DESIGN OF AXIALLY LOADED COMPRESSION PILES ACCORDING TO EUROCODE 7

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1 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 Eurocode system and application to Eurocode 7 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) E d is lower than the calculated design value of the resistance R d : E d < R d 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 R d and E d. 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 : 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 c u ). 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 : 2001(E) Actions or action effects Ground parameters Piles permanent permanent variabel Tan ϕ c c u Resistance unfavourable favourable Set ( tanϕ & c :1.0) Set

2 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 :2001(E). They may be modified by national determination. Table 2: Partial factors in approach 2 according to Annex A of pren : 2001(E) Effect of actions Ground parameters Resistance permanent permanent variabel tan ϕ c c u unfavourable unfavourable 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 : 2001(E). They may be modified by national determination. Table 3: Partial factors in approach 3 according to Annex A of pren : 2001(E) Actions or action effects Action from permanent permanent unfavourable favourable The structure From or through the ground Ground parameters Resistance variable tan ϕ c c u (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: γ Sd applied either to the actions or to the actions effects; - at the resistance side: γ Rd 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: a d = a nom + Δ a where Δ a takes account of the possibility of unfavourable deviations from the characteristic (nominal) value. Δ a 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 Spatial variability of pile resistance over the site due to variability of soil Reliability of the predicted bearing capacity Base level Soil investigation: the more extensive, the better the variability is known - Pile load test: effect may be neglected - Semi-empirical rule: calibration of the rule by static tests - Dynamic test partial factor - Load factors γ F γ Q - Partial factors γ m on soil shear strength parameters (when relevant) Small deviations to be included in calculation rule through γ cal Small and unexpected deviations through γ b and γ s Large deviations: Δ a 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 γ cal Calibration of the results

3 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 base resistance and on shaft resistance γ b, γ s or γ t 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 R ci (or R bi and R si ) 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 R ck (or R bk and R sk ) 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 R c,k is assessed using the equation: R c,k = min{(r c;m ) mean /ξ 1, (R c;m ) min /ξ 2 } Where: (R c;m ) mean : the mean value of the measured pile resistances; (R c;m ) min : the lowest measured pile compressive resistance; ξ 1 and ξ 2 : correlation factors relating the mean and the lowest value to the characteristic value of the pile compressive resistance. Table 5 indicates values of ξ 1 and ξ 2 proposed in pren : 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 ξ 1 and ξ 2 for pile load test, piles under structure allowing no load transfer. Number of pile load tests ξ 1 applied to the mean of the measured compressive resistances ξ 2, applied to the lowest of the measured compressive resistances 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 ξ 1 and ξ 2 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: R c,d = R bk /γ b + R sk /γ s - When the characteristic values of the base and shaft resistance are not known separately, but the characteristic value of total resistance is known: R c,d = R ck /γ t Typical values for the partial factors as proposed in prenv :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 γ t 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 is not consistent in this respect between approaches 1 and 2. ULTIMATE COMPRESSIVE RESISTANCE FROM GROUND TEST RESULTS, APPROACHES 1 AND 2 This section is devoted to the assessment of the design value of the pile compressive resistance according to

4 pren :2001, clauses (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 R c resistance is obtained as the sum of the base resistance R b and the shaft resistance R s : R ci = R bi + R si 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 or pren 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 R c,predicted / R c,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 (R c,measured / R c,predicted ) 5% in accordance to the following statistical formula:

5 (R c,measured / R c,predicted ) 5% = (R c,measured / R c,predicted ) mean n 1 1 * 1 V.t + 1 5% n Where: V: coefficient of variation of the ratio R c,measured / R cpredicted n: number of tests considered to calibrate the calculation rule n 1 t : student factor for 5% fractile, n-1 degrees of 5% freedom The value of the calibration factor is: γ cal = 1/ (R c,measured / R c,predicted ) 5% n R c;measured / R c;predicted Figure 3: Example of histogram (R c,measured / R c,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 R measured /R predicted 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 R measured /R calculated 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 R measured /R calculated of bored piles in sand is larger than the variability of the ratio R measured /R calculated 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 R ci (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

