INTRODUCTION

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A study (referred to as PISA) has been completed, employing field testing and three-dimensional (3D) finite-element modelling, to develop a new design approach for monopile foundations for wind turbine support structures in North Sea waters. A broad overview of the project, a general description of the field tests, and details of the site characterisation programme are given in the papers by Byrne et al. (2017) and Zdravković et al. (2019a).

This paper describes the field testing conducted as part of the PISA study on a set of reduced-scale monopiles at a test site at Cowden in the UK. McAdam et al. (2019) describe a similar set of tests conducted in a dense sand site at Dunkirk. The soil at the Cowden test site consists principally of a heavily overconsolidated glacial clay till, which is broadly representative of the Bolders Bank material that extends beneath the North Sea; a description of the geotechnical characterisation of the test site is given in the paper by Zdravković et al. (2019a). Testing was conducted on scaled monopiles of three diameters (0·273 m, 0·762 m and 2·0 m) using the test protocols and instrumentation described in the paper by Burd et al. (2019). Most of the tests were conducted at the same (controlled) value of ground-level pile velocity; a few tests were conducted at higher displacement rates to allow the effects of rate on the pile response to be observed. Selected tests were repeated, to allow the repeatability of the testing protocols to be assessed.

The results obtained from the Cowden field tests, together with associated 3D finite-element studies, have contributed to the development of a new design approach, termed the ‘PISA design model’. The current paper, however, is focused entirely on reporting the data that were obtained from the Cowden tests; the application of the data to model development will be the subject of future publications (although the principles that have been employed in the development of the PISA design model are outlined in the papers by Byrne et al. (2017) and Zdravković et al. (2019a)). The 3D finite-element model that has been developed to support the interpretation of the Cowden tests is described in the paper by Zdravković et al. (2019b).

There is, of course, a significant literature concerning laterally loaded piles in clay, with recent work relating to monopile applications. Previous experimental work that is applicable to the validation of design methods includes laboratory testing, typically in the centrifuge (e.g. Truong & Lehane, 2018), and field testing (e.g. Matlock, 1970; Zhu et al., 2017). The well-established ‘p–y’ method for the analysis of laterally loaded piles in clay, for example, was developed principally from pile tests conducted at two soft clay sites by Matlock (1970). These particular tests involved piles of diameter 0·324 m, but they focused on the long, relatively flexible piles (length-to-diameter L/D ratio of 40) typically used for jacket structures in the oil and gas industry. However, the geometry and size of the piles currently adopted for offshore wind applications present a significantly different design scenario; current monopiles may be 8 m in diameter, for example, with values of L/D between 3 and 6. Such piles tend to behave in an approximately rigid manner, especially at the ultimate limit state. Therefore, although the smaller piles for the PISA tests have a similar diameter to the pile diameter employed by Matlock (1970), they are specified to have significantly smaller values of L/D, consistent with current monopile designs.

Much of the current field test data for piles installed in clay soils, including the Matlock tests, are concerned with soft clays; this is in part driven by the need to understand lateral pile response for region-specific applications (e.g. Gulf of Mexico). In laboratory model tests, kaolin clay samples are typically used, being a well-established benchmark soil, with a well-described constitutive response. However, these materials have constitutive behaviours that are different from North Sea clays, which tend to be dominated by overconsolidated stiff tills. A key driver for the PISA field testing programme was to explore pile response in typical North Sea soils; this led to the choice of the stiff glacial clay till site at Cowden for the test programme. Glacial tills are difficult, if not impossible, to replicate reliably in the laboratory for model testing.

Most of the published pile tests, including the Matlock tests, employ either a free or fixed head condition at ground level. The PISA tests employed a significantly different configuration, in which loads were applied at raised elevations above the pile head; these loading conditions were designed to conform closely to the likely conditions experienced by offshore wind monopiles.

In view of the above considerations, it was considered that a new field testing programme was required to support the development of the new design method for offshore monopiles, as envisaged in the PISA research. In particular, the tests: (a) employed modern instrumentation, monitoring and loading systems to produce high-quality data for a range of test configurations; (b) addressed the typical geometric loading conditions for wind turbine monopiles; (c) focused on soil conditions at North Sea wind farm sites; (d) contributed test data at a credible scale to provide confidence in the application of the results.

