 kN; the lowest is 823
kN. The characteristic value of the pile resistance is the
minimum of (use ξ for four tests: ξ3 = 1.31 and ξ4 =
1.20):
Min {924 / 1.31 ; 823 / 1.20} = 686 kN
The characteristic value of the pile compressive
resistance is governed by the lowest value of the
calculated resistances. The stiffness of the structure is
accounted for through the coefficient 1.1, so the
characteristic value becomes 686 * 1.1 = 754 kN.
The geotechnical engineer however observes that only
one CPT governs the characteristic value over the whole
site, and that the other CPTs provide significantly higher
values of compressive resistance. It may be worth to
consider a subdivision of the site in two areas: the first in
which CPT A2 is used, and the second where the other
CPTs are used. Of course, such a subdivision has to be
supported by geotechnical considerations, not only by
manipulating numbers. This subdivision leads to
following characteristic values:
- Area 1: 823 / 1.4 * 1.1 = 647 kN: the minimum (single)
value governs;
- Area 2: min ⎧⎨ (990 + 915 + 968 ) . 1 . 1.1; 915 1.1⎫⎬ =
3
⎩
1.31
1.23
⎭
min ⎧⎨ 958 . 1.1; 915 1.1⎫⎬ = 792 kN: the mean value
⎩1.33
1.23
⎭
governs.
The definite choice of the first or the subdivision of the
site to select the characteristic value(s) is left to the
engineer’s judgement. A geotechnical analysis of the
site, including results of borings or other tests eventually
performed,
previous
experience,
considerations
regarding the structure supported by the piles may play
a role in this choice. A second test in area 1 is strongly
recommended: if it confirms the lower resistance in that
area, the design is well balanced; if it yields more
favourable results, this may lead to more economic
design (lower ξ value in area 1).
Step 3: design value of the pile compressive
resistance
Assume that the design is continued considering two
areas. The design value of the pile compressive
resistance in each of them is:
- Area 1; Set 2:
1.4 ⎞
⎛
Rck = 647 kN ⎜⎜ ξ 4 =
⎟ from the minimum
1.1 ⎟⎠
⎝
Rd = Rbd + Rsd =
133
690
. 1 .1 +
1.1 = 498 kN
1 .3 1 .4
1 .3 . 1 .4
The design value of the load requires 4940 / 498 = 10
piles.
- Area 2; Set 2:
1.33 ⎞
⎛
Rck = 792 kN ⎜ ξ3 =
⎟ from the mean
1 .1 ⎠
⎝
value
219 + 176 + 180 1
1 .1
Rbd =
.
.
= 122 kN
3
1.3 1.33
771 + 739 + 788 1
1 .1
Rsd =
.
.
= 487 kN
3
1.3 1.33
Rd = 609 kN
The design value of the load requires 4940 / 609 =
8.1, take 8 piles.
- The design values of the resistance for Set 1 are
easily found as (γb = γs = 1):
− Area 1: 647 kN
− Area 2: 792 kN
The foundation as determined for Set 1 (10 piles in area
1; 8 piles in area 2) fulfils the requirement of Set 1.
Note: the equivalent safety factor is:
Area 1: 988 / (4700 / 10) = 2.10
Area 2: compared to the mean resistance:
1149 / (4700 / 8) = 1.96
compared to the lowest resistance:
1098 / (4700 / 8) = 1.87
WORKED EXAMPLE FOR APPROACH 2
The design value of the load is: 3900 * 1.35 + 800 * 1.5
= 6450 kN
Step 1: calculation of the compressive resistance at
each of the CPT locations
The pile compressive resistance at each test location is
established on the same way as in previous. The same
value of the model factor γcal is applied, although this
value may need closer consideration.
Step 2 : selection of the characteristic value of the
compressive resistance
The characteristic value of the pile resistance is the
same as in approach 1.
Step 3: design value of the pile compressive
resistance
As γb = γ s = 1.10, the design value of the pile resistance
is readily found as
- Area 1:
Rc,d = Rc,k / 1.1 = 647/1.1 = 588 kN
The design value of the load requires 6450 / 588 = 11
piles.
- Area 2:
Rc,d = Rc,k / 1.1 = 795/1.1= 720
The design value of the load requires 6450 / 720 = 9
piles.
Note: the equivalent safety factor is:
Area 1: 988 / (4700 / 11) = 2.31
Area 2: compared to the mean resistance:
1149 / (4700 / 9) = 1.96
compared to the lowest resistance:
1098 / (4700 / 9) = 2.10