The axial behaviour of piles driven in chalk

This paper describes research into the poorly understood axial behaviour of piles driven in chalk. Comprehensive dynamic and monotonic axial testing on 27, mostly instrumented, piles undertaken for the ALPACA joint industry projects is reported and interpreted covering: diameters between 139 mm and 1·8 m; lengths from 3 to 18 m; different pile material types; tip and groundwater conditions; and ages after driving. The experiments show the factors that influence resistance most strongly are: ( a ) pile end conditions; ( b ) slenderness ratio and flexibility; ( c ) shaft material; ( d ) age after driving; ( e ) relative water table depth; and ( f ) whether loading is compressive or tensile. Varying the factors systematically identified a remarkable average long-term shaft resistance range from below 11 kPa to more than 200 kPa for piles driven at the same low-to medium-density chalk test site in Kent (UK). Dynamic and static analyses demonstrate that soil resistances to driving were generally well predicted by the Chalk ICP-18 short-term formulation. Considering the piles ’ long-term behaviour, the Chalk ICP-18 approach over-predicted capacity, while the widely used CIRIA approach proved over-conservative for most cases. The research enabled the development of a revised ‘ ALPACA-SNW ’ long-term capacity assessment method that matches the test outcomes far more faithfully.

review the considerable uncertainty that exists regarding the behaviour of piles driven in chalk and describe the design of the ALPACA (axial-lateral pile analysis for chalk applying multi-scale field and laboratory testing) and ALPACA-Plus joint industry projects (JIPs) to address shortfalls in current knowledge.This paper describes how the two JIPs identified the key factors that control the dynamic and monotonic, short-and long-term, axial behaviour of a wide range of driven piles.The paper also sets out an improved design approach.Buckley et al. (2023) report on the ALPACA studies into cyclic axial loading behaviour, while the 2022 final report of the ALPACA Academic Working Group (AWG), 'Monotonic and cyclic lateral loading of piles in low to medium density chalk', prepared for the JIP sponsors describes the JIPs' parallel investigations into monotonic and cyclic lateral loading.

BACKGROUND
Chalk occurs worldwide as a very weak to weak biomicrite limestone, composed of lightly cemented silt-sized calcium carbonate (CaCO 3 ) particles (Mortimore, 2013); it is encountered frequently at foundation depth in northwestern Europe.Conventional design rules have proved critically unable to predict adequately the behaviour of piles driven to support North and Baltic Sea offshore wind turbines (Barbosa et al., 2017;Carotenuto et al., 2018;Buckley et al., 2020a).Refusals have occurred in high-density chalks, while piles have 'run' under self-weight to depths far greater than expected at low-to medium-density sites.Local de-structuration generates thin 'putty' chalk annuli around open-ended piles with undrained shear strength S u , 10 kPa during driving (Hobbs & Atkinson, 1993;Buckley et al., 2018a;Vinck, 2021), which correlates with natural liquidity indices that are high.Doughty et al. (2018) and Vinck (2021) show that dynamic compaction of low-to medium-density chalk at natural water contents leads to similarly weak putties.Axial capacity growth, or set-up, develops after driving and Lord et al. (2002) recommend 120 kPa ultimate shaft shear resistances in highdensity chalk and 20 kPa for other grades, reducing to 10 kPa for piles with slender shafts that experience marked transient elastic lateral displacements, or 'whip', under driving.Loading tests reported by Barbosa et al. (2017) and Vinck (2021) proved capacities that were far higher than predicted, emphasising the need for more economical and reliable design methods.Buckley et al. (2018b) and Buckley et al. (2020a) demonstrated that piles driven in chalk share several of the fundamental features captured in the ICP-05 (Jardine et al., 2005) design approaches for sands and clays, as follows.
(a) Base resistances q b and local shaft radial effective stresses σ′ r and shear resistances τ rz correlate linearly with local cone penetration test (CPT) tip resistance q t .(b) Local σ′ rf and τ rzf reduce sharply as relative pile tip depth h (normalised by R* = (R 2 outer À R 2 inner ) 0•5 ) grows during driving.(c) Axial capacities vary markedly with time after installation, with long-term shaft resistances remaining affected by h/R* and local failure being governed by a Coulomb law with τ rzf = σ′ rf Â tan(δ′).(d ) Laboratory interface ring-shear tests provide accurate operational δ′ angles % 31-32°.Buckley (2018) concluded that σ′ rf also varies with pile diameter-to-wall-thickness ratio D/t w during driving.Working with a sparse set of un-instrumented tension and dynamic tests on open tubular steel piles driven at St Nicholas at Wade (SNW) in the UK and the Wikinger Baltic Sea windfarm, Jardine et al. (2018) and Buckley et al. (2020a) proposed Chalk 'ICP-18' approaches for soil resistance to driving (SRD) and long-term capacity.A tension-to-compression shaft capacity ratio of unity was assumed, as found with clays, although a ratio % 0•75 applies in sands due to principal stress axis rotation effects (Jardine et al., 2005) and 'Poisson' straining of pile shafts (De Nicola & Randolph, 1993).However, analysis of other tests on large tubular steel piles driven at French and German chalk sites by Vinck (2021) and Vinck et al. (2023) indicated a lower ratio % 0•5, including cases where the pile's internal plug had been removed by coring.Implicit in Chalk ICP-18 is marked post-installation set-up.Buckley (2018) interpreted ageing trends from multiple monotonic tension tests on small piles driven (above the water table) at SNW and compressive beginning-of-restriking (BoR) capacities established from dynamically instrumented large piles driven offshore at the Wikinger Baltic windfarm site.Buckley (2018) normalised these capacities by compressive end-of-driving (EoD) SRDs obtained by signal matching of instrumented dynamic records.Ciavaglia et al. (2017) noted similar trends from tension tests on other piles driven (above the water table) at SNW.The interpretation by Buckley et al. (2018a) of the onshore SNW tension tests' slow initial capacity growth, followed by marked gains over the subsequent months, did not recognise that the tension shaft capacities could be considerably lower than those available at the same age in compression.The like-for-like offshore EoD and BoR trends from Wikinger indicated final set-up ratios that reduced with h/R* and progressed more rapidly offshore than at SNW (see Buckley et al. (2020a)).