SMALL-DIAMETER (D = 0·273 m) TEST RESULTS

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The small-diameter piles (D = 0·273 m) were selected as the first set of tests to be conducted. This provided an opportunity to check the operation of the control system before embarking on the more valuable medium- and large-diameter pile tests. The first test, on pile CS1 (L/D = 5·25), resulted in a failure of the control system; as a consequence, the pile was loaded rapidly (at 465 mm/min) to failure. Interestingly, this unplanned event indicated the possibility that the pile performance could be significantly enhanced by increasing the rate of loading; further discussion of rate effects is given later in this paper. The other small-diameter pile tests (CS2, CS3 and CS4) provided opportunities to refine the test set-up, control and analysis procedures.

The ground-level load–displacement response of the three monotonic small-diameter pile tests (D = 0·273 m) excluding CS1 are shown in Fig. 4. Fig. 4(a) shows the response of CS2 (L/D = 5·25), in which early stages of the test exhibited significant noise on the measured response during the creep periods. This noisy response occurred due to excessive gain in the proportional component of the load feedback loop controller. The gain was adjusted for subsequent tests, resulting in improved stability during the creep periods, as shown in Figs 4(b) and 4(c).

Fig. 4. Comparison of load–displacement response for D = 0·273 m diameter piles with different length-to-diameter ratios: (a) L/D = 5·25 (CS2); (b) L/D = 8 (CS3); (c) L/D = 10 (CS4); (d) three L/D ratios

Figure 4(d) shows a comparison of the three length-to-diameter ratio tests conducted on the small-diameter piles. The effect of an increased (L/D) is clearly seen, with a strong correlation between pile length and ultimate load. The ultimate response for these piles is influenced by the marked non-homogeneity in soil strength near the soil surface (shown in Fig. 1). As a consequence, direct comparisons cannot be made between the three pile responses. The relatively low tangential stiffness of the medium length (L/D = 5·25) pile at the ultimate displacement (v_G = D/10) indicates that soil failure had occurred over a significant proportion of the embedded pile length when the test was terminated. However, the L/D = 10 pile exhibits a significant tangential stiffness when the test was terminated, suggesting that peak soil capacity would not occur until a substantially higher load is applied – before which yielding of the pile is likely to occur.

After unloading the L/D = 10 pile, it returns to a relatively small residual displacement. This observation suggests that, for the longer pile geometry, a smaller proportion of soil along the embedded pile length experiences significant plastic deformation, with the consequence that a greater amount of elastic energy in the soil–pile system is available for recovery.

Figure 5 shows the results from the small-diameter (D = 0·273 m) pile tests during the initial load stages and unload–reload loop. Fig. 5(a) illustrates the measurement noise that is also evident in Fig. 4(a). Fig. 5(b) shows that, for pile CS3 (L/D = 8), this noise has been broadly eliminated. However, an imbalance in the proportional and integral components of gain in the control system during the displacement-controlled load stages resulted in an accumulation of integrated error; causing an overshoot of the target displacement and a series of small loops in the load–displacement response. However, it is not expected that the fluctuations in load and displacement for the CS2 and CS3 tests will have had a significant effect on the overall pile response. Subsequent refinement of the control parameters resulted in a significant improvement in the system performance, as indicated in Fig. 5(c).

Fig. 5. Comparison of load–displacement response for D = 0·273 m diameter piles with different length-to-diameter ratios during initial load stages 1–4: (a) L/D = 5·25 (CS2); (b) L/D = 8 (CS3); (c) L/D = 10 (CS4); (d) three L/D ratios

Figure 5(d) shows a comparison between the initial load stages for the three small-diameter pile tests. The non-linearity in the response for CS2 suggests that, even during early stages of the test, significant plasticity occurs in the soil. The similarity in response for CS3 and CS4 suggests that the soil at an embedment length greater than L/D = 8 is not mobilised in any significant way at this relatively low level of loading.

MEDIUM-DIAMETER (D = 0·762 m) PILE TESTS

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Pile diameters of 0·762 m were adopted for the majority of tests to provide a means of exploring influences of pile length, wall thickness and loading rate. Although a considerable amount of experience on the optimisation of the control system had been acquired during the small-diameter tests, further tuning of the control system was required to enable the medium-diameter tests to proceed in a stable way.

Repeatability

To provide a check on repeatability, two similar tests, CM2 and CM8, L/D = 3, were conducted. The results, shown in Fig. 6(a), indicate that the two datasets are closely correlated, particularly up to load stage 7. Subsequent creep periods and load stages for pile CM8 were significantly affected by loading spikes, caused by a sticking ram. These load spikes probably induced additional displacements during the creep periods.

