AbstractThis paper presents the results from a prediction event, organized by the University of Western Australia (UWA) and the National Geotechnical Centrifuge Facility (NGCF), and performed as part of the International Symposium on Frontiers in Offshore Geotechnics to assess uncertainty in predicting the monotonic and cyclic lateral response of conductors. Geotechnical professionals from around the world were invited to predict the response of a model conductor (a flexible pile) subjected to a series of loading sequences in a centrifuge. A normally consolidated fine-grained soil was used in the tests, which was characterized by soil elements and in-flight T-bar penetrometer testing. While some participants provided accurate predictions, the mean response was an overestimate of the monotonic and cyclic load at the pile head, which was significant for large and very small displacements. An analysis of the submissions is presented to quantify the variability of the predictions received, assess the consequences of each design, and relay the uncertainty associated with engineering judgment in design.IntroductionPredicting the cyclic response of soft soils is a significant challenge facing offshore geotechnical engineers. This is notably the case for drilling conductors, whereby modelling soil–conductor cyclic behavior is critical in assessing the fatigue life of a system. Current API RP 2GEO guidelines (API 2014) recommend monotonic p-y curves that are based on the results of pushover testing performed on piles, and it is generally accepted that the recommended p-y curves underpredict lateral stiffness at modest displacement levels, which are the most relevant for conductor fatigue assessment. Without additional guidance, practitioners rely on past experience, published studies, and judgment to support the design, without documented consensus about methodology and choice of design parameters.Acknowledging the need for a better understanding of soil–conductor interaction and the benefit of a transparent and collegial approach, an international prediction event was conducted as part of the ISFOG (2020) conference in Austin, Texas, US. The event was managed by the National Geotechnical Centrifuge Facility (NGCF) at the University of Western Australia (UWA). Four loading scenarios were considered in the event: 1.A monotonic pushover test, up to a displacement of 1 conductor diameter (D);2.A two-way cyclic test at a displacement amplitude of ±0.02 D;3.A two-way cyclic test at a displacement amplitude of ±0.10 D; and4.A two-way cyclic test at a load amplitude of ±153 kN.Motivation for this case study was drawn from the success of previous events, such as the predictions of spudcan penetration for jack-up platforms (Van Dijk and Yetginer 2015) and footing settlement (Doherty et al. 2018), with both cases comparing practitioner estimates to field observations. While Van Dijk and Yetginer (2015) focused on the selection of parameters and method that yield the most accurate prediction, Doherty et al. (2018) focused on the variability of the predictions received. Both studies highlight the possible range in design outcomes—even when the ground conditions are well known, the load cases are clearly defined, and the calculation methods are reasonably well developed.Further motivation stems from the increasing use of probabilistic approaches in geotechnical research and practice. While these methods capture uncertainty in many aspects of the design process, they do not necessarily address the importance of judgment, as employed by practitioners. Previous studies have indicated the importance of human factors in design (Sowers 1993), while others have proposed approaches to account for uncertainty in data interpretation in design (Whitman 2000).In effect, this study is a unique elicitation exercise that helps to assign uncertainty associated with engineering judgment in design—achieved by performing highly controlled (centrifuge) tests in uniform soil, along with a ‘common’ level of soil interpretation. The observed variability in predictions is likely to represent a lower bound scenario compared with real design cases, which may involve complex stress histories and foundation geometries, along with additional (subjective) interpretation of the soil. Accordingly, while focusing on the study of a laterally loaded conductor, the findings are likely to be relevant to other scenarios.Building on the above background, a statistical analysis is first presented to quantify the variability of the predictions received. To provide insights on what could be considered best practices, a parametric analysis using LAP version 2.0 software (Doherty 2017) and adopting methods used by several predictors is then presented—and the results are explained in terms of their implication for fatigue design of conductors and ultimate lateral capacity of piles.Investigated CaseThe selected problem is the lateral cycling loading of a flexible pile (representative of an offshore conductor) under free head conditions. Data provided to the participants included: •A detailed account of the testing procedure from installation to end of loading;•Test setup, and the dimensions and mechanical characteristics of the pile; and•Soil properties as determined from centrifuge T-bar penetrometer tests, core sampling (for water content) at the end of testing, as well as advanced laboratory testing (simple shear