In-situ and laboratory characterisation of stiff and dense geomaterials for driven pile analysis and design

Abstract

Integrated field and laboratory characterisation of geomaterial behaviour is critical to foundation analysis and design for a wide range of offshore and onshore infrastructure. Challenges include the need for high-quality sampling, addressing natural and induced micro-to-macro structures, and applying soil and stress states that represent both in-situ and in-service conditions. This paper draws on the Authors’ recent research with stiff glacial till, dense marine sand and low-to-medium density chalk, and focuses particularly on these geomaterials’ mechanical behaviour, from small strains to failure, their anisotropy and response to cyclic loading. It considers a range of in-situ techniques as well as highly instrumented monotonic and cyclic stress-path triaxial experiments and hollow cylinder apparatus tests. The outcomes are shown to have important implications for the analysis of large driven piles under monotonic-and-cyclic, axial-and-lateral loading, and the development of practical design methods. Also highlighted are the needs for approaches that integrate field observations, advanced sampling and laboratory testing, numerical and theoretical modelling.

Keywords:
Laboratory testing; Glacial till; Dense sand; Chalk; Driven piles; Offshore Engineering

1. Introduction

The potential capabilities and practical values of advanced laboratory testing have been demonstrated through ISSMGE TC101’s International Symposia (IS) from Hokkaido 1994 to Glasgow 2019. Jardine (2014, 2020, 2023a) highlighted their application with large piles driven to support key offshore and onshore infrastructure, noting that geomaterial behaviour under in-situ and in-service conditions can be affected markedly by pile installation effects as well as operational and extreme loading. Representative numerical analyses rely critically on experiments that match these conditions faithfully to provide the fundamental physical basis for constitutive model development and calibration (Zdravković et al., 2021).

The worldwide drive for renewable offshore wind energy has prompted large-scale research projects to tackle offshore wind foundation design challenges; those involving advanced soil characterisation include the PISA (Byrne et al., 2017), PICASO (Byrne et al., 2020a), WAS-XL (Page et al., 2021) ALPACA and ALPACA Plus (Jardine et al., 2023b) projects. High-quality pile test databases have also been collated by Yang et al. (2017) and Lehane et al. (2020, 2022).

Establishing the behaviour of dense marine sands, stiff glacial tills, Eocene to Jurassic stiff clays and chalks has been particularly significant in developing large concentrations of offshore windfarms around the UK and northern European coastlines where such strata are often encountered. This requires: (i) high quality sampling (Hight & Jardine 1993); (ii) addressing both natural geomaterials’ properties and potential alterations induced by pile driving and soil-pile interaction; and (iii) applying appropriate effective stress states and perturbing stress paths (Jardine, 2014). This paper draws on contributions made to the PISA, ALPACA and ALPACA Plus Joint Industry Projects (JIPs) by Liu (2018), Ushev (2018) and Vinck (2021). The experiments conducted on the three formations considered below have contributed to making significant improvements in offshore wind turbine foundation design.

• Cowden clay, stiff, high Yield Stress Ratio (YSR, or apparent OCR) sandy glacial till sampled at the PISA test site, NE England;

• Dunkirk sand, fine marine predominately silica sand from the PISA site in Northern France, consisting of dense to very dense normally consolidated hydraulic fill (average relative density D_R ≈ 100%) and Flandrian sand (average D_R ≈ 75%);

• St Nicholas at Wade (SNW) chalk, low-to-medium density B2/B3 grade Margate and Seaford chalk from the Upper Cretaceous sampled at the ALPACA site in Kent, SE England.

An overview of the ground conditions at these sites is presented, before considering three topics for each geomaterial:

• Mechanical behaviour from very small to large strains, emphasising non-linearity, anisotropy as well as rate-and-time dependency, interpreted within suitable frameworks;

• Synthesis of in-situ and laboratory measurements;

• The geomaterials’ response to drained or undrained cyclic loading.

Mention is made briefly of how soil-steel interface behaviour is affected by stress level, time (ageing), displacement, surface roughness, pore water chemistry and other conditions. Attention is also drawn to how field and laboratory testing can be applied in analyses of impact driven piles subjected to general loading.

2. Geotechnical overview

2.1 Site profiles

Cowden site encounters Bolders Bank formation glacial tills, whose deposition involved cycles of ice loading and horizontal shearing and/or glaciotectonic passive pressures (Davies et al., 2011). The till comprises principally stony, sandy and silty clay units that under-drain into two sand layers (Powell & Butcher, 2003; Ushev, 2018; Zdravković et al., 2020a; Ushev & Jardine, 2022a). While a water table is encountered at 1.0 m depth, pore-pressures become under-drained at depth. The till’s index properties are summarised in Table 1 and Figure 1. Figure 2a presents typical profiles of corrected Cone Penetration Test (CPTu) resistances (q_t); the occasional spikes indicate hard stone inclusions. Triple-barrel, wireline, Geobore-S rotary coring and block sampling campaigns retrieved a sufficient stock of high-quality intact specimens, although the till’s stony nature and 8% gravel content limited the core recovery rate to ≈ 42%.

Table 1
Typical index properties of the three geomaterials.

Material	D50 (mm)	G s	wc (%)	wP (%)	wL (%)	ρbulk (g/cm3)
Cowden glacial till	0.01-0.03	2.707-2.723	16.1-20.2	14.0-23.0	32.0-45.0	1.95-2.25
Dunkirk sand	0.21-0.28	2.65-2.66	5-7 (above WT) 22.7 (Below WT)	NA	NA	1.74 (above WT) 2.03 (below WT)
SNW chalk	0.003	2.71	27.9-33.0	22.3-23.9	30.2-32.0	1.85-1.98

• Note: ‘NA’: Not Applicable.

Figure 1
Particle size distributions of Cowden till, Dunkirk sand and SNW chalk over the depths of interest.

Figure 2
Corrected cone resistances (q_t) profiles for (a) Cowden, (b) Dunkirk and (c) St Nicholas at Wade (SNW) sites.

Dunkirk conditions consist of mainly normally consolidated marine Flandrian sands down to the Ypresian Eocene marine clay found at 30 m (Brucy et al., 1991; Chow, 1997; Jardine et al., 2006; Zdravković et al., 2020a). Three metres of hydraulic sand fill of the same origin were placed over the Flandrian sands in the 1970s without compaction or surcharging. Particle size analyses indicate uniform fine-to-medium sand; see Figure 1. The sub-angular particles comprise ≈ 85% silica, plus calcium carbonate (CaCO₃) shell fragments and other minerals that leave the soil slightly alkaline (Chow, 1997). Table 1 summarises index properties, after Kuwano (1999) and Aghakouchak (2015). The site’s q_t profiles are illustrated in Figure 2b. Groundwater was encountered at 5.4 m in 2014, 1.4 m deeper than that found by Chow (1997) with hydrostatic conditions below. While rotary coring was conducted for Brucy et al.’s (1991) investigation, coring for PISA was unsuccessful due to disturbance and drilling fluid contamination. The laboratory testing therefore had to rely on reconstituted bulk samples.

St Nicholas at Wade (SNW) The chalk site was characterised by Diambra et al. (2014) and Ciavaglia et al. (2017) prior to Buckley’s (2018) and Buckley et al. (2018) investigations for the Innovate UK project and the exhaustive ALPACA and ALPACA Plus studies (Vinck, 2021; Vinck et al., 2022; Jardine et al., 2023c). Pure (98.6% CaCO₃) white Margate Chalk was found down to the Barrois’ Sponge Bed at 5.2 m Above Ordnance Datum (AOD) above the Seaford white Chalk. The chalk classifies as CIRIA Grade B3/B2 (structured, very weak to weak, low-to-medium density) over the depths of interest, with discontinuity apertures < 3 mm and fractures spaced at 60 to 600 mm. Predominantly vertical linear micro-fissures were identified at all depths with ≈ 10 to 25 mm spacings. The ALPACA team located the (fresh) water table ≈ 0.9 m AOD, with ± 0.25 m variations. The chalk grains classify as fine silts (D₅₀ 3-4 μm) with 1.43 Mg/m³ to 1.53 Mg/m³ Intact Dry Densities (IDD) and a 0.91 average liquidity index; see Table 1.

