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Enhancing CPT-Based Suction Caisson Penetration Design: Insights from Back-analysis
of Large-Scale Field Installation Data
Stephen K. Suryasentana1, Brendan F. O’Boyle2, John Davidson3, Sarunas Bartkus4, Felix
Schroeder5, Zefeng Zhou6
Affiliations
1 Senior Lecturer, Department of Civil and Environmental Engineering, University of Strathclyde,
75 Montrose St, Glasgow G1 1XJ, UK.
2 Geotechnical Engineer, SSE Renewables, 1 Waterloo St, Glasgow G2 6AY, UK.
3 Senior Geotechnical Engineer, Corio Generation, 33 Charterhouse St, London EC1M 6HA,
UK.
4 Geotechnical Engineer, SSE Renewables, 1 Waterloo St, Glasgow G2 6AY, UK.
5 Senior Partner, Geotechnical Consulting Group LLP, Cromwell Road, London SW7 5BE, UK.
6 Senior Researcher, NGI - Norwegian Geotechnical Institute, Sandakerveien 140, 0484 Oslo,
Norway.
Corresponding author information
Stephen Suryasentana
stephen.suryasentana@strath.ac.uk
Main text word count: 4987
Figures: 11
Tables: 7
Jul 30, 2024
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Abstract
This paper presents a detailed back-analysis of large-scale field data from suction caisson
installations in complex, layered soil conditions, enhancing the understanding of caisson
installation interaction through a refined assessment of the parameters for Cone Penetration
Test (CPT)-based installation calculation methods. Leveraging CPT and suction caisson
installation data from a large database, this paper proposes a more nuanced CPT-based design
approach tailored for such complex soil conditions. The findings highlight notable parameter
differences between dilative and contractive soils, suggesting the necessity of treating these two
groups distinctively. Through a comparative analysis with existing CPT-based methods, this
research highlights areas where current practices align well with field realities and identifies
areas where crucial adjustments are needed to enhance design accuracy. The paper also
proposes a quantile-based approach for high estimate installation calculations, which
demonstrates an effective balance between safety and excessive conservatism.
Keywords
Foundations, Soil-structure interaction, Back-analysis, Offshore
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Introduction
The offshore wind energy industry is experiencing rapid growth, positioning itself as a
pivotal element in the global shift towards renewable energy. The establishment of
offshore wind farms necessitates foundations that are both reliable and economically
viable to ensure the stability of structures and the reliable operation of wind turbines.
Suction caisson foundations have emerged as a popular solution for offshore wind
farms (OWA 2019; Bienen et al. 2018) in water depths ranging from about 40 to 60
meters. This preference is attributed to the benefits of the suction-aided installation
technique, which offers a cost-effective and less noisy alternative to the conventional
pile-driving methods used for monopile foundations. Despite its advantages, the
suction-aided installation process faces significant uncertainties, particularly in
complex, stratified soil conditions. While recent research has focused on improving
design methodologies for the post-installation performance of suction caissons (e.g.,
Vulpe 2015; Foglia et al. 2015; Sturm 2017; Jalbi et al. 2018; Gelagoti et al. 2018;
Efthymiou and Gazetas 2018; Skau et al. 2018, 2019; Antoniou et al. 2022;
Suryasentana et al. 2017, 2018, 2022a, 2022b, 2023a, 2023b, 2024; Yin et al. 2020;
Wu et al. 2022; Liu et al. 2023), there has been comparatively less attention on their
installation performance (e.g., Klinkvort et al. 2019; Buckley et al. 2023; Huang et al.
2024). This underscores the need for improved design methodologies for caisson
installation performance in complex interbedded layered soil conditions, particularly
those validated by real-world field data (e.g., Byrne et al. 2020a, b).
This paper delves into the back-analysis of field installation data from suction caisson
installations at the Seagreen offshore wind farm, a joint venture project between SSE
Renewables and TotalEnergies. The main objective of this paper is to refine the Cone
Penetration Test (CPT)-based approach for determining caisson penetration resistance
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during suction-aided installation, thereby improving the reliability of the installation
calculations for suction caisson foundations in challenging ground conditions.
The CPT is a widely used in-situ site investigation method that offers the convenience
of continuous soil profiling, aiding in soil classification and foundation design (e.g.,
Suryasentana and Lehane 2014a, b, 2016; Buckley et al. 2023). CPT data is utilized
within soil behavior type (SBT) classification systems, such as those developed by
Robertson (1990, 2009) and Schneider et al. (2008), to classify soil according to its
behavior characteristics. Traditionally, many of these SBT classification systems
employ textural descriptors—like sand, gravelly sand, or clay—to categorize each SBT.
Robertson (2016) introduced an updated CPT-based SBT classification that relies on
descriptors reflective of the soil behavior for each category. This updated classification
system categorizes soils based on their dilative or contractive properties, further
identifying them as predominantly sand-like, clay-like, or somewhere in between (i.e.,
transitional soils). Dilative soils are characterized by an increase in volume under large
strains, contrasting with contractive soils, which decrease in volume (Robertson, 2016).