RESEARCH AIMS
The ALPACA and ALPACA-Plus JIPs aimed to develop reliable, fundamentally based, practical design approaches.As set out by Jardine et al. (2019), multi-scale field experiments were conducted on 41 piles driven at SNW, as shown in Fig. 1(a), with their heights, diameters and relative position to the water table shown in Fig. 1(b).In addition to the cyclic and lateral loading studies, comprehensive programmes of dynamic and monotonic axial experiments were undertaken on 27 piles.Most were equipped with diametrically opposed strings of fibre Bragg grating (FBG) fibre-optical axial strain gauges, configured and processed as recommended by Doherty et al. (2015) and Burd et al. (2020).The influences of groundwater conditions, pile material, embedded length (L p ), diameter (D) and wall thickness (t w ) on SRD, set-up, loading sense (i.e.tension or compression) and long-term axial load-displacement behaviour were examined systematically over 4 years.

ST NICHOLAS AT WADE SITE
The test site comprises a former quarry, located % 2 km inland and 15 km west of Margate, Kent at UK grid TR 25419 66879.Buckley et al. (2018a) and Vinck et al. (2022) describe the Margate and Seaford white chalks encountered and provide full details of the chalk's geotechnical profiles and properties as measured through intensive in situ and laboratory testing.They also note that tectonism, periglacial activity, weathering and geomorphology control the chalk's structure.Most weathered material has been removed, leaving CIRIA grade B2 (Lord et al., 2002) structured, very weak to weak, low-to medium-density white structured chalk with closed to slightly open stained joints and beds of 250 mm average thickness, along with mainly vertically oriented micro-fissures spaced at 10 to 25 mm apart.
The water table lies at % 5•5 to 6 m depth, % 0•9 m above ordnance datum (AOD); suctions measured at 3 m depth with in situ tensiometers fluctuated around 30 kPa.Vinck et al. (2022) report on the piezocone (CPTu) and seismic CPT (SCPT) soundings undertaken close to each pile, nine of which are shown in conjunction with the pile tests reported later in this paper.Vinck et al. (2022) also report on cone pressuremeter testing, P-S logging, cross-hole and down-hole seismic testing, and provide profiles of index, oedometer, simple shear, unconfined compression and Brazilian tension tests.Multiple locally instrumented (drained and undrained) triaxial tests were conducted on block samples and cores from Geobore-S wireline rotary boreholes.Analysis of the data by Vinck et al. (2022) included detailed assessments of sample size effects and small-strain stiffness anisotropy.Liu et al. (2023) report further on the chalk's behaviour under effective stresses up to 13 MPa, as developed beneath the pile tips during driving.
An additional highly relevant topic is how effective normal stress level, interface material, ageing, corrosion and testing procedure affect the interface shearing resistance and shaft radial stress conditions developed around steel piles driven in chalk.Laboratory research by Vinck (2021) found that corrosion affects ultimate δ′ ult mildly, giving angles that exceed destructured chalk's critical state ϕ′ cs % 31°forall cases except (in the short term) stainless steel.However, corrosion is shown later to affect axial capacity markedly through, it is argued, radial effective stress growth around corroding steel piles, in a process comparable to that noted around steel bars in corroding reinforced concrete (Su & Zhang, 2015).The reactions draw in additional air, water and salt molecules to generate products of lower density that expand out, while being constrained radially by very stiff chalk.Noting that air can flow through any open fissures available above the water table, and the need to capture offshore conditions, Vinck (2021) examined howair and salinity affect surface corrosion mass loss rates of prismatic samples (termed coupons) cut from atypically rough pile shaft in contact with chalk.The reaction rates developed over periods of up to 67 days, expressed in μm steel loss per year, were (a) ten times slower in isolated tests than when exposed to air (b) three or more times faster with saline than fresh groundwater (c) comparable between various oxidisable construction steels (d ) ninety times slower with stainless steel and absent with concrete.
Other laboratory testing by Doughty et al. (2018) showed that the stiffness and shearing resistances of chalk that is destructured to putty increase over time through both consolidation and carbonate re-bonding.
TEST PILES Tables 1-4 summarise the considered test piles' sizes, tip conditions and materials.The FBG strain gauges, with the 0•15 to 0•6 m spacings detailed in Table 5, were installed and monitored following the protocols set out by Doherty  Tests reported by Vinck (2021) on other open instrumented steel piles driven in chalk, including one whose internal chalk core had been removed prior to testing, indicate that internal shaft resistance alone could not explain their higher compressive than tension axial shaft capacities.Multiple Mitutoyo SJ-210 gauge measurements were made on the ALPACA piles that indicated pre-driving centre-line-average R CLA pile shaft roughness means of 15•4, 10•1 and 14•2 μm for the oxidisable steel LD, smaller-diameter (SD) and ALPACA-Plus piles, respectively, while the stainless steel and concrete shafts gave 6•0 and 3•8 μm.Noting the chalk's % 3 μm D 50 grain size, all pile shafts provided fully rough interfaces; see Lings & Dietz (2005).