Typical CPTu profiles are presented in Figure 2c, showing ‘spikes’ in thin flint bands. Significant chalk de-structuration beneath and around CPT tips leads to excess pore pressures up to 10 MPa at u₁ (face) piezocone positions (Buckley, 2018) and ≈ 4 MPa at u₂ (shoulder) locations. Friction sleeve resistances indicate the chalk’s partial de-structuration towards the soft ‘putty’ found around driven pile shafts. CPTu dissipation tests generally showed t₅₀ times < 10 s from which Vinck et al. (2022) interpreted in-situ consolidation coefficients. Geobore-S rotary coring retrieved samples to ≈ 16 m depth, although the chalk’s fractured and brittle nature limited the solid core recovery rate to 51% and a rock quality designation of 32%. Large block samples were taken from a 4 m deep excavated pit.

2.2 Test equipment

The Imperial College London laboratory testing employed fully instrumented automated Bishop-Wesley type triaxial cells for 38 mm and 100 mm diameter specimens. Liu et al. (2022a) detail the equipment and their stress and strain sensors’ resolutions and precisions. The LVDTs employed to measure local strains offered resolutions ≈ 0.1 μm. Mid-height sensors tracked local pore water pressures in the Cowden tests and lubricated top and base platens were deployed in most tests (Vinck et al., 2019). Liu (2018) and Liu et al. (2020) provide full details of the Hollow Cylinder Apparatus (HCA) and Bishop ring shear apparatuses employed in parallel testing campaigns; supplementary experiments were undertaken at other research and commercial laboratories.

3. Cowden till

The PISA Cowden campaign first established profiles of index properties and oedometer test outcomes. Comparisons between the 1-D compression behaviours of natural and reconstituted specimens indicated a dense and insensitive natural fabric. Initial triaxial tests also provided information on the till’s initial linear elastic response through to large-strain critical states that fed into finite element modelling. Liu (2018) and Ushev (2018) extended the scope to investigate the till’s anisotropy, strain rate and pressure dependent monotonic shearing behaviour, as well its undrained cyclic loading response, while Ushev & Jardine (2022a) explored the till’s large-displacement soil-soil and soil-steel interface shearing characteristics.

3.1 Index and mechanical property profiles

The Cowden till comprises predominantly low plasticity (plastic limit ≈ 14-23%) clay over the depth of interest; the 1.95 Mg/m³ – 2.25 Mg/m³ bulk densities reflect its gravel content. Figure 3a plots the 1-D compression yield stresses, σ_vy′, and Yield Stress Ratio (YSR, or apparent OCR = σ_vy′/σ_v0′) profiles from stage-loaded and constant rate of compression oedometer tests. The high YSRs noted over the upper 4 m reflect complex glacial and post-glacial processes. Although Powell & Butcher (2003) interpreted K₀ values exceeding 2.5 from various empirical procedures, Jardine (1985) argued that glacial lodgement till deposition leads to lower K₀ values that are more compatible with the networks of open vertical fissures observed especially within the desiccated and more stony upper sections. Therefore, the laboratory triaxial tests and analyses limited K₀ to 1.5 within the upper 7 m and unity below this depth.

Figure 3
Cowden site profiles of (a) 1-D yield stress σ_vy′ and YSR and (b) S_u from triaxial compression (TXC) and extension (TXE) tests; all tests performed on high-quality intact specimens (modified from Liu et al., 2020; and Ushev & Jardine, 2022a, b).

The peak undrained triaxial compression and extension strengths (S_u) of natural specimens re-consolidated to in-situ stresses are reported in Figure 3b. The profiles exhibit similar shapes that, like the oedometer σ_vy′ profile in Figure 3a, differ markedly from the patterns expected in gravitationally consolidated waterborne sediments after monotonic geostatic loading and unloading. The compression profile indicates an average CPT N_kt ≈ 18, while the average S_u^TXC/S_u^TXE ratio is 1.25. Liu et al. (2020) argue that the latter ratio does not reflect the till’s anisotropy because the extension strengths are affected by necking and different Lode angles (or b values) applied in compression and extension. Liu et al. (2020, 2023a) report HCA experiments that investigated the till’s anisotropy more rigorously.

3.2 Triaxial monotonic shearing

3.2.1 Stiffness

The triaxial tests addressed behaviour from strains of 10^-6 up to ultimate failure with deviatoric strains ε_s >25%. The natural Cowden till only exhibited elastic behaviour under small stress and strain increments, no greater than a few kPa and 0.002% respectively, that remained within the till’s Y₁ kinematic yield surface (Jardine, 1992). Undrained vertical Young’s moduli established by regression analyses of these initial portions led to the E^u_sec profile in Figure 4a along with secant stiffness profiles for axial (or ε_s) levels of 0.001%, 0.01%, 0.1% and 1%, which indicate nearly parabolic trends with depth. Analysis confirmed that E_u scales with p' raised to a partial power, as expressed in Equation 1, where p_ref is atmospheric pressure. The exponent β can be taken as 0.5 and the α values are largely constant with depth for each strain level; see Figure 4b. Similar traces were observed for the interpreted triaxial tangent Young’s moduli (E^u_tan) (Ushev, 2018).

Figure 4
Cowden stiffness profiles of: (a) triaxial compression secant stiffness E^u_sec at axial strains of 0.001%, 0.01%, 0.1%, and 1%; (b) normalised triaxial secant stiffness [E^u_sec/p_ref]/[p′/p_ref]^0.5 at four axial strain levels, applying Equation 1 with β = 0.5; and (c) elastic shear stiffnesses from laboratory and field geophysical measurements, with E_u^TXC/3 profile from triaxial compression tests (modified from Ushev & Jardine, 2022a).

$E^u=\alpha p_{ref}{\left(\frac{p\text{'}}{p_{ref}}\right)}^{\beta }$ (1)

Figure 5 shows the degradation of normalised secant stiffness [E^u_sec/p_ref]/[p′/p_ref]^0.5 with strain, with degradation being steeper in extension than in compression.

Figure 5
Typical degradation trends for normalised vertical secant undrained Young’s moduli from anisotropically consolidated triaxial compression and extension tests on intact Cowden till from upper layers (modified from Liu et al., 2020).

As discussed in greater detail later, Cowden till shows cross-anisotropic stiffnesses. Figure 4c plots laboratory bender element G_vh, G_hv and G_hh profiles for intact specimens along with in-situ seismic CPT (SCPT) G_vh data from Zdravković et al. (2020a). The laboratory and SCPT G_vh traces plot relatively close together, although the field values are (on average) slightly higher. Also shown in Figure 4c is the equivalent isotropic octahedral shear moduli G_oct taken as E_u^TXC/3 which falls far below the bender element G_vh and G_hh trends because of the till’s anisotropy.

3.2.2 Large-strain yielding and rate-dependent behaviour

Cowden till exhibits ductile, strain hardening, triaxial compression behaviour. Stable failure states were reached after imposing large strains, with the specimens’ barrelling without any evident shear banding. These points were interpreted as critical states with M^TXC = q/p' around 1.0, equivalent to ϕ_cs′ = 25.4°, c′ = 0 and applied in constitutive modelling of the till. Figure 6 shows typical undrained effective stress paths from compression (TXC) and extension (TXE) tests in q-p′ (q = (σ_v′ - σ_h′), p′ = (σ_v′ + 2σ_h′)/3) coordinates. Also indicated are large-scale ‘Y₃ yield points’ interpreted as the points (at q ≈ 100 kPa) where the effective stress paths rotated from their initial negative dp′/dq ratios (that reflect the till’s elastic stiffness anisotropy) to follow paths with positive, dilative, dp′/dq directions. While the TXC tests progressed to stable critical states, all TXE specimens developed necking failures which lead to apparently low peak shear strengths and post-peak softening. A notional Hvorslev surface is shown that runs from the final TXC critical state point back to the no-tension cut-off and encompasses the large strain undrained effective stress paths. Similar critical states and Hvorslev surfaces were assumed to apply in extension.