tests, triaxial compressionm and extension).The data made available to the participants is provided as supplemental data to this paper.The pile geometry is shown in Fig. 1 with prototype dimensions (at a testing acceleration of 80 g) reported in Table 1. The pile was free to rotate and translate laterally at the load application point, located 3.36 m above the seabed, while the pile length and rigidity were chosen to minimize the rotation and translation at the pile toe. Participants were advised to assume the outer pile surface was fully rough.Table 1. Model and prototype dimensionsTable 1. Model and prototype dimensionsDimensionModel at 1 g (mm)Prototype at 80 g (m)Length (from hinge to toe)27021.6Outer diameter (aluminum pile)120.96Wall thickness (aluminum pile)0.450.036Wall coating (aluminum pile + epoxy coating)0.960.0768Total outer diameter13.921.114Embedment22818.24Experimental ApproachModel and InstrumentationThe model pile was manufactured from aluminum 6061T6, with a Young’s modulus of 68.9 GPa and instrumented with 13 pairs of strain gauges 20 mm apart, starting 15 mm from the toe as illustrated in Fig. 2. The pile was covered in epoxy resin, resulting in an outer diameter of 13.92 mm at model scale and 1.114 m at prototype scale. The free head (zero moment) condition was achieved by placing a hinge at the load bracket, 2.5 D from the top of the pile. Once the pile was installed, the hinge was located at 42 mm (model scale) or 3.36 m (prototype scale) above the seabed. For simplicity, throughout this paper, the location of the hinge will be referred to as the pile head. Once installed, the downward displacement of the pile was restricted with steel cables connected to the hinge pins during the test.The horizontal load applied to the pile was measured with a load cell located in the loading arm. The pile displacement and rotation at the load application point were measured using two lasers and a flat plate bracket as a target. The pile setup is shown in Fig. 2.To make their predictions, participants were provided with a rigidity (EI) of 770 MN·m2 as determined via a cantilever test that had been performed on an aluminum pile of an outer diameter and wall thickness as indicated in Table 1, but without the strain gauges. When the same test was later performed on the strain-gauged pile, it was observed that the epoxy required to cover the strain gauges and the cables had increased the rigidity of the pile by about 15% (i.e., EI=889 MN·m2). Furthermore, the actual pile roughness was measured after the prediction event had started, using a roughmeter and measuring over six different portions of the epoxy-coated pile. This yielded an average roughness of Rave=0.445 μm, resulting in a relative roughness of Rave/D50=0.44. Based on this relative roughness, a roughness factor of α=0.5 (where α=0 represents a perfectly smooth interface and α=1.0 a fully rough interface) was considered the most appropriate for the pile-soil interface—which differs from the fully rough condition advised to the predictors.To understand how these differences in stiffness and roughness would affect the results, a lateral push analysis was performed using LAP software (Doherty 2017) and p-y curves were determined following the method proposed by Jeanjean et al. (2017). The load was applied at the hinge level, and the prototype pile length and total outer diameter used were those specified in Table 1. To estimate the ultimate lateral soil pressure (Np·su) with depth, the undrained shear strength gradient (k) was set as 1.65 kPa/m, as obtained from the T-bar tests, and a no-gapping condition was assumed. The normalized p-y curve selected was the harmonized curve for clays with su≤100 kPa (Jeanjean et al. 2017). Fig. 3 compares the calculated bending moment profiles using the rigidly and interface roughness values provided to the predictors, where the values calculated using the rigidity and interface roughness values were re-evaluated after the prediction event.As shown, the effect on bending moment profile is small, with the peak bending moment for a pile with EI=889 MN·m2 and α=0.5 showing 17% higher (0.1D) and 6% lower (1.0D), respectively, than for the pile with EI=770 MN·m2 and α=1. While not shown, the comparison in terms of pile head load is even more modest, with the re-evaluated rigidity and roughness values giving 2% lower pile head load (on average) than the pile conditions used by the predictors. Therefore, it is concluded that it is appropriate to compare the model test results with the participant submissions.Centrifuge Setup and Experimental ProceduresThe centrifuge campaign was conducted in the 1.8-m radius centrifuge at the University of Western Australia (Randolph et al. 1991). Tests were performed at an acceleration of 80 g using a strongbox of internal dimensions of 650 mm long, 390 mm wide, and 325 mm height. The sample was prepared with 30 mm of sand to form a base drainage layer, on which a soil slurry (prepared with moisture content of 140%) was placed. The sample was subsequently consolidated in-flight under an acceleration of 80 g for 20 days, creating a normally consolidated (NC) sample. Full consolidation was validated using the graphical method proposed by Asaoka (1978).The piles were installed at 1 g to an embedment depth of 228 mm model scale and 18.24 m prototype scale. This installation followed a specific process to minimize soil disturbance in