Torsional installation and vertical tensile capacity of helical piles in clay

Helical (or screw) piles comprise steel helices on a central shaft (see Fig. 1) that are rotated into the ground under an applied vertical load (‘crowd force’). Although commonplace onshore, they are seldom used offshore, but are being increasingly considered (e.g. Knappett et al., 2014; Al-baghdadi et al., 2017; Huisman, 2019). Relative to offshore driven piles, helical pile installation avoids the significant acoustic emissions associated with pile driving, which can be detrimental to marine species as they use sound waves for foraging, orientation and communication (Madsen et al., 2006). Furthermore, the noise and vibration from pile driving may cause auditory injuries to marine species (Bailey et al., 2010) such that strict limitations have been put in place in some jurisdictions (Müller & Zerbs, 2011).

The helices on helical piles provide additional vertical, horizontal and moment capacity relative to an equivalent driven pile. For instance, Prasad & Rao (1996) showed that the lateral capacity of a helical pile in a fine-grained soil was about 1·5 times larger than that for an equivalent monopile, whereas Abbas & Ali (2020) showed that the vertical compressive capacities of a helical pile was between two and eight times that of the same diameter pile without helices. Much of the uncertainty associated with helical pile capacity in fine-grained soils surrounds the extent of pore pressure build-up and the associated strain softening during installation – studies to address this uncertainty are few, but emerging (e.g. Bagheri & El Naggar, 2015; Lutenegger & Tsuha, 2015; Ullah & Hu, 2020).

Numerical modelling of helical piles has mainly involved small-strain analysis, such that only pre-embedded (wished in place) helical piles could be modelled (Knappett et al., 2014; Pérez et al., 2017). Although there have been a limited number of large-deformation numerical studies of helical piles in sand, such as the recent work of Sharif et al. (2021a, 2021b), who used discrete-element modelling to simulate torque installation, to the current authors’ knowledge, there are no such equivalent studies in clay. Wished-in-place models are incapable of providing information on the installation torque, which is often used as an empirical indicator of post-installation capacity (Perko, 2009; Tsuha & Aoki, 2010; Sakr, 2012; Ullah & Hu, 2020), although the use of this approach has been cautioned for large offshore piles (Cerfontaine et al., 2023). Moreover, consolidation in fine-grained soil is expected to increase capacity, as is well established for driven piles in clay (Randolph et al., 1979; Fellenius et al., 1989) and to a more limited extent for helical piles (Lutenegger, 2019). It follows that modelling installation is an important aspect of understanding in-service capacity, as the effective stress state in the soil surrounding the pile is changed by the installation.

Helical pile installation and subsequent tensile capacity in fine-grained soil is assessed by either considering a ‘cylindrical failure’ or ‘individual plate’ failure mechanism. The former assumes that the shear surface develops as a cylinder (with the diameter of the helix) between adjacent helices, while the latter assumes that each helix works independently, with separate failure surfaces developing around each helix. Existing work in clay (e.g. Mooney et al., 1985; Mohajerani et al., 2016) suggests that the cylindrical failure mechanism is applicable when the helix spacing is no greater than 3D, with the individual plate mechanism applicable at larger helix spacings. However, Bagheri & El Naggar (2015) pointed out that there are some uncertainties regarding the optimum helix spacing, with some studies concluding that an individual plate failure mechanism occurs at a spacing ratio > 2D.

Furthermore, there are important pile geometry considerations for successfully transitioning the helical pile technology offshore. For instance, to minimise installation torque the upper helix may need to be more shallowly embedded than is recommended for onshore helical piles (e.g. an embedment depth of at least five times the helix diameter (Chance, 2006)). However, placing the uppermost helix at a shallow depth has potential repercussions on the mobilised capacity during tensile loading, as the failure mechanism that develops may be shallow rather than deep, which will reduce the tensile capacity (Spagnoli & Tsuha, 2020). This aspect is particularly relevant for installations in sand where a shallow mechanism for a single helix can prevail to depths of up to nine times the helix diameter (Hao et al., 2019).

Much of the research effort on helical piles for offshore applications has focused on sand. Cerfontaine et al. (2023) noted that a large pile head (or ‘crowd’) force would be required to achieve a pitch-matched installation, or an advancement ratio (AR) of unity, as recommended for onshore helical piles (Perko, 2009; Lutenegger, 2019), where in one full revolution of the pile, the helix advances a vertical displacement equal to the pitch. ‘Overflighting’ the pile (i.e. AR < 1) was found to be more beneficial in terms of reducing the crowd force, which may allow smaller installation vessels to be used. Consideration has also been given to the effect of multiple helices. Hao et al. (2019) reported data from centrifuge model tests, which showed that tensile capacity can increase with additional helices, but only where the additional helix is located outside the failure mechanism of the lower helix. Davidson et al. (2022) also noted that using additional helices did not provide significant capacity benefits, but did require a greater installation torque, which is evidently not preferable for an offshore installation. High installation torque is also generated when the helix is located deep on the pile, such that an optimised design – balancing capacity requirements with installation torque constraints – will lead to a helix location that is shallower than recommended for onshore helical piles (Spagnoli & Tsuha, 2020; Ullah & Hu, 2020; Cerfontaine et al., 2021; Davidson et al., 2022), although this does provide lateral capacity benefits (Al-Baghdadi et al., 2015). Relative to this body of work, the behaviour of helical piles in clay has received much less attention, and this knowledge gap is addressed by the current paper. This paper addresses the uncertainties highlighted above through a combination of centrifuge experiments and coupled Eulerian–Lagrangian–large-deformation finite-element (CEL–LDFE) analyses for torque-installed helical piles in normally consolidated clay. The centrifuge experiments involved torque installation of the helical piles followed by tensile loading after various reconsolidation periods. These data were then used to validate the numerical analyses that formed the basis for establishing an analytical model for predicting tensile capacity based on the principles of limit equilibrium.