Large-diameter ALPACA series
The open-ended, oxidisable X80 steel, FBG instrumented, tubular LD piles had 508 mm outside diameters (D) and 20•6 mm wall thicknesses (t w ), giving relatively low D/t w % 24•7.Most were driven in November 2017 to tip depths of 3•05 m (% 3 m above the water table with L p /D = 6) or 10•16 m (% 4•2 m below the water table with L p /D = 20).

Smaller-diameter ALPACA series
The SD series included 12 in number 139 mm dia.steel tubular piles (two with FBG strings) fabricated from various steels, driven to tip depths above the water table.Ten open piles were driven from ground level to 38 , L p /D , 40; their 8 to 10 mm wall thicknesses gave 14 , D/t w , 17•5.Tip conditions were investigated by driving two otherwise identical closed-ended steel SD piles.A 200 mm square pre-cast reinforced concrete pile, with D* = 226 m and L p /D* % 24, based on equivalent base area, and a pair of 'crenulated' SM-J steel sheet piles were also driven, with L p /D* % 18 to 19 when D* is defined from perimeter length/π = 290 mm.
Four further 12 m long, 139 mm OD open steel piles and one additional 200 mm factory pre-cast concrete pile, were driven to 6•15 m through pre-bored cased holes that isolated their shafts from the unsaturated chalk.

ALPACA-Plus series
The ALPACA-Plus piles had higher D/t w ratios (41 to 72) and 508 mm, 1220 mm and 1800 mm outside diameters.Axial testing in October 2021 concentrated on piles driven to L p = 18 m, with 10 L p /D 35.Table 4 details how BoR dynamic data recorded over the first blows applied after operational driving pauses, and at two later dates.

ANALYSIS OF DRIVING BEHAVIOUR
The open tubular LD and SD piles required between 9 and 55 blows per quarter metre (bpqm) with the hammers detailed in Table 6 and had total driving times from 2 to 14 min.All open piles generated chalk cores that rose well above ground level, confirming relatively little radial displacement out into the chalk mass.Fig. 2 shows how the volume extruded above ground compared to that of the embedded steel, V pag /V steel , fell systematically with L p /D; open pile cores rarely rise above ground level in sands and clays.
The 200 mm square concrete piles required up to 308 bpqm over up to 81 min to reach target depths with the hammers deployed; the sheet piles required up to 100 bpqm and % 20 min of driving.Table 6 summarises estimates for the average non-dimensional velocity V = vD*/c h (with v = final penetration/driving time) adopting piezocone dissipation test c h = 7 Â 10 À4 m 2 /year (Vinck et al., 2022), and D = 2R* for open piles, after Carter et al. (1980).Finnie & Randolph (1994) argue that penetration is fully undrained for V .30 and principally undrained beneath closed-ended piles if V ranges from 2 to 20.Table 6 indicates low degrees of drainage during driving beneath the larger open piles and higher degrees for the concrete and sheet piles.Dissipation tests at SNW with 43•7 mm dia.piezocones showed pore pressures sensed at the cone shoulders dissipating fully within 80 s.Scaling up by (D*/D CPT ) 2 leads to t 95 estimates for the pile tip areas ranging from % 400 s to % 2 h for the smallest to largest diameter piles.As listed in Table 6, substantial dissipation is likely to have occurred over the driving pauses identified in Table 4.
Pile driving analyser (PDA) strain gauges and accelerometers were mounted on all piles and recorded at 40 kHz.Iterative wave-matching analyses, which applied the shaft and base resistance models in IMPACT (Randolph, 2008), indicated how shaft shear stresses evolved locally as pile tips advanced.Buckley et al. (2020b) considered both FBG and PDA measurements and described how modelling parameters were selected and shaft resistances taken as applying over only the outside shaft areas.The FBG measurements agreed well with high-frequency conventional PDA measurements, and the EoD datasets provided key information on the piles' initial axial resistance profiles.Buckley et al. (2020b), Cathie et al. (2022) and Wen et al. (2023) showed that rigorously conducted stress wave matches provide the best available proxy means of measuring instantaneous EoD resistances, which cannot be measured statically in cases where set-up progresses rapidly.These authors showed that, if conducted and interpreted carefully, stress wave analyses of instrumented dynamic re-strike tests provide shaft capacity estimates that are compatible with trends inferred from static testing.However, dynamic testing offers the only practical means of monitoring rapid early-age set-up, such as occurs in chalks.
Tables 1-4 Buckley et al. (2018a)) giving means and coefficient of variation (CoV) of 24•8 kPa and 0•14, respectively.Also shown are representative q t traces from nearby CPTs and Chalk ICP-18 SRD predictions from equations ( 1) and ( 2), which capture the sharp reductions of local shear resistances with increasing h/R*.
Comparison of the total EoD shaft load between the predictions Q s integrated from the above expressions, taking δ′ ult = 32°and the signal-matching outcomes   q t : MPa τ rzi : kPa q t : MPa τ rzi : kPa q t : MPa τ rzi : kPa q t : MPa Figure 4 presents the signal-matched EoD q b values, evaluated over closed piles' full areas and open piles' annuli, normalised by q t (averaged within 1•5D of the pile tip) and plotted against D/t w (taking 2 for closed piles).The EoD q b /q t ratios decline with D/t w , as expected by Baligh et al. (1987), up to D/t w ratios of at least 25.Equation (3) leads to a better and more conservative fit to the data than the Chalk ICP-18's tentatively suggested q b /q t % 0•6.
Pile set-ups were gauged by monotonic and (for ALPACA-Plus) dynamic BoR tests.Noting that the 5•2 day re-strike on R2 may have set back its subsequent ageing, the 421 day BoR provides a lower bound to the long-term resistance of an equivalent 'virgin' pile, although Vinck (2021) noted that the impact of early re-strikes diminish over time.(Wang, 2021).
Further insight into early-age set-up is given in Fig. 6, where pile R2's signal-matched τ rzi EoD and three BoR τ rz profiles are compared, covering its first re-strike (with L p = 7•2 m) and two later restrikes performed after finally driving to 18 m.