There are two main types of design method (OWA, 2019) to determine the soil
resistance to caisson penetration under suction-aided installation: mechanism-based
(also known as ‘bearing capacity’-based) methods and CPT-based methods.
Mechanism-based methods (e.g., Houlsby and Byrne 2005a,b) rely on standard
geotechnical parameters obtained through in-situ or laboratory testing (e.g., undrained
shear strength ), whereas CPT-based methods employ parameters derived from CPT
(e.g., tip resistance ). This paper focuses on the CPT-based method, given the
availability of CPT data corresponding to every caisson installation data. Various
iterations of the CPT-based method exist (e.g., Andersen et al. 2008; Senders and
Randolph 2009; DNV 2021), but they all share a common approach: the correlation of
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local soil resistance to caisson penetration with local CPT tip resistance , utilizing
scale factors such as and . Here, correlates to the frictional resistance along
the caisson skirt, and to the end-bearing resistance at the caisson tip. These factors
are usually derived from the back-analysis of field data (e.g., Lunne and Kvalstad 1982;
Anderson et al. 2008).
Research focusing on the back-analysis of field data concerning soil resistance to
suction-aided penetration of caisson foundations is notably limited. DNV (2021)
references the back-analysis study of Lunne and Kvalstad (1982), which provided
estimates for the and factors based on field installation data from thirteen
concrete gravity platforms in the North Sea, which are mainly installed in dense sands
and stiff over-consolidated clays. Out of these, only seven platforms used steel skirts,
and none of the installations involved suction pressure. Therefore, these factors do not
account for the effect of suction-induced seepage on the caisson installation process.
This is particularly important due to the significant impact seepage has on installation
resistance in sand (Houlsby and Byrne 2005a). Anderson et al. (2008) performed a
back-analysis of field-scale model tests involving seventeen suction caisson
installations, primarily in sand. This analysis covered instances of suction-aided
installation and resulted in estimates for the and factors that are consistent with
the DNV (2021) guidelines. Klinkvort et al. (2019) expand on the method proposed by
Andersen et al. (2008) to account for the effects of an impermeable layer beneath the
caisson and an impermeable layer above the caisson tip. Further studies by Colliard
and Wallerand (2008) and Frankenmolen et al. (2017) have expanded our knowledge
on the and factors in normally consolidated clays and carbonate soils,
respectively. Given that the existing installation methods are largely based on the back-
analysis of a limited number of field installation data, the scarcity highlights the
importance of conducting back-analyses on a larger database of field installation data
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concerning real-world, suction-aided installations of caisson foundations. Such studies
are critical for refining and validating the and factors, ultimately leading to more
reliable suction caisson installation assessments.
The main contributions of this paper are as follows: First, it carries out a detailed back-
analysis of an extensive dataset featuring 293 suction caisson installations at the
Seagreen offshore wind farm project. This analysis aims to derive best estimates for
the and factors that correspond to the measured field data. The dataset analyzed
in this study is over ten times larger than those used in previous research, representing
a substantial expansion in the volume of data examined. Second, it explores the
variation of the and factors at different stages of the suction-aided installation
process, which provides indirect insights into the influence of suction-induced seepage
flow on these factors. Finally, it evaluates existing CPT-based design methods against
field installation outcomes, distinguishing between scenarios where these methods
demonstrate robust predictive capabilities and scenarios necessitating modifications for
improved accuracy, which includes the proposal of a new design framework to address
potential underestimation of the soil resistance to caisson penetration.
Case Study
The Seagreen offshore wind farm, located approximately 27km off the coast of Angus,
Scotland, in the North Sea (see Figure 1a), stands as Scotland's largest wind farm to
date. It comprises 114 wind turbine generators (WTGs), each boasting a capacity of 10
MW. These turbines are supported by jacket structures, each of which is anchored to
the seabed by three suction caisson foundations. These caissons have outer diameters
ranging from 10.5m to 11.5m. The skirt wall thickness is approximately 0.0052,
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and the embedded skirt length varies from 0.78 to 0.92. The installation of these
caissons spanned across water depths varying from 42 meters to 59 meters LAT.
Ground conditions
The site for the Seagreen offshore wind farm exhibits a complex and variable
stratigraphy, predominantly characterized by either mixed layers of sand, silts, and
clays, or uniform layers of sand. The geological composition of the site primarily
consists of Holocene and Pleistocene soils. A concise overview of these geological
units is detailed in Table 1.
CPTs were conducted within the planned footprints of each suction caisson installation
location. Figure 2 illustrates the variability of CPT-based normalized indices across the
site, where
and
, with and representing the tip
resistance (corrected for pore water pressure effects) and sleeve friction from the CPT
data, respectively. and
denote the current in-situ total and effective vertical
stresses, respectively. The broad range between the 5th and 95th percentiles of the
indices underscore the significant variability in soil conditions across the site.