The centrifuge experiments were conducted at the University of Western Australia (UWA) using the 3·6 m dia. fixed beam centrifuge. The centrifuge tests were conducted at 50g (i.e. 50 times Earth's gravity) in a normally consolidated kaolin clay sample. The geotechnical properties of this UWA kaolin clay are well documented in the numerous physical modelling studies where this soil was utilised (e.g. Stewart, 1992; House et al., 2001; Lehane et al., 2009; Chen et al., 2012; Colreavy et al., 2016; Wang & Bienen, 2016). The sample was prepared by mixing a kaolin clay slurry at a water content of approximately 120% (around twice the liquid limit) in a vacuum mixer for approximately 24 h before transferring the slurry into a sample container (or ‘strongbox’, see Fig. 2) with internal dimensions of 650 mm long, 390 mm wide and 325 mm deep. Two-way drainage in the sample was achieved by way of corner drains that provided a hydraulic connection between a 20 mm thick sand drainage layer (overlain by a geofabric sheet) at the base of the sample to the free water above the sample. The sample was consolidated in-flight at 50g over a period of 5 days, with additional slurry added after 2 days to ensure the targeted sample height (220 mm) was achieved. Water was added to the sample continuously during consolidation and testing to maintain 20 mm of free water above the sample surface.

In-flight consolidation resulted in a normally consolidated (NC) clay profile with undrained clay strength, s_u, increasing with depth from a zero strength at the mudline. After consolidation, T-bar penetrometer tests were conducted to assess the undrained shear strength. The model T-bar has a diameter D_T-bar = 5 mm (and is 20 mm long), and was penetrated at a velocity v = 1·5 mm/s, such that the dimensionless velocity V = vD_T-bar/c_v = 120 (where the coefficient of vertical consolidation c_v = 2 m²/year (0·0625 mm²/s) at a vertical effective stress level of 44 kPa, corresponding with the mid-height of the sample), greater than the V = 30 threshold required for undrained behaviour (Finnie & Randolph, 1994; Colreavy et al., 2016). Undrained shear strength profiles were derived from the measured T-bar penetration resistance using the commonly adopted bearing capacity factor of 10·5 (Martin & Randolph, 2006), and are provided in Fig. 3. As expected for this NC sample, the increase in undrained shear strength, s_u, is approximately linear with depth, such that it can be described as s_u = ρz, where ρ is the gradient of undrained strength with depth, z (in prototype scale). As shown by Fig. 3, ρ = 1·06 kPa/m, which is typical for UWA kaolin (e.g. Morton et al., 2014; Han et al., 2021). A cyclic remoulding phase (where the T-bar was cycled vertically by ± 3 diameters) was included in each T-bar test. The soil sensitivity was taken as the ratio of the intact to the fully remoulded penetration resistance (reached after 15 cycles), which for this kaolin clay was S_t = 2·5.

The model helical pile was fabricated from aluminium (and then anodised), and comprises a hollow aluminium shaft and three helices with a spacing equal to the helix diameter – that is, S = D. The shaft has a closed-end conical tip, and has an overall length, L = 150 mm and a shaft diameter, d = 10 mm. The helices have a diameter, D = 40 mm, with a thickness, t = 2 mm and a pitch, p = 8·4 mm. A schematic diagram of the pile and its key dimensions (in both model and prototype scale) is shown in Fig. 1(a). The helical pile shaft is instrumented with strain gauges at the shaft location shown in Fig. 1(a), which allows for measurement of both installation torque and vertical resistance during installation and loading. Data from the strain gauges are transmitted wirelessly (using the arrangement reported in Todeshkejoei (2019)) to allow continuous rotation without entanglement of the data cables (Fig. 2).