the vicinity of the pile and to ensure the pile was held in vertical position while driving/drilling. To achieve this, the pile was driven by a 2-axis actuator, while the soil at the toe of the pile was removed with a drill bit connected to a rotary actuator (Fig. 4). The rotary actuator was set to a speed high enough to ensure the soil inside the pile was being displaced upwards without being pushed into or pulled from the sample beneath the pile. When the pile reached the required embedment depth, both actuators were stopped, the lateral restrictions on the pile were removed, and the drill bit was extracted manually with the rotary actuator rotating in reverse. As a result of the installation process, the pile may be considered as wished-in-place for modelling purposes.Upon installation, the centrifuge was spun to 80 g, and a reconsolidation period of 1 to 2 h (equal to at least the time the centrifuge was stopped for pile installation) was observed before the load testing started.Once each test was finished, the centrifuge was stopped to remove the pile, and a non-instrumented tube of the same diameter and length was introduced in the hole left by the extracted pile. After the instrumented pile was cleaned, it was installed in another location in the same sample following the same procedure described above, separated at least 10 D from the locations of the previous tests and the walls of the box in the direction of loading.Soil CharacterizationThe tested soil is a reconstituted carbonate silt of low plasticity (PI=22%) and specific gravity (Gs) of 2.76. The soil is classified as a high plasticity silt (MH) under the US Classification System, although its D50 is clay-sized (0.001 mm). The profile of the moisture content, obtained from core samples extracted from undisturbed locations in the box at the end of the testing, is shown in Fig. 5(a). The repeatability of the moisture content profiles indicates a uniform sample throughout the box, ensuring that the initial soil conditions for all tests were the same.The undrained soil shear strength was inferred from in-flight (i.e., at 80 g) T-bar penetrometer tests (Stewart and Randolph 1991) using a capacity factor of NT-bar=10.5. The T-bar was 5 mm in diameter and 20 mm in length. The tests comprised a monotonic push to a depth of 16–17 m, then an extraction up to a depth of 14.5 m followed by a series of 20 cycles with a cyclic range of four T-bar diameters to assess soil sensitivity (Zhou and Randolph 2009a). Results from two T-bar tests performed at different stages during the testing campaign are shown in Fig. 5(b). The T-bar tests yield a strength gradient (k) of 1.65 kPa/m and a sensitivity (St) of 5, as observed from the degradation factor of 0.20 from Fig. 5(c), similar to those reported by Zhou et al. (2020) in the same material.In addition to the testing performed on the centrifuge sample, a number of laboratory element tests were performed on samples consolidated in tubes under a vertical pressure representing a depth of 6.0 m below the seabed. The results from CK0U simple shear tests at different strain rates and cyclic simple shear tests are shown in Fig. 6.It is important to note that while the carbonate silt was recovered offshore, its response does not directly replicate that observed in situ. Among the other differences, in situ carbonate soil typically exhibits higher sensitivity and a different response to cyclic simple shear testing at relatively low strains (Watson et al. 2019). The results from the reconstitution process used in the laboratory cannot replicate the natural deposition process and hence does not capture the influence of soil fabric. It is noted (and participants were advised) that the strength gradient and sensitivity of the soil used in the prediction event appear broadly similar to deep water Gulf of Mexico clay.Load CasesA total of four tests were performed: a monotonic pushover test and three two-way loading cyclic tests, with individual test sites separated by sufficient distance (at least 10 D from each other and from the walls of the box in the direction of loading) to avoid interaction effects. The details for each test are summarized in Table 2, and a diagram showing the loading sequences for the cyclic tests is depicted in Fig. 7.Table 2. Test type and descriptionTable 2. Test type and descriptionTestTest typeHead displacement y/DModelPrototypeMonotonic pushover (MT)Forward push1.07 D14.90 mm1.19 mCyclic test 1 (CT1)Two-way displacement-controlled0.02 D0.22 mm0.02 mCyclic test 2 (CT2)Two-way displacement-controlled0.10 D1.37 mm0.11 mCyclic test 3 (CT3)Two-way load-controlled—23.9 N153 kNThe displacement rate for the monotonic pushover test (1 mm/s), the frequency of the cycles (1 Hz for CT1 and 0.5 Hz for CT2 and CT3, model scale) and the duration of each cyclic test (6.7–13.3 min at model scale, 29.6–59.3 days at prototype scale) were selected such that the soil behavior is considered to be largely undrained—and participants were advised to ignore drainage effects in their analysis.It is important to mention that for cyclic test #1 (±0.02 D), the actual amplitude achieved at the pile head was 0.018 m (instead of 0.02 m targeted). This is not expected to change the cyclic degradation behavior significantly, although the peak load in the first cycle might be slightly lower than expected—and is to be considered when comparing test data to predictions.Prediction