MONOTONIC TESTING
The tension tests all reacted against steel, concrete or timber surface pads, except for TP1, which required reaction piles.Reaction piles and kentledge were also employed for the single compression test.Fig. 7 shows the main components of the testing systems deployed.Displacements were recorded by at least three transducers, referenced to distant datum points and placed at equal angles about the pile axis.Potentiometer devices were used for the LD series tests, while linear variable differential transformers (LVDTs) were employed for the SD tests.Awnings reduced the impact of sun and wind variations.Hydraulic jacks applied steady loading between maintained load stages, the durations of which gradually extended to an hour once creeping became significant.Load cell calibrations were checked when  4).CPT profile also shown required and failure was defined by semi-logarithmic creep movement rates (k s ) remaining . 2 mm/log (t), 1 h after applying the last load step.Most tests involved eight to ten load stages and ended within a day.The piles showed apparently near linear load-displacement behaviour up to relatively (, 6 kPa) low threshold τ avg values.Analysis of the global initial linear response stages of the ALPACA tests made through the approach of Randolph & Wroth (1978), re-derived for tension, led to the results listed in Table 7. Overall, the global operational shear moduli, covering all zones, found over the limited linear range amounted be around 1/4 of corresponding seismic CPT G vh values.Matthews et al. (2000) noted similarly marked discrepancies applying to shallow foundation loading in chalk, which they ascribed to natural discontinuities.
The piles' average shaft shear stresses τ rz values at failure varied widely, from below 11 to over 200 kPa, depending on multiple factors.The analysis below considers separately piles installed entirely (a) above or (b) below the water table and (c) those that spanned both conditions.

Above the water table
Load tests are summarised as curves of average τ rz against non-dimensional pile head displacement w/D, or w/D* for concrete and sheet piles, whose shear resistances were evaluated over their true perimeter areas.The open-ended, steel SD piles' first-time, tension loading curves are presented in Fig. 8  Oxidisable steel open piles.The oxidisable S355, L80/N80 and drill casing open SD piles developed far higher Λ(t) factors.Assuming again a compression/tension ratio = 2, piles SD12 and DP6-T1 showed, after 318 and 246 days, respectively, the highest % 154•1 ± 15•5 kPa resistances and maximum Λ(t) = 8•15.Interface shear tests against oxidisable X80 and S355 steels showed chalk δ′ ult angles growing modestly from % 32°to % 34•5°after long-term ageing with access to air and water (Vinck, 2021).So other processes, which do not act around stainless steel piles, such as radial effective stresses building as corrosion products expand out radially into the very stiff chalk mass, are required to explain the oxidisable piles' long-term set-up above the water table.
Hammer size also affected the piles' EoD resistances and long-term capacities.Buckley et al.'s (2018a) piles, driven with a 4 ton Junttan SHK100-4 hammer that was %2•9 times heavier than that adopted for the ALPACA SD installations (see Table 5), gave particularly high long-term resistances and Λ values.Carroll et al. (2020) noted similar trends with piles driven in sand.Each hammer blow applies an extreme load cycle; it is plausible that less de-structuration occurs beneath pile tips and around shafts when larger hammers deliver significantly lower blow counts.
Figure 9 explores local shaft capacity trends by comparing the 318 days age tension τ rzf profile deduced SD12's FBG strain gauges with its dynamic (compression) EoD profile from Fig. 3(a).Set-up is evident over the whole shaft and most intensive over the mid-section.Also shown is a Chalk ICP-18 prediction evaluated employing the 'long-term' expressions given by Jardine et al. (2018) and Buckley et al. (2020a) with δ′ ult = 32°.While the latter offers a similar shape to the field data, integration indicates non-conservative overall calculated-to-measured capacity ratios, Q c /Q m % 1•74 and % 1•14 for SD12 and DP6-T1, respectively.As set out further below, these and other results identified a clear need to revise the Chalk ICP-18 procedures.
Closed-ended steel and concrete piles.Sampling and laboratory testing, undertaken after the pile experiments, identified the annular zone of chalk that had consolidated to far lower water contents after being reduced to putty by The solid and inert (factory) pre-cast reinforced concrete pile, whose driving permitted greater pore pressure dissipation during driving, also showed a relatively high (125 kPa) long-term tension resistance, reflecting the combined effects of its high driving resistance, post-EoD residual excess pore pressure dissipation and potentially in situ carbonate bonding; see Neugebauer (1975).However, assuming the compression shaft capacity was double that in tension (as with steel piles) indicates a lower long-term Λ(t) % 3 than was developed by the more rapidly driven, and actively corroding, closed steel pile.The closed-end piles failed with 0•03 , w/D , 0•07 and their relatively high shaft capacities gave an average Q c /Q m % 1•0 when compared to Chalk ICP-18 predictions.
The sheet pile tests also showed remarkable set-up.SD10's tension resistance rose well above its EoD compression capacity when, after 3 days, it could not be failed with the equipment deployed.Corrosion led to a 35% stiffer loaddisplacement curve after 317 days for the twin SD9 sheet pile and a remarkable average τ rzf .205 kPa applying after a displacement ratio w/D = 0•055.
Short LD piles.Figure 11 presents the short 508 mm OD X80 steel piles' curves after driving to 3•05 m penetrations.Their τ rzf profiles, deduced from FBG gauges, are given in Fig. 12, with EoD wave matches from Fig. 3(c) and long-term Chalk ICP-18 predictions.The piles failed with w/D , 0•035 and average (tension) τ rzf around 3•9 times the compressive τ rzi values, indicating long-term 'compression' Λ(t) ratios % 7•9 slightly below the SD piles' maxima and reflecting similar long-term processes above the water table, with set-up being greatest over the mid-and lower shaft sections.Long-term ICP-18 calculations capture the maximum observed local resistances (up to 270 kPa), but