The helical pile was mounted at the base of a rotary actuator that was located on a two-axis Cartesian actuator (with degrees of freedom along the vertical axis and one horizontal axis). The helical pile was first penetrated vertically into the soil (i.e. without rotation) using the vertical axis of the actuator under displacement control at a velocity v_v = 0·2 mm/s (V = v_vd/c_v = 53 > 30 (adopting the shaft diameter, d = 10 mm, and an effective stress level appropriate c_v = 1·2 m²/year) such that the response may be considered undrained) until a small crowd force of ∼10 N was reached. At this point the vertical axis was switched to load control, holding a vertical load of 10 N, and the rotary actuator was engaged to rotate the helical pile. This process resulted in an initial vertical penetration (i.e. with no helix rotation) of ∼36 mm (∼1·8 m in prototype scale) prior to rotary installation, and was necessary to develop the lowest magnitude crowd force that could be maintained accurately during rotary installation over the remaining installation depth. The pile rotation rate was varied in the range v_r = 0·15 to 0·45 rev/s across the different tests. After installation a consolidation period in the range t = 0 to 1023 min (0 to 4·86 years in prototype scale), was allowed before the pile was extracted vertically at v_v = 1 mm/s. This gives V = v_vD/c_v = 640 > 30 (D = 40 mm, c_v = 0·0625 mm²/s), thus ensuring that the response is undrained (Finnie & Randolph, 1994). The variation in rotation rate resulted in equivalent (vertical) installation velocities in the range v_v = 1·1 to 3·3 mm/s, where higher rotation rates resulted in faster installations.

The test programme comprises seven centrifuge tests (see Table 1) that investigate the effect of rotation rate on installation torque, and the effects of rotation rate and consolidation time on vertical tensile resistance. In all the results presented and analysed throughout the paper, the load reference point (LRP) for torque, tensile capacity and depth is the conical tip of the pile (Fig. 1(a)).

Installation torque, T, and tensile resistance, Q, are normalised as T/s_uaD³ and Q/s_uaD², respectively, where s_ua ( = 4 kPa) is the average undrained shear strength over the L = 7·5 m pile length. The motivation for normalising by an average rather than a localised (to the helix) soil strength was to avoid very high normalised quantities at shallow depths (in this normally consolidated clay with a zero mudline strength), and as the ambient intact strength around the embedded helices is different, it is unclear as to which localised soil strength should be used.

In practice, installation torque is taken as an indicator of the subsequent compressive or tensile capacity of the pile (Perko, 2009), with higher installation torques leading to higher capacities and vice versa. Fig. 4(a) shows normalised installation torque for rotational velocities, v_r = 0·15, 0·3 and 0·45 rev/s. Evidently there is no apparent effect of rotation rate until the second helix enters the soil, beyond which the higher rotational velocities lead to higher installation torques, albeit that the difference in T/s_uaD³ is higher between v_r = 0·15 and 0·3 rev/s than between v_r = 0·3 rev/s and 0·45 rev/s. The increase in torque between v_r = 0·15 and 0·45 rev/s is approximately 20% for z/D > 2·5, implying an increase of around 40% per log cycle increase in strain rate. Although this is much higher than the 12–18% range reported for this soil (e.g. Lehane et al., 2009), installation torque involves mobilisation of frictional resistance, for which strain rate effects are often reported to be much higher than for mobilisation of bearing resistance (e.g. Dayal et al., 1975; Brown et al., 2004; Steiner et al., 2014; Chow et al., 2017).

As noted earlier, the variation in rotation rate between v_r = 0·3 rev/s and 0·45 rev/s led to equivalent installation velocities in the range v_v = 1·1 to 3·3 mm/s. These installation velocities result in an AR of less than unity, where, in one full revolution of the helix, the vertical installation depth is less than the helix pitch – that is, the pile is overflighted. Fig. 4(b) shows the variation in AR with depth for the different rotational velocities. Although there is some scatter in the data, after about half a helix diameter of penetration the advancement ratio is generally in the range AR = 0·7 to 1·1. The trend in the AR data on Fig. 4(b) (represented by the solid line, established using a Gaussian filter) indicates a slight reduction in AR with depth, but with no clear dependence on rotational velocity. The variation in AR with depth for a constant crowd force shown on Fig. 4(b) is consistent with work reported in sand (Cerfontaine et al., 2023), where a constant AR led to variation in crowd force with depth. Overflighting is also known to reduce the crowd force, which has been shown to be advantageous for offshore installation in sand (Davidson et al., 2022; Cerfontaine et al., 2023). These findings for sand are also consistent with the findings reported here for clay, insofar as the very low crowd force that was maintained during installation resulted in overflighting.

A short consolidation period of about 10 min (i.e. ∼17 days at prototype scale) was allowed between the end of installation and loading the pile. The normalised tensile resistance during vertical extraction is plotted in Fig. 5 (for the three installation rotation rates, tests T1, T2 and T3 of Table 1), where it can be seen that the peak tensile resistance is inversely proportional to the installation rotation rate. The peak normalised tensile resistance, Q_peak/s_uaD² = 13·12 for the highest rotation rate, v_r = 0·45 rev/s, compared with Q_peak/s_uaD² = 14·32 for the lowest rotation rate, v_r = 0·15 rev/s – that is, Q_peak/s_uaD² is 8·3% higher for the lower v_r. The inverse dependence of tensile resistance on rotation rate may be a reflection of the amount of time that passed between the initial shearing during installation and tensile loading of the pile. Although the same 10 min consolidation period was allowed in each test, the installation durations were longer for the slower rotational velocities, such that the effective consolidation time increases as the rotational velocity reduces. Although the variations in effective consolidation time between tests are slight, they may be sufficient for measurable differences in soil strength recovery, as reflected in the differing peak tensile resistances on Fig. 5.