ExerciseOutput Required from ParticipantsThe prediction event was advertised on the 4th International Symposium on Frontiers in Offshore Geotechnics webpage, as well on an individual basis. Participants were requested to make four predictions regarding the pile performance under the four loading conditions indicated in the previous section, although partial responses were also accepted. The output requested from participants for each test is indicated in Table 3. In addition, participants were asked to provide details of the method used, the parameters they adopted, and to describe what they considered to be the greatest source of uncertainty in their prediction.Table 3. Output required from participantsTable 3. Output required from participantsTestsOutput requiredMonotonic pushover (MT)(1) The load at different stages of lateral displacement, from 0.05 D to 1.07 D(2) The bending moment profile at 0.5 D and 1.0 D lateral displacementCyclic test 1 (CT1)(1) The lateral force at the pile head for 1, 40, and 400 cycles(2) The bending moment profile for 1, 40, and 400 cyclesCyclic test 2 (CT2)(1) The lateral force at the pile head for 1, 40, and 400 cycles(2) The bending moment profile for 1, 40, and 400 cyclesCyclic test 3 (CT3)(1) The lateral displacement at the pile head for 1, 40, and 400 cycles(2) The bending moment profile for 1, 40, and 400 cyclesParticipants were asked to provide the lateral force (or displacement) at the pile head for cycles 1, 40, and 400 for each cyclic test. It is assumed that participants provided their predictions at peak displacement (or load) and, considering that cycles were applied without an offset (two-way loading), this peak is produced at the first quarter of the cycle—as indicated in Fig. 7 by the red circle on each sequence plot.ResponsesA total of 29 individual predictions from 13 different countries were submitted. Some participants provided multiple submissions, meaning there were 24 individual participants, of which 15 were from industry, 6 were from academia, and 3 represented collaborations between industry and academia.Overall, 29 predictions were provided for the monotonic test, 27 predictions were provided for each of the displacement-controlled cyclic tests, and 28 predictions were provided for the load-controlled cyclic test.In 20 of the predictions, the participants modelled the soil-pile interaction using p-y curves, whereas 8 predictions used either finite element or finite difference approaches (FE/FD), and 1 prediction used a combined finite element and p-y approach.The selection of the p-y curves for the monotonic analysis varied significantly. Roughly 25% of the participants that used p-y curves indicated they used the method proposed by Jeanjean et al. (2017) in its original form (or as recommended in the draft version of API R2GEO 2020), whereas 15% used the recommendations in Jeanjean (2009). A further 25% of the participants indicated that their curves were derived from the laboratory tests data provided, using the method proposed by Zhang and Andersen (2017). Roughly 30% of the predictions that used the p-y curves were obtained using other methods proposed in the literature (API 2011; Komolafe and Aubeny 2020; Reese and Welch 1975; Wang et al. 2020; Yu et al. 2017), while the remaining participants did not specify how the curves were derived.Regarding the p-y curves used to predict the cyclic tests, roughly 15% of the participants reported to have used the method proposed by Zhang et al. (2017) and about 15% indicated they degraded their monotonic p-y curves based on the cyclic contour diagrams for Drammen clay presented by Andersen (2015). Some predictors (around 15% of the p-y predictions) used the method proposed by Komolafe and Aubeny (2020) to degrade their p-y curves, whereas 10% of the participants constructed their cyclic p-y curves using the method recommended by Jeanjean (2009). The remaining participants either derived specific cyclic p-y curves or degraded their monotonic p-y curves using other methods available in the literature (Ahmed et al. 2020; Wang et al. 2020; Yu et al. 2018; Zakeri et al. 2016), or did not specify which method they used.There was a clear trend towards performing 3D analysis by those participants who chose to use finite element/finite difference models, with only 25% of the predictions stated to be derived from 2D analysis (one participant did not specify which type of analysis was used). The adopted constitutive models varied between clay models (NGI APD, S-Clay-1S and UDCam-S), sand models (Ta-Ger), and silt models (PM4Silt), as well as general elastoplastic models with non-linear hardening behavior rules. All participants indicated they calibrated their models based on the experimental data provided and/or internal databases from soils with similar characteristics.Regarding the prediction that used a combined method, commercial finite element software was used with a constitutive model for clay (S-Clay-1S) to predict the monotonic response of the pile, with equivalent p-y curves then back-calculated from the results. These were degraded using the recommendations provided by Andersen (2015) and used to predict the cyclic behavior of the pile. The majority of both academia and industry used recently published procedures, with only 10% of the predictions using approaches published before 2000.In terms of modelling soil-pile cyclic behavior, 21% of participants