Evaluating Uncertainty Associated with Engineering Judgement in Predicting the Lateral Response of Conductors

The 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 $770\mathrm{MN}·{\mathrm{m}}^2$ 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., $\mathrm{EI}=889\mathrm{MN}·{\mathrm{m}}^2$). 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 ${\mathrm{R}}_{\mathrm{ave}}=0.445\mathrm{\mu m}$, resulting in a relative roughness of ${\mathrm{R}}_{\mathrm{ave}}/{\mathrm{D}}_{50}=0.44$. Based on this relative roughness, a roughness factor of $\alpha =0.5$ (where $\alpha =0$ represents a perfectly smooth interface and $\alpha =1.0$ 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 $({\mathrm{N}}_{\mathrm{p}}·{\mathrm{s}}_{\mathrm{u}})$ with depth, the undrained shear strength gradient (k) was set as $1.65\mathrm{kPa}/\mathrm{m}$, 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 ${\mathrm{s}}_{\mathrm{u}}\le 100\mathrm{kPa}$ (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 $\mathrm{EI}=889\mathrm{MN}·{\mathrm{m}}^2$ and $\alpha =0.5$ showing 17% higher (0.1D) and 6% lower (1.0D), respectively, than for the pile with $\mathrm{EI}=770\mathrm{MN}·{\mathrm{m}}^2$ and $\alpha =1$. 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.

The 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.

The tested soil is a reconstituted carbonate silt of low plasticity $(\mathrm{PI}=22\%)$ and specific gravity $({\mathrm{G}}_{\mathrm{s}})$ of 2.76. The soil is classified as a high plasticity silt (MH) under the US Classification System, although its ${\mathrm{D}}_{50}$ 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 ${\mathrm{N}}_{\mathrm{T}\text{-}\mathrm{bar}}=10.5$. 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 $1.65\mathrm{kPa}/\mathrm{m}$ and a sensitivity $({\mathrm{S}}_{\mathrm{t}})$ 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 ${\mathrm{CK}}_0\mathrm{U}$ 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.

A 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.

The displacement rate for the monotonic pushover test ($1\mathrm{mm}/\mathrm{s}$), 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 ($\pm 0.02\mathrm{D}$), 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.

The 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.

Participants 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.

A 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).

In 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:

The 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 $({\mathrm{P}}_{\mathrm{u}})$. 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 ${\mathrm{N}}_{\mathrm{p}}$ 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 ${\mathrm{P}}_{\mathrm{u}}$ 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.