Investigation of Cyclic Loading of Aged Piles in Sand | Journal of Geotechnical and Geoenvironmental Engineering

Introduction

Pile Installation and Ageing

Over the last 20 years, numerous research studies have been undertaken to better understand the mechanisms controlling driven pile behavior in sand. Lehane et al. (1993) proposed that the pile shaft resistance can be characterized by a Coulomb failure criteria, where the local shear stress at failure

$τf$

is dependent on the radial effective stress at the pile–soil interface at failure

$σrf′$

and the interface friction angle between the pile material and soil

$δf$

[Eq. (1)]. The radial stress at failure

$σrf′$

can be further separated into equalized radial stress values

$σrc′$

and the change in radial stress due to dilation and principal stress rotation during shearing

$Δσr′$

$τf=σrf′·tanδf=(σrc′+Δσr′)·tanδf$

As a displacement pile is installed in sand, the stresses beneath the pile tip can increase by several orders of magnitude relative to the in-situ conditions (White 2005), resulting in considerable crushing of the underlying sand particles as the pile tip approaches (White and Bolton 2001). As the pile tip advances, the sand is displaced laterally and passes around the pile tip, undergoing large reductions in the radial stresses in the process. Yang et al. (2010), using laboratory model pile testing, identified different zones of material around the shear band, characterized by different levels of particle crushing. The sand along the pile shaft is subjected to repeated cyclic shearing as the pile advances, resulting in a shear zone of varying thickness and a shear band in which the particles are aligned along the pile soil interface.

Following installation, before the main structure is assembled, there will be an ageing period where the applied loading will be small relative to the extreme design loads. The phenomenon of soil ageing in clean sands is well established, whereby an increase in strength and stiffness occurs after deposition or densification (e.g. Mitchell and Solymar 1984; Dumas and Beaton 1988; Jefferies et al. 1988; Schmertmann 1992; and others). This is thought to be due to two main mechanisms:

The mechanisms of pile ageing are less well known, although notable developments have been made in recent years (Jardine et al. 2006; Rimoy et al. 2015; Lim and Lehane 2015; Gavin et al. 2013, 2015; Gavin and Igoe 2019; and others). Chow et al. (1998) considered three possible mechanisms for pile ageing:

 1 Changes in the stress regime leading to increase in equalized radial stress $σrc′$ . 2 Ageing of the disturbed soil leading to increased constrained dilation $Δσr′$ . 3 Chemical corrosion resulting in an increased pile surface roughness and interface friction angle $δf$ .

As part of a long-term field investigation into pile ageing, Gavin et al. (2013) and Gavin and Igoe (2019) presented results from the installation, ageing, load-testing, and extraction of field-scale driven piles in Blessington, which are directly related to the field tests discussed in this paper. Based on these findings and previous work by other researchers, the authors suggest the primary mechanisms for pile ageing are increased constrained dilation (Mechanism B) and physiochemical processes (Mechanism C), resulting in cementation of the shear zone formed during pile driving. A “fresh” (un-aged) pile will experience shear failure at the pile–soil interface. The sand contained within the shear zone will have experienced extreme cyclic shearing, particle realignment, and grain crushing during driving (due to repeated hammer blows). The sand in this zone will likely contract during tension loading (i.e., negative

$Δσr′$

), where stress reversals cause a rotation of principal stresses, resulting in low end-of-driving shear stresses and shaft capacity. Over time, physiochemical processes, accelerated by particle breakage, such as the dissolution and precipitation of silica (Mitchell and Solymar 1984; Baxter and Mitchell 2004), can cause cementation of the sand in the shear zone. When axially loaded to failure, the shear failure zone moves into the sand mass, increasing the friction angle of the shear zone from the soil–steel interface value to a soil–soil value. In addition, creep-induced stress redistribution can lead to increased particle interlocking, resulting in increased dilation and large increases in radial stress during shearing (i.e., large positive

$Δσr′$

). The combination of processes can ultimately result in an up to threefold increase in shaft resistance.