Fig. 6. Repeat medium diameter (D = 0·762 m) pile tests: (a) L/D = 3; (b) L/D = 5·25

Figure 6(b) shows the loading up to stage 4 for the three medium length (L/D = 5·25) pile tests, after which the loading differed for the three tests. However, even up to stage 4, the three sets of data are not exactly similar. Possible reasons for these observed differences include the following.

•	Pile CM9 was previously used as the reaction pile for the small-diameter pile tests, and was subsequently tested using the standard monotonic load regime in Table 2.
•	Pile CM6 involved the standard monotonic load regime for the first five load stages, before being subjected to cyclic loads. In contrast to the other monotonic pile tests conducted at Cowden, a shallow reservoir of water was retained around the base of pile CM6 to ensure that any gap that developed around the pile during the test would fill with water. The additional hydrostatic force on the active face of any gap will tend to reduce the measured stiffness and capacity of the pile; this may partially explain the relatively soft response of this pile as indicated in Fig. 6(b).
•	Pile CM1 had a larger wall thickness (t = 15 mm) than CM6 and CM9 (t = 11 mm). This increased wall thickness is likely to have had a small influence on the overall stiffness of the pile response (although numerical analyses suggest that small variations in pile wall thickness of this magnitude are unlikely to have a significant effect on performance).

Response comparison

Figure 7 shows the ground-level load–displacement response for the three medium-diameter pile tests (D = 0·762 m), with L/D = 3, 5·25 and 10. The spikes in the test results for pile CM9 (L/D = 5·25) that are apparent in Fig. 7(b) occurred due to the use of an oversized hydraulic loading ram, for which the friction in the piston and seals occasionally caused stick/slip behaviour to develop. These infrequent and small-magnitude stick/slip events are not expected to have had a significant effect on the overall performance of the pile. Fig. 7(d) shows a comparison of the responses of each of the three piles. As expected, the longer pile exhibited a higher capacity and tangential stiffness when the test was terminated according to the displacement criteria described above. It is also seen that, in this case, the residual displacement reduces with increased pile length.

Fig. 7. Comparison of load–displacement response for D = 0·762 m diameter piles with different length-to-diameter ratios: (a) L/D = 3 (CM2); (b) L/D = 5·25 (CM9); (c) L/D = 10 (CM3); (d) three L/D ratios

Figure 8 shows the interpreted ground-level load–displacement response for the medium-diameter pile tests during the initial load stages. The measured response of CM2 (L/D = 3) in Fig. 8(a) shows an overshoot during each loading stage, before settling to the target load. Owing to the relatively short embedded length of this pile, the ratio of rotation to lateral displacement was relatively high. As a consequence, the loading system was required to apply large displacements at the pile head to achieve the desired ground-level displacement. This behaviour caused the loading system to overshoot. This was addressed later in the test by using a higher proportional gain in the displacement feedback loop, to minimise the accumulated integral error. The overshoot events seen in Fig. 8(a) are not expected to have affected significantly the subsequent pile performance.

Fig. 8. Comparison of load–displacement response at small displacement for D = 0·762 m diameter piles with different length-to-diameter ratios: (a) L/D = 3 (CM2); (b) L/D = 5·25 (CM9); (c) L/D = 10 (CM3); (d) three L/D ratios

Figure 8(d) indicates that the stiffness of response during the initial load stages differs significantly between the three medium-diameter pile tests of different lengths.

LARGE-DIAMETER (D = 2·0 m) PILE TESTS

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The two large-diameter (D = 2·0 m) piles were loaded against each other to provide two simultaneous tests. These large-diameter pile tests were the last to be conducted.

Figure 9 shows the load–displacement response for the large-diameter CL1 and CL2 (D = 2·0 m) piles. Fig. 9(b) indicates that the initial responses are almost identical, with pile CL2 exhibiting a marginally stiffer response after load stage 3. Pile CL2 achieved an ultimate load,

$H_{0\cdot 1D}$

(where

$H_{0\cdot 1D}$

is defined as the lateral load applied to the pile at

$v_{\mathrm{G}}=0\cdot 1D$

) that is 5·0% higher than that recorded for CL1; this close agreement provides further confidence in the consistency and repeatability of the tests.

