Effect of episodic pre-failure cyclic loading on whole-life geotechnical properties of soft clays

$cv$

coefficient of consolidation, $cv0$ value at normally consolidated condition

$e$

void ratio

$e0$

value after initial consolidation

$Gmax$

small-strain shear modulus, $Gmax⁡(0)$ value at normally consolidated condition

$Gs$

secant shear modulus

$Gs$

specific gravity of solid fraction

$N$

number of cycles per loading packet

$Nep$

number of episodes, each comprising a loading packet and a consolidation period

$Nt$

total number of cycles applied, where $Nt=Nep×N$

$su$

undrained strength

$su0$

monotonic undrained strength

$γ$

monotonic shear strain

$γcy$

cyclic shear strain

$γv$

volumetric strain

$Δs$

settlement during consolidation

$Δu$

excess pore water pressure

$κ$

slope of post-shearing recompression line

$κo$

slope of oedometer recompression line

$λo$

slope of oedometric normal compression line

$σ′v$

vertical effective stress

$σ′vc$

consolidation vertical effective stress

$σve'$

vertical effective stress after cyclic loading

$τ$

monotonic shear stress

$τav$

average shear stress

$τcy$

cyclic shear stress

$ϕ'$

friction angle

Foundations and anchoring systems supporting onshore and offshore infrastructure experience varying loads from environmental and operational conditions. These loads can alter the geotechnical properties of the surrounding soil, affecting the subsequent response and capacity. Whole-life geotechnical design couples the life cycle of imposed actions with the evolving geotechnical properties to forecast the changing response and reliability of the system throughout the design life (Gourvenec, 2020).

For normally and lightly overconsolidated fine-grained soils, a key mechanism in whole-life analysis is the beneficial consolidation effects that cause hardening, and an increase in strength, stiffness and consolidation coefficient, following dissipation of excess pore pressures generated from loading. Such whole-life effects have been quantified experimentally in penetrometer tests (Hodder et al., 2013; O’Loughlin et al., 2017), element tests (Yasuhara & Andersen, 1991; Laham et al., 2021) and large-scale and centrifuge-scale modelling of pipelines (Smith & White, 2014), sliding foundations (Cocjin et al., 2014, 2017), anchors (Han et al., 2016; Zhou et al., 2020) and piles in clay (Lai et al., 2020; White et al., 2022). These examples illustrate how whole-life changes in geotechnical properties influence the optimisation and reliability of geotechnical designs. These effects offer opportunities for more efficient systems, including reductions in foundation or anchor size, reduced fatigue risk and reassessment for late life reassessment or decommissioning choices (Gourvenec, 2020).

The study presented here provides insights relevant to a range of infrastructure, although the testing was targeted towards floating offshore wind, which is a topical challenge that could benefit by embracing whole-life geotechnical design. A rapid acceleration of offshore wind development is required for the energy transition, as indicated by a global ambition to install 2000 GW of capacity by 2050, which is 35 times the current installed capacity (IRENA, GWEC, 2021). The corresponding geotechnical requirements have been estimated to include the design and installation of up to 4500 anchors annually (Gourvenec, 2024; Cerfontanie et al., 2023). This creates impetus for more efficient foundation and anchor systems and more efficient seabed characterisation methods. Whole-life geotechnical design is one of the tools available to support this.