There have been ongoing efforts to improve cyclic axial pile design in sands, with the most notable contributions from Imperial College London (ICL), Institut National Polytechnique de Grenoble (INPG), and others on the grouted offshore piles alternating loading (GOPAL) and piles under cyclic solicitations (SOLCYP) research projects (Jardine and Standing 2012; Tsuha et al. 2012; Rimoy et al. 2013; Puech et al. 2013). The cyclic response of piles in sand has been shown by Tsuha et al. (2012) to be primarily affected by the number (

$N$

$Qmean$

, and cyclic amplitude

$Qcyc$

(Fig. 1) relative to the static capacity immediately preceding the test

$Qs(t)$

$100

. The limited number of piles and wide range of cyclic loading combinations led to multiple tests being performed on the same piles. The influence of prior testing history was accounted for by tracking changes in the tension capacity; however, unavoidable ambiguities were acknowledged by the authors (Jardine and Standing 2012). The analysis of the Dunkirk tests led to the development of cyclic interaction diagrams (discussed later) and a widely used global pile approach for estimating the average degradation of shaft capacity due to cyclic loading. The Jardine and Standing (2012) approach for estimating cyclic degradation stems from the Imperial College pile (ICP) design guidelines (Jardine et al. 2005), which expresses the change in local radial stress acting on the pile shaft due to cyclic loading

$Δσr,cyc′$

as

$Δσr,cyc′σrc′=A(B+τcycτf)NC$

where

$τcyc$

= locally applied cyclic shear stress;

$N$

= number of cycles for a given load level; and A, B, and C = calibration coefficients. By conservatively ignoring the base resistance, neglecting the effect of constrained interface dilation (

$Δσr′$

) on the pile shaft, and assuming that the local reduction in shaft resistance can be applied globally to cover the average degradation of shaft resistance (

$ΔQs$

), Jardine and Standing (2012) proposed the following equation:

$ΔQsQs(t)=A(B+QcycQs(t))NC$

Direct calibration from the Dunkirk results gives the following:

$A=−0.126$

,

$B=−0.10$

, and

$C=0.45$

. A lower limit was applied for one-way cycling when

$Qcyc/Qs,t=Qmean/Qs,t=0.25$

, below which cycling improves rather than degrades capacity. The previous approach is widely used in design practice for estimating the degradation of offshore piles, despite being based on a limited number of tests from a single site. Neglecting the effect of constrained interface dilation (

$Δσr′$

) may be a valid assumption for recently driven piles (due to its small contribution to capacity), but this assumption may no longer be valid for aged piles, where

$Δσr′$

may have a large contribution to the shaft capacity. This paper aims to provide much-needed field test data to inform the axial design of aged piles in sand under cyclic loading. The axial capacity of five steel piles was accurately tracked using a carefully planned load testing regime that considered both ageing and cyclic effects and also the influence of testing on the capacity itself. This paper aims to fill in the gaps in the literature, namely:

 • Investigate the link between ageing and the effects of cyclic loading on the pile capacity. • Investigate the effects of testing to failure and retesting on pile capacity. • Propose new cyclic interaction diagrams and an updated cyclic degradation approach based on the findings in this paper.

Experimental Testing at Blessington

In this paper, axial load testing on open-ended steel piles driven into a dense sand deposit near Blessington, Ireland, is described. Multiple static and cyclic loading tests performed on four steel piles, designated S2, S3, S4, and S6, are discussed in this paper. First-time “fresh” tension tests from each of these piles have been previously reported in Gavin and Igoe (2019) and Igoe et al. (2013). Tension testing was preferred over compression testing to reduce the uncertainty related to separating the shaft and base resistance components for open-ended piles. All piles had identical geometries with an outer diameter

$D$

of 340 mm, wall thickness of 14 mm, and embedded length of 7 m. Pile S6 had two diametrically opposite steel channels welded onto the outer shaft to house strain gauges, and radial stress sensors were embedded in the pile wall at locations offset circumferentially at 90° to these channels, as described in Gavin and Igoe (2019).