The analysis of the CPT data, guided by the Robertson (2016) SBT classification
system, discerns soil behaviors into seven categories based on the and values,
as outlined in Table 2. The distribution of soil behavior types with depth across the site,
as summarized in Figure 3, reveals that dilative sand is the predominant soil behavior
at all depths, followed by dilative clay and transitional soil. Deeper layers frequently
contain contractive clays, whereas contractive sand and transitional soils are primarily
encountered at shallow depths.
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Methodology
The primary objectives of installation design calculations for suction caisson
foundations are twofold: Firstly, to estimate the caisson penetration behavior in
scenarios where suction is not applied, effectively when only the self-weight of the
caisson and its supporting structure are considered — this is referred to as ‘self-weight
penetration’ (SWP). Secondly, to estimate the suction-aided caisson penetration
response, which involves determining the suction pressures necessary to achieve the
desired penetration depth. This step includes evaluating the predicted suction
pressures against potential limitations arising from phenomena such as cavitation and
structural buckling, ensuring that the design remains within safe operational thresholds.
The basic equation for suction caisson installation calculation is based on the following
force equilibrium equation:
(1)
where and are the submerged vertical load (considering buoyancy
effects), internal plan area of the caisson lid, suction pressure applied (calculated as
the difference between the pressure outside and inside the caisson), and total soil
resistance to caisson penetration (which includes the soil resistance along the inner
and outer walls of the caisson skirt, and at the tip of the caisson skirt).
This paper focuses on the CPT-based method recommended by DNV (2021), as
follows:
(2)
where the right-hand side of Eq. 2 represents . is depth below seabed, is depth
of the caisson tip below seabed, is the inner caisson diameter, and
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, as shown in Figure 1b. and are the factors for the frictional
and end-bearing component of the soil resistance, respectively. The DNV suggested
values for and are summarized in Table 3. For the purposes of this study, in the
absence of DNV suggested factor values for transitional soils, the assumed factors for
these soils are derived as the average of the factors provided for sand and clay. This
approximation acknowledges the intermediate nature of transitional soils, positing that
their behavior under caisson penetration might similarly lie between that of purely
sandy or clayey soils. Moreover, as the DNV suggestions do not distinguish between
dilative and contractive soils, the same suggested factors are assumed for both soil
groups.
The aim of this paper is to conduct a detailed back-analysis to determine the best
estimates of the and factors in Eq. 2 that best match the full-scale, field
observations of the suction caisson installations. Notably, this analysis deviates from
existing approaches by not solely relying on broad soil categories (e.g., clay, sand) as
prescribed in Table 3. Instead, it adopts a more nuanced approach, aligning with the
Robertson (2016) SBT classification system. This approach is adopted to investigate if
substantial differences exist between dilative and contractive soils regarding the and
factors.
To achieve these aims, the study compiled a dataset that matches the caisson
installation data with proximate CPT data. The caisson installation data provides
structural information such and , as well as measurements of the suction
pressure and the corresponding penetration depth. This dataset focuses exclusively
on caisson installation under non-cyclic suction pressure. The assembled dataset
encompasses data from 293 caisson installations, yielding approximately 123,000 data
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points corresponding to the force equilibrium condition represented by Eq. 2. Note that
there are no data points for sensitive contractive clay-like (SCC) soils.
The dataset is partitioned as follows: (i) 80% of the caisson installation locations are
randomly selected to form the training dataset. This subset is used to back-analyze the
and factors; (ii) the remaining 20% serve as the test dataset, used to evaluate the
reliability of caisson installation calculations based on the back-analyzed factors. This
approach allows for validation of the factors when applied to similar, but previously
unseen, ground conditions. Figures 2 and 3 compare the CPT-based indices and the
Robertson (2016) classifications for the training and test datasets, which indicate that
the two datasets are broadly similar.
Figure 4a, which outlines the distribution of these data points from the training dataset
across the various SBT categories, reveals a predominant representation of dilative
soils, particularly dilative sand (SD). This distribution pattern aligns with observations
from Figure 3a. To account for the different and factors pertaining to each SBT
category, Eq. 2 can be rewritten as:
(3)
where refers to the set of Robertson (2016) SBT categories i.e., {SD, TD, CD, SC,
TC, CC, SCC}.
and
are the values of and for SBT category .
if
the SBT category at depth is , else
.
is the total resistance along the
caisson skirt till depth for SBT category , which is calculated as follows:
(4)
where and refer to the top and bottom depth of the th soil layer that has
been classified as SBT category . Note that only layers encountered from depth 0 to
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are considered in the integration i.e.,
. If there is no soil layer of SBT
category encountered from depth 0 to , then
.
To minimize the caisson dimensions from biasing the regression analysis when
determining the best estimates for the and factors, the following stress-based
form of Eq. 3 is used:
(5)
For regression analysis, it is convenient to express Eq. 5 in vector form as follows:
(6)
where and are both 14x1 vectors and is a scalar. They are defined as:
(7)
(8)
(9)
Here, represents the unknown and factors for the SBT categories.