Adoption of whole-life geotechnical design principles requires a systematic approach to characterise whole-life parameters. The direct simple shear (DSS) element test protocol is widely used in offshore site investigation because it is cost-effective, requiring smaller specimens compared to triaxial testing (Airey et al., 1985; Dyvik et al., 1987), while also allowing systematic investigation of cyclic shearing behaviour. The DSS apparatus also mobilises an intermediate soil strength between triaxial compression and extension, which is often adopted as an average value throughout a failure mechanism for capacity assessment (Kinner & Ladd, 1973; Mayne, 1985; Randolph, 2000). Previous uni-directional cyclic DSS tests have characterised the cyclic softening response to build cyclic strain or excess pore pressure accumulation contour diagrams ‘SN-curves’ (Andersen, 2009, 2015; Zografou et al., 2019) or to investigate the influence on sample disturbance on their cyclic response (Yang et al., 2020). Multi-directional cyclic DSS tests have also been performed to understand the cyclic softening response during earthquakes (Ishihara & Yamazaki, 1980; Boulanger et al., 1993; Kammerer et al., 2004; Yang et al., 2019) and for cyclic multidirectional loading on foundations (DeGroot et al., 1996; Sibley, 2016) and shared anchors (Herduin, 2019). Episodic DSS tests have explored the effect of consolidation episodes on soil recompression response (Yasuhara & Andersen, 1991), stiffness and strength (Laham et al., 2021). These studies involved episodic loading consisting of pre-failure shearing where the applied shear stresses applied cyclically (Yasuhara & Andersen, 1991) or monotonically (Laham et al., 2021) are a fraction of the monotonic undrained shear strength, at constant volume, interspersed by consolidation periods, to represent, for example, multiple storm events.

This study explores the response of soft clays to episodes of pre-failure undrained cyclic shearing with intervening periods of consolidation through a suite of DSS tests. This study considers a wider range of loading histories and focuses on the evolution of strength, stiffness and consolidation properties, which has not been systematically addressed. The principles explored are relevant to a range of clays and applications, while the specific loading histories and normally consolidated clay considered are particularly relevant to the emergent challenge of floating offshore wind. Variables explored include (a) the number of undrained cycles of loading per packet, $N$⁠; (b) the number of cyclic loading episodes, $Nep$⁠; and (c) the amplitude of the applied cyclic shear stresses, $τcy$⁠.

The DSS tests were performed at the NGI Oslo laboratory, Norway, using the Geonor DSS apparatus (Fig. 1). The apparatus has two load cells (labelled (4) and (12) in Fig. 1) that measure vertical and horizontal loads on the specimen (1). A wire-reinforced rubber membrane (2) imposes a zero lateral strain boundary condition on the specimen. Vertical and horizontal displacements are measured by displacement transducers (8), (9) and (10). During consolidation, the vertical load is applied using dead weights (15) by way of a lever arm (14). During a constant volume stage, active height control is achieved using the in-house control system (Modlab) that drives the motor (17) to maintain a specified specimen height (Dyvik & Suzuki, 2019). The specimen height is measured by a displacement transducer (10). Any change in vertical load to maintain the set height is equivalent to the excess pore pressure generation in an undrained condition (Dyvik et al., 1987). Monotonic horizontal movement is imposed by controlled displacement (13), while cyclic horizontal loads are applied by a pneumatic control system.

During re-consolidation, the height control is turned off and excess pore pressure is permitted to dissipate, and the specimen changes height under the applied consolidation stress. The parameter $κ,$the slope of the post-shearing recompression line, is derived from the change in void ratio and the change in the natural log of the vertical effective stress. The coefficient of consolidation $cv$ is calculated using the Taylor root time method from the settlement response during each re-consolidation period (Taylor, 1948).

Bender elements were embedded in the top and bottom platens providing a direct measurement of small-strain shear stiffness through the test (Dyvik & Madshus, 1985).

Reconstituted normally consolidated Onsøy clay, with properties listed in Table 1, was prepared from a slurry at a water content of twice the liquid limit. The slurry was mixed under a vacuum for 8 h and then consolidated in a steel tube of 76 mm inner diameter and 300 mm tall. Consolidation was carried out in four load increments. The vertical load was doubled in each increment to reach a final consolidation stress of 50 kPa after 1 month. This stress level was chosen to target the minimum strength that is practical for specimen preparation. Individual specimens were extruded from the prepared tubes of consolidated clay and trimmed to a diameter of 66·7 mm and a height of 16 mm.

The extruded specimen was prepared between the top cap and the bottom pedestal, each with embedded porous filters with small pins, and the wire-reinforced membrane was stretched over the specimen. The specimen was then gently placed in the DSS apparatus and consolidated to 100 kPa in four load increments with the load doubled at each increment. The displacement during consolidation was recorded to calculate the specimen height before shearing (ASTM, 2017).