Close inspection of the loading curves on Fig. 5 (see inset) reveals that the peak tensile resistance is mobilised at a normalised displacement, Δz/D ∼ 0·12, with no apparent dependence on installation rotation rate. Beyond the peak capacity, the normalised resistance response is marked by a rapid post-peak reduction with depth, with an available tensile resistance of 35 to 38% of the peak value when the pile is extracted by half its overall length, consistent with the reduction in mobilised s_u as the pile becomes shallower, and also as the soil softens due to the movement of the pile.

The effect of consolidation time (i.e. the time between installation and the start of tensile loading), on the measured tensile resistance is shown in Fig. 6. The dimensionless time factor, T_h, is given as

where t is consolidation time varying between 10 and 1023 min (0·04 and 4·86 years in prototype scale); D_a is the average diameter of the pile shaft and the helix plate taken as 1·25 m; and c_h is the coefficient of horizontal consolidation taken as 7·88 m²/year (0·25 mm²/s) at a vertical effective stress level of 26 kPa (Colreavy et al., 2016), corresponding with the mid-length of the installed pile. Fig. 6(a) shows the tensile loading curves for each consolidation duration, which are characterised by a sharp increase in tensile resistance to a peak value that is dependent upon consolidation time, before reducing sharply after the peak is mobilised. Close inspection reveals that this post-peak reduction is more significant for the tests with longer consolidation times. Fig. 6(b) plots the normalised peak tensile capacity ratio, Q/Q₀ (where Q₀ is the tensile capacity measured in the test with the shortest consolidation time, test T3), against the dimensionless time factor, T_h. Q/Q₀ almost doubles as T_h increases from 0·02 to 24·56. The increase in tensile capacity with consolidation time shown on Fig. 6 is due to the time-dependent dissipation of excess pore pressures that develop during installation and result in increases in undrained shear strength that is subsequently mobilised as the pile is loaded. Evidently, the longest consolidation time allowed in these tests was not sufficient for full consolidation, as the response on Fig. 6(b) does not plateau at the higher T values. The increases shown on Fig. 6 are consistent with the so-called ‘set-up’ effects for driven piles and suction caissons (e.g. Whittle & Sutabutr, 1999; Abu-Farsakh et al., 2015).

All simulations were conducted using Abaqus/Explicit with parallel processing using 24 central processing units (CPUs) for faster computation (Abaqus, 2018).

Figure 7 shows the mesh configurations used in the finite-element model. A three-dimensional (3D) cylindrical model was developed in Abaqus, which allowed torque installation of the helical pile to be modelled, avoiding the simplification of needing to wish the pile in place. The soil is modelled as an Eulerian material and the helical pile is modelled as a rigid body, which is considered reasonable given the range of clay strengths considered in this paper (and in the centrifuge tests reported earlier). A void region (no material zone) with a length equal to that of the pile was provided above the Eulerian material region to accommodate the pile as it was pulled out of the soil and any soil movement above the clay surface (surface heave and clay extracted with the pile). The overall helical pile geometry was exactly the same as in the centrifuge tests, but with either one, two or three helices (see Fig. 1(b)). The soil was discretised using eight-noded Eulerian brick elements (EC3D8R), whereas the pile was discretised using four-noded 3D rigid elements (R3D4). To avoid potential boundary effects, the lateral and bottom boundaries were set at 4D and 3·22D from the fully installed pile tip, respectively, consistent with Ullah et al. (2014, 2017a, 2017b, 2017c). The lateral boundaries were restricted in the radial and circumferential directions and the base was restrained in the vertical (downward) direction. A refined mesh was used in the vicinity of the Lagrangian pile over a radial distance of 0·75D from the pile centre. The element size in this refined mesh zone was D/32 (following mesh sensitivity studies of tensile loading of a pile reported in Kwon et al., 2019), progressively increasing to D/4 at the boundary. The element thickness in the vertical direction was D/36 with a total of 984 912 elements in the whole domain.

The soil was modelled as an elastic–perfectly plastic Tresca material with an undrained shear strength matching that in the centrifuge tests reported earlier – that is, s_u = 1·06z. However, a zero mudline (surface) shear strength can cause numerical instability due to the potentially high strain generated and result in unrealistic surface heave prediction during pile touchdown. To avoid this, a non-zero surface strength of s_u = 0·5 kPa was specified over a depth z = 0·5 m. Initial results showed that this avoided numerical instability and produced surface heave amounts that matched the centrifuge experiments. Adopting s_u = 0·5 kPa over the upper 0·5 m (i.e. ρ = 0 for 0 m ≤ z ≤ 0·5 m) and s_u = 1·06z (i.e. ρ = 1·06 kPa/m for z > 0·5 m) thereafter resulted in an average undrained shear strength of s_ua = 4 kPa over the length of the fully installed pile (i.e. identical to that in the centrifuge tests). Thus, s_ua = 4 kPa was used to normalise the numerical results presented later. Additional analyses considered a variation in soil strength over the range of 30 to 40 kPa for clays of uniform strength (i.e. ρ = 0 and s_ua = s_u).