Figure 6
Typical undrained triaxial compression and extension effective stress paths for Cowden till samples from 3.0 to 3.5 m depth (Axial shear strain rate: 5%/day) (modified from Ushev & Jardine, 2022b).

Noting that rapid lateral pile loading tests at Cowden delivered markedly higher peak loads and stiffness than slower stage-loaded experiments (Byrne et al., 2020b), Ushev (2018) investigated the till’s rate-dependency. Triaxial tests run at axial strain rates of 5%/day, 50%/day and 500%/day showed S_u and secant stiffness increasing by ≈ 6% and 10% respectively per tenfold rate change. Compatible rate trends and reversible isotach behaviour were observed in other tests that alternated between 5% and 500%/day shearing rates.

3.3 Anisotropic stiffness and shear strength characteristics

Differences observed in the till’s triaxial compression and extension shear strengths and the triaxial and field stiffness profiles in Figures 3 and 4 prompted Liu et al. (2020) to investigate the till’s stiffness anisotropy. Suites of triaxial probing tests on samples from 4 depths applied drained vertical (dσ_vʹ), horizontal (dσ_hʹ) and undrained vertical (dq) stress increments (of typically 2 kPa) at rates of 0.1-0.2 kPa/hour established the till’s stiffness anisotropy. A suite of undrained HCA ‘α_dσ-controlled’ experiments that achieved five final σ₁ axis orientations with respect to the vertical (α_f values) spaced equally between 0 and 90˚. HCA simple shear (HCASS) and HCA triaxial compression tests (HCA TXC) performed on block sample specimens from 2.9 m established in this way the till’s anisotropy up to shear failure. The α_dσ-controlled and HCASS tests were controlled to keep the intermediate principal stress parameter (b) close to 0.5.

3.3.1 Cross-anisotropic elastic stiffnesses

Treating the till’s linear elastic behaviour as cross-anisotropic and strain-rate independent allows dynamic and static measurements to be considered as compatible and inter-comparable. The cross-anisotropic stiffness matrix has five independent parameters, E_vʹ, E_hʹ, ν_hvʹ (or ν_vhʹ), G_vh, G_hh (or ν_hhʹ) that can be determined experimentally (see for example Kuwano & Jardine, 2002). Three independent parameters, E_v^u, E_h^u and G_vh apply under undrained conditions that can be established from the drained set (see Brosse et al., 2017) or the combined drained and undrained probing approach proposed by Nishimura (2014) that places emphasis on the higher quality axial strain measurements.

The profiles with depth of G_hh/G_vh, E_hʹ/E_vʹ and E_h^u/E_v^u derived from Liu et al.'s (2020) triaxial and HCA tests plotted in Figure 7 show a generally consistent trend for a stiffer response under horizontal than vertical loading, which is important to recognise when analysing lateral pile loading. Also shown are G_hh/G_vh and G_hh/G_hv ratios from in-situ down-hole and cross-hole shear velocity tests by Powell & Butcher (2003); stiffness anisotropy clearly diminishes with depth.

Figure 7
Anisotropic stiffness ratio profiles for Cowden site (modified from Liu et al., 2020).

3.3.2 Non-linear stiffness characteristics over full strain range

Following Brosse et al. (2017), the α_dσ-controlled Cowden HCA tests allowed undrained vertical and horizontal Young’s moduli and torsional shear stiffness to be tracked over a wide strain range. The till’s marked elastic-plastic stiffness degradation under HCA conditions is demonstrated in Figure 8 by plotting E_v^u and E_h^u against vertical strain ε_z and average horizontal strain (ε_r + ε_θ)/2, respectively. Despite showing initial scatter, the moduli exhibit consistent degradation trends. Narrow spreads apply to each component, suggesting that the cross-anisotropic stiffness components are relatively insensitive to the shearing path followed. The two HCA triaxial tests, which employed pre-shearing b = 1.0 and ultimate b_u = 0, showed overlapping E_v^u trends that fall slightly below those of most b = 0.5 tests. Overall, the E_h^u curves plot above the E_v^u data trends, confirming that stiffness anisotropy persists as strains grow.

Figure 8
Cowden stiffness degradation from HCA tests: (a) undrained vertical secant Young’s moduli E_v^u against vertical (axial) strain; (b) undrained horizontal secant Young’s moduli E_h^u against mean horizontal strain (modified from Liu et al., 2020).

When taken to failure, under nominally plane strain conditions, in HCA tests, the highest shear strengths developed when σ₁ acted horizontally (b = 0.5, α_f = 90˚) and the lowest when σ₁ acted vertically; the shear strengths specimens applying at intermediate α_f values spanned these limits, confirming that any S_u anisotropy inferred from comparing triaxial compression and extension strengths (see Figure 3b) would be misleading.

3.4 Response to undrained cyclic loading

Cyclic loading, which can be critical for offshore structures, was addressed in the PISA field pile testing. Ushev (2018) and Ushev & Jardine (2022b) supported this work by investigating Cowden till’s response to undrained triaxial cyclic loading, considering multiple nominally identical samples from 3.4 mbgl re-consolidated to in-situ stresses q₀ = -25 kPa, p₀′ = 67 kPa. Mean (q_mean) and cyclic (q_cyc) deviatoric stresses, in the -25 to 200 kPa and 10 to 150 kPa respective ranges, were applied to populate the q_mean-q_cyc interactive loading plane and investigate how the combinations affected the evolving trends for effective stress, cyclic strain and stiffness, damping ratios and any cyclic failures.

3.4.1 Number of cycles to failure and cyclic interaction diagram

The influences of the mean q_mean and cyclic q_cyc deviatoric stresses were considered in both (i) the conventional total stress q_cyc/(2S_u) and q_mean/(2S_u) interactive loading space and (ii) alternative ‘effective-stress’ normalised q_cyc/p′_in-situ and q_mean/p′_in-situ space, as shown in Figure 9. Five of the higher amplitude cyclic tests failed after the indicated number of cycles (N_f). All other specimens remained un-failed when loading halted after 1500 to 3500 cycles. Interpreted contours are shown of the conditions under which failure can be expected at N_f = 10, 100 or 1000. A stable zone is indicated where cyclic failure is not expected within 1000 cycles, and regions where failures occurred by either (i) large cyclic and average strains that led to “abrupt failure” or (ii) mean strains accumulating and samples “creeping towards failure”.

Figure 9
Contours of number of cycles to failure for intact Cowden till in normalised stress space (modified from Ushev & Jardine, 2022b).

3.4.2 Evolution of effective stress, cyclic strain and stiffness

Cowden till’s cyclic effective stress path and overall cyclic loading behaviour varied systematically with the normalised loading parameters. Typical ‘stable’ and ‘unstable’ responses are illustrated in Figure 10 for specimens cycled under q_cyc = 25 kPa and a single test involving q_cyc = 150 kPa from ‘in-situ’ q_mean = -25 kPa. Also shown are the no-tension lines, the Hvorslev surfaces and M lines identified from the static tests. Figure 10a illustrates the stable outcomes of experiments involving q_cyc = 25 kPa (q_cyc/(2S_u) = 0.1). Shifts can be seen from an initially “dilative” drift trend to one indicating slightly “contractive” behaviour. In contrast, the higher amplitude q_cyc = 100 and 150 kPa (q_cyc/(2S_u) = 0.4 and 0.6) experiments conducted from q_mean = -25, 50 and 125 kPa all initially violated the ‘slow shearing’ Hvorslev surface and subsequently progressed to fail within 1000 cycles. One example is given in Figure 10b. The final stages of ‘unstable’ experiments could involve axial strain rates up to 200 times higher than the reference monotonic experiments, explaining why they were able to sustain transient conditions that could not be sustained under slow monotonic loading. The specimens’ p′ values fell more significantly on unloading than they rose during loading, leading to an overall contractive trend with the paths heading leftward towards the origin, developing irregular loops and broad “butterfly-wing” shapes.