Site Description

The pile tests were performed at the upper geotechnical test site located in the Redbog quarry in Blessington, 25 km southwest of Dublin, Ireland. The ground conditions at the site and the sand properties have been reported in Doherty et al. (2012), Igoe et al. (2011), and Igoe and Gavin (2019). Details of the site layout are shown in Fig. 2. The ground conditions were dense to very dense glacially deposited overconsolidated fine sand. Eight cone penetration tests (CPTs) were performed in the area of the pile tests (Fig. 3), and the cone resistance

$qc$

values increased from

$∼10 MPa$

close to ground level to

$∼20 MPa$

at the pile toe 7 m below ground level (bgl). The sand had a mean particle size

$D50$

between 0.1 and 0.15 mm and a fines content (percentage of clay and silt particles) of between 4% and 13%. The water table was well below the base of the piles discussed in this paper, at approximately 13 m bgl.

Pile Installation

Piles S2–S4 were driven using a Junttan PM16 pile-driving rig that had a 4-t hammer and a 0.3-m stroke. Driving was paused every 1 m in order to allow measurements of the stationary radial stress and soil plug length until the target penetration depth of 7 m bgl had been achieved. Pile S6 was driven using a Junttan PM20 piling rig with a 5-t HHK-5A hammer (Junttan Oy, Kuopio, Finland). A stroke length of 0.2 m was used for the first 4 m of installation; this was then increased to 0.35 m for the remainder of the driving process. The installation of Pile S6 was paused every 0.25 m during driving to measure the soil plug length and stationary radial stress.

The driving records for each pile are shown in Fig. 4. The total blow counts required to reach the final penetration of 7 m varied between 529 and 739 blows for Piles S2–S4 using the 4-t hammer and

$∼1,500$

blows for Pile S6 with the 5-t hammer, albeit at a lower hammer drop height for most of the installation. The maximum energy transferred into the piles (EMX) was estimated using the approach adopted in Gavin and Igoe (2019), which was based on linear fit to measured EMX data for the same piling hammers from Flynn and Mccabe (2016). A comparison of the estimated EMX is provided in Fig. 4(b), and it is clear that Pile S6 has significantly lower average EMX for most of installation, which explains the significantly higher number of blows required for installation of Pile S6.

The degree of pile plugging during installation was measured for Piles S3 and S4 using the incremental filling ratio (IFR, incremental change in plug length with respect to penetration), as shown in Fig. 4(c). Due to the difficulty in measuring IFR, the plug length ratio (PLR, ratio of total plug length to pile embedded length) is often used because it can be measured at the end of installation. Piles S2, S3, and S6 developed similar PLRs with a final plug length of

$4.48+–0.02 m$

(

$PLR=64%+–0.5%$

). Pile S4 had a final plug length of 4.75 m (

$PLR=68%$

). A comparison of the IFR profiles from Piles S3 and S4 indicated that all the piles had a similar IFR profiles to 6 m bgl, below which the IFR of Pile S4 deviated and increased over the final 1 m of penetration, resulting in a final

$IFR≈75%$

. The ultimate tension capacity of Pile S4 measured from static load tests (discussed later) was also significantly lower. Although the exact reason for the low capacity of Pile S4 compared with the other piles is unclear, it is postulated here that Pile S4 may have been affected by a local silt pocket at the base of the pile, which could have significantly reduced both the internal and external skin friction over the bottom few meters of the pile. This could explain the change in plugging behavior and also the much-reduced tension capacity, where the bottom 3 m of the pile provides the majority of the shaft resistance.

After installation, the piles were load tested in tension at various time intervals after driving. The tests were scheduled to (1) capture the ageing effects on previously untested fresh piles following driving, (2) to capture the effects of static loading retesting, and (3) to quantify the impact of cyclic loading on aged piles. Full details of the experimental testing program are provided in Table 1. The tension static load tests were performed by Lloyds Acoustics Ltd. using a 5-m loading frame that transferred the load through reaction beams positioned

$≈2.5 m$

$≈1 min$

. The length of the maintained load hold periods did not appear to have a significant influence on the load-displacement response, in agreement with the findings of Jardine and Standing (2012).