The normalised stiffness ratio at each depth within the soil was set at E/s_u = 500; Poisson's ratio for the clay was set to 0·49 to model undrained conditions; and the submerged density was set at 700 kg/m³, such that the effective unit weight was 7 kN/m³. To reduce computational time most of the analyses used a mass scaling factor of between 1·6 and 3·32 (submerged density of 1120 and 2324 kg/m³, respectively), effectively increasing the soil density. Although this artificially high density is higher than plausible for a soil, the benefit of the reduced computation time (through a reduction in the dilatational wave speed, c_d, and increases in the minimum stable time increment) was deemed to outweigh the marginal effect that the higher density had on the measured response (as shown later in the paper). No material properties were specified for the rigid helical pile.

The analyses were conducted in two steps. In the first step, after establishing the in situ geostatic stresses, the pile was rotationally installed at a fixed vertical and rotational speed. Once the pile was fully embedded, it was extracted vertically at a constant speed. Contact was modelled using a penalty contact model with a hard contact defined in the normal direction and tangential slip controlled by the traditional Coulomb friction law with the coefficient of friction set to a small value, μ = 0·45, to prevent generation of large interface shear stresses.

The centrifuge test involving a rotational speed v_r = 0·45 rev/s (reported in Fig. 5) was used to validate the numerical model. As noted previously, the CEL analyses were conducted by imposing a fixed rotational and vertical velocity. This validation exercise involved a similar rotational velocity as the centrifuge test, v_r = 0·42 rev/s, and a vertical velocity v_v = 0·1 m/s. This higher vertical velocity was selected based on past experience (see Ullah et al., 2020) to balance computational time and accuracy. This resulted in AR = 0·57, which although lower than the average AR in the centrifuge tests (see Fig. 4(b)), is not expected to be of consequence for these simulations that do not allow for strain softening and strain rate dependency. The pile geometry in the numerical model consists of three helices with diameter D = 2 m, a pitch p = 0·42 m ( = 0·21D) and with a shaft of diameter d = 0·5 m, identical to the prototype dimensions in the centrifuge test. A mass scaling factor of 3·32 was adopted for this validation case, with the effect of mass scaling considered later in the paper.

Figure 8 shows the comparison of installation torque measured in the centrifuge test and produced by the numerical model (s_ua = 4 kPa, D = 2 m, n = 3). There is reasonable agreement between the numerical result and the centrifuge test data. Qualitatively the responses are very similar, albeit that the numerical result overpredicts the measured torque by an amount that increases slightly with increasing penetration depth up to a maximum of 17% at the end of the installation. The overpredicted torque in the CEL model is considered to be because the Tresca model does not allow for soil softening, whereas the kaolin clay in the centrifuge test would have experienced some degree of remoulding during installation. Additional analyses were conducted to check if the difference is partly due to the initial penetration of the pile in the centrifuge test (i.e. without rotation as discussed previously). The results of these additional analyses are also provided in Fig. 8, and show that the initial penetration does not affect the torque that subsequently develops during rotation.

The CEL simulation shows that torque is negligible up to approximately z = 0·9 m (z/D = 0·45; Fig. 8). Over this depth only the shaft below the bottom helix is in contact with the clay, and as the average strength of the clay over this depth is very low (s_u < 1 kPa), the measured torque is negligible. At z/D = 0·45, the bottom helix enters the soil, at which point the (normalised) torque starts to increase at a gradient with depth that appears to be linear between helix locations, indicating that the change in torque response is controlled by the (linear) strength profile. However, the overall response is non-linear with depth as the other helices become embedded, as also demonstrated by the centrifuge data.

The CEL tensile resistance is compared with the centrifuge data and theoretical solutions in Fig. 9. Theoretical models for helical pile compressive and tensile capacity in clays are based on either (a) the cylindrical shear surface method, applicable when the normalised helix spacing S/D < 3 or (b) the individual bearing capacity method, applicable when S/D > 3 (Mooney et al., 1985; CGS, 2006; Merifield, 2011; Mohajerani et al., 2016) (see Fig. 10). In this instance, the normalised plate spacing ratio S/D = 1, such that the cylindrical shear surface method is considered to be applicable, where a cylindrical shear surface forms between the top and lowermost helix together with bearing failure at the top helix (Fig. 10(a)). It is worth noting that the cylindrical shear surface method (as described by Mooney et al. (1985) and Mohajerani et al. (2016)) for tensile loading does not allow for reverse end bearing mobilised at the pile tip or below the lowermost helix, such that the peak tensile resistance would be given by

where A is the projected area of the helix (i.e. A = πD²/4); s_u is the undrained shear strength relevant for each capacity component; L_c is the length of the cylindrical shear surface (in this case L_c = 2S = 2D); L_s is the length of shaft above the top helix; and N_cu is the bearing capacity factor for tensile loading of the top helix. The value 0·5D accounts for a reduced effective shaft length considering the vertical extent of the shallow bearing mechanism above the top helix. Allowing for reverse end bearing (Fig. 10(c)) leads to

where N_cr is a bearing capacity factor for reverse end bearing at the lowest helix.