Figure 10
Effective stress paths of Cowden till under undrained cyclic triaxial shearing: (a) typical stable response under low amplitude cycling; (b) unstable cycling response under high q_cyc level of 150 kPa (Ushev & Jardine, 2022b; Liu et al., 2023a).

Typical patterns of permanent axial strain (ε_mean) accumulation with N are plotted in Figure 11a on logarithmic scales. The strains developed under the lowest (10 kPa) cyclic amplitudes tended to stabilise after 100 to 1000 cycles to rates comparable to the slow residual creep rates (< 0.005%/day) applying before cycling started. Empirical power law relationships were found that relate the strain development of stable and metastable tests to their normalised cyclic loading parameters. Figure 11b presents the cyclic peak-to-trough secant stiffnesses trends for tests performed at in-situ q_mean. The tests that manifested stable effective stress loops showed stiffness either growing slightly with N or falling modestly before stabilising; unstable cycling response led to cyclic stiffness falling sharply with N.

Figure 11
Evolution trends for (a) mean (permanent) axial strain and (b) cyclic secant stiffness against number of cycles for intact Cowden till specimen cycled from in-situ mean q_mean = -25 kPa (Ushev & Jardine, 2022b, Liu et al., 2023a).

3.4.3 Cyclic kinematic yield surfaces

The cyclic responses observed in the stable and metastable tests can be related to two kinematic yield surfaces that, once engaged, move with the current effective stress point; Jardine (1992). The first elastic, Y₁, region is approximately elliptical in shape and has a maximum height of only about ± 2.5 kPa in-situ for the cyclic series’ specimens. The second Y₂ kinematic yield surface (KYS), defined here as the threshold limit to: (i) stable effective stress conditions that involve less than 5% variation in p′ over 2000 ± 500 cycles and (ii) practically constant cyclic stiffness. Figure 12 marks the approximate boundaries of the Y₁ (red circles) and Y₂ (black ellipses) surfaces that surround each q_mean point. The Y₂ surfaces’ vertical dimensions diminished as the pre-loading effective conditions approached the Hvorslev surface, even though p′ increased as the samples moved along this undrained loading path. While cyclic loading within the initial Y₂ kinematic yield surface does not appear deleterious, paths that engage Y₂ on each loading and unloading stages dissipate far more energy and provoke marked stiffness degradation and strain accumulation.

Figure 12
Y₂ kinematic yield surfaces for Cowden till interpreted from cyclic undrained triaxial tests at four mean deviatoric stress (q_mean) points along a slow compression test path to failure (modified from Ushev & Jardine, 2022a, b).

4. Dunkirk sand

The Dunkirk PISA triaxial testing focused initially on calibrating the Taborda et al. (2014) state parameter-based bounding surface plasticity model employed to design and model lateral pile tests. The research scope extended later to consider stiffness anisotropy and long-term drained cyclic loading behaviour, again aiming to support cyclic pile tests. Liu (2018) and Liu et al. (2019a, b) report on the sand’s interface shearing behaviour.

4.1 Site stiffness profiles

Extensive field SCPT and laboratory bender element and small-stress probing tests led to the stiffness profiles plotted in Figure 13. The 2016 PISA SCPT tests indicated higher G_vh profiles than those reported by Chow (1997) at a location 100 m distant, potentially reflecting local ground variability and/or the effects of ageing over ≈ 20 years under the hydraulic fill (Zdravković et al., 2020a). Drained triaxial tests indicated consistently higher vertical (E_vʹ) than horizontal (E_hʹ) moduli, reflecting the applied K₀ = 0.4, although the G_vh and G_hh components showed less difference. The in-situ SCPT G_vh profiles plotted distinctly above laboratory bender element (BE) values, especially above the water table, which was ascribed to long-term ageing, partial saturation in-situ and seasonal water table fluctuations. Checking for, and addressing, such discrepancies is crucial to successful practical modelling of laterally loaded monopiles.

Figure 13
Dunkirk stiffness profiles from in-situ SCPT, laboratory bender element (BE) and triaxial small-stress probing tests (Liu, 2018).

4.2 Full strain mechanical behaviour under monotonic loading

4.2.1 Linear elastic stiffness anisotropy

Liu (2018) undertook stress-path probing tests on fully instrumented 100 mm diameter specimens that were consolidated and swelled along five constant K (= σ_hʹ/σ_vʹ) stress ratio paths. The following functions were fitted to correlate the cross-anisotropic stiffnesses with the principal stresses σ_vʹ and σ_hʹ.

$$E_{\text{v}}\text{'}=f(e)C_{\text{v}}{\left(\frac{{\sigma }_{\text{v}}\text{'}}{p_{\text{ref}}}\right)}^{a_{\text{v}}}$$ (2)

$$E_{\text{h}}\text{'}=f(e)C_{\text{h}}{\left(\frac{{\sigma }_{\text{h}}\text{'}}{p_{\text{ref}}}\right)}^{b_{\text{h}}}$$ (3)

$$G_{\text{vh}}=f(e)C_{\text{vh}}{\left(\frac{{\sigma }_{\text{v}}\text{'}}{p_{\text{ref}}}\right)}^{a_{\text{vh}}}{\left(\frac{{\sigma }_{\text{h}}\text{'}}{p_{\text{ref}}}\right)}^{b_{\text{vh}}}$$ (4)

$$G_{\text{hh}}=f(e)C_{\text{hh}}{\left(\frac{{\sigma }_{\text{v}}\text{'}}{p_{\text{ref}}}\right)}^{a_{\text{hh}}}{\left(\frac{{\sigma }_{\text{h}}\text{'}}{p_{\text{ref}}}\right)}^{b_{\text{hh}}}$$ (5)

where C_v, C_h, C_vh, C_hh, a_v, b_h, a_vh, b_vh, a_hh and b_hh are material coefficients and f(e) is taken as (2.17-e)²/(1+e).

Table 2 summarises the cross-anisotropic stiffness coefficients determined from Liu's (2018) study and Kuwano's (1999) earlier Dunkirk sand probing tests. C_h/C_v and C_hh/C_vh, were invariably greater than unity, indicating inherent anisotropy induced by grain orientation during water (or air) pluviation. Although the simple treatment generally works well, the experiments indicated coefficients that varied moderately with K with C_v values from K = 0.5 tests around 15% above those from K = 1 experiments; see Figure 14.

Table 2
Cross-anisotropy stiffness coefficients of Dunkirk sand.

Sand batch	DR (%)	Method	K	Stiffness parameters
Batch 1 (5.85-11.9 m bgl.)	57-65	AP	1, 0.53, 0.35	Cv: 225 av: 0.55	Ch: 228 bh: 0.50	Cvh: 70 avh: 0.36 bvh: 0.20	Chh: 105 ahh: 0.05 bhh: 0.46	Ch/Cv: 1.01 Chh/Cvh: 1.5
Batch 3 (0-0.8 m bgl.)	73-92	WP	1, 0.5	Cv: 154 av: 0.51	Ch: 166 bh: 0.50	Cvh: 49 avh: 0.30 bvh: 0.19	Chh: 63 ahh: 0.10 bhh: 0.42	Ch/Cv: 1.08 Chh/Cvh: 1.29

• Notes: (1) Batch 1 data from Kuwano (1999); (2) Sample preparation method: AP = air pluviation; WP = water pluviation; (3) parameters _v, _h, _vh and _hv in MPa; (4) All tests performed with lubricated platens.