The training dataset contains approximately 99,000 instances of Eq. 6, which can be
collectively expressed in the following general matrix form:
(10)
where is a rectangular matrix whose rows are made up of from Eq. 7 pertaining to
different installation locations and depths, while is a vector whose components is
made up of from Eq. 9 corresponding to those installation locations and depths.
As represents an overdetermined system of equations (i.e., there are more equations
than unknowns), Eq. 10 does not have an exact solution and thus, the least squares
12
method is used to determine the best estimates for the and factors. However,
ordinary least squares (OLS) solution may result in negative values for these factors,
which are not physically meaningful given that these factors represent resistance and
should inherently be non-negative. To address this issue, the current study employs
the Non-Negative Least Squares (NNLS) technique, which is an extension of the OLS
problem that adds a constraint: every element of the solution vector must be greater
than or equal to zero. The NNLS problem can be mathematically formulated as a
convex optimization problem, as follows:
(11)
The convex nature of the problem ensures that a globally optimal solution exists and
can be efficiently found (Boyd and Vandenberghe, 2004). For the current study, the
solution to Eq. 10 is obtained using the algorithm proposed in Bro and De Jong
(1997). If there are no negative components in under OLS, then the NNLS solution
will be similar to the OLS solution. In practical terms, any components in that are
negative under OLS are usually set to zero in the NNLS solution.
Using the solution (i.e., the best estimates for the and factors), the best
estimate for the stress-based soil resistance
can be calculated as:
(12)
For installation calculations, it is common practice to predict both ‘best estimate’ (BE)
and ‘high estimate’ (HE) calculations. The HE calculation represents a conservative
approach, essentially preparing for more challenging soil conditions than those typically
anticipated. DNV (2021) suggests the use of the ‘Highest Expected’ factors in Table 3
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to determine this HE calculation. The current paper, however, proposes an alternative
quantile-based approach to determine the HE calculation:
(13)
where is a high estimate (e.g., 95th) percentile of the residual error that defines the
desired level of conservatism. The residual error is defined as follows:
(14)
The residual error quantifies the mismatch between the field measurements and the
model calculations using the back-analyzed factors. The purpose of the quantile-based
approach is to address potential underestimation by the back-analyzed model when
compared to field measurements. This underestimation can occur because the model
has a limited number of adjustable parameters and is calibrated to best match field
measurements in a least-squares sense. Consequently, while the model aims to
minimize the overall error, it may still underpredict some field measurements. The
quantile-based approach compensates for this potential underestimation, ensuring that
the HE calculation will meet or exceed the field measurements at a chosen target
confidence level. For example, if the 95th percentile of the residual error is used for the
HE calculation in Eq. 13, then there is only a 5% chance that the HE calculation is
lower than the field measurement.
Bootstrapping
The bootstrap method (Efron 1979) is a powerful resampling technique for assessing
the sensitivity of regression analysis results to changes in dataset composition. This
approach involves generating numerous bootstrap samples from the original dataset by
sampling with replacement, followed by the computation of regression solutions across
these samples (Efron and Tibshirani 1994).
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The current study generates 20,000 bootstrap samples by randomly sampling the
caisson installations in the training dataset. Each bootstrap sample contains a random
subset of these installations, meaning some installations may be omitted. This
simulates the back-analysis outcomes if fewer caisson installations had been available.
The best estimate for the and factors are determined for each bootstrap sample
by solving the corresponding Eq. 11 problem. Through this process, the variability and
reliability of the estimated parameters can be evaluated, offering insights into how the
regression outcomes might vary with different subsets of the data. This will facilitate an
assessment of whether additional caisson installation data collection might significantly
alter the regression results.
Variation of factors during suction-aided installation in sand
During suction-assisted caisson installation in sand, the applied suction can induce
changes in the soil properties which can influence the caisson penetration resistance
as the installation progresses. The reduction in the caisson installation resistance is
attributable to the induced seepage field and decreased effective stresses within the
internal soil plug. While this physical phenomenon is understood qualitatively, precise
quantitative analysis remains challenging due to the complex stress states involved.
This phenomenon, which is not captured in the DNV model (i.e., Eq. 2), was
considered in the mechanism-based method (Houlsby and Byrne 2005a) and CPT-
based method (e.g., Andersen et al. 2008; Senders and Randolph 2009) for sand.
Senders and Randolph (2009) propose a model based on the following assumptions:
(i) external friction along the caisson skirt remains constant regardless of applied
suction; (ii) internal friction along the caisson skirt and tip resistance decrease linearly
with the degree of mobilized critical suction , which is defined as the suction
pressure level at which piping occurs. The model can be described as follows:
15
(15)
where
(16)
The application of the
multiplier effectively reduces the factor for internal
friction and the factor for tip resistance to zero when
.
Eq. 2 does not capture the effect of applied suction for caisson installations in sand.