Table 2 summarises the DSS tests performed in this study. An initial test determined the monotonic undrained strength after consolidation to $σ′vc=$100 kPa, at a shear strain rate of 4%/h to 20% shear strain. This consolidation stress is within the range of effective stresses found in soft clays at depths typically relevant to anchors for floating offshore wind turbines (FOWTs). This study also focuses on clays that are initially normally consolidated, since these are the conditions most conducive to changes in properties through episodic loading. Clays with a low overconsolidation ratio are found in many European offshore wind frontiers, including the Irish Sea (Coughlan et al., 2023) and the North Sea, for example in the Witch Ground (Paul & Jobson, 1991) and the Norwegian Channel (Petrie et al., 2022), as well as the region of the Hywind Tampen floating offshore wind farm (RevOcean, 2024).

Test sets 2 to 5 comprised stress-controlled episodic cyclic tests with a loading pattern illustrated in Fig. 2. These tests investigated the evolution of undrained strength, stiffness and consolidation coefficient through episodes of undrained cyclic loading and intervening full consolidation. All specimens were consolidated to $σ′vc=$100 kPa, before being subjected to $Nep$ loading and consolidation episodes. The cyclic loading was performed under a constant volume condition with $N$ cycles per episode at a constant cyclic stress amplitude $τcy$ spanning a range of proportions of the monotonic strength. The cyclic stress was symmetric for all tests (i.e. average shear stress $τav$ = 0 kPa) and was applied at a frequency of 0·1 Hz, which is typical of a wave period (Andersen et al., 1988). During the consolidation periods the specimen was allowed to settle under $τ=$ 0 kPa. The consolidation phase was terminated when the settlement over 30 min was less than 0·01% of the specimen height. The episodic loading was followed by a displacement-controlled monotonic shearing stage, at the same rate as the monotonic test in set 1. In test sets 2 to 5, various combinations of $Nep$⁠, $N$ and $τcy$were applied.

A long-term episodic cyclic test was performed first to explore the number of episodes required to approach a stable soil response (E055_10_100 in test set 2, for $Nep =$10, $N =$100 $and τcy =$0·55$su0$⁠). Tests with different $Nep$⁠, and the same $τcy$ were also performed to identify the change in $su$ from $Nep =$1, 3, 5 and 10 (Table 2).

Eight other stress-controlled episodic cyclic tests with the same number of episodes (⁠$Nep =$5) were performed and have been grouped in Table 2 by test set based on $τcy$⁠. These tests capture the effect of varying $N(=$10, 50, 100 and 1000) at different cyclic stress amplitudes (⁠$τcy =$0·35, 0·55 and 0·70$su0$⁠). After the 5th episode, all of these tests were sheared monotonically to failure to determine the change in strength. Each of these tests involved extensive testing times of up to 2 weeks and it is recommended that further testing should involve non-symmetric loading cycles.

The range in the applied cyclic stress ratio (CSR = $τcy/su$⁠) and the number of cycles per packet, $N,$ were also selected to span a variety of responses and to achieve good coverage of the shear stress ratios required to build SN curves (e.g. similar to Skau et al. (2023)). The chosen CSRs and value of $N$ = 100 are similar to the CSRs and equivalent number of cycles, $Neq$ in design storms, albeit at the high end (Andersen, 2015; Randolph & Gourvenec, 2011; Allen et al., 2020; Kwa et al., 2023; Skau et al., 2023). This bias towards the high range of the selected CSRs and $Neq$ towards a higher range of practical relevance is for two reasons: (a) to make response effects more discernible and (b) because the aim of the study is to unlock the use of reduced partial factors in design (i.e. higher CSRs), taking account of gains in strength that are shown later.

The effective stress path (ESP) during monotonic shear demonstrates the usual fall in effective stress due to a rise in excess pore pressure as the stress path bends left to the critical state line (CSL) (Fig. 3(a)). The CSL was determined from the final shearing stage at 20% shear strain in all tests (see the open dots in Fig. 3). The solid data markers indicate the initial state of the normally consolidated specimens when first consolidated to $σ′vc$ = 100 kPa. The one-dimensional normal consolidation line (NCL) is shown dotted in Fig. 3(b), based on an oedometer test, where two unloading–reloading loops of 1280 to 160 kPa and 5120 to 1280 kPa were applied on soil specimen to measure an average value of unload–reload line.