Figure 14
Correlations between E_vʹ/f(e) and σ_vʹ/p_ref and the stiffness coefficients for the K = 1 and 0.5 small-stress probing tests on Dunkirk sand (Liu, 2018).

4.2.2 Non-linear stiffness and yielding

Vinck (2016) and Liu (2018) investigated Dunkirk sand’s behaviour from its linear elastic range through to critical state conditions in over sixty locally instrumented tests, varying D_R, effective stress level (p₀′) and OCR as well as platen configurations. Figure 15 illustrates the effects of OCR on E_v,tan′/f(e) through samples tested at p₀ʹ = 50 and 150 kPa after unloading to a range of OCRs. While over-consolidation affected the initial E_v,tanʹ values by only 5%, it extended the initial linear tangent stiffness plateau through changes in the granular contacts and micro-structure that were accompanied by minimal volume changes and so cannot be captured by, for example, applying a simple f(e) function.

Figure 15
Effects of effective stress level and history on the pre-failure small strain stiffnesses of Dunkirk sand (Liu, 2018).

Rowe & Barden (1964), Bishop & Green (1965) and Koseki (2021) identified how end friction affects large-strain triaxial behaviour and shear strength of sands. However, its impact on small-strain behaviour was only recently investigated experimentally (with peat) by Muraro & Jommi (2019) and numerically by Cui et al. (2021), considering stiff, high OCR, London clay. Liu et al. (2022a) explored the impact of platen roughness on the pre-failure stiffness of siliceous sand and Figure 16 demonstrates how end constraint affects Dunkirk sand’s stiffness and degradation trends even when specimens had 2:1 initial height-to-diameter ratios and strains were gauged locally over the central ≈ 50 mm height. Figure 16 plots E_v,tan′/f(e) against σ_v′/p_ref for medium dense specimens, considering axial strains of 0.001%, 0.01%, 0.1% and 1%. Medium density specimens tested at relatively low stress levels were most heavily affected by sample end constraints at low to modest strain levels.

Figure 16
Effects of platen conditions on the pre-failure small strain stiffnesses of medium dense (D_R ≈ 53%) Dunkirk sand specimens (Liu, 2018; Liu et al., 2022a).

4.2.3 Large-strain and critical state behaviour

End constraint also influences medium-to-large strain behaviour. Full end constraint leads to misleadingly high peak stress ratios and shear strengths, at apparently smaller strains, and ultimate stress ratios that did not tend to converge to a unique M with medium dense specimens. Deformation was more uniform in tests employing enlarged lubricated platens, although bulging about the vertical axis was observed with these specimens, but without visible bifurcation even with very dense specimens.

Liu (2018) interpreted Dunkirk sand’s large strain and ultimate shearing behaviour within the state parameter critical state framework, providing the basis for bounding surface plasticity (Taborda et al., 2014) and Nor-Sand (Jefferies & Been, 2015) modelling. Taborda et al. (2020), Castillo-Fuentes et al. (2023) and Selby et al. (2023) demonstrated these models’ application in the simulations of the PISA Dunkirk pile tests.

4.3 Long-term drained cyclic loading behaviour

Aghakouchak (2015) and Aghakouchak et al. (2015) conducted cyclic triaxial and hollow cylinder (HCA) tests to model axial cyclic pile loading and showed how to cater for the ‘near-shaft’ conditions, stress and loading histories that govern field behaviour. Lateral cyclic pile loading engages larger volumes in the passive, active and side shear reaction regions located around the pile circumference. Predominantly drained conditions applied in the PISA Dunkirk tests; conditions are expected to be substantially drained under long-term cyclic loading around even larger monopiles.

Liu’s (2018) cyclic triaxial testing programme for Dunkirk therefore focussed on long-term drained constant σ_r′ experiments, aiming to produce a benchmark dataset against which cyclic constitutive models could be validated, calibrated, and applied in boundary value problems. The tests applied the cyclic and mean deviatoric stress combinations (q_cyc, q_mean) as defined in q_cyc/p₀ʹ-q_mean/p₀ʹ (or CSR-η) space in Figure 17. Specimens were consolidated to, and allowed to creep at, initial (q_mean, p₀′) states before constant amplitude cycling to target conditions with N > 10⁴. All but two specimens survived cycling and were subsequently sheared monotonically to failure to assess how cycling had modified their behaviour. Figure 18 illustrates the q–ε_a trends shown for a typical test on a very dense (D_R = 92%) specimen that started from (q_mean, p₀′) = (100, 133.3) (kPa) with q_cyc = 40 kPa (CSR = 0.3). The local axial strains recorded with high resolution sensors manifested the accumulation trends plotted logarithmically in Figure 19, considering each of the 10⁴ cycles. Also annotated are power law equations that fitted the experimental trends. Liu (2018) further related the fitting parameters to the q_cyc/p₀ʹ-q_mean/p₀ʹ loading conditions and showed how to interpret ratcheting, cyclic stiffness, damping and other cycling characteristics from the high-resolution cycle-by-cycle stress-strain data.

Figure 17
Normalised q_cyc/p₀ʹ-q_mean/p₀ʹ (CSR-η) stress states with reference to the peak and critical state envelopes of Dunkirk sand (Note (q/pʹ)_peak^TXC = 1.5, M_cs^TXC = 1.31, (q/pʹ) _peak^TXE = -1 and M_cs^TXE = -0.9) (Liu, 2018).

Figure 18
Deviatoric stress strain (q-ε_a) trends for a typical long-term drained cyclic triaxial test involving two sets of stress-controlled consolidation and creep stages, a cyclic shearing stage and post-cyclic monotonic shearing to failure (Liu, 2018).

Figure 19
Accumulated cyclic axial strains for very dense (D_R = 92%) triaxial Dunkirk sand specimens cycled from (q_mean, p₀ʹ) = (100, 133.3) (kPa) under fully drained conditions (Liu, 2018).

Post-cyclic shear stiffness trends are considered in Figure 20, plotting normalised secant Young’s moduli E_v,secʹ against axial strain for specimens cycled from the same (q_mean, p₀′) = (100, 133.3) (kPa) mean conditions but with different amplitudes (q_cyc). Applying f(e) accounted for void ratio changes under cycling, showing how cycling led to higher initial stiffness, longer linear plateaux and more gradual stiffness degradation. These changes grew markedly with the prior cyclic stress ratio, reflecting micro-fabric optimisation under cycling. The significantly better organised internal particle force chains and contact distributions also relocated and expanded the sand’s Y₁ and Y₂ kinematic yield surfaces.

Figure 20
Effects of cyclic loading history on the post-cyclic monotonic stiffness degradation trends for Dunkirk sand (Liu, 2018).

5. St Nicholas at Wade (SNW) chalk

Extensive laboratory and in-situ characterisation were conducted for the ALPACA piling JIP. Noting that pile driving alters chalk properties significantly, the testing considered the behaviour of both intact chalk and the de-structured ‘putty’ material that formed adjacent to the pile shafts during driving and controlled their axial behaviour. The programme encompassed monotonic and undrained cyclic triaxial loading, supported by geological logging, index, unconfined compression strength (UCS), oedometer, direct simple shear (DSS), Brazilian tension (BT) and interface shear tests (Vinck, 2021). A metallurgical corrosion study was also undertaken by Vinck et al. (2023b) to provide fundamental insights into the piles’ highly age-dependent axial shaft capacity trends (Buckley et al., 2018, 2020; Jardine et al., 2023b, c; Vinck et al., 2023a).