Thus, the current study investigates how the best estimates of the and factors for
sand change as the applied suction increases. The analysis begins by creating a 'sand-
only' dataset, extracted from the training dataset to include only caisson installation
data from locations with uniform sand conditions. The resultant 'sand-only' dataset
contains only caisson installations in dilative sand. Thereafter, multiple subsets of the
'sand-only' dataset are formed, each containing installation data up to progressively
advanced stages of the suction-aided installation process. For each subset, a NNLS
regression analysis is performed to determine the best estimates of the factors. By
examining the variations in these factors, the study identifies how they change as
applied suction increases.
Results
Table 4 shows the NNLS solutions for the best estimates of the and factors
(rounded to two significant figures) across the Robertson (2016) SBT categories. A
significant finding is the marked difference in these factors between dilative soils (SD,
CD, TD) and contractive soils (SC, CC, TC).
is approximately 100 times larger than
, while
and
are broadly similar. Contractive soils exhibit significantly higher
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factors than their dilative counterparts. Notably, the and factors for both
dilative and contractive transitional soils (TD, TC) are close to the average of the
corresponding factors for sand and clay.
In comparison to the DNV suggested values in Table 3, the back-analyzed factors
for dilative soils are in very close agreement. However, the factors for dilative soils
diverges from the DNV suggested values, with
being smaller, while
is larger.
For contractive soils, the and factors are much larger than the DNV suggested
values, except for
which is comparable.
Figures 5 and 6 show the histograms of the bootstrap estimates for the and
factors as obtained from the NNLS solutions for the bootstrap samples. The best
estimates for these factors obtained using the full dataset (as detailed in Table 4) are
also included in these figures (as vertical dashed lines) for comparison. It is evident
that these best estimates are very close to the modes of the histograms. The best
estimates for
and
are slightly away from the modes but they are similar when
comparing them to two significant figures. These results suggest that the dataset has
reached a critical volume sufficient for deriving robust estimates, at least for the ground
conditions encountered at the site. This robustness enhances confidence in the
reliability of the back-analyzed factors and their resilience against dataset variability,
thereby mitigating concerns about overfitting. Nevertheless, the variability of the factors
for the contractive soils is greater than that for the dilative soils. One possible
explanation for this is the much smaller volume of data for the former compared to the
latter. Another possible explanation is that there are other effects contributing to the
observed variability. These effects could include a changing relationship between skin
friction and tip resistance with depth or latent relationships between resistance and
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caisson geometry. These effects are masked by the modeling assumption that and
factors remain constant regardless of depth or geometry. The current study’s back-
analysis is based on a narrow range of caisson geometries and is therefore most
applicable to installations with similar dimensions. Future work could benefit from an
expanded dataset that includes a wider variety of geometries, allowing for refined
calibration of these factors and investigation of possible geometry-specific effects.
Figure 7 presents the best estimates of the and factors obtained for dilative sand
using the subsets of the ‘sand-only’ dataset that corresponds to progressively
advanced stages of the suction-aided installation process. These estimates highlight
notable trends. The factor at the end of SWP (i.e., before suction is applied) is
almost double the corresponding value in Table 4. As the applied suction increases,
the factor initially increases slightly from 0.0022 to 0.0028 before gradually
decreasing and stabilizing at 0.0011 (the value in Table 4). In contrast, the factor at
the end of SWP is almost half the corresponding value in Table 4. As the applied
suction increases, the factor initially decreases slightly from 0.062 before gradually
increasing and stabilizing at 0.12 (the value in Table 4).
Figure 8 provides an overview of the accuracy of the caisson installation calculations
for the training dataset using the DNV and back-analyzed factors. Figure 8a shows the
histogram of the normalized residual errors (see Eq. 14) of the installation calculatons
using the best estimate and factors in Tables 3 and 4. The errors based on the
back-analyzed factors are approximately normally distributed, while those based on the
DNV factors have a left-skewed distribution. This indicates that the measured values
are generally smaller than those predicted using the DNV factors. This observation is
supported by Figure 8b, which shows the mean, 5th and 95th percentile for the residual
18
errors. Figure 8b also shows that the range between the 5th and 95th percentile for the
DNV residual errors is much greater than that for the back-analyzed residual errors.
Figure 9 compares the installation calculations using the best estimate factors in
Tables 3 and 4, across some varied ground conditions within the training dataset. The
figure also shows the ground conditions of the installation locations, according to the
Robertson (2016) SBT system. The colors of the SBT categories in Figure 9 are based
on the same legend shown in Figure 3. Figure 9 presents the installation calculations in
terms of normalized applied suction , which is defined as follows:
(17)
Figure 9a represents the base case with uniform dilative sand conditions. It shows that
the installation calculations using the back-analyzed factors from Table 3 closely match
the measured values. In contrast, the DNV calculations predict larger suction pressures
than the measured values.
Figure 9b represents a location with dilative clay at shallower depths and primarily
dilative sand below the SWP depth. The figure shows that the calculations using the
back-analyzed factors underpredict the measured values at the shallower depths but
match the measured values at the deeper depths. In contrast, the DNV calculations
underpredict at the shallower depths and overpredict at the deeper depths.