The episodic cyclic response of the normally consolidated specimens all followed similar trends with increasing $N$ and $Nep$⁠. An example of results from a selected test, with the highest applied $τcy/su0$ = 0·70 (test set 5) is described in detail first, as it has the clearest trend in episodic cyclic responses, prior to a comparison of all tests. The selected test, E070_5_50 (⁠$τcy/su0$ = 0·70, with $Nep$ = 5 packets of loading of $N=$ 50 cycles each, is shown in Fig. 4.

During each packet, softening was observed, demonstrated by a decrease in small-strain shear modulus, $Gmax$ (Fig. 4(a)), relative to the normally consolidated condition, $Gmax⁡(0)$⁠, measured at $σ′vc$ prior to shearing. The shear strain amplitude, $γ$ (Fig. 4(b)) and excess pore water pressure, $Δu$ increase during each packet (Fig. 4(c)), but reductions occur in each subsequent episode after the intervening consolidation. The resulting ESP is shown in Fig. 4(d).

During the consolidation periods, the pore pressure dissipation led to settlement (Fig. 4(e)) and densification, quantified by the reduction in void ratio (Fig. 4(f)) and accompanied by a rise in normalised shear modulus, $Gmax /Gmax⁡(0)$ – by a greater amount than the fall during the previous cyclic loading, leading to a net rise in stiffness (Fig. 4(a)). In this figure, the episode count, $Nep$ is defined such that half values represent the state at the end of the cyclic loading and whole values represent the end of the following consolidation period, which completes each episode. Consolidation coefficient $cv$ also increased with each consolidation period (Fig. 4(g)). The reduction in void ratio during the consolidation stage, $Δe$ (Fig. 4(f)), was used to calculate the post-shearing recompression modulus, $κ=Δe/ln⁡σ′ve/σ′vc$⁠, where $σ′ve$ is the vertical effective stress after cyclic loading, prior to consolidation, and decreased with each episode (Fig. 4(h)).

The softening and hardening effects became very small after five episodes. For example, for the test shown in Fig. 4, $Δu$ in the last episode was 0·3% of the value in the first episode (Fig. 4(c)). Similarly, the settlement in episode 5 was 7% of the settlement in the first episode (Fig. 4(e)).

A single test was carried out for ten episodes of cyclic loading and intervening consolidation, that is $Nep$ = 10, (E055_10_100), and confirmed that negligible changes (⁠$Δu$ < 0·1 kPa) occurred after $Nep$ > 5, as shown in Fig. 5. A summary of the episodic results (Figs 5(a)–5(f)) shows that the softening and hardening effects stabilise for $Nep$ > 5. The remaining tests in the programme were therefore subjected to five episodes of cyclic loading and consolidation (see Table 2). The next sections discuss those results and examine the effects of varying $N$ and (⁠$τcy/su0$⁠) on the soil response. The response under cyclic shear is considered first (in the next section ‘Episodic cyclic response: shearing’), followed by the response during subsequent consolidation (section ‘Episodic cyclic response: consolidation’) then finally the evolution of geotechnical parameters (section ‘Evolution of engineering properties’).

The excess pore pressure generated in a packet depended on $N$ and (⁠$τcy/su0$⁠), as illustrated in Fig. 6. Specimens loaded at a higher cyclic amplitude experienced larger increase in excess pore water pressure for the same number of cycles and each consolidation phase led to reduced excess pore pressure in subsequent packets – as shown by the trend in all tests in Fig. 6. The specimen loaded at $τcy/su0$ = 0·70 (test set 5 in Table 2) could not withstand 100 cycles of continuous loading, failing after 71 cycles in the first packet, at an excess pore water pressure of 58 kPa (Fig. 6(b)). The excess pore pressure generated in each episode for each test is presented in Fig. 7, showing that the build-up always reduced in subsequent packets, for all numbers of cycles of loading in each packet.

The shear strain increased with the applied cyclic amplitude and the number of cycles per packet as shown in Fig. 8, mirroring the excess pore pressure generation (Fig. 6). A progressive decrease in cyclic shear strain was also observed with each packet, as is also evident in Fig. 8, again mirroring the excess pore pressure response (Fig. 7).