Details of pile tests

Table 1. Details of pile tests

Pile (test) Date Age (days) Test type Load (and permanent displacement)
S2 April 28, 2011 0 Driving (Junttan PM16) 695 blows (400-mm drop height)
(S2.Stat1) April 29, 2011 1 Maintained load Capacity = 344 kN (34 mm)
(S2.Stat2) April 29, 2011 1 Quick load Capacity = 332 kN (18 mm)
(S2.Cyc1) April 29, 2011 1 Cyclic load test (20 cycles) Load = 0–220 kN (0 mm)
(S2.Stat3) April 29, 2011 1 Quick load Capacity = 351 kN (16 mm)
(S2.Stat4) May 9, 2011 11 Maintained load Capacity = 430 kN (36 mm)
(S2.Stat5) August 31, 2011 125 Maintained load Capacity = 752 kN (31 mm)
(S2.Stat6) August 31, 2011 125 Maintained load Capacity = 600 kN (23 mm)
(S2.Cyc2) August 31, 2011 125 Cyclic load test (170 cycles) Load = 0–380 kN (0 mm) (stable)
(S2.Cyc3) August 31, 2011 125 Cyclic load test (170 cycles) Load = 0–520 kN (4.7 mm) (metastable)
(S2.Stat7) August 31, 2011 125 Maintained load Capacity = 600 kN, drops to 440 kN (23 mm)
S3 April 28, 2011 0 Driving (Junttan PM16) 739 blows (400 mm drop height)
(S3.Stat1) May 09, 2011 11 Maintained load Weld failed at 525 kN (4.1 mm)
(S3.Stat2) May 11, 2011 13 Maintained load Capacity = 665 kN (59 mm)
(S3.Stat3) May 11, 2011 13 Maintained load Capacity = 595 kN (37 mm)
(S3.Cyc1) May 11, 2011 13 Cyclic load test (20 cycles) 0–440 kN (0 mm) (stable)
(S3.Cyc 2) May 31, 2011 33 Cyclic load test (83 cycles) 0–580 kN (0.25 mm) (metastable)
(S3.Stat4) October 19, 2012 540 Maintained load Capacity = 1,192 kN (28 mm)
(S3.Stat5) October 19, 2012 540 Maintained load Capacity = 875 kN (8 mm)
S4 April 28, 2011 0 Driving (Junttan PM16) 529 blows (400-mm drop height)
(S4.Stat1) May 31, 2011 33 Maintained load Capacity = 385 kN (42 mm)
(S4.Stat1) May 31, 2011 33 Quick maintained load Capacity = 348 kN (30 mm)
(S4.Stat3) July 29, 2011 92 Maintained load Capacity = 520 kN (17 mm)
(S4.Stat4) August 26, 2011 120 Maintained load Capacity = 462 kN (24 mm)
(S4.Stat5) August 26, 2011 120 Maintained load Capacity = 450 kN (17 mm)
(S4.Cyc1) August 26, 2011 120 Cyclic load test (105 cycles) 0–300 kN (

$<0.1 mm$

)

(S4.Cyc2) August 26, 2011 120 Cyclic load test (105 cycles) 0–350 kN (0.6 mm)
(S4.Cyc3) August 26, 2011 120 Cyclic load test (18 cycles) 0–400 kN (63 mm)
S5 April 28, 2011 0 Driving (Junttan PM16) 630 blows (400-mm drop height)
(S5.MLT1) December 4, 2011 220 Maintained load Capacity = 990 kN (20 mm)
S6 May 28, 2012 0 Driving (Junttan PM20) 1,501 blows (200–300 mm drop height)
(S6.Stat1) September 21, 2012 116 Maintained load Capacity = 1,050 kN (28 mm)
(S6.Stat2) September 24, 2012 119 Quick load Capacity = 870 kN (20 mm)
(S6.Cyc1) September 25, 2012 120 Cyclic load test (400 cycles) 0–300 kN (0.05 mm)
(S6.Cyc2) September 26, 2012 121 Cyclic load test (100 cycles) 0–400 kN (0.1 mm)
(S6.Cyc3) September 26, 2012 121 Cyclic load test (750 cycles) 0–520 kN (1.8 mm)
(S6.Cyc4) September 27, 2012 122 Cyclic load test (8 cycles) 0–620 kN (20 mm)
(S6.Stat3) September 27, 2012 122 Quick load Capacity = 620 kN (19 mm)

Cyclic load tests were applied using a specially fabricated cyclic loading unit that consisted of an electronically controlled two-way hydraulic actuator with pressure control and release valves, powered by an electric motor. The cyclic setup was programmed to ramp between predetermined hydraulic pressures (loads) with fixed cyclic periods of 10 s (0.1 Hz), which is typical for offshore environmental loading (Jardine et al. 2012).

