OTC A4 OTC-24063-MS Lacasse Reliability Final - Corrected

OTC-24063-MS

Reliability of API, NGI, ICP and Fugro Axial Pile Capacity Calculation Methods S. Lacasse, F. Nadim, K. H. Andersen, Siren Knudsen, Unni K. Eidsvig, Norwegian Geotechnical Institute (NGI), Gülin Yetginer, Tom R. Guttormsen and Asle Eide, Statoil.

Copyright 2013, Offshore Technology Conference This paper was prepared for presentation at the Offshore Technology Conference held in Houston, Texas, USA, 6–9 May 2013. This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.

Abstract The API RP2A (RP2GEO) and ISO 19902 guidelines include four CPT-methods for calculating the axial capacity of piles in sands. The guidelines require that if newer methods are to be implemented in design, the same level of safety shall be docu-mented for these methods as for existing methods. The designer is required to select an appropriate safety factor when using the newer design methods. The challenge lies in deciding which safety factor will ensure a consistent safety level for different soil conditions and pile dimensions. To evaluate the required material factor, the probability of failure was quantified in two case studies for piles designed with the API method and with the newer NGI, ICP and Fugro methods. A calibration of the required material factor for a target probability of failure of 10-4/yr was also performed. The results show that the annual relia-bility index and probability of failure vary with the axial pile capacity calculation method. The study provides a contribution to the discussion on the reliability of the API, the NGI, the ICP and the Fugro methods. The material factor needs to be associated with the characteristic soil parameters selected for design. A large number of case studies should be added to quantify the reli-ability and the required material factor for each pile capacity method. The findings on margin of safety and the definition of the characteristic shear strength have important implications for the design of piles offshore and can result in significant savings.

Introduction Ensuring adequate reliability under severe loading conditions is a necessary consideration for offshore platforms, and the safe-ty margin depends on the uncertainty in the parameters entering the analyses, in addition to the model uncertainty. The design engineer attempts to compensate for the uncertainties by introducing an appropriate "factor of safety" in design. There will always be a finite probability that the forces of the environment can cause damage, or the total collapse, of an offshore struc-ture. Defining the level of finite probability that is tolerable is the challenge.

The API RP2A (RP2GEO) (1) and ISO 19902 (2) guidelines included four CPT-methods for calculating the axial capacity of piles in sands in 2007. The designer is required to select an appropriate safety factor when using the newer design methods. The difficulty lies in deciding which safety factor will ensure a consistent safety level for different soil conditions and pile dimensions. The axial capacity of tubular steel piles for offshore installations is frequently based on the Recommended Prac-tice of the American Petroleum Institute (API) (1). To evaluate the required material factor, the probability of failure was quantified for piles designed with the API method and with the NGI, ICP and Fugro methods. A calibration of the required material factors for a target probability of failure of 10-4/yr was also carried out. The paper presents the results of the reliability analyses and the calibration of the material factor for each axial pile capacity method. The approach is illustrated with two case studies of jacket on piles, the first on a mainly clay profile and the second on a very dense sand profile. Scope of Study The study was undertaken to document that the pile foundations were designed according to governing regulations. The goal was to make a recommendation on the appropriate material factor and minimum pile length to use for the design of the piles on an offshore jacket. The reliability study of the axial capacity of the piles considered two jackets on two very different soil pro-files. For each of the case studies, the assessment included:

Statistical evaluations of the soil and load parameters, Statistical analyses of the model uncertainty associated with each of the pile capacity methods, Deterministic and probabilistic analyses of the axial pile capacity with different pile capacity methods to determine

the annual reliability index and the annual probability of failure for each axial pile capacity calculation method, and

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Calibration of the required material factor for a target annual probability of failure. Table 1 lists the axial pile capacity methods considered: the API method, the NGI-05 method, the ICP-05 method and the

Fugro-96/05 method. For the ICP method in sand, the simplified method relevant for large diameter piles was used as described in API and ISO (1; 2). Table 2 lists the soil parameters required for each method. The unit weight of the soil is also required to calculate the total or effective stress versus depth.

Table 1. Axial pile capacity methods included in the study. Methods References for methods in clay References for methods in sand API API-RP2A, 20th edition 1993 (3) API-RP2A, 20th edition, 1993 (3) NGI-05 Karlsrud et al 2005 (4) Clausen et al (2005) (8) ICP-05 Jardine et al 1996; 2005 (5; 6) Jardine et al 2005; API 2011; 2007 (6; 1; 9)) Fugro-96/05 Kolk and van der Velde 1996 (7) Kolk et al 2005 (10)

Table 2. Required soil parameters for each pile capacity method considered in the study. Soil type

Method

Sand Clay Cone

resistance qc

Relative density

Dr

Effective internal friction angle

'

Effective interface friction angle

Undrained shear strength

suUU

Cone resistance

qc

Plasticity index

Ip

Overconsoli-dation ratio

OCR(or pc')

Sensi-tivity

St API (✓) ✓ (✓) ✓ ✓

NGI-05 ✓ (✓) ✓ ✓ ICP-05 ✓ (✓) ✓ (or d50) (✓) ✓ ✓ ✓ Fugro-96/05 ✓ ✓ Parenthesis indicates that the parameter is derived from another parameter. d50 = Diameter of particles at 50% passing on grain size distribution curve. su

UU = Undrained shear strength from unconsolidated undrained (UU) tests.

Load and Material Factor In a deterministic design, the load and material factors are applied as follows:

[l stat • Pstat + l env • Penv100-yr] = Qult/m

where l stat = Load factor on static load

Pstat = Selected characteristic static load l env = Load factor on environmental load

Penv100-yr = Selected characteristic environmental load (typically the environmental load with 100-yr return pe-

riod, Penv100-yr, is used as the characteristic load)

Qult = Selected deterministic ultimate axial pile capacity

m = Material factor

Procedure to Evaluate the Reliability of Axial Pile Capacity Methods The definition of failure has a significant impact on the failure probability that comes out of the reliability analysis. In general for pile design, one can use one of two failure criteria:

(1) the capacity of the most heavily loaded pile is exceeded, or

(2) the capacity of the entire pile system is exceeded after full redistribution of loads among the piles (i.e. fully utilized pile system)

Criterion (1) leads to a higher failure probability than Criterion (2), because it implies a significant non-mobilized reserve capacity, whereas Criterion (2) does not. In this paper, Criterion (2) with the most heavily loaded pile group was used.

The reliability analyses of the axial pile capacity methods included the following steps:

1) Establish the mean and standard deviation and the probability density function of the soil parameters. Evaluate correla-tion among parameters and include if applicable.

2) Establish model uncertainty for the different pile capacity calculations methods used.

3) Establish the effect of cyclic loading on the axial pile capacity and determine whether the piles in compression or ten-sion are governing the design.

4) Develop a model for the statistics of the static (permanent) and environmental loads on the top of the piles.

5) Do deterministic analysis of the axial pile capacity.

6) Do probabilistic analyses of axial pile capacity and obtain the probability density function of the ultimate capacity.

7) Calculate the annual reliability index and probability of failure by combining the statistical description of the loads and the probabilistic description of the ultimate axial pile capacity.

The effects of cyclic loading and of time on the ultimate pile capacity are not included in this paper. The effect of cyclic loading should always be accounted for. It can be determinant on whether the loading in compression or in tension is critical

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for design, because the effect of cyclic loading is normally more severe in tension than in compression. Screening analyses showed that for the two case studies in this paper, the compression piles were critical for design. The effect of cyclic loading was small for Case Study A and negligible for Case Study B.

The effect of time should also be considered, and a decision should be made on whether to include this effect or not. This effect can be important, especially for piles in sands on the short term. The effect of time would be the same for each of the calculation methods used.

Case study A - Piles in Mainly Clay Profile Description of Case Study A The structure in Case Study A is a four-leg jacket supported on tubular steel piles. The water depth is 119 m. Each pile group consists of four piles with 96" (2.438 m) diameter and 90-mm wall thickness. The static load on the most heavily loaded pile group was 116.1 MN (including pile weight). The 100-yr environmental load on the most heavily loaded pile group was 101.9 MN.

The soil conditions are characterized by alternating sand and clay layers. Intermittent sand and silt layers were found within the clay units, and intermittent clay layers were identified within the sand units. The very dense sand layer at a depth of 92 m was based on one boring only.

The characteristic undrained shear strength for preliminary design was selected as a carefully assessed value, as required by NORSOK N-004 (11). Figure 1 presents the soil layering and the selected characteristic profile of undrained shear strength. The “low” su

UU refers to the characteristic value from unconsolidated undrained laboratory tests (UU) (other values would be used for the calculations of pile driving resistance).

The preliminary pile capacity analyses, using the NGI-05 method, required a pile length of 107 m for a material factor m of 1.5. Pile driving analyses suggested that refusal during driving would occur in the 4-m thick sand layer 92 m below seafloor.

Figure 1. Selected characteristic undrained shear strength profile Figure 2. Mean and standard deviation of undrained shear strength for the deterministic design of piles, Case Study A. compared with characteristic untrained shear strength. Uncertainty in Soil Parameters The parameters were established with statistical analyses of the available soil data, combined with well-documented correla-tions, experience and engineering judgment. The soil data were analysed unit by unit. The parameters were taken to either vary linearly with depth within the one unit (dependent soil variable) or be constant within the unit (independent soil variable). The procedures for estimating the mean and standard deviation for independent and dependent soil variables used the recom-mended practice described in DNV (12). Appendix A describes briefly the approach. A summary of the mean and coefficient

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of variation for the clay and sand parameters is given in Table 3. PDF of Soil Parameters. The probability density functions (PDF) are listed at the top of the columns for each soil parame-

ter in Table 3. The PDFs were selected as either normal (N), lognormal (LN) or beta (), based on a study of the best fit of the data. To ensure that the parameters would not become negative in the probabilistic analyses, parameters like undrained shear strength and sensitivity were given a lognormal PDF. The best fit of the data was done with the commercial program EasyFit, produced by Mathwave (13). In many layers however, there were too few data to establish a good fit of the data.