5.1 Elastic stiffness profiles

The chalk’s elastic stiffnesses were examined by laboratory and field testing and Figure 21 considers the shear stiffness profiles measured at the smallest strains offered by various techniques. As emphasised by Clayton et al. (2003), the chalk’s meso-to-macro fabric plays a dominant role. The mean SCPT G_vh and cross-hole G_hv trends amount to around 2/3 of the shallow triaxial tests’ BE G_vh measurements and converge more closely at depth, reflecting the reducing occurrence of open fissures, which are naturally excluded from laboratory specimens. The direct simple shear (DSS) G_vh maxima and the pressuremeter G_hh values fall far below those interpreted from shear wave velocities, due to their low resolution and the chalk’s brittle response to the non-uniform straining imposed by these tests. Triaxial BE measurements made on the same samples indicated G_hh/G_vh ≈ 0.5 in the shallow layers, which gradually rose to unity at depth; the field seismic data show a similar, but more muted, trend. Also plotted in Figure 21 is the E_h′/E_v′ profile developed from four suites of triaxial probing tests by Vinck (2021). Horizontal loading from in-situ stresses provokes a far softer response than vertical compression, which is important when analysing lateral pile loading. This aspect of the chalk’s marked anisotropy contributed to undrained and drained triaxial compression paths following similarly inclined effective stress paths (Vinck et al., 2022).

Figure 21
SNW profiles and ratios of maximum stiffnesses: (a) laboratory and in-situ measurements of G_vh and G_hv; (b) G_hh profiles; (c) ratios between laboratory and in-situ stiffnesses; and (d) profiles of stiffness anisotropy ratios (modified from Vinck et al., 2022).

5.2 Chalk’s response to monotonic triaxial loading

5.2.1 Pressure-dependent yielding and failure

The SNW chalk’s cemented open micro-structure (Alvarez-Borges et al., 2020) leads to significant sensitivity, brittleness and pressure-dependent behaviour. Figure 22 shows example loading curves up to 0.5% axial strain from locally instrumented triaxial and UCS tests conducted from in-situ p₀′ and 300 kPa + p₀′ stresses. Very stiff and nearly linear pre-failure behaviour is evident, as well as a notably brittle post-peak response that involved tensile fracturing and led to low low strengths at large strains. High pressure triaxial tests that explored conditions from in-situ p₀′ (≈ 63 kPa) up to p₀′ = 12.8 MPa identified a gradual transition (shown in Figure 23) from brittle to ductile behaviour under increasing p′ levels. The chalk’s highly curved failure envelope (Figure 24) reaches an ultimate (q/p′)_ult = 1.25, equivalent to critical state ϕ′ ≈ 31^o, that matches (as shown later) that of fully de-structured chalk.

Figure 22
Example stress-strain curves up to 0.5% axial strain from locally instrumented triaxial and unconfined compression (UCS) tests on intact SNW chalk from in-situ p₀′ and 300 kPa + p₀′ (Vinck et al., 2022).

Figure 23
Full-strain triaxial compression behaviour of intact SNW chalk under a wide range of pressures (Liu et al., 2023b).

Figure 24
Peak and ultimate shear strength envelope for intact SNW chalk (Liu et al., 2023b).

Figure 25 depicts how the initial Y₁ and Y₃ yield loci of unfractured chalk may be represented with near elliptical surfaces in triaxial q-p′ space. Intact (cemented) chalk displays linear behaviour over a far larger region of q-pꞌ space than soils such as the unbonded Cowden till or Dunkirk sand. Laboratory elastic vertical Young’s moduli E_v,max′ are comparatively insensitive to applied p₀′, with modest increases up to the peak (7.7 GPa) found with p₀′ = 650 kPa before falling to a 4 MPa plateau as bonds break under increasing p₀′ (Liu et al., 2023b). However, the chalk’s systems of micro-to-macro fissures, which gradually close under normal stress, lead to the maximum mass chalk stiffnesses invoked by pile loading being four times lower than the laboratory values (Jardine et al., 2023c).

Figure 25
Yield stresses and interpreted pre-failure Y₁ and large-scale Y₃ loci for intact SNW chalk (Liu et al., 2023b).

Chalk’s propensity to tensile fracture leads to BT and DSS strengths 90% and 50% lower respectively than those from UCS or triaxial compression tests, with many implications for the modelling of geotechnical problems that involve multi-directional loading.

5.2.2 Fully de-structured chalk’s response to undrained monotonic shearing

Laboratory dynamic compaction, applied at in-situ water content, was employed to de-structure low-to-medium density chalk in an analogous way to pile driving, producing uniform chalk putty with 9 ± 3 kPa fall-cone shear strengths and liquid and plastic limits of 30.6% and 24.2% respectively. Instrumented, consolidated, triaxial specimens were formed with (pre-shearing) void ratios and effective stress states matching those noted in the de-structured annuli identified around driven pile shafts several months after driving (Buckley et al., 2018).

The de-structured chalk’s undrained triaxial compression and extension behaviour is demonstrated first in Figure 26 by considering the q-p′ effective stress paths. These are initially nearly vertical, suggesting that the re-consolidated and (mildly aged) putty’s initial stiffness response was largely isotropic. The effective stress paths rotated to follow leftward (contractive) stages after mobilising modest ‘peak’ resistances (at ε_a < 0.2%) and showed strain softening as shearing continued up to phase transformation (PT) points at which their paths rotated abruptly and climbed towards ultimate (critical state) conditions. Continued straining led to markedly higher ultimate strengths as the specimens attempted to continue dilating. Extension tests indicated similar, yet not fully symmetric, paths and shear strengths. The ultimate critical states gave ϕ_cs′ ≈ 31°, matching the high-pressure intact tests in Figure 24.

Figure 26
Effective stress paths of de-structured chalk under undrained triaxial compression and extension (modified from Liu et al., 2022b).

5.3 Response to undrained cyclic triaxial loading

5.3.1 Intact chalk’s failure patterns

Undrained cycling affects intact chalk differently to saturated sedimentary sands or clays (Ahmadi-Naghadeh et al., 2022). Figure 27 presents a typical unstable response observed with a specimen loaded from p₀′ = 42 kPa, q_mean = 1225 kPa by high-level cycling with q_cyc = 950 kPa and q_max/(2S_u) = 0.91. The axial strain and pore pressure records show little or no sign of impending instability; little change was seen in either the damping ratio (which remained at around 4%) or the cyclic stiffness, until degradation set in over the last 30 cycles and brittle failure occurred abruptly after 181 cycles. In contrast, specimens that sustained large number (> 4,000) of cycles developed minimal straining and excess pore pressure accumulation and manifested nearly visco-elastic behaviour.

Figure 27
Typical unstable cycling response of intact chalk: Variation of axial strain and pore water pressure against number of cycles (Test conditions: p₀′ = 42 kPa, q_mean = 1225 kPa, q_cyc = 950 kPa and q_max/(2S_u) = 0.91) (Ahmadi-Naghadeh et al., 2022).

The experimental outcomes allow cyclic interaction diagrams to be established in q_cyc/(2S_u)–q_mean/(2S_u) space, as in Figure 28. A tentative fan of linear N_f contours indicates the main trends applying between 1 and 3000 cycles. The region below the 3000-cycle contour in Figure 28 signifies the stable region within which undrained cycling improved stiffness without any loss of undrained shear strength.

Figure 28
Cyclic interaction diagram for intact SNW chalk tested from p₀′ = 42 kPa, showing the interpreted contours of number of cycles to failure for specified q_cyc-q_mean conditions (Ahmadi-Naghadeh et al., 2022).

Overall, the intact chalk’s behaviour appears more like that of crystalline rocks or metals than sedimentary soils. Repeated loading prompts progressive wear and shearing between grains, forming microcracks that may coalesce into macrocracks (Cerfontaine & Collin, 2018). The outcomes can be interpreted as ‘S-N’ curves that plot the maximum cyclic load (q_max = q_mean + q_cyc) against log N, with contours interpolated to show how the q_max/(2S_u) curves fall as q_cyc/q_mean rises, expressed as:

$$\frac{q_{\max }}{2S_{\text{u}}}=f(N)\cdot \frac{1+q_{\text{cyc}}/q_{\text{mean}}}{f(N)+q_{\text{cyc}}/q_{\text{mean}}}$$ (6)

in which f(N) represents for each N_f line its projected intercept on the vertical axis of the interactive q_cyc/(2S_u)-q_mean/(2S_u) diagram and is expressed as:

$$f(N)=0.35+\frac{1}{1.54+0.37\times {[{\log }_{10}(N_{\text{f}})]}^{2.75}}$$ (7)

A lower limit of f(N) = 0.35 is incorporated in this expression which corresponds to a fatigue limit (or fatigue strength) of q_max/(2S_u) = 0.52, below which specimens could sustain cycles indefinitely under the most critical q_cyc/q_mean = 1 one-way loading condition. The above two equations lead further to a three-dimensional representation of intact chalk’s undrained cyclic failure characteristics in a q_max/(2S_u)-q_cyc/q_mean-log₁₀(N) space, as shown in Figure 29.