reported degrading the response using a cycle-by-cycle approach, whereas 27% followed cyclic strain accumulation procedures. From the information submitted, 24% derived parameters for their model from the simple shear test results, and 21% determined the strength profile was depth based on the T-bar data provided. Additionally, 24% of participants indicated they incorporated rate effects in their analysis, with the majority stating they had increased the ultimate lateral resistance.The greatest source of uncertainty in the prediction (reported by over 40% of the participants) was the applicability of the model selected for the particular soil and cycling loading regime. Participants stated that the model used was either calibrated from data for another soil type [kaolin, sand, or Gulf of Mexico (GoM) clay] or adapted from analysis of smaller displacements, or from cases with different cyclic loading regimes, or that they had to adapt the model in some way to apply it to the prediction event problem. The second greatest source of uncertainty (reported by 28% of the participants) was interpretation of the laboratory and centrifuge characterization test data. In this case, uncertainty related to the conversion of soil behavior at an element level to the p-y response, and considerations of loading rate, is thought to be critical to the predictions provided. Nonetheless, relatively few participants (28%) reported they had insufficient data to assign parameters for their models. Around a quarter of the participants noted they were uncertain of the performance of their adopted method to account for the cyclic degradation of the soil, with 20% of the participants also suggesting that drainage might have occurred (introducing discrepancies between their predictions and the test results).Experimental and Prediction ResultsIn this section, results from the centrifuge tests (at prototype scale) are compared to the predictions. No manipulation was performed to the predictions provided, with the exception of the following: 1.When the depth provided was not aligned with the depth requested, a linear interpolation was performed between the closest neighboring depths.2.When the maximum bending moment of the profile provided was negative, the convention was modified to exhibit a positive peak bending moment.Monotonic TestingFig. 8 presents the load-displacement curves for the centrifuge results and all predictions. The bending moment profiles for a lateral displacement of 0.5D and 1.0D at the pile head are presented in Fig. 9. Note that for 1.0D, one prediction is only partially shown as it lays outside the margins selected for the figure. As will be discussed in more detail in the statistical analysis and discussion, the predictions generally indicate higher pile head load for a particular displacement level, as well as higher peak bending moment.Cyclic TestsThe pile head response against cycle number is presented in Fig. 10, while the bending moment profiles (for N=1 and 400) are presented in Fig. 11.Statistical Analysis and ObservationsStatistical Analysis of the Monotonic TestThe pile head load predictions for monotonic displacements of 0.1 D and 1.0 D are presented using a bar plot in Fig. 12(a), along with the median of the predictions and the measured load. Note that individual predictors are designated by an individual number, allowing changes in position (relative to other predictions) to be tracked.Roughly 70% of the submissions overpredicted the load, with the median values up to 22% higher than the measured load. For 0.1 D displacement at the pile head, the median value of pile head load from both p-y and finite element/finite difference (FE/FD) predictions are similar. However, for higher pile head displacements, the median value of the load predicted from FE/FD analysis jumps to 44% higher than the measured load. This suggests either that the soil constitutive models require better calibration for large displacement cases, or that other issues such as mesh distortion/mesh lock are influencing the results.To identify trends representing the majority of the predictions, outliers were removed to obtain the coefficient of variation (COV) of the data. Outliers were identified for all tests and stages as those values outside the average value +/− two standard deviations. The impact of these outliers on the values of COV is illustrated in Fig. 13, along with the median of the predictions normalized by the measured load.Fig. 13 indicates that the load predictions are best at a displacement of 0.40 D, for which the COV and normalized median pile head load are 0.20 and 1.11, respectively. The comparison is worse (higher COV and normalized pile head load) for both smaller and large displacements.Fig. 14 shows the load-displacement curves grouped according to the p-y methods that most participants used for their prediction. Fig. 14(a) shows the predictions that used the method proposed by Zhang and Andersen (2017) for p-y scaling from simple shear test results, combined with other methods in the literature to obtain the ultimate soil pressure (Pu). Two participants indicated they obtained the ultimate soil pressure with the guidelines provided in Jeanjean et al. (2017), whereas another participant indicated they used Murff and Hamilton (1993). The latter lies slightly below the test results, whereas the former two lie on the high side, possibly indicating that the