Key Soil Parameters. Figures 2 to 4 illustrate key results of the statistical analyses. Figure 2 compares the mean and stand-ard deviation of the undrained shear strength with the characteristic shear strength (p'o is the in situ effective vertical stress). Figure 3 compares the mean and standard deviation of the undrained shear strength with the results of piezocone tests, where the qc measurements were converted to the triaxial compression undrained shear strength (su

C), and not the UU-strength (suUU).

Figure 4 presents the mean and standard deviation of the plasticity index.

Table 3. Input parameters for clay and sand used in probabilistic analyses of axial pile capacity, Case Study A.

Soil Unit

Depth to

bottom of soil unit, z

Soil type

Submerged unit weight, (kN/m3)

Undrained shear strength, Top-bottom

suUU ( kPa)

CPTU Top-bottom

qc (MPa)

Presonsolidation (Lower–Upper)

p (kPa) Sensitivity, St

Plasticity index, Ip

(%)

Mean; CoV (%) PDF=N

Mean; CoV (%) PDF=LN

Mean; CoV (%) PDF=N

Mean (range) PDF=



I 1.0 SAND 10.0; 6% - 1 – 5; 20 % - - - II 3.6 CLAY 11.3; 4% 38 – 108; 30 – 40 % 0.7 – 2 300; (200 - 400) 1.7-1.9; 20-40% 13.4; 25 %

IIIa 18.6 CLAY 11.2; 4% 108 – 172; 25 – 30 % 2 – 3 300; (200 - 400) 1.5-1.6; 20-30% 18.7 – 22.8; 10 % IIIb 24.1 SAND 10.7; 7% - 70 – 70: 20 % - - - IIIc 32.3 CLAY 11.4; 4% 192; 10 % 3 – 3 300; (200 - 400) 2.1; 15 – 20 % 19.6; 10 % IVa 38.6 CLAY 10.5; 3% 342; 25 – 30 % 6 – 6 550; (400 - 700) 1.5; 20 – 30 % 33.2; 20 % IVb 50.0 CLAY 10.7; 5% 342; 25 – 30 % 6 – 6 550; (400 - 700) 1.5; 20 – 30 % 17.0; 40 % IVc 56.3 CLAY 11.2; 3% 492; 35 % 40 – 15 550; (400 - 700) 1.5; 20 – 30 % 13.3; 40 % IVd 69.5 CLAY 9.7; 6% 288 – 240; 25 % 7.5 – 7.5 550; (400 - 700) 1.5: 20 – 30 % 30.7; 10 % IVe 91.9 CLAY 11.2; 5% 337; 25 – 30 % 8 – 8 550; (400 - 700) 1.5: 20 – 30 % 19.3; 20 % IVf 96.0 SAND 11.5; 4% - 50 – 50 - - - V 102.0 CLAY 11.7; 2% - 8 – 11 550; (400 - 700) - 20

PDF = Probability density function: N=normal; LN= lognormal; = beta

Figure 3. Mean and standard deviation of the undrained shear Figure 4. Mean and standard deviation of the plasticity index strength compared with su

C from CPTU tests. compared with values used for preliminary design.

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Other parameters are also required for the calculation of axial pile capacity. These include specific parameters for the sand

layers, such as the coefficient of horizontal stress (K), the friction angle and the API limiting skin friction. Bias and coefficient of variation were obtained from the survey done of 40 offshore pile specialists summarized by Lacasse and GOULOIS (14). A summary of these additional parameters is given in Table 4. The values of the friction angle in the sand are based on the rec-ommendations by the current API-guidelines. For very dense sand, the friction angle would be expected to be at least 45 °, but the API guidelines were followed in the reliability study. The values of relative density were obtained from the procedure in PACER (15) to obtain relative density from CPTU tests. Values of Dr greater than 100% were derived. More discussion of this aspect can be found under Case Study B.

Scour and gapping. Gapping at the top of the pile may occur under horizontal loading. In the deterministic analysis, the axial pile capacity in the top 1.7 m was taken as zero. A study of the gapping was not included in the reliability analyses. In principle, one should analyze the possibility of loss in capacity due to gapping or scour at the top of the pile.

Table 4. Additional parameters for the sand layers.

Unit ' (°) Flim (kPa) δwall (°) K Dr

Mean CoV Mean CoV Mean CoV Mean CoV Mean CoV I 30 5% 81.3 15% 29 15% 0.8 10% 0.93 15%

IIIb 40 5% 115 15% 29 15% 0.8 10% 1.20 15% ' = friction angle Flim = limiting skin friction δwall = effective stress shaft friction angle K = coefficient of horizontal stress Dr = relative density

Statistical Representation of Loads for Foundation Reliability Analysis

Static Loads. Very little uncertainty was expected in the static loads induced by gravity (weight of the platform and piles themselves) on the pile group. The uncertainty in the gravity-induced loads was hence taken as 0 in the analyses.

Environmental Loads. The procedure used a recommendation by (16) for the statistical representation of the maximum storm-induced compression loads on the foundation. The procedure is described in Appendix B. The parameters of the extreme value distribution were estimated from the extreme loads. The resulting Gumbel distributions for the loads in compression are shown in Figure 5a. In the reliability analyses of axial pile capacity for Case Study, the distribution fitted to q1/q2 = 0.01/0.0001 was used. This fit provides a good approximation of the extreme loads with return periods between 10 and 10,000 years, which is the range of the value of the storm-induced load at the design point in the reliability analyses. Analyses were also done with a shifted exponential distribution function which provided a reasonably good fit for the annual storm-induced loads on the pile group (black dashed line on Fig. 5b). The results did not change significantly with the second approximation.

a) Fitted Gumbel distributions for environmental loads (ref 16). b) Storm-induced loads with shifted exponential distribution.

Figure 5. Statistical representation of environmental loads for Case Study A Model Uncertainty in Pile Calculation Analysis Methods An extended study of the model uncertainty was carried out for the different axial pile capacity calculation methods. The de-tails of this study are presented in a companion paper to the OTC session (17). The model uncertainty used in the reliability analyses for Case Study A, expressed as a bias (mean), standard deviation, coefficient of variation and probability density function (PDF) are summarized in Table 5. The analyses were done with both the normal and lognormal PDF for the model uncertainty. The model uncertainty values were obtained by comparing the predicted to the measured axial pile capacity from relevant and reliable pile model tests. The NGI database of "super pile" load tests (18; 19; 17) was used. Each calculation method showed different bias and variability when analyzed statistically with NGI’s reference database of reliable pile load tests.

Several options exist to describe model uncertainty. The ratio of measured capacity to calculated capacity (Qm/Qc) was se-lected herein, based on the study in (17).For all the methods in Table 5, the NGI database was used, except for the Fugro-96/05

Dashed curves are the shifted exponential distri‐bution fitted to the data on the full curves. The fitting was governed by a best fit for return periods greater than 100 years.

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method, where the original data were not available and the uncertainty was estimated from the results published by the authors (7). The axial pile capacity methods were used as described by the references in Table 1. No bias to account for the effects of plasticity (for the API methods) or increasing pile diameter (ICP and Fugro methods) was included in this paper.

Most effort for Case Study A was spent on the model uncertainty for the prediction of skin friction, since the friction capac-ity was the most important component of the pile capacity. The uncertainty in the end bearing was taken as a large value and the same for all methods for the study of the reliability of the methods. For Case Study A, introducing a relatively large uncer-tainty in the end bearing model did not have a significant effect on the annual probability of failure.

Table 5. Model uncertainty Qm/Qc used for each pile capacity method in reliability analyses, Case Study A

Axial pile capacity method Model uncertainty, Qm/Qc, in clay layers Model uncertainty, Qm/Qc, in sand layers

Skin friction End bearing Skin friction

API Bias = 1.09; SD = 0.26 CoV = 0.24; PDF = LN or N

Bias = 1.0; SD = 0.30 CoV = 0.30; PDF = LN or N


NGI-05


Bias = 1.0: SD = 0.30 CoV = 0.30; PDF = LN or N


ICP- 05




Fugro-96/05 method




Bias Qm/Qc > 1.0 means that method under-predicts measured capacity in pile load tests Bias Qm/Qc < 1.0 means that method over-predicts measured capacity in pile load tests SD = Standard deviation CoV = Coefficient of variation LN or N = Lognormal or normal PDF

Deterministic Analyses of Axial Pile Capacity

The axial pile capacity in compression and tension was analyzed deterministically using the software PACER (15) and RELPAX (20). The calculated ultimate axial pile capacity curves in compression using the different axial capacity methods in Table 1 for the characteristic soil profile and for the statistical mean values are presented in Figures 6 and 7. The results are summarized in Table 6. The Pre 1987 API- method predicts the lowest capacity. With the characteristic shear strength, the API-method, the NGI-05, the ICP-05 and the Fugro-96-05 methods yield capacities between 100 and 134 MN for a 90-m long pile. With the mean undrained shear strength, the capacities ranged between 119 and 139 MN. For low plasticity clays such as found for Case Study A, the NGI-05 method predicts significantly lower -factors as compared to the API method, which results in less skin friction resistance and hence less axial capacity. The deterministic analyses showed that the mean undrained shear strength gives up to 20% higher capacity compared to characteristic shear strength profile. The calculations confirmed that the end bearing contributed very little to the total capacity.

Table 6. Results of deterministic axial pile capacity for 90m long pile, Case Study A Method

Su-profile

API NGI-05 ICP-05 Fugro-96/05 Compression1) (MN)

Characteristic su 124.7 100.1 133.5 117.5 Mean 138.6 118.7 133.2 136.1

1) Compression = Qskin compression + Qtip Pile weight and plug weight are not included in the ultimate pile capacity

Probabilistic Analyses The annual probability of pile foundation failure was estimated using a two-stage approach. In the first stage, the uncertain-

ty in the ultimate axial pile capacity was evaluated and quantified by a probability distribution function. The NGI software RELPAX (20) was used. In the second stage, the results of the first stage were combined with the probabilistic description of the maximum annual axial load on the pile to calculate the annual probability of failure. The commercial software COMREL (21) was used. Appendix C describes the approach in more detail. Table 7 presents a selection of the probabilistic RELPAX and COMREL analyses done.