6 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 R c,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: R c,k = min{(r c,cal ) mean /ξ 3, (R c, cal ) min /ξ 4 } Where ξ 3 and ξ 4 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: (R c;cal ) mean = (R b;cal + R s;cal ) mean = 1/N*Σ i (R b;cal;i +R s;cal;i ) = 1/N*Σ i R b;cal;i +1/N*Σ i R s;cal;i = (R b;cal ) mean + (R s;cal ) mean, it follows that: R c,k = (R c;cal ) mean /ξ 3 = (R b;cal + R s;cal ) mean /ξ 3 = (R b;cal ) mean /ξ 3 + (R s;cal ) mean /ξ 3 - To the lowest value: (R c;cal ) min = (R b;cal + R s;cal ) min : the lowest of the calculated compressive resistances at all the tested profiles, thus: R c,k =(R b;cal + R s;cal ) min /ξ 4 (R b;cal ) min /ξ 4 + (R s;cal ) min /ξ 4 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 ξ 3 and ξ 4 are proposed by pren :2001(E) in the table below; they may be modified by national determination. Table 6: values of ξ 3 and ξ 4 when ground test results are used, piles under structure allowing no load transfer Number of tested profiles ξ 3 applied to the mean ξ 4, applied to the lowest 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 ξ 1 and ξ 2. Clearly this ratio increases with the number of tests as the statistical population increases. The value of ξ 3 and ξ 4 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 ξ 3 and ξ 4 are given in (Bauduin, 2001). The values of ξ 3 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 ξ 3 and ξ 4. Then the value of ξ 3 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

7 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 allows to assess the characteristic values by: R b,k = A b. q b,k and R s,k = Σ A s;j. q s,k;j Where q b,k and q s,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 q b,k and q s,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 (c k and ϕ k or c u;k ) valid over the site considered. Variability, # of tests Stiffness of structure Measured soil parameter Shear strength parameters ϕ, c;c u "characteristic value" of parameter Tables; charts Characteristic value ϕ k, c k; c u;k Variability, # of tests Stiffness of structure Rck = R b,k + R s,k = A b * q b,k + Σ A s;j. q s,k;j Calculation rule ( l ti l) Calibrated value of the characteristic pile resistance Reliability of prediction; model Uncertainties: partial factors f t b d Design value R c,d = R b,k /γ b + R s,k /γ s Figure 4: Design procedure using semi-empirical methods alternative to the model pile procedure. The value of q b,k and q s,k;j (tabulated or chart values or derived from characteristic values of the shear strength parameters c k and ϕ k or c u;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 q b,k and q s,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: R c,d = R bk /γ b + R sk /γ s 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 :2001(E) Approach 1, set 2 Appr. 1, set 1 Approach 2 Type of pile γ b γ s γ t γ b γ s γ t γ b =γ s =γ t Driven piles Bored piles Continuous flight auger Combining the equation for characteristic value and the equation above delivers ( model pile procedure ): - When the mean value governs the characteristic value: R c,d = R bk /γ b + R sk /γ s = (R b;cal ) mean /(ξ 3. γ b ) + (R s;cal ) mean /(ξ 3. γ s ) - When the lowest value governs the characteristic value: R c,d = R bk /γ b + R sk /γ s = (R b;cal /γ b + R s;cal /γ s ) min /ξ 4 where (R b;cal + R s;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 R measured / R calculated 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