Results of Repeated Static Load Testing

The results of the multiple static reload tests on each pile are described in this section. Pile S2 was initially load tested 1 day after driving and was used as the reference pile for the 1-day capacity. The complete load-displacement response for all tests conducted on Pile S2 is shown in Fig. 6(a). Multiple static tension tests to failure 1 day after installation (S2.Stat 1–3) did not result in any reduction in pile capacity, indicating that the 1-day capacity

$Qs,1–day$

may represent a lower-bound limit for the pile capacity. Static tension tests on the same pile conducted after an ageing period of 11 and 125 days (S2.Stat4 and Stat5) showed an increase in capacity due to ageing; however, the capacities remained lower than fresh piles, indicating that performing multiple tests to failure on the same pile had reduced the ageing effect. Two further static tension tests performed at 125 days (S2.Stat6 and Stat7) to assess the effect of the retesting on the aged pile capacity showed a significant reduction in pile capacity, with the final capacity only 30% higher than

$Qs,1–day$

. The findings from Pile S2 indicate that cyclic degradation only affects the ageing component of pile capacity (

$Qs,ageing=Qs(t)–Qs,1–day$

).

Multiple static tests performed on Piles S3, S4, and S6 are provided in Figs. 6(b–d), respectively, and show the same trends for increase in capacity due to ageing and reduction in capacity due to static testing to failure. Further discussion and interpretation of the static test results are provided in the following sections.

The results of the cyclic load tests on all piles are presented in Fig. 7, where the applied head load (gray lines) and displacement (black lines) are plotted against cumulative number of cycles. A summary of the cyclic tests including load levels and pretest capacities is provided in Table 2. The cyclic behavior of the test piles is described in terms of stable, metastable, and unstable behavior. The majority of cyclic tests exhibited stable behavior with no accumulated displacements or failure. Three tests, S2.Cyc3, S4.Cyc2, and S6.Cyc3, exhibited apparent metastable behavior, where displacements continue to accumulate, but were not cycled long enough to reach failure. A problem with the displacement transducers during S2.Cyc3 resulted in some data loss for the first 50 load cycles, but an estimate of the initial displacements based on the remaining load cycles suggests a metastable loading response with

$≈3 mm$

of permanent displacement accumulated during the test. Only two cyclic tests, S4.Cyc3 and S6.Cyc4, were cycled to failure, where capacity reduction led to large plastic displacements.

Blessington cyclic tests

Table 2. Blessington cyclic tests

Test No.

$Qs,1–day$

(kN)

$Qs,measured$

(kN)

$Qs,ageing$

(kN)

$Qs(t)$

(kN)

$Qmean/Qs(t)$

$Qcyc/Qs(t)$

$Nf$

Stability
S2.Cyc1 338 340 2 339 0.32 0.32 No failure Stable
S2.Cyc2 338 600 262 600 0.33 0.33 No failure Stable
S2.Cyc3 338 600 262 600 0.43 0.43 No failure Metastable
S3.Cyc2 347 595 248 751 0.38 0.38 No failure Metastable
S4.Cyc1 337 450 113 438 0.34 0.34 No failure Stable
S4.Cyc2 337 450 113 438 0.40 0.40 No failure Metastable
S4.Cyc3 337 450 113 438 0.46 0.46 18 Unstable
S6.Cyc1 343 870 527 689 0.22 0.22 No failure Stable
S6.Cyc2 343 870 527 689 0.29 0.29 No failure Stable
S6.Cyc3 343 870 527 689 0.38 0.38 No failure Metastable
S6.Cyc4 343 870 527 689 0.45 0.45 8 Unstable