Table 7.Results of probabilistic analyses of axial capacity for 90 m pile, Case Study A.

No

Method Ultimate pile capacity

Mean ± SD (CoV) PDF = LN

Deterministic capacity *

(MN)

Annual Pf and

Scaling factor on capacity

for Pf=10-4/yr

Calculated load factor

for Pf=10-4/yr

Relative contribution to Pf

Loads Soil resistance

(Model uncertainty)

I API 151.7 ± 31.1 (21 %) 138.6 Pf = 2.010-7 = 5.0

0.67 1.116 51 % 49 %

(40 %)

II NGI-05 120.5 ± 20.0 (17 %) 118.6 Pf = 1.310-6 = 4.7

0.76 1.259 67 % 33 %

(24 %)

III ICP-05 136.8 ± 25.4 (19 %) 136.8 Pf = 3.910-7 = 4.9

0.705 1.186 63 % 37 %

(30 %)

IV Fugro-96/05

114.6 ± 30.8 (27 %) 136.1 Pf = 2.410-4 = 3.5

1.07 0.926 68 % 32 %

(24 %) * With mean soil parameters

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Figure 6. Ultimate axial pile capacity in compression with the Figure 7. Ultimate axial pile capacity in compression with the characteristic undrained shear strength, Case Study A. mean undrained shear strength at Case Study A.

Axial Pile Capacity and Annual Probability of Failure. The ultimate axial pile capacity for a 90-m long pile, with a Lognormal distribution, had a coefficient of variation between 16 and 20 % for the API, the NGI-05 and the ICP-05 methods. The annual probability of failure was between 10-6 and10-7. The coefficient of variations for the Fugro methods was closer to 30 %, and the probability of failure was significantly higher.

Table 8 lists the axial pile capacity and annual probability of failure as a function of pile length between 75 and 90 m. The numbers are for the NGI-05 method. The calculations show that a 75-m long pile had an annual probability of failure of about 10-5. The table shows only small changes in the annual probability of failure when the second-order reliability method (SORM) was used instead of the first-order reliability method (FORM) (Appendix C) and when a normal PDF for the axial pile capacity was used instead of the lognormal PDF.

Table 8. Axial pile capacity and annual probability of failure as a function of pile length, NGI-05 method, Case Study A. Depth (m) Qult char (MN) Qult mean (MN) Annual Pf - FORM, QLN Annual Pf - SORM, QLN Annual Pf - FORM, QN

75 77.8 96.6 2.110-5 2.110-5 5.210-5

80 84.1 103.9 2.310-5 2.510-5 2.310-5

90 96.8 118.6 1.210-6 1.310-5 1.310-5

In the COMREL analyses (21), a scaling factor was established to calculate the probabilistic foundation capacity required for an annual failure probability of 10-4. The scaling factors shown in Table 7 represent the factor by which one needs to multi-ply the axial pile capacity (the mean or the characteristic capacity) to bring the probability of failure to 10-4/yr. The environ-mental load in the probabilistic analyses giving an annual failure probability of 10-4 related to the 100-year deterministic envi-ronmental load was also found through a scaling factor. These scaling factors are used for the calibration of the material factor.

Influence factors. The FORM analyses with RELPAX and COMREL provided sensitivity factors for each random varia-ble. The sensitivity factors describe the relative contribution of the random variables to the total uncertainty. The influence factors of the uncertainties in the loads and the uncertainties in the soil resistance on the probability of failure, Pf, are given in Table 7. For the NGI-05 method, the uncertainties in the loads influence the probability of failure with 67 % weight, while the uncertainties in the soil parameters and pile capacity calculation model influence the probability of failure with 33% weight, whereof 24 % was due to the uncertainty the capacity calculation method. Model uncertainty in the capacity calculation meth-ods, mainly the skin friction, was important for all methods, contributing more than 50 % of the uncertainty in the capacity, thereby contributing to increasing the probability of failure.

Observations. The results of the probabilistic analyses indicate that (1) the deterministic capacity calculated by RELPAX with the mean values of the soil parameters were in general quite close to the probabilistic mean for the NGI-05, ICP-05 and Fugro-96/05 methods; (2) the model uncertainty for each of the calculation methods was by far the most important contributor to the uncertainty in the capacity; and (3) the probabilistic distribution of the axial pile capacity was best modeled with a lognormal distribution.

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Case study B - Piles in Mainly Sand Profile Description of Case Study The structure is a four-leg jacket supported on tubular steel piles to be installed at a site with water depth of about 92 m. Each foundation pile group consists of six piles with 96" (2.438 m) diameter and 100-mm wall thickness. The static load on the most heavily loaded pile group was 221.0 MN (including pile weight). The 100-yr environmental load on the most heavily loaded pile group was 97.1 MN. Table 9 describes the soil. It consists of mainly dense to very dense sand layers, with rather thin clay layers in between. Figure 8 provides the results of CPTU tests near the footprint of the jacket. The sand is very dense, with the cone tip resistance reaching maximum pressure in several segments (see also Figure D1 in Appendix D). This would indicate that the strength of the sand is even higher than that measured at those depths.

Table 9. Soil description for Case Study B. Unit Depth range (m) Description

I 0.0 – 0.5 Loose to medium dense silty fine to medium SAND locally with shell fragments and pockets of clay. II 0.1 – 9.9 Dense to very dense slightly silty fine to medium SAND, traces of medium sand-sized to coarse gravel-sized shell fragments.

IIIb 7.9 – 23.5 Dense to very dense fine to coarse slightly silty fine to coarse SAND with traces of medium sand-sized to coarse gravel-sized shell fragments with a thin to thick bed of hard sandy clay at base of unit.

IVb 21.5 – 46.6 Dense to very dense, locally loose, silty slightly gravelly fine to medium SAND with shell fragments and traces of pockets of clay and with a thick bed of very stiff to hard clay.

IVa 45.7 – 51.1 Very stiff to very hard slightly sandy to sandy CLAY locally with extremely closely spaced partings of fine silt and sand, and traces of shell fragments and fine gravel.

IVb 47.1 – 67.2 Very dense slightly silty to silty fine to medium SAND, traces of shell fragments locally very clayey and silty, few cobbles. Va 59.3 – 80.8 Very hard foliated slightly sandy CLAY, pockets, laminae and thin beds of silt and fine sand, traces of black staining pockets.

The characteristic shear strength in the sand, based on the measured cone resistance from CPTU tests, was selected as a carefully assessed value as required by NORSOK (11). Figure 9 presents the soil layering used and characteristic cone resis-tance profile. For piles loaded in compression, a penetration depth of 51 m was originally required to ensure the required bear-ing capacity. The NGI-05 method, giving in this case the lowest capacity among the CPT-methods, was used for this evalua-tion of pile length.

Uncertainty in Soil Parameters

The statistical procedures were the same as those used for Case Study A. The soil data were analysed layer by layer. The parameters were taken to either vary linearly with depth within the one unit (dependent soil variable) or be constant within the unit (independent soil variable). In addition, a procedure was developed to statistically process the cone resistance qc from the CPTU data in very dense sand. Five CPTU borings closest to the footprint of the jacket were used for the statistical estimates. The procedure is summarized in Appendix D.

Table 10 lists most of the soil parameters required for the probabilistic pile capacity analyses The table gives the mean and the coefficient of variation. The probability density functions (PDF) for the soil parameters are also listed. The best fit of the data was done as for Case Study A with EasyFit (13). There were more data points available for the Case Study B statistical analyses than for Case Study A, but judgment still had to be used.

Figures 9 illustrates the statistical analyses of the cone resistance qc, with mean ± one standard deviation. In Figure 10, the single points with qc>100 MPa give the maximum capacity of the cone penetrometer and do not reflect the actual in situ re-sistance. The actual in situ qc is higher than measured. The averaging used the measured maxima. To partly account for this, a lognormal PDF was used to describe the cone resistance probabilistically (see also Fig. D1 in Appendix D).

Table 10. Input parameters for sand and clay in the probabilistic analyses of axial pile capacity, Case Study B.

Soil Unit

Depth to top of unit

(m)

Soil type

Total unit weight, (kN/m3)

Undrained shear strength (top-bottom), su

UU ( kPa) qc (top-bottom)

(MPa) Relative density

Dr (%) Plasticity index, Ip (%)

Mean ± SD (CoV=2-7 %); PDF=N


Mean; CoV (%) PDF = LN

Mean; CoV(%) PDF = N


I 0 SAND 18.6 ± 0.47 - 0 – 4.5; 17 % 0.94; 7 % - II 0.3 SAND 18.6 ± 0.47 - 4.5 – 12.5; 17 % 1.15; 6 % - II 0.8 SAND 18.6 ± 0.47 - 12.6 – 52.9; 13 % 1.25; 4 % -

IIIb 8.7 SAND 18.8 ± 0.51 - 74.2; 25 % 1.36; 7 % - IIIb 21.7 CLAY 21.2 ± 0.47 415-478; 6.5 % 10; 68 % - 16.3; 15 % IVb 22.2 SAND 19.0 ± 0.64 - 60.6 – 94.8; 25 % 1.28; 8 % - IVb 25.0 SAND 19.0 ± 0.64 - 112.9 - 83.3; 32 % 1.37; 9 % - IVb 33.2 SAND 19.0 ± 0.64 - 67.2; 43 %- 1.15; 15% - IVb 34.9 CLAY 20.2 ± 0.24 277-294; 34 % 4 – 6.6; 33 % - 29.5; 3 % IVb 36.1 SAND 19.0 ± 0.64 - 20.6 – 51.0; 42 % 0.88; 19 % - IVb 38.5 SAND 19.0 ± 0.64 - 65.3; 27 % 1.09; 10 % - Iva 46.2 CLAY 22.2 ± 1.6 324-1471; 38 % 7.4 – 30.4; 49 % - 14; 19 % IVb 49.4 SAND 19.0 ± 0.64 - 112.9 - 90.5; 34 % 1.27; 11 % - Preconsolidation stress (p’) is 1800 kPa in clay layer IIIb, 1000 kPa in clay layer IVb and 3300 kPa in clay layer IVa. Sensitivity in clay layers: mean =1.5, CoV = 25 %; su in clay from qc trend using = 20.0 kN/m3 and N = 20. su ~ (qc – v0)/N. PDF = Probability density function: N = normal; LN = lognormal

OTC-24063-MS 9

Figure 8. Cone resistance versus depth, Case Study B. Figure 9. Mean and characteristic cone resistance, Case Study B

Figure 10. Undrained shear strength of clay layers, Case Study B Figure 11. Relative density implied by the NGI 05 method for the deterministic and statistical qc profiles, Case Study B.