Figure 29
Three-dimensional representation of the undrained cyclic failure characteristics of intact SNW chalk in q_max/(2S_u)-q_cyc/q_mean-log₁₀(N) space (Ahmadi-Naghadeh et al., 2022).

5.3.2 Cyclic failure characteristics of de-structured chalk

Liu et al. (2022b) show that fully de-structured, re-consolidated, chalk putty responds to undrained cyclic loading similarly to silts and silty sands, and markedly differently to the intact chalk. As illustrated in Figure 30, de-structured specimens respond to high-level cycling by generating excess pore pressures that shift their effective stress paths leftwards. Both contractive and dilative phases occur within individual cycles. Cyclic phase transformation lines with (q/p′) gradients of ≈ 0.54 and 0.38 can be identified in compression and extension respectively, following Mao & Fahey (2003), that fall well below the monotonic phase transformation lines. The transient cyclic effective stress paths can also cross the monotonic critical state gradients M.

Figure 30
Effective stress paths for typical unstable tests on de-structured chalk and the identified cyclic phase transformation lines (Liu et al., 2022b).

The full suite of one- and two-way cyclic tests is set-out in an interactive loading diagram in Figure 31, which adopts both q_cyc/(2S_u)-q_mean/(2S_u) and q_cyc/(p₀′)-q_mean/(p₀′) axes. A tentative family of contours is shown for number of cycles to failure (N_f); the lower-levels, high N_f, contours show less curvature and tighter spacings than those representing high-level cycling. As with all soils, chalk putty is more susceptible to high-level two-way (compression and extension, with q_mean ≤ q_cyc) loading than one-way compression cycling.

Figure 31
Cyclic interaction diagram for de-structured chalk expressed in normalised q_cyc/(2S_u) - q_mean/(2S_u) and q_cyc/p₀′ - q_mean/p₀′ stress space for p₀′ = 200 kPa and p₀′ = 400 kPa test series (Liu et al., 2022b).

Significant axial strain development and stiffness losses occur in unstable tests that accelerate markedly as cyclic failure approaches. Liu et al. (2022b) report on these features and the specimens’ damping ratios. Cycle-by-cycle effective stress changes were tracked in the experiments, enabling the development of a laboratory-based global prediction method for axial shaft capacity under cyclic loading (Jardine, 2020; Buckley et al., 2023). All tests showed Δp′/p₀′ decreasing continuously with N, although it is possible that cycling at lower levels than those applied would identify conditions under which no reduction occurs. Liu et al. (2022b) show that the mean effective stress drifts of tests run with (q_cyc+ q_mean)/p₀′ < 0.4 can be related to the number of cycles applied by the power-law Equation 8.

$$\frac{p\text{'}}{p_0\text{'}}=A\times (B+\frac{q_{\text{cyc}}}{p_0\text{'}})\times N^C$$ (8)

Parameters A, B and C define the rates of p′ degradation and the maximum cyclic stress ratio that could lead to beneficial, null, or deleterious cycling effects. Higher level cyclic tests that failed within just a few cycles show more complex trends. Figure 32 reports the outcomes of cyclic tests on samples consolidated to p₀′ = 200 kPa and shows how Equation 8, applied with A = -0.05 and B = -0.12 and C = 3.48×q_cyc/p₀′ fits the experimental trends well.

Figure 32
Mean effective stress trends during cycling and fitted trends (in dashed lines) for ‘putty’ tests with p₀′ = 200 kPa and mostly (q_cyc+ q_mean)/p₀′ < 0.4 (Liu et al., 2022b).

6. Applications of the research

The Cowden, Dunkirk and SNW characterisation programmes were vital to interpretating the high-value, large-scale, instrumented pile experiments run at the three sites. They also led to new site investigation and practical pile design approaches that are being applied widely in major offshore wind projects. As noted below, advances have flowed in four main areas.

6.1 Pile behaviour under monotonic axial loading

Jardine et al. (2005) and Jardine (2014) showed that advanced finite element (FE) modelling based on the glacial tests by Jardine et al. (1984) and sand tests by Kuwano (1999) offered good matches to full-scale field observations made at North Sea clay till sites and tests to failure on 19 m long, 457 mm diameter piles driven at Dunkirk. The most significant new findings to emerge regarding axial load-displacement behaviour, which is central to jacket supported structures, therefore concern the chalk, about which little information was available previously. Wen et al. (2023a, b) employed the laboratory testing to calibrate new 1D load transfer and advanced 2D/3D FE models that provide generally good fits to the ALPACA and ALPACA Plus field tests on piles with diameters up to 1.8 m and embedded lengths up to 18 m.

6.2 Pile behaviour under cyclic axial loading

Buckley et al. (2023) and Liu et al. (2023c) report on how the laboratory chalk putty cyclic testing contributed to a simplified yet accurate global prediction method for axial cyclic pile design in chalk, which is now available for use by industry. Jardine (2020) and Jardine et al. (2012) have reported previously on the use of undrained cyclic tests on sands and clays to predict pile response to axial loading, showing how the laboratory experiments by Aghakouchak et al. (2015) on Dunkirk sand enabled accurate predictions of the cyclic axial pile tests reported by Jardine & Standing (2012). The Cowden till cyclic testing data is also now available to aid back-analysis of earlier cyclic axial pile tests (see Ove Arup and Partners, 1988) as well as monotonic axial tests reported by Karlsrud et al. (2014).

6.3 Pile behaviour under monotonic lateral loading

Modelling of field lateral pile loading response is critical to the efficient design of monopile supported offshore wind turbines. Taborda et al. (2020) and Zdravković et al. (2020b) describe how the site characterisation described above was central to advanced 3D FE analyses that aided the design and interpretation of the PISA lateral loading tests on instrumented piles with diameters up to 2 m driven at Dunkirk and Cowden. The resulting PISA design approach (Byrne et al., 2020c) has offered a step change in design practice that has been applied internationally. Pedone et al. (2023) describe how still more advanced 3D FE analyses developed from the chalk testing captured accurately the lateral loading behaviour shown by ALPACA tests in the fractured, highly brittle SNW chalk. These experiments and analyses are now being applied in the design of major new windfarms at offshore chalk sites.

6.4 Pile behaviour under cyclic lateral loading

It is essential to consider lateral cyclic loading cases when designing monopile foundations. The PISA cyclic pile tests are applied widely as benchmarks against which alternative modelling strategies are routinely calibrated and tested. The Authors’ recently published cyclic laboratory test programmes offer a basis for re-analyses of the Cowden and Dunkirk cyclic PISA pile tests, as well as the recent PICASO tests (Byrne et al., 2020a) at Cowden. The cyclic laboratory programmes on chalk will also pave the way for well-calibrated lateral cyclic analyses at chalk sites.

7. Summary and conclusions

This paper summarises recent research into the stiff glacial till, dense marine sand, and low-to-medium density chalk encountered at the PISA, ALPACA and ALPACA Plus JIPs instrumented pile test sites. Coordinated field and laboratory studies investigated the materials’ stiffness patterns, full strain mechanical behaviour, anisotropy and response to cyclic loading. Their outcomes are being employed widely to aid the modelling of field behaviour under axial-and-lateral, monotonic-and-cyclic loading. By enabling more efficient driven pile foundation design, the research is contributing significantly to more efficient offshore wind energy generation and CO₂ emission reductions. The large volume of new findings supports four general conclusions.