Figures 9c and 9d illustrate complex cases with many interbedded layers below the
SWP depth. In Figure 9c, the calculations using both the back-analyzed and DNV
factors generally underpredict the measured values for most of the installation depth. In
Figure 9d, the calculations using both the back-analyzed and DNV factors are generally
19
in line with the measured values, although the DNV calculations slightly underpredict
the measured values in the dilative clay layers.
Beside the calculations using the best estimate factors in Tables 3 and 4, Figure 9 also
includes the HE calculations, where the Highest Expected factors in Table 3 are used
for the DNV HE calculations. Table 5 presents various percentile values derived from
the histogram of residual errors in the back-analyzed calculations, as displayed in
Figure 8a. These values are used for the proposed quantile-based HE calculation
approach (i.e., Eq. 13). In Figure 9, the 95th percentile of the residual errors (i.e., Eq.
13, with from Table 5) is employed for the back-analyzed HE
calculations as an example. Figure 9 shows that the back-analyzed HE calculations is
greater than the measured values for most depths across all locations. In contrast, the
DNV HE calculations can be overly conservative (see Figures 9a and 9b).
To evaluate the reliability of the back-analyzed factors for caisson installation
calculations in new, unseen data, they are applied to the test dataset. Figure 10
provides an overview of the accuracy of the caisson installation calculations for the test
dataset using the DNV and back-analyzed factors. A comparison of Figure 8 and 10
demonstrates that the accuracy of calculations using the back-analyzed factors is
consistent between the test and training datasets. The residual error skew and the
range between the 5th and 95th percentiles are similar in both cases. This consistency
confirms the reliability and applicability of the back-analyzed factors in new locations
with comparable ground conditions. Additionally, Figure 11 shows the caisson
installation calculations for some locations in the test dataset. Figure 11a represents
the base case with uniform dilative sand conditions, while Figure 11b represents a
location with dilative clay and transitional soils in the shallower depths but mainly
dilative sand below the SWP depth. These figures illustrate that, under primarily dilative
20
sand conditions, the calculations using the back-analyzed factors from Table 4 closely
match the measured values, whereas the DNV calculations are generally more
conservative.
Figure 11c represents a location with dilative sand at shallower depths and mainly
dilative clay below the SWP depth. The figure shows that the calculations using both
the back-analyzed and DNV factors tend to underpredict the measured values for most
of the installation depth. Figure 11d represents a complex case with many interbedded
layers, where a significant portion of the ground conditions below the SWP depth
consists of contractive clay. The figure demonstrates that at shallower depths,
calculations based on the back-analyzed factors underestimate the measured values
but align more closely at greater depths. In contrast, the DNV calculations consistently
underestimate the measured values throughout the entire installation depth.
Regarding HE calculations, Figure 11 indicates that HE calculations using the back-
analyzed factors generally exceed the measured values for most depths across all
locations. On the other hand, the DNV HE calculations are either overly conservative
(as shown in Figures 11a and 11b) or insufficiently conservative (as shown in Figure
11d).
Discussion
The results reveal a notably distinction between the and factors for dilative versus
contractive soils. Specifically, contractive soils exhibit significantly higher factors than
dilative soils, suggesting that using the same factors for dilative and contractive soils
may not be appropriate. The higher factor for contractive sand aligns with the
recommendation of Senders and Randolph (2009), who suggested that the factor
21
for loose sand should be higher than that of dense sand. However, it is important to
acknowledge that the current study includes significantly less data on contractive soils
compared to dilative soils. Nevertheless, the installation data in contractive soils still
encompasses a total penetration depth of approximately 30m, which provides a
substantial basis for preliminary analysis. Future research with a larger dataset on
contractive soils would help to confirm these findings more conclusively.
The close alignment of the back-analyzed factors for dilative soils with the DNV
suggested values affirms the reliability of the DNV values. The back-analyzed and
factors for dilative transitional soils also agree with the simplistic assumption of the
values being the average of the corresponding sand and clay factors. However,
discrepancies in the factors highlight areas for potential adjustment. The DNV
suggested value for
may be too high, while its
suggested value may not be
high enough. The implications of the overly high
is evident in Figures 9a and 9b,
which illustrate the over-conservatism of the DNV calculations for locations
predominantly composed of dilative sand, despite the DNV
factor aligning closely
with the back-analyzed value. On the other hand, the implications of the too low
is
evident in Figure 9d, which shows that the DNV installation calculations underestimate
in layers of dilative clay, despite the DNV
factor aligning closely with the back-
analyzed value.
Figure 7 hints at the changing soil-caisson interaction during installation. The reduction
of the factor for dilative sand with increasing applied suction likely stems from the
influence of seepage flow due to suction, which lowers the effective stress in the sand
and, consequently, its resistance to caisson penetration. This is consistent with the
findings of previous research (e.g., Senders and Randolph 2009). This suggests that
22
the best estimates of the back-analyzed factors in Table 4 already represent
conservative lower-bound values that account for the effect of suction. However, it is
noted that the observed increase in the factor in Figure 7b is unexpected, as Eq. 15
suggests that the factor should decrease as applied suction increases. The reason
for this is uncertain. It could be a modeling artifact of the and indirect estimation
procedure, or it might represent a physical phenomenon that previous experimental
studies did not capture. Further research is needed to clarify the underlying causes.