Figure 10 gives the average shear strength in the "clay" layers. The clay did not contribute significant resistance to the ul-

timate pile capacity. The plasticity index was assumed to be constant with depth within each clay layer. Other parameters re-quired for the calculation of axial pile capacity in the clay layers were the difference in effective stress between the preconsoli-dation stress and the overburden stress, Δp', and the sensitivity, St. Standard deviation and coefficient of variation were esti-mated on the basis of experience and engineering judgment, and earlier published results (22; 23).

Dep

thbe

low

seaf

loor

,m

0 25 50 75 100 125 150

Relative density, Dr , %

60

55

50

45

40

35

30

25

20

15

10

5

0

Dep

thbe

low

seaf

loor

,m

Characteristic Dr

Mean Dr

0.00.2

8.7

21.4

22.5

34.8

36.1

46.2

49.3

60.0

10 OTC-24063-MS

Relative Density Dr.The relative density of the sand, Dr, was estimated from the cone resistance (8):

0.4ln22 ′ ∙ .

where qc is the cone resistance, σ'vo the vertical effective stress and σatm the atmospheric reference pressure (100 kPa). Using the First Order Second Moment (FOSM), and neglecting the uncertainty in the vertical effective stress, the relationship be-tween the standard deviation (SD) of Dr and the coefficient of variation (CoV) of qc was SD (Dr) = 0.4·CoV(qc). The choice of a lognormal distribution for qc implies a normal distribution for Dr, due to the logarithmic relationship between Dr and qc.

The resulting relative density of the sand, used by the NGI-05 and API methods, was in some layers as high as 135 %. Fig-ure 11 presents the inferred relative density with depth, for both the characteristic and the mean profiles, and the measured cone resistance. The very high relative densities are directly related to the very high values of cone resistance measured. It is not unusual that the relative density in situ is higher than what can be achieved in the laboratory, especially considering the ASTM and British Standard laboratory techniques that were used to establish the correlation among qc-Dr and effective stress. The above expression is a compromise between the two diagrams recommended in Lunne et al (24), which were based on work done by Baldi et al (25). Relative densities greater than 100 % are not unrealistic (8). Laboratory testing techniques used at NGI can give relative densities that are 20 percentage points higher than the standard ASTM and British standards methods. Relative densities measured in a recovered tube from the Frigg field have also shown relative densities that were higher than what could be achieved in the laboratory. Although the calculated Dr may be correct with respect to the reliability of the empir-ical NGI method to predict axial pile capacity, sensitivity analyses were made and it was decided to limit the maximum rela-tive density to 120 %.

Evaluation of other parameters for sand. As for Case Study A, other parameters are required for the calculation of axial pile capacity. The type of required parameters depend on the method of axial pile capacity calculation used. These additional parameters include specific parameters for the sand layers, such as the coefficient of horizontal stress (K), the friction angle ('), and the API specified limit on the skin friction (flim). The mean and coefficient of variation were obtained from the survey done of 40 offshore pile specialists summarized by (14). The values from this survey for very dense sand, in terms of mean and coefficient of variation (CoV), are presented in Table 11. The total unit weight was assumed to be constant with depth within each layer. The values of the friction angle in the sand were based on the recommendations by the API-guidelines (9). For very dense sand, the friction angle would be expected to be 45° or even more, but the API guidelines were followed in the reliability study of the API methods.

Table 11. Mean and CoV for additional parameters in sand in pile capacity analyses. Unit ' (°) Flim (kPa) K δwall (°)

Mean CoV Mean CoV Mean CoV Mean CoV I 40 15% 115 15% 0.8 25% 28 15% II 40 15% 115 15% 0.8 25% 28 15% IIIb 40 15% 115 15% 0.8 25% 28.8 15% IVb_i 40 15% 115 15% 0.8 25% 28.8 15% IVb_ii 40 15% 115 15% 0.8 25% 28.8 15% IVb_iii 40 15% 115 15% 0.8 25% 28.8 15% ' = friction angle Flim = limiting skin friction δwall = effective stress shaft friction angle K = coefficient of horizontal stress Dr = relative density

Statistical Representation of Loads for Foundation Reliability Analysis The same procedure as for Case Study A was used (Appendix B). The static compression load on the piles had very little un-certainty and was modeled as a deterministic value in the calculations. The resulting Gumbel distributions shown on Gumbel probability paper in Figure 12. In the reliability analyses of axial pile capacity for Case Study B, the distribution fitted to q1/q2 = 0.1/0.001 was used, except for two cases. In two cases, the value of the storm-induced load at the design point was greater than the 10,000-year extreme load. For these two cases, the distribution fitted to q1/q2 = 0.01/0.0001 was used. The results did not change significantly with the alternative approximation.

Figure 12. Fitted extreme value Gumbel distributions for annual maximum load, Case Study B.

OTC-24063-MS 11

Model Uncertainty in Pile Calculation Analysis Methods The selection of the model uncertainty values was done as for Case Study A. The details of the study are presented in a com-panion paper in the same OTC session (17). The model uncertainty used in the reliability analyses, expressed as a bias (mean), standard deviation, coefficient of variation and probability density function (PDF) is summarized in Table 12. The analyses were done with both the normal and lognormal PDF for the model uncertainty. Deterministic Analyses of Axial Pile Capacity The axial pile capacities for pile penetration depths of 51 m, 39 m and 26 m for the characteristic and the mean soil profiles and for the different calculation methods are listed in Table 13. The capacities were obtained with the software PACER (26). Figure 13 presents the calculated axial pile capacities in compression for the characteristic soil parameters and Figure 14 does the same for the mean soil parameters. For the CPT-methods, there is an increase in capacity due to the higher mean qc com-pared to the characteristic qc. For the NGI method, the increase in capacity is between 12 and 23 % depending on the depth of the pile, and for the ICP-method there is an increase in capacity between 28 and 47 %. The API method predicts essentially the same axial capacity with the two strength profiles. The slight reduction in Qult is caused by the reduction in total unit weight in the statistical mean profile.

Table 12. Model uncertainty Qm/Qc used for each pile capacity method in reliability analyses, Case Study B.

Axial pile capacity method Model uncertainty, Qm/Qc, in sand layers Model uncertainty, Qm/Qc, in clay layers

Skin friction End bearing Skin friction

API Bias = 1.27; SD = 0.81 CoV = 0.64; PDF = LN or N



NGI 05


Bias = 1.02: SD = 0.17 CoV = 0.17; PDF = LN or N


ICP 05




Fugro-96/05 method




Bias Qm/Qc > 1.0 means that method under-predicts measured capacity in pile load tests Bias Qm/Qc < 1.0 means that method over-predicts measured capacity in pile load tests SD = Standard deviation CoV = Coefficient of variation LN or N = Lognormal or normal PDF

Table 13. Results of deterministic axial pile capacity, Case Study B. Method

Strength profile Pile length

(m) API NGI-05 ICP-05 Fugro-96/05

Compression1) (MN) Characteristic values

51 85.1 C 107.3 P 143.9 C 128.2 P

Mean values 83.3 C 122.7 P 200.7 C 155.5 P Characteristic values

39 57.9 C 85.2 P 110.7 C 114.6 P

Mean values 55.8 C 95.7 P 141.9 C 140.3 P Characteristic values

26 34.9 C 71.0 P 99.0 C 116.0 P

Mean values 32.8 C 87.2 P 145.7 C 155.5 P 1) Compression = Qskin compression + Qtip (

C = coring pile tip, P = plugged pile tip Pile weight and plug weight are not included in the ultimate pile capacity.

With the selected characteristic parameters and the NGI-05 axial pile capacity calculation method, a pile penetration depth of 51 m was required for a material factor of 1.5, whereas a pile penetration depth of 39 m was required for a material factor of 1.3. With the ICP-05 method, a pile penetration depth of 26 m was required for material factors of 1.5 and 1.3. This unusual effect is due to the particular profile and the application of API’s transition rules between layers. Large decreases in capacities were associated with the presence of very thin layers of clay. The required pile penetration depths can be from 26 m to 51 m, depending on the method and material factor used. For the API method, the limit end bearing, qlim, was not reached until the pile penetrated 54.2 m depth.

Effect of pile tip embedment and punch-through. The plugged pile tip resistance values computed by the axial pile capaci-ty calculation methods include reduction factors to account for the embedment and punch-through, as recommended by (1; 2).

Figure 15 shows the interpretation of the API recommendations for the reduction in pile tip bearing in a sand layer when the pile tip is near the top or the bottom of a sand layer. With large diameter piles and thin weak layers, the effect of punch-through shown on Figure 15 is believed to be conservative, as the punching hypothesis assumes that a failure surface can be mobilized in the weaker layer. For Case Study B, the layers at 22 and 35-m depths are too thin to allow such surface to mobi-lize. The pile will have already found bearing in the next competent sand layer before the soil can fail in the very thin layer.

To study the effect of thin clay layers on the axial pile capacity, the entire soil profile was modeled as continuous sand, us-ing qc as input. The results of the deterministic analyses with the NGI-05 method are presented in Figure 16 for the characteris-tic and the mean qc profile. The analyses were done with two assumptions of qc in the clay layers: the bounds represent includ-ing and neglecting the clay layers at 22, 35 and 48 m. It is believed that with the thin weaker layers at 22 and 35 m, the actual capacity will be closer to that of the full sand profile (upper bound) than that of including the thin clay layers (lower bound). The capacity will be in between the curves presented on Figure 16. Considering the above and using Figures 13, 14, 15 and 16, the required pile lengths for different material factors for the API, NGI-05 and ICP-05 methods are given in Table 14.