Piles driven entirely below the water table
The ALPACA programme included five piles driven through holes pre-bored and cased to avoid contact with unsaturated chalk.As shown in Fig. 13(a), the slowly driven, closed-ended, solid concrete SD17 (L/D* % 47) developed higher long-term resistance below the water table than the equivalent concrete pile (SD19) above the water table.While tensile straining in SD17's 6•5 m of free shaft length led to larger pile head movements, this inert pile's development of a 'compression equivalent' Λ .3•3 was not affected by being submerged.
In contrast, the far higher L/D (% 90) and consequent flexibility of the 139 mm OD steel tubes led to these piles 'whipping' during driving which, as noted by Lord et al. (2002), can halve capacity in low-to medium-density chalk.The piles' 6•5 m unrestrained free lengths allowed them to deflect easily during assembly and testing, potentially further damaging their axial capacity.tension load-displacement curves after 126 to 129 days of ageing, all failing at average low τ rzf (10•7 to 18•7 kPa) and w/D , 0•03.Stainless steel SD13 showed the lowest resistance.Assuming a compression-to-tension ratio of 2 indicates Λ = 0•9, well below the 2•4 applying (at a similar age) to the shorter and less flexible stainless steel SD18 driven above the water table.The oxidisable high L/D piles showed greater capacities below the water table, indicating that corrosion also contributed (albeit modestly and slowly) to their set-up.
Highly flexible piles driven with long unsupported sections clearly develop abnormally low capacities.Much of the compression pile's greater resistance developed over its 0•005 , w/D , 0•075 range, where tangent stiffness slowly reduced towards zero at failure.This is interpreted as reflecting outward Poisson pile straining gradually raising shaft σ′ r and hence τ rzf stresses as growing shaft and base loads compress the shaft and expand it radially.The ratio of compression to tension shaft capacity from LD5 and LD6 is displayed in Fig. 16 together with Vinck's (2021) assessment from similarly paired tests undertaken near Dieppe (France) and Hamburg (Germany) with comparable piles and chalks.An average ratio of at least 2 is indicated, which, as discussed later, was confirmed by long-term ALPACA-Plus tests.
The base capacity (1251•3 kN) mobilised at w/D = 0•075 was found by projecting loads to the tip depth.It exceeds the driving and short-term re-drive tip loads detailed in Tables 1-4, indicating significant set-up and a resistance q b = 6•2 MPa over the entire base area % 0•4q t .Significant loads may have been transferred into the lowest section of the pile shaft through local internal shaft friction, as argued for sands by Jardine et al. (2005).Any internal shaft friction that develops above the lowest strain gauge level is effectively counted as combined with the external shaft resistance.Vinck (2021) provide further guidance based on long-term tests at other sites.
Local τ rzf profiles are plotted in Fig. 17 for LD5, 6 and 7. Also shown are the typical EoD profile from Fig. 3(c) and long-term Chalk ICP-18 predictions.The compression test shows notably higher shaft resistance over its top half, where corrosion was most active, and the pile axial loads (and hence Poisson strains) were greatest.Nevertheless, the long-term Chalk ICP-18 predictions exceed the compression shaft capacity by 60% and those of the tension tests by a larger margin.