Fig. 9. Large-diameter pile response: (a) overall monotonic response; (b) small displacement response

RATE EFFECTS

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As described earlier, the rapid loading of pile CS1 (D = 0·273 m, L/D = 5·25) provided an unplanned, but nevertheless useful, indication of the significance of loading rate. Test CS1 was followed by an equivalent test (CS2). Testing on CS2 proceeded as originally planned (i.e. according to the loading schedule in Table 2). As a consequence, comparisons between CS1 and CS2 provide an indication of the influence of the rapid rate of loading applied in CS1. The responses are compared in Fig. 12(a). The increase in loading rate by a factor of 510 resulted in an about 90% increase in the pile capacity, equivalent to a 33% increase in strength per log₁₀-cycle of loading rate.

Fig. 12. Varied loading rate tests: (a) CS1 and CS2 (D = 0·273 m, L/D = 5·25); (b) CM1 (D = 0·762 m, L/D = 5·25)

The test programme was therefore adjusted to allow a further investigation on rate effects, as follows. A bespoke experiment was devised for pile CM1 (D = 0·762 m, L/D = 5·25). In this test, the first five load stages of the standard monotonic loading regime (Table 2) were applied. Immediately following stage 5, consecutive ground-level displacement increments of approximately 23 mm were applied, alternating between a ‘fast load rate’ (average of 430 mm/min) and a ‘slow load rate’ (average of 1·65 mm/min). The results are shown in Fig. 12(b). Individual cubic spline fits to the first five load stages and the subsequent fast and slow load stages suggest a difference in load of about 20% between the inferred backbone curves for the fast and slow phases. This corresponds to an increase in capacity of about 8% per log₁₀-cycle, a rather less significant effect than observed in the CS1/CS2 tests.

It is well established that the strength of clay depends on the rate at which it is loaded. It is typically understood that a 10–20% increase in undrained shear strength occurs for each cycle of loading rate (Dayal & Allen, 1975). Brown & Hyde (2008) report rate effects for the axial capacity of piles from field tests in a similar till at a site near to Cowden. Although the current results are insufficient to quantify the effects of loading rate for incorporation within design methods, it is clear that monopile foundations in clay, designed on the basis of the strength of the ground under slow loading conditions, may have significant reserves of strength in cases (e.g. storm wave or ship impact) when significant loads are applied for only a short duration.

PILE GAPPING

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During the pile tests a gap was invariably seen to develop on the active face of the pile (and sometimes also on the passive face after unloading). Table 4 shows the depth of the gap below ground level on the active pile face, measured using a metal tape at the end of each test (i.e. after the final unload stage). Typically, a significant gap that is of the order of half the embedded depth of the pile is seen to occur (L_G/L varies from 0·43 to 0·74). The possibility of gap formation is regarded as an important feature of monopile behaviour, as the presence of a gap may have a significant influence on the pile response. Lack of contact between the pile and the soil over a significant proportion of its surface area will reduce the pile stiffness, which in turn may influence the overall dynamics of the pile/tower system. Note, however, that the gaps reported in Table 4 were developed after the application of loads that substantially exceed the likely in-service conditions for a prototype foundation. The tendency for gaps to form around a monopile under normal working loads is likely to be considerably less marked than indicated in the data in Table 4.

Table 4. Test pile active face gap depths

INFERENCES ON THE EMBEDDED PILE RESPONSE

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Embedded instruments (inclinometers and strain gauges) were installed in all of the large-diameter piles and most of the medium-diameter piles (Table 1). Careful consideration was given to (a) the range of useful data on pile performance that can be inferred from these measurements and (b) the development of appropriate techniques to establish robust information on pile performance (e.g. for incorporation within the design model development scheme shown in Fig. 2 of the paper by Zdravković et al. (2019a)). Note that below-ground strains were measured using two independent systems, fibre optic (FO) strain gauges and extensometers (see Burd et al. (2019)). As discussed in the paper by Burd et al. (2019), a review of the strain data led to the conclusion that the extensometer measurements were significantly less reliable than the fibre optic data. As a consequence, the data analysis presented here is based solely on strain data from the fibre optic sensors.