The reducing strain is reflected in increased stiffness after each re-consolidation phase, as illustrated by the secant shear modulus in the final cycle of each episodic test (Fig. 9). A lower secant shear modulus results from a higher number of cycles per packet. However, the shear modulus increases with each packet due to stiffening during consolidation, and a reduced tendency for softening during subsequent cycles. This is a further quantification of the changing soil response and increasing resilience from intervening consolidation.

Dissipation of the excess pore water pressure led to volumetric strain and a reduction in void ratio during each consolidation phase. The shear–volumetric strain paths from each test illustrate that specimens loaded to a higher shear stress and subjected to a greater number of cycles per packet experienced a correspondingly larger volumetric strain on consolidation (Fig. 10). The reduction in void ratio reduces in successive consolidation periods (Fig. 11), as each specimen becomes denser and stiffer. This is consistent with the observed trends of reducing excess pore pressure generation following consolidation (Figs 6 and 7).

The volumetric response through episodic loading can be followed in e–ln $σ′v$ space (Fig. 12). This form of representation shows the recompression response as a sloping line joining horizontal lines that represent the excess pore pressure generation during adjacent packets of cyclic loading. The post-shearing recompression paths, which have a gradient of $κ/log10⁡e=2·3κ$ on a log plot to base 10 (Burland, 1990), are not parallel. This indicates that the post-shearing recompression modulus, $κ$⁠, is influenced by the previous loading history, and specifically the loading amplitude and the number of preceding loading and consolidation episodes.

Changes in recompression modulus, $κ,$ show an increasing stiffness with increasing episodes for all loading levels (Fig. 13). Also, lower values of $κ$ – meaning a stiffer response — are associated with recompression following higher cyclic stress amplitude and more cycles per packet. This trend is also highlighted in Fig. 12(b), comparing the indicated values $κAA', κBB''$ and $κCC'.$

The varying recompression modulus from reconsolidation following cyclic shearing is compared with the recompression modulus observed in an oedometer test, $κo$⁠, which relates to reloading after one-dimensional unloading without shearing. It has been previously recognised that the stiffness during post-shearing recompression differs from the reloading stiffness seen in an oedometer (Yasuhara & Andersen, 1991; Yasuhara et al., 1992). The measured post-shearing $κ$ varies in magnitude from ten times $κo$ for early episodes and small-amplitude cycles, to half $κo$ for later episodes under high cyclic loading (Fig. 13).

The duration of the re-consolidation phase is affected by the increase in recompression stiffness (i.e. reduction in $κ$⁠, Fig. 13). The calculated consolidation coefficient, c_v, increased by factors between 10 and 30 by the end of five episodes of cyclic shear and consolidation (Fig. 14). Specimens subjected to higher cyclic amplitudes and more cycles experienced greater increases in $cv$⁠. This trend is connected to the greater densification and stiffening following reconsolidation after severe loading conditions (as seen in Figs 12 and 13). An implication of the trend of increasing $cv$ with episodes of loading and reconsolidation is that changes in strength and stiffness will occur more quickly after each loading episode, due to the faster consolidation.

The increases in undrained shear strength from episodes of loading and re-consolidation are shown in Fig. 15, from the monotonic shearing stage at the end of each episodic test, normalised by $su0$ measured from the initial monotonic test.

The results show a consistent trend of increasing strength following episodes with higher cyclic stress amplitude and more cycles per packet, consistent with the observed greater densification (Fig. 12). For the highest cyclic stress amplitude and the greatest number of cycles per packet (E055_5_1000), a 70% increase in $su$ was observed. Tests at the intermediate level of cyclic amplitude and cycles per packet typically showed increases in $su$ of 20–30%, with the lowest load level and shortest packets still exhibiting ∼10% gain in strength (E035_5_10).

These observations from pre-failure loading conditions show that the excess pore pressure generation and cyclic softening is mirrored by the level of strength gain from subsequent consolidation, since the level of softening affects the potential for subsequent densification and hardening.