1. Monotonic laboratory testing to failure showed how the geomaterials behave over their full strain range, including the distinct properties of the fully de-structured chalk putty. Combining these data with in-situ measurements enables representative modelling of the pile test outcomes and shows the way forward for their practical application;

2. Laboratory and field measured elastic stiffnesses may show significant divergence. While broadly similar profiles applied at Cowden, triaxial tests on reconstituted Dunkirk sand underpredicted the site’s field stiffnesses, which had grown after 20 years of ageing under hydraulic fill. In contrast, the chalk’s mass field stiffness fell far below the measurements made from laboratory tests on intact samples because they did not capture the important effects of partially open meso-to-macro fractures;

3. All three geomaterials displayed elastic stiffness anisotropy. Vertical stiffnesses exceeded horizonal moduli in the normally consolidated dense Dunkirk sand and in the high YSR intact SNW chalk, while the opposite applied in high YSR Cowden glacial till;

4. The cyclic programmes showed a wide range of behaviours and provide vital new evidence to aid the development of suitable predictive approaches. While the intact chalk’s response was distinctly different to that of the till and sand, resembling that of crystalline rocks or metals, the chalk putty’s cyclic behaviour was closer to that shown by the glacial till and marine sand.

List of symbols and abbreviations

a_v, a_vh, a_hh Cross-anisotropy stiffness parameters; see Equations 2-5

b Intermediate principal stress factor (= (σ₂ - σ₃)/(σ₁ - σ₃))

b_h, b_vh, b_hh Cross-anisotropy stiffness parameters; see Equations 2-5

c′ Soil cohesion

e Void ratio

e₀ Specimen initial void ratio

p′ Mean effective stress

p′_in-situ In-situ mean effective stress

p₀′ Initial mean effective stress

p_ref Reference atmospheric pressure (= 101.3 kPa)

q Deviatoric stress

q_c, q_t Measured cone resistance and cone resistance corrected for pore pressure respectively

q_cyc Cyclic deviatoric stress amplitude (= (q_peak – q_trough)/2)

q_f Deviatoric stress at failure

q_mean Mean q applied in stress cycle

q_max Maximum q applied in stress cycle (= q_mean + q_cyc)

q_trough Minimum q applied in stress cycle (= q_mean – q_cyc)

q_PT Deviatoric stress at the phase transformation state

wc Water content

w_L Liquid limit

w_p Plasticity limit

ALPACA Axial-Lateral Pile Analysis for Chalk Applying multi-scale field and laboratory testing

AOD Above ordnance datum

BE Bender element test

CPTu Cone penetration test with pore pressure measurement

CSR Cyclic stress ratio (= q_cyc/p₀′)

C_v, C_h, C_vh, C_hh Cross-anisotropy stiffness parameters, see Equations 2-5

D_R Relative density

DSS Direct simple shear

D₅₀ Mean particle diameter

E_v′, E_h′ Drained vertical and horizontal Young’s moduli respectively

E_v^u, E_h^u Undrained vertical and horizontal Young’s moduli respectively

E_u^TXC Undrained Young’s modulus determined from triaxial compression tests

E_sec^u Undrained secant Young’s modulus

G_hh Shear modulus in horizontal plane

G_hv, G_vh Shear modulus in vertical plane

G_zθ (= G_vh) Shear modulus in vertical plane

G₀ Elastic shear stiffness

G_oct Octahedral shear modulus

G_s Specific gravity

HCA Hollow Cylinder Apparatus

IDD Intact dry density

JIP Joint industry project

KUC K_o-consolidated undrained compression

KUE K_o-consolidated undrained extension

K₀ Coefficient of earth pressure at rest

LVDT Linear variable differential transformer

M Critical state q/p′ stress ratio

M_cs^TXC, M_cs^TXE Critical state stress ratio under triaxial compression and extension

N Number of cycles

N_f Number of cycles to failure

N_kt Cone factor defined as N_kt = (q_t – σ_v0)/S_u

OCR Over-consolidation ratio

PI Plasticity index

PISA PIle Soil Analysis

PT Phase transformation

SCPT Seismic cone penetration test

S_r Saturation degree

S_u Undrained shear strength

S_u^TXC, S_u^TXE Undrained shear strength under triaxial compression and extension

TXC, TXE Triaxial compression and extension respectively

YSR Yield stress ratio

α Angle between the vertical and the direction of σ₁ axis

α_dσ Angle between the vertical and the direction of Δσ₁ axis

α_f Angle between the vertical and the direction of σ₁ axis at ultimate failure

γ_zθ Torsional shear strain

Δu Excess pore water pressure

δ_ult′ Ultimate soil-structure interface shear resistance angle

ε_a, ε_v Axial (vertical) strain

ε_mean Permanent axial strain accumulated in cyclic tests

ε_r Radial (horizontal) strain

ε_s Shear strain (= ε_a for undrained triaxial condition)

ε_z, ε_r, ε_θ Axial, radial and circumferential strains respectively in HCA space

ε_v, ε_h Vertical (axial) and horizontal (radial) strains respectively in triaxial space

ε₁, ε₃ Major and minor principal strain respectively

η Mean stress ratio (= q_mean/p₀′)

ρ_bulk Bulk density

σ₁, σ₂, σ₃ Major, intermediate and minor principal stresses respectively

σ_vʹ, σ_hʹ Vertical and horizontal effective stress respectively

σ_vyʹ One-dimensional (1-D) compression yield stress

σ_v0ʹ In-situ vertical effective stress

τ_zθ Torsional shear stress

ϕ' Effective angle of shearing resistance

ϕ'_cs Critical state shear resistance angle

ϕ′_peak Shear resistance angle at peak

Data availability

Some data that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgements

The first author is deeply grateful to Lidija Zdravković, Erdin Ibraim and Andrea Diambra who provided essential guidance for writing up this paper and lecture. Parts of the laboratory testing campaigns on Cowden till and Dunkirk sand were undertaken to support the PISA JIP project managed by Ørsted. The PISA sponsors’ and Academic Working Group’s support is acknowledged thankfully, as is the financial support provided by Ørsted for the later Post-PISA Experimental Project. The studies on St Nicholas at Wade (SNW) chalk were undertaken as part of the ALPACA project funded by the Engineering and Physical Science Research Council (EPSRC) grant EP/P033091/1 and Royal Society Newton Advanced Fellowship NA160438. The authors acknowledge gratefully additional financial and technical support from Atkins, Cathie Associates, Equinor, Fugro, Geotechnical Consulting Group (GCG), Iberdrola, Innogy, LEMS, Ørsted, Parkwind, Siemens, TATA Steel and Vattenfall. Ken Vinck acknowledges Imperial College’s EPSRC Centre for Doctoral Training (CDT) in Sustainable Civil Engineering and the DEME Group (Belgium) for supporting his doctoral research. The kind support and contributions of many collaborators are acknowledged gratefully including those of Amin Aghakouchak, Reza Ahmadi-Naghadeh, Amandine Brosse, Róisín Buckley, Byron Byrne, Matteo Ciantia, Matthew Coop, Wenjie Cui, Pedro Ferreira, Stavroula Kontoe, James Lawrence, Ross McAdam, Satoshi Nishimura, Catherine O’Sullivan, Giuseppe Pedone, David Potts, David Taborda, Kai Wen, Hongjie Zhou and others. Invaluable technical support by Steve Ackerley, Graham Keefe, Prash Hirani, Stef Karapanagiotidis, Graham Nash and Gary Jones is acknowledged gratefully. Finally, the authors thank their families for their patient and essential support, which was crucial to enabling the presented research.

• Discussion open until November 30, 2024.

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Publication Dates

• Publication in this collection
  20 May 2024
• Date of issue
  2024

History

• Received
  23 Aug 2023
• Accepted
  19 Feb 2024