ALPACA-Plus piles driven to 18 m depth
The 18 m long TP1 and TP3 piles' tension tests, conducted 373 and 380 days after driving, reached failure with w/D % 0•02, as shown in Fig. 14.Their set-up trends are identified in Fig. 5, while Fig. 18 presents their EoD and monotonic test τ rzf profiles.The 421 day re-strike on the 18 m long, 1220 mm OD, R2 pile indicated average τ rzf = 117•4 kPa in compression, 2•1 times TP1's tension resistance (57•0 kPa), supporting the trend of compression to tension capacity in Fig. 16.A still higher ratio may be inferred if allowance is made for R2's higher, and less advantageous, L p /D.

Overall trends
The ALPACA and ALPACA-Plus axial tests identified ten clear trends.The ALPACA and ALPACA-Plus axial tests confirmed key general features of ICP-18's long-term shaft capacity formulation.However, they also proved the approach required significant recalibration to address the ten points itemised above.The first step was to expand the Coulomb criterion applied to characterise local shaft failure to recognise the impact of loading sense (compression or tension) on shaft capacity, as shown in equation ( 4).
For simplicity, loading factors f L of 2/3 and 4/3 are taken for tension and compression that ensure a shaft capacity ratio of 2. These factors could be refined as further field or theoretical evidence emerges.
Updating is also required for the Δσ′ rd interface dilation term.As highlighted in Table 7, elastic analysis of the pile tests shows the operational shear modulus G ope under pile loading is only 1/4 of that expected from seismic CPT testing.Adopting the finding by Lings & Dietz (2005) that shearing against fully rough interfaces induces a normal (dilative) displacement Δr in granular media comparable to their D 50 grain size under the stress levels applying around pile shafts in chalk, leads to equation ( 5).Iterative analysis indicates that Δr may be taken as % 5 μm and % 3 μm above and below the water table, respectively.
Applying Vinck's (2021) δ′ = 32°and equations ( 4) and ( 5) to the τ rzf -depth profiles presented in Figs 9, 12, 17 and 18 leads to the pre-loading σ′ rc /q t plotted against h/R trends in Figs 19(a) and 19(b) for conditions above and below the water table, respectively.The fitted power law relationships, given as equations ( 6) and ( 7), are subject to h/R minima, below which σ′ rc /q t is constant.They capture markedly steeper σ′ rc /q t decays with pile tip depth than Chalk ICP-18.They also employ h/R without any effective area term being required to avoid skewing with respect to D/t w over the range considered of 15•4-80•8.Alternative correlations with h/R* lead to marginally less satisfactory outcomes.

Above water table
Below water table : The pile-tip factor f tip is 1 for the open piles considered and 3 for closed-ended piles.Intermediate factors may apply over the unexplored 2 D/t w 15•4 range.Any 'internal' shaft resistance developed by open piles under compression loading is assumed to be built into these shaft and end bearing expressions; both sides of sheet piles are considered.
Integrating equations ( 4)-( 7) over the pile shafts provides capacity predictions for 16 ALPACA, ALPACA-Plus and Innovate UK (Buckley et al., 2018a) axial pile tests conducted at ages !120 days at the SNW site.Two deliberately 'non-standard' stainless steel piles (SD13 and 18) were excluded, so were the very high L p /D open-ended steel SD piles driven through cased holes that had experienced whipping during installation.Table 8 summarises the mean Q c /Q m found with the recalibrated long-term approach for this dataset, showing unbiased means and relatively low CoVs for piles driven either entirely above or below the water table, as well as those that span both conditions.In comparison, the CIRIA (Lord et al., 2002) method is systematically over-conservative and Chalk ICP-18 nonconservative, largely because of the latter's assumption of equal tension and compression shaft capacities and less steep 'friction-fatigue' relationship.Set-up factors Λ, which vary strongly with L p /D, may be assessed by dividing the calculated long-term capacities by the SRD values, which are generally well predicted by Chalk ICP-18.
The individual pile test points plotted in scatter diagrams in Fig. 20 confirm that the new method gives no significant bias with diameter D, length L p , L p /D, wall thickness ratio, D/t w or time over the !120 days age range.
Research remains active to assess how well the ALPACA-SNW approach predicts pile tests at other chalk sites, drawing on the case studies collated and reviewed by Vinck (2021) and other data.Further checking at other locations and in denser chalk strata is recommended.

SUMMARY AND CONCLUSIONS
The ALPACA and ALPACA-Plus JIP programmes addressed the uncertain behaviour of piles driven in lowdensity to medium-density chalks through comprehensive dynamic, cyclic, monotonic, axial and lateral testing of piles covering a wide range of scales, materials, groundwater conditions, ages and loading modes, generating a unique high-quality experimental database against which design approaches may be assessed and developed.Buckley et al. (2023) reported the cyclic axial pile loading experiments and showed how their responses may be predicted from laboratory element tests and the 2022 final report of the ALPACA AWG to the JIP sponsors summarised the lateral loading study.
The main outcomes regarding monotonic axial loading are given below.
summarise the interpreted overall EoD shaft and base resistances, while Figs 3(a)-3(e) illustrate the various series' EoD shaft friction profiles.Piles SD20 (open steel), SD5 (closed steel) and SD19 (concrete) represent the SD cases.The long and short 508 mm piles are typified by LD5 and LD13; traces are also shown for the TP1 and TP3 ALPACA-Plus piles.The open piles' average, compressive, τ avg EoD values range from 19•8 to 32•2 kPa (including six 'SD' piles from indicated a mean calculated-to-measured (Q c /Q m ) ratio of 1•00 (with CoV = 0•38) for the open-ended piles listed in Tables 1-4 with reliable τ avg EoD values.Open piles with the lowest L p /D (= 6) values developed the highest EoD resistances, reflecting their lower h/R* values and consequently smaller local τ rzi reductions.Closed-ended steel SD5 showed the lowest (reliable) τ avg EoD value, which fell well below the ICP-18 predictions, reflecting the larger strains and greater destructuration that develop beneath closed pile tips.Baligh et al.