Discussion

Interpretation of Pile Ageing and Static Testing to Failure

By performing a comprehensive load test program involving multiple static and cyclic tension load tests on four separate piles, the effects of ageing and cyclic loading on the piles were accurately assessed. Fig. 8(a) shows an intact ageing trend from the untested fresh pile tension capacities, previously described in Gavin and Igoe (2019). It is clear that Pile S4 is an outlier, where the capacity falls significantly below the intact ageing trend. Fig. 8(b) shows the pile tension capacities for all static tests described in this paper normalized by their respective 1-day capacity

$Qs,1–day$

. Because only Pile S2 was load tested 1 day after driving, and in order to account for soil variability between the piles,

$Qs,1–day$

was calculated for each pile using the CPT-based UWA-05 axial pile design method (Lehane et al. 2005) and applying an ageing factor of 0.65 to account for the reduced capacity 1 day after driving. The UWA-05 method was favored over other methods, such as the ICP-05 method (Jardine et al. 2005), due to its ability to account for partial plugging through the IFR term and its excellent match with the 1-day capacity from Pile S2 (

$Qs,UWA×0.65/Qs,measured=0.99$

).

For aged piles, multiple static load tests to failure can result in significant capacity degradation. However, for piles that have not experienced capacity increases due to ageing, no decrease in capacity was noted, as seen from the multiple static failures performed on Pile S2 1 day after driving. This would suggest that the 1-day tension capacity

$Qs,1–day$

represents a lower-bound capacity for cyclic degradation. This seems logical, considering: (1) the dynamic shear stress cycles imposed during pile driving are likely to be significantly more severe than those during in-service cyclic loading, and (2) the radial stress reduction due to principal stress rotations that occur during tension static loading is not likely to be amplified by cyclic loading. In all cases, even after severe cyclic loading and multiple failures, the capacity of the piles never dropped below the reference 1-day capacity. Similar behavior at Dunkirk was noted by Jardine et al. (2006) and Jardine and Standing (2012).

Even after the piles had experienced multiple failures, large capacity increases due to ageing were noted. The slopes of the normalized capacity–time plots [Fig. 8(b)] were similar between fresh and prefailed piles, the difference being that each failure on an aged pile caused significant reductions in the aged capacity. One exception to this was the rate of capacity growth for Pile S2 over the first 11 days after driving. In order to quantify the shaft capacity degradation caused by large displacement single-cycle static failures on aged piles, the capacity change measured between two consecutive static failures (

$ΔQs$

) is plotted against the pretest capacity gains due to ageing (

$Qs,ageing$

) in Fig. 9. A linear trend-line provides an excellent fit to the data and suggests a strong correlation between capacity degradation and ageing, such that each single-cycle static test caused an average 35% drop in the ageing component of the capacity:

$ΔQs=−0.35×Qs,ageing=−0.35×(Qs(t)−Qs,1–day)$

However, after two successive failures (with no ageing in between), no further capacity reductions were seen to occur, as was the case for Piles S4 and S6. Similar reductions in the aged pile tension capacity were noted during two consecutive tension load tests on Pile R6 at Dunkirk (Jardine and Standing 2000).

Interpretation of Cyclic Tests

In light of the previous observations, the

$Qs(t)$

values from the Dunkirk load tests were reinterpreted on the basis that a static load test would result in an average 35% drop in the aged component of pile capacity. In the cases where the static load test immediately preceding cyclic loading did not reach failure, or where there was a significant ageing period between static testing and cyclic loading, the best estimate

$Qs(t)$

values originally proposed by Jardine and Standing (2012) were used. Table 3 provides the new reinterpreted

$Qs(t)$

values compared with the original values. The reinterpreted Dunkirk data (square symbols) and new Blessington test data (circle symbols) were compared with cyclic interaction diagrams proposed by Jardine and Standing (2012) in Fig. 10. The data are plotted as the mean (

$Qmean$

) and cyclic (

$Qcyc$

) amplitudes normalized by the available tension capacity

$Qs(t)$

(accounting for the effects of prefailure) with stable behavior noted by open symbols, metastable with gray symbols, and unstable with black symbols. Despite the difference in the sand state and pile geometry (and therefore pile capacities) at the two sites, the data are remarkably consistent. The new data suggest the boundary lines proposed by Jardine and Standing (2012) are slightly conservative and new boundary lines, 15%–20% higher, appear to offer a better fit to the data.