12 OTC-24063-MS

Scour and gapping. To partly account for scour, the cone resistance was reduced to a minimum of 0.1 MPa in the upper 1.5 m. Gapping caused by the horizontal load should be considered, especially for piles in clays. For Case Study B with sand in the top 20 m, the sand will probably fill in the gap if gapping should occur. The very dense sand will also have a tendency to dilate under loading, which should tend to reduce any gapping. Gapping is therefore not considered to be an issue.

Observations. There was a large difference in required pile length depending on the method used. The API method re-quired much longer piles than the other methods. It is not a reliable method for very dense sands. The nature and strength char-acteristics with depth in Case Study B (very dense sand with considerably weaker thin clay layers) made for an unusual in-crease in capacity from 26 m to 51 m. The assumptions in the analyses to account for the effect of transition from one layer to the other and the possible effect of punch-through tend to give too low ultimate axial pile capacity, because the thin weaker layers at 22 and 35 m are too thin to allow full mobilization of a failure surface beneath the 2.4-m diameter pile.

Figure 13. Ultimate axial pile capacity in compression with the Figure 14. Ultimate axial pile capacity in compression with the characteristic qc for Case Study B. mean qc (right diagram) for Case Study B.

Table 14. Required pile length, deterministic analyses with the API, NGI and ICP methods. Method Strength profile Required pile length form = 1.5 Required pile length form = 1.3 API Statistical mean > 51 m 51 m API Statistical mean, all sand* > 51 m 55 m NGI-05 Characteristic 51 m 39 m NGI-05 Characteristic all sand* 39 m 27 m NGI-05 Mean 39 m 25 m NGI-05 Mean, all sand* 26 m 23 m ICP-05 Characteristic 26 m 26 m ICP-05 Characteristic all sand* ≈23 m ≈18 m ICP-05 Mean 23 m 13 m ICP-05 Mean, all sand* 17 m 13 m * Intermediate value between "low" qc and "high" qc

Probabilistic Analyses

Results. The annual probability of pile foundation failure was estimated with the same two-stage approach as for Case Study A (Appendix C). Table 15 presents a selection of the probabilistic RELPAX and COMREL analyses done. The table also shows the scaling factors for capacity and load established from the COMREL results to calculate the probabilistic foun-dation capacity for an annual failure probability target of 10-4.

OTC-24063-MS 13

Figure 15. Reduction in end bearing for pile tip embedded in sand Figure 16. Ultimate axial pile capacity in compression with charac- layer, as recommended by API (1) and used in PACER (15). teristic and mean qc "all sand" profile, Case Study B.

Table 15. Results of probabilistic analyses of axial capacity for Case Study B

No

Method Ultimate pile capaci-

ty Mean ± SD (CoV); PDF = LN

Deterministiccapacity *

(MN)

Annual Pf and

Scaling factor on capacity for

Pf = 10-4/yr

Calculated load factor

for Pf=10-4/yr

Relative contribution to Pf

Loads Resistance

(Model uncertainty) I API

(51-m pile) 106.9 ± 37.6

(35%) 83.3

Pf = 1.310-2 = 2.2

1.676 0.700 -- ---

III NGI-05 (26-m pile)

83.5 ± 12.0 (14 %)

80.7 Pf = 5.810-6 = 4.4

0.976 0.923 45 % 55 %

(45 %) IV ICP-05

(26-m pile) 162.0 ± 29.0

(18 %) 148.4

Pf = 2.710-11 = 6.6

0.569 0.831 28 % 72 %

(58 %) V Fugro-96/05

(26-m pile) 160.9 ± 34.0

(21 %) 155.3

Pf = 5.610-9 = 5.7

0.644 0.783 15 % 85 %

(70 %) * With mean soil parameters

Observations. The probabilistic analyses of ultimate axial pile capacity, including all uncertainties in the soil parameters

gave coefficients of variation of 15 to 20 %, except for the API method. Model uncertainty in the pile capacity calculation methods, either on the skin friction or the end bearing, was overwhelmingly the most significant random parameter contri-buting most to increasing the probability of failure. The model uncertainties used are believed to be on the conservative side (with a CoV larger than in reality) (17).

The results confirm the importance of quantifying this uncertainty parameter as realistically as possible. A parametric study was also done with a 20-30 % increase in the model uncertainty. This increased the standard deviation and coefficient of varia-tion of the ultimate axial pile capacity by about 5%. The model uncertainty was modeled with a lognormal PDF. NGI believes this assumption to be more realistic than a normal PDF, because the normal distribution allows the calculations to select values of biases (Qm/Qc) which are unrealistically high (and unrealistically low), which led to unrealistically low probabilities of fail-ure. Calibration of material factor Approach A calibration of the required material factor was done, with target annual probability of failure of Pf = 10-4 (corresponding to an annual reliability index of 3.75). This target is an example for this paper, other targets could have been selected.

The calibration procedure used (1) the results of the deterministic analyses giving the ultimate axial pile capacity with the characteristic strength parameters (Qult char); (2) the RELPAX probabilistic analyses giving the PDF of the ultimate axial pile capacity (Qult mean); and (3) the results of the probabilistic COMREL analyses giving the annual probability of failure, Pf.

The calculation included nine steps. Figure 17, showing a two-dimensional simplification of the overlap of the probabilistic

Pile tip stress, q (MPa)

Pile

tip

de

pth

be

low

se

aflo

or

(m)

c:\cjfc\text\figures\pile-tip-stress.grf

3 Pilediameters

2 Pilediameters

q q

Plugged

Coring

Cla

yS

an

dC

lay

14 OTC-24063-MS

ultimate pile capacity (Qult) and probabilistic environmental load (Penv), may help explain Steps 1 to 4 below. The PDF for the Penv was taken as the same for Pf1 and Pf2 in the calculations. The calibration of the material factor should be consistent with the definition of characteristic design load and the characteristic soil strength profile used for the calculation of axial pile ca-pacity. Steps 5 to 9 below explain how the calibration is done for different ultimate capacities.

1) Obtain the scaling factor required to shift the PDF from the calculated annual Pf to the target Pf of 10-4 /yr; 2) Find the ultimate axial pile capacity, Qult mean, for the target Pf with the scaling factor; 3) Find the load on the pile (static, Pstat, + environmental, Penv⃰) at the design point for the target Pf; 4) Find the ultimate axial pile capacity at the design point, Qult⃰, for the target Pf; 5) Calculate the required material factor for Qult mean for Penv⃰ (design point); 6) Calculate the required material factor for Qult char for Penv⃰ (design point); 7) Calculate the load factor on Penv at the design point, l env ⃰ (relative to the 100-yr characteristic load); 8) Calculate the required material factor for Qult mean for a load factor, l env, set to 1.3 (l stat is 1.0); 9) Calculate the required material factor for Qult char for a load factor, l env, set to 1.3 (l stat is 1.0).

Figure 17. 2D simplification of the PDFs of the environmental load Penv and ultimate pile capacity Qult.

Results Tables 16 and 17 present the results of the calibration of the material factor for Case Studies A and B. The first column gives the pile capacity method used; the second column, the characteristic and mean ultimate capacity from the RELPAX analyses. The next six columns present the results for the capacities and the derived material factor and load factor for the target annual probability of failure of 10-4/yr. Two material factors were obtained: one for the axial pile capacity calculated with the mean undrained shear strength (Qult mean), and one for the axial pile capacity calculated with the characteristic undrained shear strength (Qult char). The last two columns in the tables give the required material factor for a load factor on the environmental 100-yr load set to 1.3. The load factor at the design point was less than 1.3. In design however, the material factor would be expected to be associated with a load factor of 1.3 on the 100-yr environmental load.

Table 16. Results of calibration of material factor for Case Study A (pile length 90 m).

Method RELPAX Pf = 10-4/yr l env = 1.3

Qult char

(MN) Qult mean

(MN) Scaling factor

Qult mean

(MN) Qult ⃰ (design point)

(MN) m

(Qult mean) m

(Qult char) l env ⃰

Design point m

(Qult mean) m

(Qult char) API 124.7 151.7 0.671 101.8 57.5 1.77 1.46 1.12 1.64 1.35 NGI-05 100.1 120.5 0.762 91.8 61.2 1.50 1.25 1.26 1.48 1.23 ICP-05 133.5 136.8 0.706 96.6 59.2 1.63 1.59 1.19 1.55 1.52 Fugro-96/05 117.5 114.6 1.077 123.4 52.6 2.34 1.34 1.25 1.49 1.31

Table 17. Results of calibration of material factor for Case Study B (pile length 26 m, except for API, 51 m).

Method RELPAX Pf = 10-4/yr l env = 1.3

Qult char

(MN) Qult mean

(MN) Scaling factor

Qult mean

(MN) Qult ⃰ (design point)

(MN) m

(Qult mean) m

(Qult char) l env ⃰

Design point m

(Qult mean) m

(Qult char) API 83.3 106.9 1.676 179.2 48.2 3.72 2.90 0.70 3.09 2.41 NGI-05 87.9 83.5 0.976 81.5 50.4 1.62 1.56 0.92 1.44 1.40 ICP-05 148.4 162.0 0.569 92.2 48.9 1.89 1.73 0.83 1.63 1.50 Fugro-96/05 155.3 160.9 0.644 103.6 48.1 2.15 2.08 0.78 1.84 1.77

OTC-24063-MS 15

For both case studies, the calibrated material factors apply to those sites only, and cannot be transferred to other sites with-out site-specific reliability studies. The calibrated material factor varies with the method of axial pile capacity used. The fac-tors reflect the varying influence of the uncertainty in the soil parameters and of the model uncertainties for the different meth-ods. The results present generally consistent trends, where the axial pile capacity methods predicting higher axial pile capacity require a higher material factor to ensure that the probability of failure does not exceed 10-4/yr. The calibrated material factor depends on the strength parameters used in the equilibrium equation to do the deterministic analyses, and should be used only with the strength parameters it was derived from.

Case Study A. Using the NGI-05 pile capacity method, the required material factor is 1.50 if the mean undrained shear strength is used, and the required material factor is 1.25 if the characteristic undrained shear strength (Fig. 1) is used. The load factor,l env, was then 1.26. If the load factor is increased to 1.3, the material factors reduce to 1.48 and 1.23. With the ICP-05 method, which gave significantly higher capacity than the NGI-05 method, the calibrated material factor was 1.5 with a load factor of 1.3. With the Fugro-96/05 method, a material factor of 1.3 seems appropriate with a load factor of 1.3. These numbers apply to Case Study A only.