8 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 = γ cal. γ b and γ cal. γ s 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 :2001 stresses that when the alternative method is used, the values of the partial factors γ b and γ s 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 R c, measured /R c, 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 γ tanϕ γ c or γ cu before entering the calculation rule. This provides design values of the base and shaft resistance. The figure 5 illustrates different steps of the procedure. N tested profiles giving values of shear strength parameters Design values of Characteristic Step 1 Step 2 shear strength value ϕ Step 3 k, c k ; parameters ϕd, c d c u;k or c u;d Variability, # of tests Stiffness of structure Uncertainties: partial factors γ tanϕ γ c or γ cu Calculation rule (analytical) Reliability of prediction; model factor Figure 5: Design procedure for approach 3. Design value R cd = R b (ϕ d, c d ; c ud )/γ cal + R s (ϕ d,c d ;c ud )/γ cal 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: c d = c k /γ c = c /1.25 and tanϕ d = tanϕ k / γ tanϕ = tanϕ k / 1.25; c ud = c uk / γ cu = c u,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: R c,d = R b,d + R s,d Where: R bd = R b (c d, ϕ d ; c ud ) and R sd = R s (c d, ϕ d or c ud ) If model (calibration) factors are needed, they should be applied on the design value of the pile resistance.

9 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: R b = α b.β.ε b.a b.q b q b ultimate unit bearing resistance derived from the E1 cone resistance according to the calculation method of De Beer ( ), which has been established for cylindrical driven piles; A b nominal cross section of the base of the pile deduced from the largest nominal diameter of the base screw; α b 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; ε b 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; ε b = (D b /d c 1) where D b /d c is the ratio of the largest pile base diameter to the diameter of the CPT cone. - Shaft resistance: R s = χ s.σh i η pi. q ci χ s nominal pile shaft perimeter, deduced from the nominal shaft diameter: χ s = π D s H i thickness of layer i q ci mean cone resistance in layer i η pi global empirical factor allowing to transform the cone resistance to local shaft friction q su ; the factor depends on the soil type, the pile installation method and the roughness of the shaft;: η pi = ( for q c between 1.5 and 3 MPa) Remarks: calculation rules which account explicitly for each q c 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 D b 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 Rc;predicted = εb.αb.qb.ab measured + χσηpiqcihi Rc; Ratio [m] [m] [kn] [kn] [kn] [kn] [kn] [kn] (measured/ predicted) A A B B B B C C C C Mean Std. deviation The mean value of the ratio R c,measured / R c;predicted is equal to 1.03 and the standard deviation is This allows to calculated the 5% fractile (n = 10) of the ratio R c,measured / R c;predicted :(R c,measured / R c;predicted ) 5% = ( ) 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

10 were taken equal to: α b = 1.0 and η pi = All the results are gathered in figure 6 below. measured Summary of predicted and measured ultimate compressive resistance predicted Precast pile Screw pile Screw pile, steel shaft Screw pile, St. Katelijne Waver Measurement = prediction Calibration 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 R c,measured / R c;predicted for the supplementary tests on the screw piles does not deviate significantly from the ratio found at Sint Katelijne Waver. The variabilty of R c,measured /R c;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 (R c,measured / R c;predicted ) ~mean is than equal to 1.02; - The coefficient of variation of R c,measured / R c;predicted is than equal to 0.10; - The calibration factor remains equal to 1.20 The coefficient of variation of the ratio R c,measured /R c;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 R c,measured /R c;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 R b,measured / R b;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 R c,measured / R c;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 R i /s i Where: F : effect of the actions (representative values) R i : representative value of component i to the resistance s i : global safety factor applied to component i of the resistance In approaches 1 and 2 one can define an equivalent deterministic safety factor s eq as: s eq = γ cal. γ pile.ξ.γ F Where: γ cal : calibration factor γ pile : partial factors on the pile resistance ( γ pile weighted value of γ b & γ s if relevant) γ F : weighted load factor = P/(P + Q) γ G + Q/(P+Q).γ Q ) In common design practice, the global safety factor is constant. The value of s eq will not be constant as γ pile may depend on the relative parts of shaft and base resistance, as γ F 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 γ cal = 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