A typical set of below-ground data, for CM3, is shown in Fig. 13. In processing these data, two separate issues are considered. First, curvatures inferred from inclinometer data are expected to correlate with the bending moments inferred from strain gauge data. It is desirable therefore, when assessing the below-ground pile behaviour, to combine the inclinometer and bending moment data to obtain a unified representation of performance. Second, consideration needs to be given to the scope of the information on embedded pile performance that can realistically be determined from the available measurements. Data on below-ground inclination and bending moment are regarded as ‘primary data’ in the sense that they are determined directly from the field instrumentation. The primary data are of particular significance in the validation process indicated in Fig. 3 of the paper by Zdravković et al. (2019a). In addition, data on lateral pile displacement (which can be inferred from the field measurements by applying an appropriate structural model for the pile and the soil/structure interaction) are of interest for the purposes of visualising the below-ground response, although these ‘secondary data’ are of less significance in the validation process.

Fig. 13. Rotation and bending moment profiles for pile CM3 at H = 113 kN and H = 395 kN. Bending moment data are inferred from the fibre optic strain gauge measurements

Note that some previous authors (e.g. Haiderali & Madabhushi, 2013; Lau et al., 2014; Choo & Kim, 2015) have attempted to determine the lateral pressures acting on laterally loaded piles instrumented with strain gauges when tested in the centrifuge. These lateral pressures are then used to determine representative p–y curves for the test (although Haiderali & Madabhushi (2013) indicate that considerable care is needed to obtain reliable results). No attempt has been made here to derive p–y curves directly from the field data.

Field tests and centrifuge studies on laterally loaded monopiles are often instrumented only with strain gauges. In the processing of these data, the Euler–Bernoulli theory is usually assumed for the pile. As a consequence, straightforward relationships are obtained between the bending strains (determined from the strain gauges), the lateral pressures (determined by double differentiation of the bending moment profile) and the lateral displacement (determined by double integration of the bending moment). This simplified approach has not been used in the current work for two reasons. First, the testing included inclinometer measurements (as well as strain gauges), and these have been combined with the strain gauge data to provide a unified representation of behaviour. Second, since the length-to-diameter ratio L/D of the piles is relatively small, shear strains within the pile (as well as bending strains) may contribute significantly to the overall pile performance (see e.g. the discussion by Gupta & Basu (2018)). Timoshenko theory (in which shear strains are incorporated in an approximate way) is therefore adopted to represent the pile behaviour. In this case, the simple relationships implied by Euler–Bernoulli theory do not apply. The work has not explored in any systematic manner whether the simpler Euler–Bernoulli theory would have been sufficient, as the a priori assumption was to include shear displacements by way of Timoshenko theory in the analysis.

To infer the embedded pile displacements from the field instrumentation, an optimisation approach was used in which the embedded pile was represented by a series of n Timoshenko beam elements (Fig. 14). A horizontal force and moment is applied at the pile head and an assumed distribution of soil reactions (linear across each element) is applied to the embedded pile. The model also includes a base moment

$M_{\mathrm{B}}$

and a base horizontal force

$H_{\mathrm{B}}$

. Ideally, the model would also include a distributed moment component, thereby corresponding directly to the four-component PISA design model (Byrne et al., 2017; Zdravković et al., 2019a). However, without any direct measurement of the shear forces in the pile it is not possible to distinguish between the influence of the lateral distributed load and a distributed moment on the pile performance. Consequently, the distributed moment is excluded from the model and the lateral distributed load is regarded as being an ‘equivalent’ load, representing the combined influence of the lateral distributed load and the distributed moment.

Fig. 14. Discretisation of the pile into a series of Timoshenko beam elements

The behaviour of each element is represented using Timoshenko beam theory

$$M=-EI\frac{\mathrm{d}\psi }{\mathrm{d}z}$$

1

where

$M$

is the induced bending moment (a positive moment is associated with tension on the left side of the structure) and

$\psi$

is the (clockwise) rotation of the beam cross-section. The (clockwise positive) inclination of the structure,

$\theta =-(\mathrm{d}v/\mathrm{d}z)$

is given by

$$\psi =\theta -{\gamma }_{xz}$$

2

where

${\gamma }_{xz}$

is the shear strain, assumed to be uniform across the section and given by

$${\gamma }_{xz}=\frac{S}{\kappa AG}$$

3

where

$S$

is the shear force; EI is the local flexural stiffness;

$\kappa AG$

is the local shear stiffness (where

$\kappa$

is a shear factor taken in the current calculations to be 0·3); and

$v$

is the lateral displacement in the

$y$

-direction. It is assumed that

$E=210\mathrm{GPa}$

and

$G=80\cdot 77\mathrm{GPa}$

. Together, these equations give

$$\frac{M}{EI}=\left(\frac{{\mathrm{d}}^{2}v}{\mathrm{d}{z}^2}+\frac{1}{\kappa AG}\frac{\mathrm{d}S}{\mathrm{d}z}\right)$$

4

The lateral distributed soil reaction acting on the pile is assumed to vary linearly across each pile element. For each element (

$i=1,n)$

the lateral load is

$$p=-a_{i}z-b_i$$

5

where (

$a_i,b_i$

) are constants relating to pile element i.