Figure 8b and 10b show that the DNV installation calculations are considerably more
conservative than the actual measurements. Additionally, the broader range between
the 5th and 95th percentiles of the error histograms for the DNV installation calculations
points to a higher likelihood of extreme prediction errors across various ground
conditions. This contrasts with the narrower error range for the back-analyzed
installation calculations, which implies that using the back-analyzed factors in Table 4
provides potentially more robust and consistent performance, with fewer instances of
extreme prediction errors. Furthermore, the similarity between the residuals errors of
the calculations for the training and test dataset (compare Figures 8 and 10) provides
more confidence in the reliability of the back-analyzed factors listed in Table 4. This
reliability suggests that these factors can be effectively applied to ground conditions
similar to those investigated in this study. This assertion is supported by the
observation of similar and ranges in the training and test datasets, as depicted in
Figure 2.
Figures 9c and 11c reveal a significant discrepancy between the back-analyzed model
calculations and the field-measured data. This discrepancy arises because the model
is based on a limited set of adjustable parameters (i.e., the and factors), which
restricts its ability to match all field data precisely. Consequently, some model
23
predictions may under- or overestimate the observed values, as reflected in Figure 8.
The model parameters were optimized to best fit the field data using a least-squares
error approach, which inherently introduces some degree of mismatch. To address
potential underestimations of soil resistance during installation, which are generally
more critical than overestimations, this paper has proposed the quantile-based
approach for HE calculations (Eq. 13). Another possible reason for this discrepancy
could be lateral variation in soil conditions within the caisson footprint, which are not
captured by the representative CPT data.
Figures 9 and 11 illustrate that the proposed quantile-based approach for HE
calculations effectively addresses potential underestimations using the best estimate
factors in Table 4, without being overly conservative. This approach compares well
against the DNV approach to HE calculations, which can result in either extreme
conservativeness (see Figures 9a, 9b, 11a and 11b) or insufficiency (see Figure 11d).
Although this paper employs the 95th percentile of the residual errors for the HE
calculations, other percentile values in Table 5 may be used to determine the HE
calculations at the desired level of conservatism. Therefore, the quantile-based
approach provides a balanced and pragmatic solution to accommodate significant
deviations from anticipated outcomes during caisson installation, especially in ground
conditions similar to those in the study.
This study has some limitations. The failure mechanism of soil at the skirt tip differs
between SWP and suction-aided penetration, which would affect the penetration
resistance and change the factors. In the current study, the proposed CPT-based
model does not explicitly account for this difference in failure mechanisms. Instead, for
simplicity, it assumes identical factors for all stages of penetration, similar to existing
CPT-based installation design methods (e.g., DNV 2021). Although this idealization
24
may introduce some inaccuracy in SWP calculations, Figures 9 and 11 suggest that the
resultant SWP calculations are reasonable. Another limitation of the current study is
that previous research (e.g., Klinkvort et al. 2019) has shown that when a caisson skirt
penetrates from a sand layer into a clay layer, suction-induced seepage flow may
diminish, which would change the and factors in the sand layer. However, the
current study does not quantify changes in the and factors under varying
seepage flow conditions during soil layer transitions, mainly due to the complexity of
the soil layering configurations (e.g., see Figure 9c). Furthermore, for ease of
application, the proposed model assumes that these factors remain constant for each
soil type, regardless of seepage flow conditions, aligning with the DNV (2021) CPT-
based design method. Nevertheless, the back-analysis effectively accounts for different
seepage flow conditions as it determines the constant and factors that best
match the field observations across the range of seepage flow conditions encountered
in different soil layer configurations during installation. However, it is acknowledged that
a more detailed model that incorporates seepage flow-dependent and factors, as
in the model proposed by Klinkvort et al. (2019), could provide more accurate
estimates, presenting an area for future research.
Conclusion
This paper presents a detailed back-analysis of field data from suction caisson
installations at a site with complex, multi-layered soil conditions. It refines the estimates
of the and factors for a CPT-based suction caisson installation calculation
method, using a nuanced soil classification system that differentiates between dilative
and contractive soil behaviors as suggested by Robertson (2016). The study confirms
the reliability of DNV's suggested values for the factors for dilative soils but suggests
that the DNV factor for dilative sand may be too high. The findings highlight
25
significant differences in the back-analyzed and factors for dilative versus
contractive soils and reveal the variable nature of the factors for dilative sand during
different stages of the suction-aided installation phase.
To address potential underestimations using the back-analyzed factors, a quantile-
based approach for high estimate installation calculations is proposed. This approach
ensures safety without excessive conservatism. Overall, the insights from this research
contribute to the development of more precise and effective design strategies for
suction caisson installations, especially in soil conditions similar to those examined in
this study.