The calculations made the following assumptions: the case applies to a 90 m long pile. The calibrated factors represent an approximation for the methods other than the NGI-05 method which determined the pile length of 90 m. A more complete analysis would need to calibrate the material factor for the pile lengths required by each of the calculation methods.

Case Study B. Similar trends are seen for the pile capacity methods investigated for Case Study B. Because of the larger model uncertainties in the axial pile capacity calculations, the calibrated material factors are higher than in Case Study A. Case Study B is difficult to interpret, in terms of pile length and probability of failure, because of the relative little gain in capacity as the pile length increases and the effect of the transition to and from the weaker layers.

For Case Study B and using the NGI-05 pile capacity method, the calibrated material factor is 1.62 if the mean soil parame-ters are used, and the calibrated material factor reduces to 1.56 if the characteristic parameters selected for design are used. The load factor, l env, was then 0.92. If the load factor is set to 1.3, the respective material factors reduce to 1.44 and 1.40. With the ICP-05 method, which gave higher capacity than the NGI-05 method, the calibrated material factor was 1.6 with a load factor of 1.3. With the Fugro-96/05 method, a material factor of 1.8 seems appropriate with a load factor of 1.3. Again, these num-bers apply to Case Study B only.

The calibrated material factor of 1.40 with the NGI-05 method applies to the characteristic capacity in Figure 16. The actu-al capacity in situ is believed to be closer the upper bound shown in Figure 16. One should do a reliability analysis with this profile to complete the reliability study and to conclude on the required material factor.

Recommendations for Practice The reliability study gives insight in what could be the required material factor for different methods of axial pile capacity calculation. The study was not meant to favor an approach, it illustrates the state of knowledge today. More case studies are needed to draw general and non site-specific conclusions. One would need to do 15 to 20 (or more) analyses of this type on a variety of soil profiles to enable a general recommendation on the material factor for each of the methods. The results also depend strongly on the model uncertainties used, especially for sand profiles, and this should also be studied in more detail.

It may well be that some methods are better suited than others for specific soil conditions, pile lengths or pile diameters. This could be established by calibrating the methods for different soil, pile and loading conditions.

It is recommended that the profession make a joint effort to calibrate a series of cases such as Case Studies A and B to cal-culate the probability of failure and examine how the derived calibrated material factor may vary with soil type, profile and analysis method. It is further recommended, in agreement with (17), to look in detail into the database(s) of reliable pile model tests and to establish a consensus on the database(s) to use and on the interpretation of the pile model tests. A joint industry project should be set up with wide international participation to study these aspects.

Because of time and space constraints, the UWA pile capacity method (27; 28; 1; 9) was not included in this paper, but the method should also be considered as part of the calibration exercise.

When doing an axial pile capacity analysis, the following aspects should be included: (1) a careful selection of the charac-teristic soil parameters; (2) the effect of cyclic loading on the characteristic shear strength or ultimate pile capacity, for both piles loaded in compression and in tension; (3) the effect of gapping and/or erosion at the top of the piles on the axial pile ca-pacity; and (4) a decision on whether to account or not for the effect of time after pile installation on the axial capacity.

Selection of characteristic shear strength parameters. The selection of the characteristic parameters to use in the deter-ministic analysis is often a source of uncertainty, and can be very subjective, varying from one engineer to the other. In con-nection with Eurocode developments, Simpson (29) reported that characteristic values tend today to be selected in Europe at about 0.5 times the standard deviation below the mean. In the USA, the characteristic values are selected at values between 0.50 and 0.75 times the standard deviation below the mean. Lacasse et al (30; 31) observed similar trends (½ - 1 standard devi-ation below the mean) from a review of several clay sites in the North Sea and the Gulf of Mexico. Figures 2 and 9 compared characteristic values selected for design with the means and standard deviations from statistical analyses for Case Studies A and B. Based on those two cases (albeit limited data), the characteristic shear strength for the deterministic design of axial pile capacity could be selected at a value corresponding to about 0.5 times one standard deviation below the statistical mean.

16 OTC-24063-MS

It could be worthwhile to also consider using the mean of the soil parameters in the deterministic analyses and rather ad-justing the required material factor. For example, in Case Study A, with the NGI-05 method, the material factor would be 1.5 rather than 1.3 if the mean undrained shear strength was used. For Case Study B, the material factor would be 1.45 rather than 1.4 if the mean strength parameters were used. Using mean values would have the advantage of removing the subjectivity in the selection of the characteristic strength parameters. In addition, the mean is simpler to quantify and it is more objective.

Summary and Conclusions The paper presented the results of reliability studies of the axial pile capacity of piles at two sites. Reliability methods provide a basis for the rational and systematic treatment of the uncertainties associated with the offshore environmental loadings and the uncertainties in the geotechnical parameters and the calculation models, and it circumvents the use of safety factors. Relia-bility logic and technology also provide a useful and powerful tool essential for developing cost-effective offshore platform design criteria.

The two case studies showed that the annual probability of failure depends greatly on the values of model uncertainty used for each axial pile capacity method, especially in sand profiles. Further work to better define these values is warranted. The newer design methods need further validation with large scale tests, especially with diameters and loadings comparable to that used offshore, in order to serve as consistent design methods. Alternatively or in addition, the methods should to be qualified with respect to range of validity and extrapolation in practice, considering parameters such as pile diameter, relative density of sand and plasticity index of clay. The current state-of-the-art design seems to rely highly on qualified engineering judgement to assess and ensure a consistent safety level.

The material factors calibrated with the methodology proposed in the paper appear reasonable and suggest that the CPT-methods are as reliable as the current API method. The calibration suggest however that required material factors will differ for each of the pile capacity methods, given a target probability of failure. The approach offers an alternative to estimate the annual probability of failure and the required material factor. The target annual probability of failure of 10-4 is an example for this paper, other targets could have been selected.

The material factors and the reliability indices and probabilities of failure computed are specific for each of the sites stud-ied, and cannot be directly transferred to other sites. The methodology developed is however general and is applicable to other sites. The documentation of the annual probability of failure can lead to a significant reduction in the required length of piles, which can mean greatly reduced costs. This however, depends on the selected target annual probability of failure.

The reliability study gives insight in what could be the required material factor for different methods of axial pile capacity calculation. More case studies are needed to draw non site-specific conclusions. One would need to do 15 to 20 analyses of this type on a variety of soil profiles to enable a recommendation on the material factor for each of the methods. It is recommended that the profession initiate a joint industry project with wide international participation calibrate the required material factor. The project should also aim at establishing a consensus among experts on the database, the soil characteristics and the interpre-tation of the reliable pile model tests that can be used to establish model uncertainty.

The analyses also demonstrate the importance of how the characteristic shear strength parameters are defined. It is recom-mended to define the characteristic strength in specific terms, e.g. selecting the characteristic shear strength for the determinis-tic design of axial pile capacity at a value corresponding to about 0.5 times one standard deviation below the statistical mean.

Until additional evaluated pile load tests or the results of the proposed joint-industry project become available, one should consider using simplified statistical and reliability analyses to estimate the margin of safety and ensure approximately same margin of safety for comparable offshore installations, and at the same avoid over-conservative designs.

Acknowledgments The authors wish to acknowledge Statoil for the permission to present this work. The authors thank Gisle Håland, Gunnar Lian and Bjørn Ivo Krokeide from Statoil, Knut O. Ronold from DNV, Marc Lefranc, Rolf Hansson and Hans Jørgen Mikkelsen from FORCE Technology, Patrick Joyce, Ping Lu, Neil Glover and David MacLaren from SNC-Lavalin, and Pasquale Carocanuto, Birger Hansen, Morten Saue, Thomas Langford, Maarten Vanneste and Amir Rahim from NGI, for their assis-tance with the work. References (1) American Petroleum Institute (2011). Geotechnical and Foundation Design Considerations. ANSI/API Recommended practice 2GEO.

ISO 19901-4:2003 (Modified), Petroleum and natural gas industries–Specific requirements for offshore structures, Part 4–Geotechnical and foundation design considerations. 1st edition, Washington, April 2011.

(2) ISO 19902 (2007). Petroleum and natural gas industries - Fixed Steel Offshore Structures. 1st ed., Switzerland, Dec. 2007. (3) American Petroleum Institute (1993). Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms -

Working Stress Design. API RP 2A-WSD, 20th Edition, Washington, 1 July 1993. (4) Karlsrud K., C.J.F.Clausen, and P.M. Aas (2005). Bearing Capacity of Driven Piles in Clay, the NGI Approach. Proc., International

Symposium on Frontiers in Offshore Geotechnics, Perth Sept. 2005, A.A. Balkema Publishers, ISBN 0 415 39063 X. (5) Jardine, R.J., and F.C. Chow (1996). New design procedures for offshore piles. Marine Technology Directorate. Publ. 96/103, London,

UK. (6) Jardine R.J., F.C. Chow, R.F. Overy and J.R. Standing (2005). ICP design methods for driven piles in sands and clays. Imperial Col-

lege, Thomas Telford Publishing, London.

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(7) Kolk H.J. and E.v.d. Velde (1996). A Reliable Method to Determine Friction Capacity of Piles Driven into Clays.OTC paper no. 7993, Houston, May 1996.

(8) Clausen, C., P.M. Aas and K. Karlsrud (2005). Bearing Capacity of Driven Piles in Sand, the NGI Approach. Proc. 1st International Symp. on Frontiers in Offshore Geotechnics, ISFOG, Univ. of Western Australia, Perth, Taylor & Francis, London, pp. 677-681.

(9) American Petroleum Institute (2007). Recommended Practice for Planning, Designing and Construction Fixed Offshore Platforms – Working Stress Design. API RP 2A-WSD, 21st Edition, Washington, August 2007.