The shear force and moment within each element are

$$S=-\int p\mathrm{d}z=\frac{a_i{z}^2}{2}+b_{i}z+c_i$$

6

$$M=\int S\mathrm{d}z=\frac{a_i{z}^3}{6}+\frac{b_i{z}^2}{2}+c_{i}z+d_i$$

7

From equation (5), for each element

$$EI\frac{{\mathrm{d}}^{2}v}{\mathrm{d}{z}^2}=M-\lambda \frac{\mathrm{d}S}{\mathrm{d}z}=\frac{a_i{z}^3}{6}+\frac{b_i{z}^2}{2}+c_{i}z+d_i-\lambda \left(a_{i}z+b_i\right)$$

8

with

$\lambda =EI/\kappa AG$

. The cross-section rotation,

$\psi$

, overall (neutral axis) rotation,

$\theta$

, and lateral displacement, v, are obtained as

$$-EI\psi =\frac{a_i{z}^4}{24}+\frac{b_i{z}^3}{6}+\frac{c_i{z}^2}{2}+d_{i}z+e_i$$

9

$$-EI\theta =\frac{a_i{z}^4}{24}+\frac{b_i{z}^3}{6}+\frac{c_i{z}^2}{2}+d_{i}z+e_i-\lambda \left(\frac{a_i{z}^2}{2}+b_{i}z+c_i\right)$$

10

$$\begin{array}{rl}EIv=& \frac{a_i{z}^5}{120}+\frac{b_i{z}^4}{24}+\frac{c_i{z}^3}{6}+\frac{d_i{z}^2}{2}\\ & +e_{i}z+f_i-\lambda \left(\frac{a_i{z}^3}{6}+\frac{b_i{z}^2}{2}+c_{i}z\right)\end{array}$$

11

When the coefficients

$a_i$

to

$f_i,i=1,\dots ,n$

have been computed, the lateral deflection

$v$

can be determined at all points along the embedded pile. The coefficients are computed by solving the following set of equations.

(a)	Set A – Continuity at the connection between adjacent elements. At the $(n-2)$ connection points, it is assumed that lateral deflection, cross-section rotation, bending moment, shear force and lateral load are all continuous. This gives a total of $5\times (n-2)$ independent relationships between the parameters.
(b)	Set B – Continuity at ground level. Four further relationships between the parameters are formulated by equating the lateral displacement, overall rotation, shear force and bending moment to values determined from the above-ground instrumentation.
(c)	Set C – Embedded instrument data. A further set of equations is formulated in which the inclinometer data are equated to the values of overall rotation implied by the model and bending moments inferred from the field data are equated to the bending moments implied by the model.

Values for the parameters

$a_i$

to

$f_i,i=1,\dots ,n$

are determined by solving equation set C in a least-squares sense, subject to the constraint equations in sets A and B. In achieving this solution, it is necessary to apply two further constraints. First, the horizontal force acting at the base of the pile,

$H_{\mathrm{B}}$

, is constrained to act in an opposite direction to the pile base displacement, with magnitude less than the product of the pile section area and the local undrained strength

$$0<H_{\mathrm{B}}<\frac{1}{4}\pi D^2{s}_{\mathrm{u}}$$

12

Second, the lateral distributed load,

$p$

, at ground level is constrained to positive values (i.e. to act in an opposite direction to the local pile displacement) to prevent sensor noise from providing a non-realistic negative soil reaction.

A detailed set of data interpreted using this approach for CM3, for

$v_{\mathrm{G}}=99\mathrm{mm}$

(i.e. at the largest displacement applied in the test) is shown in Fig. 15. It is clear from Figs 15(b) and 15(c) that the optimised model provides a good representation of the primary data (rotation and bending moment). Also shown in Fig. 15(a) are the inferred displacements (seen to coincide at the ground surface with data from the above-ground instrumentation) and inferred shear force (which also coincides at the ground surface with the value of the applied load measured from the above-ground instrumentation). The displacement profile in Fig. 15(a) indicates the ‘toe kick’ phenomenon that typically occurs in stiff laterally loaded piles. Fig. 15(e) indicates the inferred distribution of equivalent distributed lateral load determined from the optimisation process.