Data Availability Statement
Some or all models, or code that support the findings of this study are available from
the corresponding author upon reasonable request. The data used during the study are
proprietary or confidential in nature.
Acknowledgments
The first author would like to thank EPSRC Supergen ORE Hub for supporting this
work through the Flexible Funding scheme (FFF2023-1009). Additionally, the first
author would like to thank SSE Renewables and TotalEnergies for providing the
necessary data for this work.
26
List of notation
submerged vertical load
internal plan area of the caisson lid
total soil resistance to caisson penetration
applied suction pressure
atmospheric pressure
normalized by
factor for soil resistance along caisson skirt
factor for soil resistance at caisson skirt tip
factor for dilative sand
factor for dilative clay
factor for dilative transitional soil
factor for contractive sand
factor for contractive clay
factor for contractive transitional soil
factor for dilative sand
factor for dilative clay
factor for dilative transitional soil
factor for contractive sand
factor for contractive clay
factor for contractive transitional soil
residual error in caisson installation calculations
caisson outer diameter
caisson inner diameter
caisson skirt length
depth below seabed
depth of the caisson tip below seabed
CPT tip resistance
CPT sleeve friction
normalized CPT tip resistance
normalized CPT sleeve friction
27
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33
Table 1. Main geological units encountered at the site.
Geological Units
Description
Holocene marine sands
Sand with occasional gravel or silts.
Forth Formation
(Pre-Holocene and Early Holocene deposits)
Soft clays, silts and sand with some
organic content.
Marr Bank and Wee Bankie Formations
Poorly to well sorted fine-grained sand,
with layers of silts, gravels and clays
Table 2. Soil behavior type categories according to Robertson (2016).
Symbol
Description
SD
Sand-like - Dilative
TD
Transitional - Dilative
CD
Clay-like - Dilative
SC
Sand-like - Contractive
TC
Transitional - Contractive
CC
Clay-like - Contractive
SCC
Clay-like - Contractive - Sensitive
Table 3. DNV (2021) suggested values for the and factors for clay and sand.
Soil type
Best Estimate
Highest Expected
Clay
0.4
0.03
0.6
0.05
Sand
0.3
0.001
0.6
0.003
Table 4. Best estimate of and factors obtained using the full training dataset.
Soil type
Soil behavior type
Back-analyzed (Best Estimate)
Sand
SD
0.12
0.0011
Clay
CD
0.66
0.028
Transitional
TD
0.47
0.018
Sand
SC
1.1
0.13
Clay
CC
4.6
0.019
Transitional
TC
2.5
0.074
Table 5. Percentile values for the histogram of the residual errors of the back-analyzed
calculations shown in Figure 8a.
Percentile
90th
0.88
95th
1.14
99th
1.66
100th
2.96
34
(a)
(b)
Figure 1. (a) Seagreen wind farm location, off the east coast of Scotland (b) Schematic
diagram of a suction caisson installation
35
(a)
(b)
(c)
(d)
Figure 2. Depth profiles of the CPT-based indices, and , for the CPT data in the:
(a)-(b) training dataset; (c)-(d) test dataset. The mean profile, together with the 5th to
95th percentile interval, is shown here.
36
(a)
(b)
Figure 3. Distribution of the Robertson (2016) classification for every 1m depth interval
for the CPT data in the: (a) training dataset; (b) test dataset
37
Figure 4. Distribution of data points for each Robertson (2016) SBT category for the full
training dataset
38
(a)
(b)
(c)
(d)
(e)
(f)
Figure 5. Histograms of the bootstrap estimates for the factors.
39
(a)
(b)
(c)
(d)
(e)
(f)
Figure 6. Histograms of the bootstrap estimates for the factors.
40
(a)
(b)
Figure 7. Changes in the best estimates for the (a) factor, and (b) factor for
caisson installations in dilative sand (SD) as the applied suction increases.
41
(a)
(b)
Figure 8. (a) Histogram of the residual errors of the calculations using the back-
analyzed and DNV factors, relative to the measured values, for the training dataset; (b)
Error bars of the residual errors. The circle marker represents the mean, while the end
bars represent the 5th and 95th percentiles.
42
(a)
(b)
(c)
(d)
Figure 9. Comparison of required suction pressure vs penetration profiles for several
locations in the training dataset, as calculated using the DNV and back-analyzed
factors. Refer to Figure 3 for the color legend of the Robertson (2016) SBT categories.
43
(a)
(b)
Figure 10. (a) Histogram of the residual errors of the calculations using the back-
analyzed and DNV factors, relative to the measured values, for the test dataset; (b)
Error bars of the residual errors. The circle marker represents the mean, while the end
bars represent the 5th and 95th percentiles.
44
(a)
(b)
(c)
(d)
Figure 11. Comparison of required suction pressure vs penetration profiles for several
locations in the test dataset, as calculated using the DNV and back-analyzed factors.
Refer to Figure 3 for the color legend of the Robertson (2016) SBT categories.