In equations (2) and (3), the first term accounts for the bearing capacity at the top helix, the second term arises due to cylindrical shear and the third term accounts for frictional resistance along the effective shaft length above the top helix. The additional fourth term in equation (3) accounts for reverse end bearing. To be consistent with the existing literature, potential frictional and reverse end bearing resistance due to the shaft beneath the bottom helix is ignored in equation (2), noting that this would be negligible relative to the total capacity. Frictional resistance along the shaft beneath the bottom helix is also excluded from equation (3) as this rather short section of shaft would be consumed within the reverse end bearing mechanism (as shown later in the paper) such that frictional resistance would not develop. Following Skempton (1984), the bearing capacity factors, N_cu and N_cr, are calculated according to the depth of the helix

Values computed from equations (2) and (3) using N_cu = 7·4 and N_cr = 9 are expressed in the dimensionless form, Q/s_uaD² (as used earlier in the paper), where the average undrained shear strength s_ua = 4 kPa, and are presented as the dashed lines in Fig. 9. Fig. 9 shows excellent agreement between equation (3) (accounting for reverse end bearing) and the CEL peak tensile capacity, whereas when reverse end bearing is ignored (equation (3)) the normalised peak capacity is nearly halved, such that it falls well below the CEL test curve. Although the tensile capacity measured in the centrifuge test peak is lower than that produced by the CEL (and equation (3)), this is expected, as in this centrifuge test there was minimal reconsolidation time between installation and loading (T_h = 0·23), such that the softening that would have occurred during installation should be reflected in the soil strength mobilised in capacity. Equating the peak capacity from equation (3) to the centrifuge peak capacity (Fig. 9) indicates that the back-calculated mobilised soil strength is about 35% of the intact value. This is broadly consistent with the expected remoulded soil strength, calculated using the sensitivity for this clay, S_t = 2·5, albeit that an adjustment in s_u may also be warranted to account for differences in the average strain rate associated with T-bar penetration and extraction of the helical pile.

The failure mechanism for the centrifuge test conditions is shown in Fig. 11, by taking a cross-section at the midplane of the pile at the point of peak capacity. A cylinder is seen to form between the top and bottom plates with a reverse end bearing mechanism clearly visible. The mechanism above the top helix indicates lifting of a zone of soil above the helix, with curvilinear shear planes extending from the circumference of the helix to the free surface of the seabed. The mechanism above the top helix depends mainly on normalised depth as well as on the surrounding soil strength (Merifield, 2011). The failure surface is seen to reach the soil surface, indicating a shallow mechanism (Merifield & Smith, 2010). This contrasts with current onshore practice, where a deep localised bearing failure is assumed above the top helix and the failure surface does not reach the soil surface (see Chance, 2006; Spagnoli & Tsuha, 2020). However, offshore use will require that installation torque is minimised to enable the use of low-cost installation equipment, such that it is more likely that the top helix will be at a shallow embedment, mobilising a shallow failure mechanism such as that shown in Fig. 11.

As noted earlier, the mass of the soil was scaled by a factor of 3·32 in the validation results discussed above and in the parametric studies that are presented later in the paper. Figs 11 and 12 show the effect of mass scaling on the installation torque and the tensile resistance, respectively, for both the normally consolidated strength profile considered earlier (identical to that measured in the centrifuge tests; s_u = 1·06z, s_ua = 4 kPa) and a uniform soil with a constant undrained shear strength with depth s_ua = 40 kPa (i.e. an order of magnitude higher than the average soil strength in the normally consolidated case). Evidently the effect is depth dependent and more prominent for the stronger clay (Fig. 12(a)). The final torque (i.e. at z/D = 3·75) is higher for the simulation with mass scaling, by 16% for the stronger uniform clay and by ∼5% for the softer NC clay. A similar effect is evident in the loading response on Fig. 13. For the normally consolidated softer clay, the peak tensile resistance appears to be unaffected by the mass scaling (Fig. 13(b)), whereas for the stronger clay of uniform strength mass scaling increases the peak tensile resistance by ∼10% (Fig. 13(a)). The computational times with parallel processing using 24 CPUs with and without mass scaling were approximately 4 days and 7 days respectively. Therefore, mass scaling by a factor of 3·32 reduced the computation time by around 3 days. Stronger (and hence stiffer) clays have a higher elastic modulus resulting in an increase in the dilatational wave speed, therefore reducing the stable time increment, which is why the mass scaling effect is more evident. However, for the normally consolidated strength profile of interest here, the very small effect of mass scaling is considered acceptable.

The centrifuge studies reported earlier considered a single helical pile with three helices attached along the shaft with a spacing ratio S/D = 1 and a helix pitch-to-diameter ratio p/D = 0·21. Having validated the CEL model against the centrifuge data, the CEL simulations are extended to cover a broader parametric space with respect to number of helices and their spacing, helix pitch and shaft–helix diameter ratio. Each simulation case modelled both the installation and loading phase, such that installation torque and tensile resistance data are generated.