Fig. 2 .
Fig. 2. Variation of the ratio between the above-ground chalk plug volume (V pag ) and embedded steel volume (V steel ) against L p /D

Fig. 3 .
Fig. 3. Profiles of CPT resistance and shaft friction from end-of-driving (EoD) PDA analyses compared against short-term Chalk ICP-18 predictions: (a) SD seriesopen-ended piles; (b) SD seriesclosed-ended piles; (c) LD series; (d) ALPACA-Plus TP1; (e) ALPACA-Plus TP3 Fig. 5 plots against age the average re-strike set-up factors derived from BoR tests conducted on piles whose capacities were primarily developed below the water table, divided by the EoD value from the last blow before any pause commenced, along with t 95 times estimated by scaling up the piezocone dissipation test t 95 times by (D*/D CPT ) 2 as explained earlier.The normalised depths L p /D, to which tips had advanced before each 'test' are also indicated.Table 6 identifies the early-age time ranges over which re-consolidation contributed to set-up.Set-up varies with L p /D, as noted in full-scale offshore Wikinger pile tests by Buckley et al. (2020a).The average set-up trend from eight Wikinger piles covering 0•26 L p /D 14•9 with a mean % 6•8 is shown plotting close to the L p /D = 10 SNW trend curve in Fig. 5. Tentative L p /D contours are plotted whose interpretation combined: (a) BoR data; (b) trends from the monotonic tension tests described below (accounting for the tension-to-compression shaft capacity ratio); and (c) BoR tests on multiple 0•61 m dia.open steel piles driven in 2021 at Tilbury % 70 km east in the (same) Margate and Seaford formations

Fig. 5 .τ
Fig.4.Normalised bearing pressure (q b /q t ) plotted against piles' D/t w at EoD (note: q b evaluated over the closed piles' full areas and the open piles' steel annuli; D/t w taken as 2 for closed piles) along with tests byBuckley et al. (2018a) on identical piles.Average τ rzf failure values varied from 30•2 to 142•3 kPa, with the w/D ratios at which the maximum load was obtained increasing from % 0•02 to 0•07 as the piles aged.Inert stainless steel open pile.The stainless steel SD18 pile developed the lowest tension τ rzf , which was only 20% greater than its (compressive) EoD τ rzi .If, after Vinck (2021), compression shaft capacities are treated as double those in tension, then the like-for-like set-up ratio Λ(t) is 2[τ rzf (tension)/τ rzi (compression)] % 2•4 after 125 days.

Fig. 8 .Fig. 9 .
Fig. 8. Trends for average shaft resistance (τ avg ) plotted against normalised pile head displacement (w/D) for open-ended SD piles embedded fully above water table

Fig. 11 .SD5Fig. 10 .τFig. 13 .
Fig. 11.Trends for τ avg plotted against w/D for LD12 and LD13 (D/t w % 24•7; L p /D = 6) embedded fully above water table.ICP-18 predicts τ avg = 162•0 and 155•2 kPa for LD12 and LD13 Piles with shafts above and below the water table Long LD piles.Tension tests on open 508 mm LD piles driven to 10•16 m (L p /D = 20) are presented in Fig. 14, all failing with w/D , 0•02.Average τ rzf grew from 21•2 kPa (after 66 days) to 39•1 kPa at t .200 days, while the 'equivalent compression' long-term Λ(t) values grew from % 1•8 to % 3•3 over the same age interval.Fig. 5 collates their trends with those from other piles whose shaft capacities developed mostly below the water table.The compression test pile, LD7, illustrated in Fig. 15, indicated Λ = 3•45 at 260 days, although the assessment depends on how loads are extrapolated over the lowest (0•65 m) shaft length.Fig. 15 also shows the average shear stresses evaluated for LD5, LD6 and LD7 down to the deepest strain gauge; the indicated tension τ rzf values are lower than those shown in Fig. 14 because the final 0•65 m contributes so heavily to capacity.