selection of the Np value with depth plays a role as important as the shape of the p-y curve on the overall load-displacement behavior.The predictions that used the p-y methods based on Jeanjean (2009) or Jeanjean et al. (2017), either as published originally or as the modified version in the draft ISO guidelines (currently under review by member countries), are shown in Fig. 14(b). The predictions shown in this figure generate p-y curves based on parameters selected by the practitioner. Although the methods suggest a preferred laboratory test to determine the input parameters, the selection process is affected by the judgment of the practitioner with respect to rate effects and past experience on similar soils.In Figs. 14(a and b), it is observed that the predictions that incorporate rate effects using the methods mentioned above (or at least where this was reported) all lie considerably higher than the test results. Here, the participants used two different approaches: they either increased the undrained shear strength profile by a percentage (based on the rate of the test compared to the rate of the provided laboratory tests), or they adjusted Pu by some multiplier.Peak bending moments for monotonic pile head displacements of 0.5 D and 1.0 D are presented in Fig. 12(a), along with the median of the predictions and the measured value. Around 62% of submissions overpredict the peak bending moment, although the median value is only 6% higher than that measured and the associated COV (excluding outliers) is only 0.17. The median depth at which the peak bending moment is estimated is 10.5 m [Fig. 15(a)]. This is close to the depth of 10 m obtained from centrifuge testing, noting that the range in peak bending moment depth from all predictions is between 7.0 m and 13.0 m, with a COV of 0.13.At 1.0 D pile head displacement, however, 72% of the submissions overpredicted the peak bending moment, with the median value of all predictions being 19% higher than the measured value, and the COV increasing slightly to 0.20. The median depth to peak bending moment increases to 12.0 m, compared to a test measurement of 11.0 m. The range of depths below the seabed to peak bending moment ranges between 5.0 m and 14.0 m, with a COV of 0.11.While it appears that the prediction of peak bending moment increases in scatter and degree of overprediction with increasing displacement, the depth to the peak is predicted accurately.Statistical Analysis of Cyclic TestsCyclic Test: Displacement-Controlled CT1 (±0.02 D)The comparison between prediction and model testing for CT1 is summarized in Table 4, and in Figs. 12(b) and 15(b). It can be observed that roughly 80% of the predictors overestimated the pile head load, with significant scatter in the data as demonstrated by the high reported COV. However, it is also noted that the magnitude of overprediction reduces with cycle number—from 46% at N=1 to only 19% at N=400.Table 4. Summary of results for CT1Table 4. Summary of results for CT1Cycle #Predicted/measuredAllp-yFE/FDAllNo outliersAllAllNo outliers11.461.281.720.480.361.290.470.28401.241.111.400.480.291.150.550.304001.191.161.320.500.311.030.570.30With respect to the prediction method used, Fig. 12(b) and Table 4 indicate that for N=1 the p-y methods outperformed the FE/FD methods, which is consistent with the monotonic push over test. The median value of the head load from p-y based predictions is 28% higher than the measured value, versus 72% higher for FE/FD based predictions. As also observed for the monotonic test, the predictions improve with increasing cycle numbers.The majority of predictors (over 90% for N=1 reducing to around 60% for N=400) over predicted the peak bending moment, with the median value reducing from 1.29 to 1.03 times the measured value as N increases from 1 to 400. While the predictors appear to have estimated the peak bending moment somewhat better than the pile head load, the COV values show a similar scatter for both. As for the monotonic test, the predictors accurately estimated the depth to the peak bending moment [Fig. 15(b)] at all cycles except N=400.Cyclic Test: Displacement-Controlled CT2 (±0.10 D)The results of the statistical analysis on CT2 are summarized in Table 5, and in Figs. 15(c) and 16(a). More than 70% of the predictors overestimated the pile head load with high scatter, as demonstrated through the COV. The overprediction is lowest for low numbers of cycles but increases for N=400.Table 5. Summary of results for CT2Table 5. Summary of results for CT2Cycle #Predicted/measuredAllp-yFE/FDAllNo outliersAllAllNo outliers22.214.171.1240.430.301.160.360.18401.161.031.530.390.321.050.390.214001.241.141.640.370.281.090.220.17Similar to CT1, the median pile head load for N=1 determined using p-y methods is closer to the measured value than that derived using finite element/finite difference methods. As the number of cycles increases, the median value from p-y analysis remains low, while that obtained from FE/FD analysis increases up to 1.64 times the measured value—indicating that less degradation was considered in the FE/FD models.Also consistent with CT1 is the observation that the majority of predictors overestimated the peak bending moment. However, unlike CT1, the median prediction of the depth to peak bending moment was 1 m higher than the measured depth for all cycles.Cyclic Test: Load-Controlled CT3 (±153 kN)The results of the