Figure 14 shows the installation torque and tensile capacity for a single-, double- and triple-helix pile, with all helices having the same diameter, D = 2 m. Spacing effects were examined for a double-helix pile by considering spacings of S = 2 and 4 m ( = 1D and 2D). Vertical and rotational velocities were set at v_v = 0·41 m/s and v_r = 1 rev/s, corresponding to a neutral rotation (AR = 1), such that in one full revolution the pile advances a distance equal to the pitch distance. The depth profile of undrained shear strength was identical to that considered in the previous simulations (and the centrifuge tests); s_u = 1·06 kPa/m (s_ua = 4 kPa). Fig. 14(a) shows that installation torque is identical for all four piles up to z/D = 1·5. At this depth, the second helix for the piles with helices spaced at S = 2 m (and with more than one helix) enters the soil and the torque response diverges. A further divergence occurs when the next helix enters the soil at z/D = 2·5. The torque required to fully install the pile is seen to be controlled by both the number of helices and their spacing. For instance, the torque needed to install the triple-helix pile is approximately 1·24 and 1·96 times that to install the double- and single-helix piles, respectively. For piles with the same number of helices, the installation torque is higher when the spacing is lower as the helices mobilise stronger soil at greater depths.

Figure 14(b) shows the corresponding tensile capacity for all four piles considered. It can be seen that the majority of the resistance is mobilised by a single-helix pile (n = 1) as the addition of another helix only contributes an additional 11% to the tensile capacity, with no benefit obtained when a third helix is added or when the spacing of the second helix is changed. These marginal to nil changes in tensile capacity can be explained by considering the failure mechanism for each pile shown in Fig. 15. For n = 1, the bulk of the tensile resistance is derived from end bearing and a soil flow-around mechanism above the helix. For n = 2, the soil flow-around mechanism is prevented due to the formation of a cylinder between the helices, in addition to the reverse end bearing. These competing mechanisms are responsible for limiting the increase in tensile resistance to about 11% (Fig. 14(b)).

In summary, these CEL analyses demonstrate that although additional helices require higher installation torque, this is not necessarily translated to an increase in tensile capacity. This contrasts with current best practice, where a higher installation torque is perceived to be an indicator of higher compressive and tensile capacity. A similar conclusion was reached by Lutenegger (2019), but attributed to the increased installation disturbance caused by the extra helices rather than the change in capacity mechanism revealed by the CEL simulations.

All the previous results relate to a single pitch, p = 0·21D (0·42 m), consistent with the centrifuge tests reported earlier. The effect of helix pitch on installation torque and tensile capacity for a single-helix pile is shown in Fig. 16 for a soft clay (s_u = 1·06z; s_ua = 4 kPa). The pitch is varied as 0·21D and 0·42D, whereas the installation corresponds to a neutral rotation such that in one full revolution both piles advance a distance equal to the respective pitch distance (i.e. AR = 1). It is seen that alterations to the pitch have no practical implications for installation torque and tensile resistance.

Figure 17 shows the effect of the shaft-to-helix diameter ratio, d/D, on installation torque. Varying d/D over 0·25 to 0·50 was achieved by keeping the helix diameter constant at D = 2 m, while increasing the shaft diameter, d, from 0·5 to 1 m. Although installation torque increases with increasing d/D, the increase is most pronounced for the single-helix case (n = 1), where the final torque increase is around 46%. For n = 2 and 3, the increase is about 7% and 16%, respectively. The effect of shaft diameter is highest for the single-helix case, as much of the installation resistance is generated from friction between the soil and the shaft.

Increasing the shaft diameter has only a marginal effect on tensile capacity for the single-helix pile (Fig. 18). For double- and triple-helix piles the peak tensile capacity is similar for the same d/D, but decreases in magnitude with increasing d/D. Hence, the effect of an increase in the shaft diameter ratio, d/D, is a reduction in tensile capacity for multi-helix piles and no discernible change for single-helix piles. This is consistent with findings from laboratory tests conducted in sand, where the tensile capacity was also found to decrease with increasing shaft diameter ratio, d/D (Nagata & Hirata, 2005; Spagnoli et al., 2015). A larger diameter shaft reduces the effective helix area, π/4(D² − d²), which in turn reduces the weight of the soil that must be lifted with the multi-helix pile, causing a net reduction in the tensile capacity. The effect is minimal for a single-helix pile when the failure mechanism is localised around the helix, as the soil above the helix is not lifted and does not contribute to tensile capacity.

As noted earlier in the paper, analytical tensile resistance models for helical piles are based on either the cylindrical shear surface mechanism or the individual plate bearing mechanism (see Fig. 10). These models assume no reverse end bearing and, as a result, can be overly conservative. Results (and observations) from the numerical analyses allow for the refined tensile capacity model illustrated in Fig. 19. The model is appropriate for tensile loading when the plates are closely spaced (such that a cylindrical shear resistance mechanism develops) and the uppermost helix is shallowly embedded (such that shear planes extend from the top helix to the ground surface).

To simplify implementation of the model, linear slip planes are assumed that are inclined at an angle, θ, from the vertical. Observations from the numerical analyses indicate that θ = 8° is appropriate for the clay considered here. This approach is similar to that proposed for the uplift capacity of anchors in sand (Vermeer & Sutjiadi, 1985; Ghaly et al., 1991; White et al., 2008). For sand, it has been found that the inclination of the slip plane is closely related to the dilation angle (Lee et al., 2013; Ullah et al., 2017a, 2017b; Hao et al., 2019).