Fig. 15. Embedded pile response for pile CM3 (D = 0·762 m, L/D = 10) at H = 425 kN, v_G = 99 mm. Parts (a) and (b) indicate the inferred data on ground-level displacement and rotation (indicated as ‘Surface v’ and ‘Surface

$\theta$

’, respectively) determined from the above-ground instrumentation, using the methods described in the paper by Burd et al. (2019). Parts (c) and (d) indicate ground-level bending moment and shear force (indicated as ‘Surface M’ and ‘Surface S’, respectively) determined directly from the applied load. Part (e) indicates the equivalent distributed lateral load determined from the optimised model

Plots of lateral deflection and bending moment for CM3, determined at other stages in the test, are shown in Fig. 16. Also shown in Fig. 16(b) are the bending moments inferred from the fibre optic strain gauges at

$H=395\mathrm{kN}$

. During the initial load stages, the pile exhibits a flexural mode of deflection, with the depth of the pivot point (i.e. the point at which the lateral displacement is zero) progressively increasing as the load is increased. The pivot point reaches an asymptotic value of approximately z/D = 0·64 as the load is increased, after which a toe kick develops and the deflected shape becomes a combined flexural and rotational mode. Fig. 16(b) shows that, as the load is increased, the depth of the peak bending moment also increases, due to the transfer of the applied load to soil reactions at greater depths.

Fig. 16. Profiles of (a) displacement and (b) bending moment for pile CM3, including bending moment data inferred directly from the fibre optic strain gauges at

$H=\mathbf{395}\mathbf{k}\mathbf{N}$

Figure 17 shows that pile CM2 (D = 0·762 m, L/D = 3) exhibits a rigid rotational deflection at all values of applied load, with a normalised pivot depth of approximately z/D = 0·79. The location of the pivot point does not appear to change as the test progressed. As shown in Fig. 17(b), as the load applied to this shorter pile is increased, the bending moment profile increases along the entire embedded length, reaching an asymptote in the moment capacity at the toe as the load is increased. As the soil capacity is progressively exceeded from the pile toe to shallower depths, the position of peak moment migrates slightly to shallower depths. Also shown on Fig. 17(b) are the bending moments inferred from the fibre optic strain gauges at

$H=31\mathrm{kN}$

. These data agree well with the corresponding bending moment data determined from the structural model. Fig. 17(b) indicates that a significant bending moment develops near the pile toe. However, the magnitude of this moment is within realistic bounds when compared to estimates of the likely moment bearing capacity at the pile toe, based on the total cross-section of the pile. The magnitude of the maximum base moment in CM2 (of the order of 50 kNm, interpreted from the structural model) is consistent with the interpreted base moment for the final loading stages of the longer pile, CM3, shown in Fig. 16(b) (although the horizontal scale of Fig. 16(b) means that the value of the base moment cannot easily be visualised in this case). These data confirm that a significant base moment reaction can develop in laterally loaded monopiles.

Fig. 17. Profiles of (a) displacement and (b) bending moment for pile CM2, including bending moment data inferred directly from the fibre optic strain gauges at

$H=\mathbf{31}\mathbf{k}\mathbf{N}$

Data from one of the large-diameter piles (CL2, D = 2·0 m, L/D = 5·25) are shown in Fig. 18. Also shown, in Fig. 18(b), are bending moment data inferred from the fibre optic strain gauges at

$H=2166\mathrm{kN}$

. These data indicate that the response develops from behaviour that is initially relatively flexible, to a rigid rotational mode with toe kick as the load is increased, with a final pivot depth of approximately z/D = 0·7. Consistent with CM3, the depth of the peak moment gradually increases as the load is increased.

Fig. 18. Profiles of (a) displacement and (b) bending moment for pile CL2, including bending moment data inferred directly from the fibre optic strain gauges at

$H=\mathbf{2166}\mathbf{k}\mathbf{N}$

These data provide a pattern of behaviour that is consistent with the centrifuge tests of monopiles in clay reported by Haiderali & Madabhushi (2013) in which the depth of the pivot point increases as the lateral pile deflection increases, reaching a limiting depth of the order of

$0\cdot 7D$

.