(10) Kolk, H.J., A.E. Baaijens and M. Senders (2005). Design criteria for pipe piles in silica sands. Proc. 1st International Symp. on Fron-tiers in Offshore Geotechnics, ISFOG, Univ. of Western Australia, Perth, Taylor & Francis, Lon-don, pp. 711-716.

(11) NORSOK (2004). NORSOK N-004, Design of steel structures. Rev.2, October 2004. (12) DNV (2012). Recommended Practice DNV-RP-C207: Statistical representation of soil data, January 2012. (13) Mathwave. www.mathwave.com/products/easyfit.htm. (14) Lacasse, S. and A. Goulois (1989). Uncertainty in API parameters for prediction of axial capacity of driven piles in sand. Proc., 21st

Annual OTC, Houston, Texas, pp. 353-358. (15) NGI (2011). PACER – A Computer Program for Calculation of Axial Capacity of Driven Piles. Program Documentation. NGI Report

No. 20061125-1, Rev.2 dated 1 November 2011. (16) Haver. S. (2012). Personal communication. April 2012. (17) Lacasse, S. F. Nadim, T. Langford, S. Knudsen, G. Yetginer. T.R. Guttormsen and A. Eide (2013). Model Uncertainty in Axial Pile

Capacity Design Methods. Paper OTC-24066-MS. Houston, Texas. May 2013. (18) NGI (2000). Bearing Capacity of Driven Piles in Clay. Report 525211-1. 23 March 2000. Norwegian Geotechnical Institute. Oslo. (19) NGI (2001). Bearing Capacity of Driven Piles in Sand. Report 525211-2. 21 Jan. 2001. Norwegian Geotechnical Institute. Oslo. (20) NGI (1999). Deterministic and probabilistic analysis of an offshore pile. NGI report 514161-1, 23 March 1999. (21) RCP GmbH (1999). STRUREL – A Structural Reliability Analysis Program System. RCP GmbH, Munich, Germany. (22) Keaveny, J.M., F. Nadim and S. Lacasse (1989). Auto-correlation functions for offshore geotechnical data. Proc. 5th ICOSSAR, San

Francisco, USA, pp. 263–270. (23) Lacasse, S. and F. Nadim (1996). Uncertainties in characterizing soil properties. Uncertainty in the Geologic Environment: From Theo-

ry to Practice. Proc. Uncertainty '96. Madison, WI. American Society of Civil Engineers. Geotechnical Special Publ., 58. pp. 49-75. (24) Lunne, T., P.K. Robertson and J.J.M Powell (1997). Cone Penetration Testing in Geotechnical Practice. Blackie A&P. LondonUK. 312p. (25) Baldi, G. Bellotti, R. Ghionna, V., Jamiolkowski, M. and Pasqualini, E. (1986). Interpretation of CPTs and CPTUs; 2nd Part: drained

penetration of sands. Proc. 4th International Geotechnical Seminar, Singapore. pp.143-156. (26) NGI (2008). PACER – A Computer Program for Calculation of Axial Capacity of Driven Piles. Program Documentation. NGI Report

No. 20061125-1, Rev. 1 dated 23 March 2008. (27) Lehane B.M., J.A. Schneider and X. Xu (2005). A Review of Design Methods for Offshore Driven Piles in Siliceous Sand. UWA

Report No. GEO 05358, The University of Western Australia, Perth, Australia, Sept. 2005. (28) Schneider J.A., X. Xu and B.M. Lehane (2008). Database Assessment of CPT-Based Design Methods for Axial Capacity of Driven

Piles in Siliceous Sands. ASCE Journal of Geotechnical and Geoenv. Eng. 134(9): 1227-1244, Sept. (29) Simpson, B. (2012). Eurocode 7. Fundamental issues and some implications for users. Keynote Lecture, NGM 2012. Proc. DGF Bulle-

tin 27. V 1. pp. 29-52. (30) Lacasse, S., F. Nadim, A. Rahim and T.R. Guttormsen (2007a). Statistical description of characteristic soil properties. Offshore Tech-

nology Conference, 37. Houston 2007. Proceedings paper 19117. (31) Lacasse, S., T.R. Guttormsen, F. Nadim, A. Rahim and T. Lunne (2007b. Use of statistical methods for selecting design soil parame-

ters. International Offshore Site Investigation and Geotechnics Conference, 6. London 2007. Proceedings, pp. 449-460. (32) Lacasse, S. (1988). Uncertainty in offshore geotechnical engineering - Deterministic and probabilistic analysis of axial capacity of

single piles. NGI report 525285-8, 1 May 1988. (33) Gollwitzer, S., T. Abdo, and R. Rackwitz (1988). FORM (First-Order Reliability Method) Manual. RCP GmbH, Munich, Germany. List of Appendices Appendix A. Statistical Analyses of Soil Data - Recommended Practice by DNV-RP-C207 Appendix B. Statistical Representation of Loads for Foundation Reliability Analyses Appendix C. Reliability Analysis of Axial Pile Capacity Appendix D. Procedure for the Statistical Treatment of CPT Data

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Appendix A. Statistical Analyses of Soil Data - Recommended Practice by DNV-RP-C207 (12) Independent Soil Variables. Let x be an independent soil variable, represented with n observations x1,...,xn. The mean

value of x is estimated by the sample mean: ̅ ∑ / .The standard deviation of x is estimated by the sample standard deviation:

Dependent Soil Variables. Let Y be a dependent soil variable, with linear variation with depth. It is assumed that n obser-vations of pairs (zi, yi) where i = 1, 2, 3, ...n are available from the soil investigations. The variation of Y with depth can be expressed as , where the term represents the linear mean variation with depth, the term ε the natu-ral variability of Y about the mean, and z denotes the depth below the soil surface. The coefficients and represent the surface intercept and the depth gradient of the mean of Y. The standard deviation of Y is assumed to be constant, i.e. to be in-dependent of the depth z. Estimators for the coefficients a0 and a1 (denoted â0 and â1 respectively) for the line with the best fit to the data can be found from:

∑ ̅

∑ ̅ and ̅

in which ∑ and ̅ ∑ . The standard deviation of Y is estimated by the sample standard deviation:

12

For comparison of uncertainties for each soil parameter in the different layers, the coefficient of variation, CoV, is useful. The CoV expresses the standard deviation as a fraction of the mean, often in percent. An estimator for CoV is not specified (12) for dependent soil variables. The coefficient of variation could in principle vary with depth for dependent soil variables. For the present study, the CoV-value (denoted ), was estimated for each layer as a value representative for the entire depth of each layer with the following equation: CoV s/y. For simplicity, CoV was denoted CoV in the paper. Appendix B. Statistical Representation of Loads for Foundation Reliability Analyses

Fitted extreme value model. The procedure used for statistical representation of the maximum storm-induced loads on the foundation followed the recommendation made by (16) of Statoil. The annual maximum storm-induced load on the pile fol-lows a Gumbel (Type I) extreme value distribution:

The extreme value, xq, corresponding to an annual exceedence probability q, is given by:

1

If the q-probability extreme values, xq1 and xq2, for respectively two exceedance probability levels q1 and q2 are given, then α and β can be estimated from:

and 1

The extreme loads corresponding to 0.63, 0.1, 0.01, 0.001 and 0.0001 exceedence probability per year were provided by the structural engineer. The parameters of the extreme value distribution can be estimated from any two of these extreme loads. Figures in the main text provide the parameters corresponding to the various two-by-two combinations and the corresponding Gumbel distributions. Table B1 provides the parameters corresponding to the two-by-two combinations for Case Study A. Table B2 provides the parameters corresponding to the two-by-two combinations for Case Study B.

Uncertainty in environmental loads, Case Study A. At a given return period, there is some uncertainty in the calculated loads due to the uncertainties in wave height and period, as well as the mathematical idealization. It was beyond the scope of the study to do a detailed assessment of these uncertainties. Their effect were however included in the analyses. According to (16), the model uncertainty for the storm-induced loads varies for different return periods. This uncertainty could be as high as 30% for the 10,000-yr return period, 25% for the 1,000-yr, 20 to25% for the 100-yr, and 10 to 15% for the 10-yr and 1-yr return periods. The-se values reflect the range (upper and lower bounds), not the standard deviation of the model uncertainty, and they comprise both the statistical uncertainty in wave height and period, and the modeling uncertainty of the mathematical idealization. For the plat-form analyzed, the estimated uncertainty bands were within a range of ±10 to 16% for extreme loads with return periods of 100 to 10,000 years (16). To account for this, a modeling uncertainty parameter with mean of 1, standard deviation of 0.1, and normal distribution was assumed for the storm-induced loads in the foundation reliability analyses. Sensitivity analyses were done where this uncertainty was modeled by a Beta-distribution with a variable standard deviation as function of the load level. The results of the analyses were not sensitive to how the uncertainty in the calculated loads was modeled.

Uncertainty in environmental loads, Case Study B. The uncertainty in the calculated environmental loads for Case Study B was not assessed in detail. Based on discussions with the structural engineers, a modeling uncertainty parameter with mean

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of 1, standard deviation of 0.1, and normal distribution was assumed for the storm-induced loads in the foundation reliability analyses to account for this uncertainty.

Formulation in the pile foundation analysis. The annual axial load on the pile group in the pile foundation reliability analyses was formulated as X1 + X2X3, where X1 is the static axial load due to gravity (submerged weight of platform and piles) and is a deterministic variable, X2 the storm-induced loads on the pile and X3 the modeling uncertainty with normal distribution N(1, 0.1), or a Beta distribution with mean value of 1 and variable standard deviation as function of the load level.

Table B1. Gumbel parameters, annual maximum storm-induced load on most heavily-loaded pile group, Case Study A.

Case q1/q2 xq1

(MN) xq2

(MN)

(MN) β

(MN) Mean (MN)

Standard deviation (MN)

0.1/0.01 75 800 101 900 50 804 11 107 57 215 14 245 0.1/0.0001 75 800 167 600 46 118 13 190 53 731 16 917 0.01/0.001 101 900 132 300 41 285 13 177 48 891 16 900

0.01/0.0001 101 900 167 600 36 342 14 251 44 658 18 278 0.001/0.0001 132 300 167 600 26 428 15 327 35 275 19 658

Table B2. Gumbel parameters, annual maximum storm-induced load on most heavily-loaded pile group, Case Study B.