The small-strain shear stiffness evolves with episodes of cyclic loading and consolidation, as was observed for undrained strength. The decrease in the cyclic shear strain $γcy$ and post-shearing recompression modulus κ between episodes indicate stiffening (Figs 8, 9 and 13). In test sets 4, 5 and 6, bender element measurements at the end of each packet of loading and consolidation period revealed the changes in small-strain shear modulus $Gmax$relative to the initial value $Gmax⁡(0)$ (Fig. 16). $Gmax$ increased with episodes, with a higher gain in tests subjected to higher cyclic stress amplitudes and number of cycles. The highest gain was in the test with the greatest number of cycles and highest stress level and showed a 50% increase in $Gmax$ (E055_5_1000). Specimens subjected to intermediate amplitude and numbers of cycles experienced a 20–25% increase in $Gmax$⁠, while the lowest cyclic amplitude with the fewest cycles (E035_5_10) experienced a 10% gain.

The observed changes in shear stiffness are much smaller than the changes in volumetric recompression stiffness (Fig. 13) but are similar to the observed changes in undrained strength (Fig. 15). The relationship between $Gmax/Gmax⁡0$and $su/su0$ at the end of each test is shown in Fig. 17, with a linear trend of

such that changes in one parameter can support an estimate of the other.

This study has systematically explored the changing properties of normally consolidated clay when subjected to alternating stages of cyclic undrained shearing and re-consolidation, in a test format referred to as episodic cyclic loading. The results demonstrate the capability of DSS element tests to explore the evolution in soil properties for different loading scenarios that mimic realistic design conditions, where the influence of realistic long-term cyclic actions can be simulated along with the drainage and consolidation processes over the same timescale. Systematic variations in the soil response are evident across a range of cyclic loading levels and durations, and it is found that the specimens reach a relatively stable long-term state after five episodes of cyclic loading and full consolidation.

The results from the suite of DSS tests quantify changes in shear and volumetric response with different episodes of undrained cyclic loading interspersed with consolidation, due to sequential softening during cyclic loading and hardening during consolidation.

Significant changes in the geotechnical properties were observed through each episodic test, including increases in strength, stiffness and coefficient of consolidation. Changes observed included gains relative to the initial condition of up to 70% in strength, 50% in small-strain shear stiffness, a five-fold increase in volumetric reloading stiffness and a rise in consolidation coefficient by a factor of 30. These significant changes highlight the importance of accounting for whole-life effects in geotechnical design.

Accounting for these enhancements provides the opportunity for more efficient structures including reductions in foundation or anchor size. For example, if the seabed around an anchor strengthens from experiencing low-level loading early in life, prior to the maximum design load, the required design capacity can be reduced in proportion to the gain in strength. This also translates to reduction in the materials required to fabricate anchors and therefore lighter anchors which are easier to transport to site. Accounting for changes in anchor capacity and seabed stiffness also provide opportunities for reduced risk of fatigue and better-informed decommissioning processes for offshore infrastructure. The methods outlined in this testing procedure and the trends shown in these results can be used directly to expand current methods of cyclic strength assessment to incorporate consolidation and densification effects in soft clays. In addition, these results provide an extensive dataset to assist the enhancement of constitutive models to capture the detailed response of soft soil through episodic loading.

This study forms part of the activities of the Royal Academy of Engineering Chair in Emerging Technologies Centre of Excellence for Intelligent & Resilient Ocean Engineering (IROE) at the University of Southampton, UK through a collaboration project ‘Characterisation of Geotechnical Properties for Whole-Life Design’ with the Norwegian Geotechnical Institute (NGI). Financial support of the Norwegian Research Council under their basic funding programme for NGI is acknowledged. Noor Laham is supported through a Rayleigh Scholarship administered by the University of Southampton, and by the Norwegian Geotechnical Institute. Susan Gourvenec and Katherine Kwa are supported by the Royal Academy of Engineering, with Susan Gourvenec supported under the Chairs in Emerging Technologies scheme and Katherine Kwa holding a RAEng Research Fellowship. David White is supported by the EPSRC Offshore Renewable Energy Supergen Hub (EPSRC grant EP/Y016297/1).