statistical analysis on the load-controlled cyclic test are summarized in Table 6, and in Figs. 15(d) and 16(b). In this case, it can be seen that roughly half of the predictors accurately predicted the pile head displacement, but with relatively high scatter in the submissions (and high COV values). The comparison appears to worsen with an increase in cycle number, leading to underprediction of displacement. This indicates that cyclic degradation is somewhat underpredicted relative to the test. When comparing prediction methods, the p-y method seems to (on average) overpredict pile head displacement, while the FE/FD method seems to underpredict it.Table 6. Summary of results for CT3Table 6. Summary of results for CT3Cycle #Predicted/measuredAllp-yFE/FDAllNo outliersAllAllNo outliers11.021.050.881.570.401.050.140.07400.941.050.811.790.440.980.170.134000.900.980.841.790.471.070.180.13Regarding peak bending moment, the median value is close to the measured value with low COV, implying that load-controlled cyclic tests can be more accurate than displacement-controlled tests. The median depth to the peak bending moment is also well predicted.Discussion and ImplicationsTo understand better how the selection of parameters and analysis method influence the predicted soil–conductor behavior, a parametric analysis was performed using LAP software (Doherty 2017) and considering variations in Np, adopted p-y curve shape, and su profile. In this case, the pile-soil interface was assumed partially rough (α=0.5) and the pile stiffness was set as 889 MN·m2 (consistent with the measured values for the conductor). The load was applied at the hinge level, and the prototype pile length and outer diameter used were those specified in Table 1. The studied cases are reported in Table 7. The undrained shear strength gradient (k) shown in Table 1 was determined from the average of the strength from the CK0U simple shear tests at the slow rate, divided by the representative depth of the laboratory tests (6.0 m), and assumed a seabed strength of 0 kPa. It is noted that the T-bar strength gradient (1.65 kPa/m) yields a very similar value as the strength gradient calculated from the simple shear tests at a slow rate (1.66 kPa/m)—despite the T-bars being performed at (considerably) higher strain rate than the slow simple shear tests. While not fully understood, this is thought to be attributed to partial soil softening induced during initial penetration of the T-bar (Einav and Randolph 2005; Zhou and Randolph 2009a, b), thereby offsetting the increase due to loading rate.Table 7. Data for parametric analysisTable 7. Data for parametric analysisCaseUndrained shear strength gradient, k (kPa/m)Rate effectsShape of p-y curveLateral bearing capacity factor, Np1k=1.66 kPa/mNot consideredFrom Jeanjean et al (2017), recommended curve for su<100 kPaFrom Jeanjean et al. (2017), no gap assumedAverage su from simple shear tests at slow rate2k=1.66 kPa/m49.4% increase (based on 17.3% increase per log cycle from SS tests at slow and fast rate)From Jeanjean et al. (2017), recommended curve for su<100 kPaFrom Jeanjean et al. (2017), no gap assumedAverage su from simple shear tests at slow rate3k=1.66 kPa/mNot consideredScaled from simple shear test at slow rate using Jeanjean et al. (2017)From Jeanjean et al. (2017), no gap assumedAverage su from simple shear tests at slow rate4k=1.66 kPa/mNot consideredFrom Jeanjean et al. (2017), recommended curve for su<100 kPaFrom Murff and Hamilton (1993)Average su from simple shear tests at slow rateThe p-y curves used in the parametric analysis are shown in Fig. 17 and were either scaled from the simple shear test at slow rate (Zhang and Andersen 2017; Jeanjean et al. 2017) or from the literature (Jeanjean et al. 2017). The head loads and bending moments using the p-y curve scaling from Zhang and Andersen (2017) are observed to be very similar to the ones using the scaling from Jeanjean et al. (2017), and hence only the results using Jeanjean et al. (2017) are provided in this study (Case 3). The results of the parametric analysis are shown in Figs. 18 and 19 in terms of load-displacement curves and bending moment profiles, respectively.At 1.0 D displacement of the pile head, Case 2 and Case 3 estimated head loads above the measured values in the test by 40% and 10%, respectively. This overestimation is also observed in the bending moment profiles for the same level of displacement (Fig. 19) in which the estimated peak bending moment is about 35% and 10% higher than the measured values for Case 2 and Case 3, respectively. The head load from Case 1 was within 5% of the measured load, and the peak bending moment within 4%. The closest match to the experimental data was also obtained from Case 4, yielding a head load and peak bending moment within 2% of the measured values.A head displacement of 1.0 D is considered more relevant to pile foundations than it is to conductor fatigue life estimation.For displacements less than 0.1 D (relevant for conductors), the measured load-displacement lies between the analyzed cases, with Case 2 and Case 3 predicting a stiffer response and Case 1 and Case 4 predicting a softer response.As observed in the bending moment profile from Fig. 19, at 0.02 D and 0.10 D pile head displacement, stiffer p-y curves produce bending moment profiles whose peaks are greater than the measured data. This is particularly true for Case 3, where the