Case q1/q2 xq1

(MN) xq2

(MN) α

(MN) β

(MN) Mean (MN)

Standard deviation (MN)

0.1/0.01 78 307 97 174 8 029 60 238 64 873 10 298 0.1/0.001 78 307 122 444 9 478 56 978 62 449 12 155 0.1/0.0001 78 307 159 172 11 619 52 161 58 867 14 901 0.01/0.001 97 174 122 444 10 953 46 788 53 110 14 047

0.01/0.0001 97 174 159 172 13 448 35 310 43 073 17 247 0.001/0.0001 122 444 159 172 15 948 12 290 21 494 20 453

Appendix C. Reliability Analysis of Axial Pile Capacity

Ultimate Pile Capacity. The ultimate pile capacity, defined as the axial load on the pile head leading to excessive dis-placement, depends on the limit skin friction, pile tip capacity, and the submerged weight of the pile. It can be evaluated from simple equilibrium consideration as shown on Figure C1. The deterministic model for the calculation of axial pile capacity can be used in conjunction with structural reliability methods to obtain the component reliability of a pile foundation in terms of its axial capacity when subjected to axial loading transferred to the pile head via the jacket.

Probability of Failure. In previous studies, NGI developed models for probabilistic analysis of axial and lateral capacities of single piles (32; 20). The RELPAX model was used (20). The more recent CPT-pile capacity calculation methods were implemented. The analyses consisted of (1) a deterministic analysis of the axial pile capacity with the best estimate of the soil properties with each of the methods and (2) a quantification of the uncertainty in the ultimate pile capacity, including its prob-ability density function.

The deterministic values of the axial pile capacity in compression, Pult comp, and in tension, Pult tens were evaluated. A limit state function was defined as:

g = Pile capacity - (Deterministic value of pile capacity)

where is a factor less than 1. Using the first-order reliability method, FORM (33), the probability of failure Pf was defined as:

Pf = P [g 0 ] (-)

where is the reliability index and is the normal distribution function. The limit state function g and probability of failure Pf were obtained for 8 values of . Normal and Lognormal PDFs were fitted to the computed values. The better fit of the two distribution functions as calculated by RELPAX was used for the probabilistic description of the axial pile capacity. Since the axial pile capacity being evaluated probabilistically is related to resistance rather than loading, the best fit to the lower tail (values below the mean) of the distribution function was the more relevant for foundation reliability analyses. The -fractions of the deterministic value of 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8 and 0.85 were therefore used in the calculations.

FORM Approximation. The probabilities were calculated with the first-order reliability method, FORM. The first step in the FORM approximation is the definition of a performance function, g(X), such that g(X) 0 means satisfactory performance and g(X) < 0 means failure. X is a vector of basic random variables including soil properties and modeling uncertainty. If the joint probability density function of all basic random variables Fx(X) is known, then the probability of failure Pf is given by:

Pf = L

x dXXF )(

where L is the domain of X where g(X) < 0. In general the above integral cannot be solved analytically, and an approximation is obtained by the FORM approach. In this approach, the general case is approximated to an ideal situation where X is a vector of independent Gaussian variables with zero mean and unit standard deviation, and g(X) is a linear function. The probability of failure Pf at the "design point"(where the probability of failure is highest) is:

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Pf = P [ g(X) < 0 ] = P [

n

i 1

iUi – < 0 ] = (-)

where P[…] reads “the probability that”, i is the direction cosine of random variable Xi, Ui is the transformation of variable Xi in the standard normal space, is the distance between the origin and the hyperplane g(U) = 0 in the standard normal space, n is the number of basic random variables Xi (and its transformation in the standard normal space U), and is the standard nor-mal distribution function. The vector of the direction cosines of the random variables (i) is called the vector of sensitivity factors, and the distance is called the reliability index. The relationship between the reliability index, , and the probability of failure, Pf, is shown in Figure C2.

The direction cosines or sensitivity factors are an important by-product of the FORM analysis. The square of the sensi-tivity factors (i

2), which sum is equal to unity, quantifies the relative contribution of the uncertainty in each random variable Xi to the total uncertainty. The statistical subroutine packages FORM and SORM developed by (33) are implemented in RELPAX software. Spot verifications were done with the second-order reliability method (SORM) and the changes in the results were found to be small.

Evaluation of the Annual Probability of Pile Foundation Failure. The assessment of the annual probability of foundation failure used the FORM approximation in the COMREL-Symbolic software package (21). The following limit state function g was used in the calculation of the annual foundation failure for a group of four piles in compression:

g = scale*capacity – pile_weight – (storm_load*errload + perm_load) /4 where capacity = Axial pile capacity from RELPAX probabilistic analyses storm_load = Sum of annual maximum storm-induced loads on pile group

perm_load = Sum of permanent static loads on pile group (deterministic) errload = Random variable describing the epistemic uncertainty in load calculation model pile_weight = Net sum of submerged weight of a 90-m steel pile and soil plug, and their buoyancy (deterministic) scale = Scaling factor on capacity (set to unity in first analysis)

The limit state function g is based on the following assumptions: (1) failure of the most heavily-loaded pile in the foundation system does not mean that the foundation system has failed. The jacket and the pile group are capable of redistributing the load to other piles in the group once the axial capacity of a pile is fully mobilized. This assumption may be non-conservative; (2) the uncertainty in gravity-induced loads is negligible. The variables used for the base case analyses of Case Studies A and B are summarized in Table C1.

Figure C1. Ultimate axial capacity of a pile. Figure C2. Relationship between probability of failure, Pf, and reliability index . Pult + W’ = Qs + Qtip Qs = Ultimate skin friction Qtip = Ultimate tip capacity Pult = Axial pile capacity

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Table C1. Parameters used of the evaluation of the annual probability of failure for Case Studies A and B Case Study

Variable

Case Study A (90- m long pile) Case Study B (26-m long pile)

PDF Mean SD PDF Mean SD

Capacity Lognormal or Normal See main text See main text Lognormal or Normal See main text See main text

storm_load Gumbel

= 36 342, = 14 251 44 658 kN 18 278 kN

Gumbel = 9 478, = 56 978

62 449 kN 12 155 kN

storm_load (Sensitivity analysis)

Shifted exponential 50 467 kN 14 267 kN Gumbel

= 13 448, = 35 310 43 073 kN 17 247 kN

errload Beta with = 3, = 3 1.0 Variable * Normal 1.0 0.1

pile_weight ** -- 3 253 kN -- -- 1 490 kN --

perm_load * -- 103 300 kN -- -- 203 561 kN --

* Function of the load level, see main text PDF Probability density function SD Standard deviation ** Deterministic parameter

Appendix D. Procedure for the Statistical Treatment of CPT Data A procedure was developed to treat the cone resistance qc from the CPTU data in very dense sand. The procedure can be sum-marized in nine steps. Results for Case Study B are illustrated in Figure D1. In Figure D1, the peak qc is the value reached when the cone reached maximum capacity and could not be pushed further.

1. For each CPTU test, obtain the measured qc versus depth. Plot qc versus depth individually at large scale.

2. Eliminate non relevant data where the qc-values rising from 0 to qc as a new push is started. All points in the rising CPTU are removed up to the point where the following criteria are met:

a. the increase in qc ceases to be “uniform”, smooth, compared to the qc-data close by (either above or below considered depth). (To limit subjectivity, have several persons agree on the data to be removed).

b. the probe has penetrated a minimum 10 to 15 cm into the soil (about four times the diameter of the probe).

c. a local maximum is reached: below the depth of this local maximum value, all measured qc-values are kept.

3. When the maximum capacity of the cone was reached (actual in situ qc-value is higher than measured, but the equipment could not measure higher cone resistance), use this value, noting though that the resistance is in reality higher. This max-imum measurement is represented by one data point only.

The criteria in Steps 2 and 3 were coded as follows: (a) for each of the qc-data files for a given borehole (i.e. for each push), sort the input data versus depth; (b) data from unique depth levels were subsequently re-sampled (linear interpola-tion) at regular 1 cm depth intervals; (c) the processed and re-sampled data for each CPT stroke were then catenated, one file for each borehole; (d) the data from depth intervals flagged for removal were skipped and only the peak values were added, from the raw data files, for the intervals flagged for peak scanning. The re-sampling in (d) prevents unequal weighting of the data points, e.g. at locations where the number of qc-points per meter is much larger than at other loca-tions in the same depth interval.

4. Do Steps 1 to 3 for all CPTU borings considered. Check on a graph how the depths overlap.

5. Reexamine the data for each boring and check that the actual data have been sampled correctly.

6. Divide profile in soil layers; use existing soil layering as a starting point and adjust layering as indicated by the qc-data.

7. Where sufficient data are available, calculate the mean and standard deviation (uncertainty) in each layer for each bore-hole. Establish either a constant or linearly varying qc for each layer by finding the best fit to the CPTU data.

8. Check that the results show a plausible variation with depth, adjust and correct as needed (e.g. consider whether qc should be constant with depth instead of decreasing with depth, whether qc should increase with depth, whether two layers should be merged, etc.).

9. Merge the processed CP data from each borehole and determine for each soil layer the trend line and as done in Step 7.

The procedure used the measured qc-values when the probe reached its maximum capacity. The mean value of qc will then be on the conservative side. The spatial trends are not accounted for in this procedure. They probably exist, but they tend to be small over small depth intervals. Measurement uncertainty is not accounted for either. The measurement uncertainty in qc is relatively low. In deterministic analyses, the use of a material factor and characteristic values allows to avoid addressing this uncertainty explicitly.

In some cases the qc-values is used in a calculation to derive another parameter. In such a case, a FOSM (First-Order Se-cond-Moment) analysis of the formulations should be done, e.g. in the clay layers where qc is converted to undrained shear strength su. The FOSM analysis propagates the uncertainty in the inferred parameters used as input to the pile calculations. (This last step does not apply when the qc-value is used as a direct input in the calculations of pile capacity).

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Figure D1. Filtered, re-sampled and merged cone resistance qc with mean and ±one standard deviation.

OTC A4 OTC-24063-MS Lacasse Reliability Final - Corrected

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