11 are likely to occur when using the partial factors γ cal, γ pile, ξ, and γ F. 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 R mobilised /R ultimate (thus considering the values α b = 0.8 and η= 0.033; γ cal = 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 D b. Such relative settlements are in line with the SLS requirements often used in Belgium (for a summary, see e.g. Holeyman et al. 1997). Rmobilised/Rultimate (-) s 0/D b (%) Screw piles Precast concrete piles seq = 1.8 seq = 2.2 Figure 7: R mobilised /R ultimate as a function of relative pile settlement s o /D b. REFERENCES ENV , Eurocode 7 Geotechnical design, part 1: General rules. CEN/TC 250/SC7. Bruxelles: Comité Européen de Normalisation. BAUDUIN, C., 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 CALLE, E., Toepassing van statistiek en stochastiek in de grondmechanica, Stichting postdoctoraal onderwijs in de civiele techniek. Cursus nieuwe ontwikkelingen in de geotechniek. DE BEER, E., 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 ), 5 (p ) & 6 (p ), Brussels. DE COCK, F., LEGRAND C., 1997 (editors). Design of axially loaded piles. European Practice. Rotterdam, Balkema. FRANK, R., Some comparisons of safety for axially loaded piles. In De Cock & Legrand, (eds), Design of Axially Loaded Piles : European Practice. Rotterdam: Balkema. pp HUYBRECHTS, N., 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. March 15 th 2001, Brussels. pp MAERTENS, J., HUYBRECHTS, N Results of the static load tests. Proceedings of the symposium on Screw Piles: Installation and design in stiff clay. Rotterdam, Balkema. March 15 th 2001, Brussels. pp 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 Design of Axially Loaded Piles. In De Cock & Legrand (eds). Rotterdam, Balkema. pp PrEN final draft doc 355 version h. October Eurocode 7 Geotechnical design, part 1: General rules (working document towards transformation of ENV to EN ), CEN/TC 250/SC7/PT 1. TOL, A.F., Hoe betrouwbaar is de paalfundering? Intreerede, Technische Universiteit Delft, Faculteit der Civiele Techniek. 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 D b = 400mm, D s = 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 q k = 3900 kn, variable load Q k = 800 kn. The design values become: Approach 1, set 2: 390 * * 1.3 = 4940 kn Approach 1, set 1: 390 * * 1.5 = 6450 kn Step 1: calculation of the compressive resistance at each of the CPT locations Using De Beer's method, one calculates q b for piles with base diameter of 400 mm. The base compressive resistance is obtained as R b = q bu. A b. α b. ε b in which : - α b = 0.8 (value hereabove suggested for screw piles in OC clay) - ε b = (D b /d c 1) = (400/37 1) = A b = π/4 = m² The shaft compressive resistance is calculated using: R s = η pi. q ci. χ where: - η pi = χ = π. D s = π. (0.360) = 1.13 m²/m The value of the calibration factor γ cal is assumed to be 1.20 (see previously).

12 The calculation results are summarised in the table below. Table 9: Calculation results of predicted and calibrated compressive resistance at each CPT CPT q b (MPa) α b. ε b.a b q b (kn) Σχ. η pi.h I. q c (kn) R c (kn) R c / γ cal (kn) A = = A = = B = = C = = 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: ξ 3 = 1.31 and ξ 4 = 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 ( ) ; = min ; 1.1 = 792 kn: the mean value 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 R ck = 647 kn ξ4 = from the minimum 1.1 R d = R bd + R sd = = 498 kn The design value of the load requires 4940 / 498 = 10 piles. - Area 2; Set 2: 1.33 R ck = 792 kn ξ3 = from the mean 1.1 value R bd =.. = 122 kn R sd =.. = 487 kn R d = 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 (γ b = γ s = 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 * * 1.5 = 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 γ cal 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 γ b = γ s = 1.10, the design value of the pile resistance is readily found as - Area 1: R c,d = R c,k / 1.1 = 647/1.1 = 588 kn The design value of the load requires 6450 / 588 = 11 piles. - Area 2: R c,d = R c,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