peak bending moment at 0.02 D head displacement is roughly 45% higher than the measured value. Overly stiff p-y curves could lead to an underestimation of the bending stresses on the lower components and an overestimation on the bending stresses in the upper components—which may be important for design, depending on where the structural joints (along the conductor) are located.Overall, the parametric study shows that selection of the undrained strength profile and stiffness of p-y curves requires careful consideration. Of importance is the observation that the range of predictions (presented earlier) is considerably wider than the range of results from the parametric study—highlighting that judgment and experience play large roles in the final results—with the same input data potentially leading to a large range in prediction.ConclusionsThis paper presents the results of a prediction exercise undertaken by the National Geotechnical Centrifuge Facility at the University of Western Australia. The problem chosen is the response of a model conductor in normally consolidated fine-grained soil, subjected to sequences of monotonic and cyclic loading in a centrifuge.Across all tests, the participants tend to predict higher pile head capacity/stiffer response than seen in the experimental observations, albeit with some of the provided predictions being (very) close to the model response. The median of the predicted pile head load for the monotonic test is up to 46% higher than the measured value and was closest at displacements between 0.2 D and 0.7 D. Similarly, the peak bending moment is best predicted for low displacement, with the depth to reach the peak bending moment well predicted. Under cyclic loading, participants were able to predict the response more accurately during the load-controlled test, and in all cases, the p-y approach outperforms the FE/FD approach. A closer look at the results provides some potential avenues for improvement of conductor and pile design. Note that these observations are based on the median values of the predictions and do not address individual cases: •In all cases, the prediction of the peak bending moment is more accurate than the prediction of the head load, with this remaining the case even at high cycle numbers.•The better performance of the p-y approach (constituting 20 of the 29 predictions) is a testimony to the experience gathered by the geotechnical community over the last 3 decades, and of the general robustness of this approach. Further improvements will likely rely on more accurate estimation of p-y curves for given materials.•While limited in number, the accuracy of the FE/FD approach reduces with increasing displacement. It is uncertain whether this is associated with numerical artifacts (i.e. mesh locking) or calibration of the constitutive models. Regarding the cyclic tests, the FE/FD approach seems to decrease in accuracy with cycle number for the load-controlled test and the displacement-controlled test at ±0.1 D, but provides better predictions with cycle number for the displacement-controlled test at ±0.02 D. While not specifically explored in this event, it is considered likely that FE/FD approaches are more time consuming than p-y analysis—suggesting the latter is a better tool for these design problems.•Care must be exercised when incorporating judgment in the analysis. It is noted that several participants chose to include rate effects—consistent with the parametric analysis, it appears that including rate effects leads to an overestimation of stiffness, resulting in predictions with higher pile head capacity/stiffer response—although other factors may also have influenced the results provided.The significance of overpredicting pile head loads or peak bending moments is likely to be specific to the application. Use of an overly stiff p-y curve in conductors analysis may lead to an overprediction of the bending moment in the upper section, which is potentially conservative (and possibly cost prohibitive) for fatigue assessments; while at the same time may underpredict the bending moment over the lower section and lead to an aggressive outcome.Given this was a highly constrained problem, using a uniform and relatively well characterized soil sample, and well controlled installation methodology, the level of scatter in the predictions indicates there is room for improvement—particularly with respect to recommended practice. The professional judgment of each engineer plays an important role in selecting the soil parameters for calculations, and this is reflected in the variability of the predictions. This variability is explored in the statistical analysis included in this paper and may help assign uncertainty associated with engineering judgment in the design of conductors and piles.AcknowledgmentsThe authors would like to thank all the participants for their contribution and the organizers of ISFOG (2020) for their support of this prediction event. The first author is supported by the ARC Industrial Transformation Research Hub for Offshore Floating Facilities which is funded by the Australian Research Council, Shell Australia, Woodside Energy, Bureau Veritas, and Lloyd’s Register (IH140100012). The fourth author leads the Shell Chair in Offshore Engineering research team at the University of Western Australia, which is sponsored by Shell Australia. 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