Re-interpretation of Dunkirk cyclic tests

Table 3. Re-interpretation of Dunkirk cyclic tests

Test No.

$Qs,1–day$

(kN)

$Qs,measured$

(kN)

$Qs,ageing$

(kN)

$Qs(t)$

old (kN)

$Qs(t)$

new (kN)

$Qmean/Qs(t)$

$Qcyc/Qs(t)$

Stability

$Nf$

2.C1.CY3 437 820 259 840 696

$−0.06$

0.86 Unstable 41
2.C1.CY5 437 696 181 620 619 0.02 0.66 Unstable 12
3.R2.CY2 904 3,210 1,499 2,500 2,403 0.42 0.42 Unstable 9
2.R3.CY2 930 2,315 1,078 2,315 2,008 0.35 0.35 Metastable 200
2.R3.CY3 930 2,315 1,121 2,050 2,050 0.46 0.46 Unstable 13
2.R4.CY2 1,105 2,000 1,858 2,963 2,963 0.34 0.34 Metastable 221
2.R4.CY4 1,105 2,000 995 2,100 2,100 0.60 0.36 Unstable 3
3.R4.CY6 1,105 2,100 1,005 2,110 2,110 0.19 0.19 Stable No failure
2.R5.CY2 923 2,000 1,542 2,465 2,465 0.41 0.41 Metastable 345
2.R5.CY3 923 2,000 720 2,000 1,643 0.43 0.43 Unstable 27
2.R6.CY2 826 2,450 1,175 2,000 2,000 0.63 0.38 Unstable 1
2.R6.CY4 826 1,585 760 1,585 1,585 0.44 0.44 Unstable 24
3.R6.CY6 826 1,325 825 1,650 1,650 0.42 0.42 Metastable 206

In order to calculate the global degradation due to cyclic loading, the approach proposed by Jardine and Standing (2012) in Eq. (3) can be modified to account for the new findings in this paper by including a normalized ageing term as follows:

$ΔQsQs(t)=a(Qs,ageingQs(t))(b+QcycQs(t))Nc$

The average

$Qs,ageing/Qs(t)$

for original Dunkirk piles was 0.54, and therefore adopting values of

$a=−0.234$

,

$b=−0.1$

, and

$c=0.45$

will match the original Eq. (1) calibration well. For one-way cycling where

$Qcyc=Qmean$

, failure will occur when

${(ΔQs)/[Qs(t)]}=2{(Qcyc)/[Qs(t)]}−1$

, and therefore Eq. (5) can be rearranged to calculate the number of cycles to failure as follows:

$Nf=[(2QcycQs(t)−1)a(Qs,ageingQs(t))(b+QcycQs(t))]1c$

Direct calibration against the Dunkirk and Blessington field test results was undertaken using constrained optimization, minimizing the square of the difference between the calculated and measured

$Nf$

values for each cyclic test. The calibration gives the following values:

$a=−0.206$

,

$b=−0.100$

, and

$c=0.390$

. The combined contribution of number of cycles, cyclic amplitude, and ageing using Eq. (5) to predict cyclic degradation can be visualized using a three-dimensional (3D) surface plot, as shown in Fig. 11. The different surfaces in the plot represent different levels of ageing contribution to pretest capacity. Standard axial pile design methods, such as the ICP-05 and UWA-05 design approaches, are calibrated to predict the medium-term (10–30-day) capacity. Although these methods do not explicitly consider ageing affects in the standard calculations, they have an inherent ageing component

$Qs,ageing/Qs(t)≈0.33$

based on their calibration, which is the top dark gray surface shown in Fig. 11. Piles designed with larger ageing components

$Qs,ageing/Qs(t)=0.5$

and 0.67 are also shown, along with the cut-off surface representing the number of cycles to failure from Eq. (6) (black surface). It is clear from the figure that the rate of capacity degradation is highly dependent on the ageing and that cyclic capacity degradation for piles that are designed without ageing effects may be significantly lower than currently considered.

References

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