Fig. 14 .Fig. 15 .Fig
Fig. 14.Trends for tension τ avg plotted against w/D for the long LD piles and ALPACA-Plus piles.ICP-18 predicts τ avg = 141•5, 115•1, 99•5 and 144•5 kPa for LD5, LD6, TP3 and TP1, respectively (a) Open-ended and sheet steel piles develop notably lower driving resistances than closed steel and concrete piles.(b) Piles driven at the same site show average long-term τ rzf values ranging from , 11 kPa to .200 kPa.(c) Closed-ended piles displace and de-structure a more extensive region of chalk than open piles.This feature may explain their far higher driving and long-term shaft resistances, as implied, for example, by cylindrical cavity expansion analyses of pile installation effects; see Randolph et al. (1979) or Carter et al. (1980).(d ) Highly flexible piles that 'whip' during driving develop anomalously low long-term shaft capacities.(e) Short-term and long-term shaft resistances fall steeply with h/R* or h/R in all cases.( f ) Marked set-up commences immediately after driving as pore pressures dissipate and total stresses evolve towards equilibrium values under the highly kinematically constrained conditions applying near the pile shafts.(g) Further long-term set-up takes place above and belowthe water table at gradually slowing rates.(h) Corrosion reactions lead to set-up being notably faster (i) around oxidisable steel piles driven above the water table and (ii) with saline rather than fresh groundwater.(i) Compression shaft resistances appear to be at least twice as high as those available in tension.( j) Chalk ICP-18 predicts driving SRD resistances with no overall bias and relatively low scatter, but over-predicts long-term capacity in most cases, indicating a need for careful re-calibration.

Fig. 20 .
Fig. 20.Ratios between calculated and measured capacity (Q c /Q m ) plotted against (a) D, (b) L p , (c) L p /D, (d) D/t w and (e) ageing days: open symbols represent open-ended piles; closed symbols signify closed-ended tubular, concrete and sheet piles.Covers all piles tested at ages !120 days except stainless steel cases and high L/D cased piles that showed whipping on driving (a) Evidence of, and explanations for, a remarkably wide range of axial shaft resistances are provided, with: (i) pile end conditions and material; (ii) L p /D ratio and flexibility; (iii) relative water

Table 2 .
Summary for ALPACA SD steel tubular piles Buckley's (2018)ht above the original ground level.†Tests in tension unless otherwise noted.‡PDAdataquality judged as poor followingBuckley's (2018)approach.Tabulated values represent: (a) either the average EoD τ avg for all open-ended tubular pile cases, = 24•8 kPa, or (b) EoD τ avg of 'twin' pile(s) with similar geometry.

Table 3 .
Summary for ALPACA SD closed-ended sheet and precast concrete piles w : mm L p : m EoD τ avg : kPa EoD q b /q t Age: days Test τ avg : kPa Comment †

Table 5 .
Fibre Bragg grating (FBG) sensor configuration *Number of sensors in one FBG string; all piles instrumented with two diametrically opposite strings.†Value in parentheses is the number of fibre optic temperature sensors.

Table 6 .
Ranges of normalised velocity V and upper-bound full drainage elapsed times after end of driving

Table 7 .
Operational shear moduli derived from linear elastic analyses of initial loading stages of monotonic pile tests again overestimate the overall tension capacities, giving below water table table depth; (iv) age after driving; and (v) whether loading is compressive or tensile.(b) Parallel information is revealed on load-displacement behaviour in tension and compression.(c) It is demonstrated that driving resistances are generally well predicted by Chalk ICP-18, while long-term capacities are over-predicted by this approach.The CIRIA approach is shown to be generally over-conservative.(d ) A new ALPACA-SNW approach is proposed, which fits far more satisfactorily the widely ranging axial capacities measured at SNW on piles driven above or below the water table, when tested after at least 120 days after driving.(e) Independent checking is underway to explore how well the approach performs in predicting research tests conducted at other sites in France, Germany and the UK; further high-quality testing at other sites is strongly recommended.supported by EPSRC grant EP/L016826/1, DEME and Imperial College.The provision of additional financial and technical support by the following project partners is also acknowledged gratefully: Atkins, Cathies, Equinor, Fugro, GCG, LEMS, Ørsted, Parkwind, RWE, Siemens-Gamesa, Scottish Power Renewables and Vattenfall.The authors also wish to acknowledge: Socotec UK Ltd as their main contractor for the field-testing programme; Marmota Engineering AG as the fibre optic strain gauge specialists; Cambridge in situ for the pressuremeter tests; and Lankelma UK and Fugro Geo-services for in situ testing and rotary boreholes.NOTATION c h coefficient of horizontal consolidation D diameter of pile or penetrometer D* equivalent pile diameter based on base area for cylindrical and square piles, and perimeter area for sheet piles D 50 mean particle diameter D/t w pile wall thickness ratio f L axial compression or tension loading factor f s cone penetration test (CPT) sleeve friction f tip open-or closed-end tip condition factor G max maximum shear modulus G ope operational shear stiffness G vh shear modulus in the vertical plane h distance from the pile tip k s increment of creep displacement per log cycle of time L p pile embedded length L p /D pile length ratio Q b pile base capacity Q c /Q m calculated to measured pile capacity q t CPT cone resistance R pile radius R* open-ended pile effective radius R CLA centre-line-average surface roughness S u undrained shear strength t 100 full drainage elapsed time after end of driving t w pile wall thickness V normalised velocity (= vD/c h ) v average pile penetration velocity W pile head displacement Δr radial dilation at pile interface Δσ′ rd change in radial effective stress due to interface dilation δ′, δ′ ult ultimate interface friction angle Λ set-up factor σ′ r radial effective stress σ′ rf radial effective stress at failure σ′ z vertical effective stress τ avg average shaft resistance τ rzi shaft resistance at end of driving τ zf mobilised shaft resistance at failure ϕ′ cs critical state shear resistance angle