The tensile capacity equation taking explicit account of the clay strength gradient can be derived for the cylindrical bearing mechanism. The peak tensile capacity, Q_peak, is given by equation (5) and comprises reverse end bearing resistance at the lowest helix, Q_end, shear resistance along the vertical ‘soil cylinder’ that forms between helices, Q_sc, (shallow) vertical component of the shear resistance acting along the inclined slip planes (Q_sf(v)), the weight of soil in the cone frustum, W_c, developed by the shallow bearing mechanism and the weight of soil trapped between the helices, W_s, in the cylindrical shear mechanism

This leads to the following equation for peak tensile resistance Q_peak (the full derivation is given in the Appendix)

Table 2 summarises the performance of the analytical model (i.e. equation (6)) relative to the numerical and centrifuge results for cases where the mechanism assumed in the analytical model is applicable – that is when helices are closely spaced (S/D < 3·0) and the top helix is shallowly embedded (L_T/D < ∼1·5). Five calculation scenarios are considered, with variations on the seabed strength profile and helical pile geometry. Overall, the analytical model predicts the numerical and experimental results to within 23%, with a mean measured-to-calculated ratio of 0·87 (where measured refers to both the experimental and numerical results). The prediction accuracy improves to ±3% when only the two stronger seabed profiles are considered.

In this paper, the results from centrifuge tests and CEL–LDFE simulations that modelled installation and tensile loading of helical piles in clay have been considered. The centrifuge experiments investigated the effect of the rate of rotation on installation torque and tensile undrained capacity, and the effect of post-installation consolidation time on pile capacity. These experiments provided a means of validating CEL 3D finite-element analyses, which were subsequently extended to consider other pile geometries. The following conclusions can be drawn.

• (a)

  Simplified analytical calculations based on cylindrical shear resistance and reverse end bearing provide agreement with measured tensile resistance when the remoulded soil strength is used as input. This indicates that the installation process fully remoulds the soil that is mobilised in undrained tensile capacity. Existing approaches used in onshore practice do not allow for reverse end bearing at the lowermost helix, which is an overly conservative assumption for offshore applications in clay, where an undrained response is expected.

• (b)

  Post-installation consolidation leads to significant tensile capacity gains, with a consolidation period of about 5 years (at field scale) leading to a doubling of the undrained tensile capacity.

• (c)

  Installation torques calculated in the numerical simulations are broadly similar to those measured in the centrifuge experiments, with differences due to the non-softening soil model adopted in the finite-element simulations. Similarly, tensile capacities calculated by the finite-element simulations are consistent with those calculated analytically using intact soil strength as input to the calculations, but over-predict the measured tensile capacity by an amount that is controlled by the soil sensitivity. These comparisons indicate that the numerical techniques adopted are appropriate for a qualitative assessment, but would require an appropriate strain-softening constitutive relationship to provide accurate predictions of absolute installation torques and capacities.

• (d)

  For piles where the helices are spaced at up to twice the helix diameter, increasing the number of helices has a significant effect on the torque required to install the pile, but has a minor effect on tensile capacity. This finding challenges the practice of inferring capacity from installation torque.

• (e)

  Numerical simulations indicate that installation torque increases as the shaft diameter increases relative to the helix diameter, and that the increases become more moderate for piles with more helices. However, the effect on tensile capacity is nil for single-helix piles and a reduction for multi-helix piles, due to the differing capacity mobilisation mechanisms for single- and multi-helix piles.

These observations are reflected in a simplified analytical model for calculating tensile capacity, which is shown to calculate the numerically and experimentally determined capacities to a mean accuracy of 13%. Further data for other pile geometries and soil strength profiles would allow the merit of the model to be explored further.

Data are available from the corresponding author by request.

The research presented here is supported by Central Queensland University, research grant RSH/4730. This support is gratefully acknowledged. The authors wish to thank the technical team at the National Geotechnical Centrifuge Facility – Manuel Palacios, Adam Stubbs, Dr Guido Wager and John Breen – for their contributions to the experimental work presented here. Thanks are due to Mr Jason Bell of the Central Queensland University for the supercomputing support. The authors acknowledge the open access publication fund provided by the Research Division, Central Queensland University.

Considering Fig. 19, the reverse end bearing resistance at the bottom helix is given by

where A is the projected area of the helix ( = π/4(D² − d²)); N_cr is the bearing capacity factor defined previously in equation (4); and s_u is the undrained strength taken at the position of the bottom helix – that is, at z = L_B.

The cylindrical shear term can be derived as

where s_um is the undrained shear strength at the mudline; ρ is the gradient of undrained shear strength with depth; and L_B and L_T are the distances from the bottom and top helices to the mudline, respectively.

To calculate the shear resistance due to the inclined slip plane mechanism assumed above the top helix, an infinitesimal strip of height, d_s, with a width, 2r, located at an arbitrary depth, z, from the mudline is assumed (Fig. 19). The total shear resistance can then be expressed as

r can be expressed as a function of depth z as

Substituting r from equation (11) into equation (10) and integrating (for a constant θ) gives the total shear resistance along the slip plane Q_sf as

The vertical component of Q_sf, Q_sf(v) is then simply

It is worth noting that Q_sf(v) calculated using equation (13) is independent of the mechanism considered (bearing on individual plates or cylindrical shear) and is also valid for the individual bearing capacity method provided that L_T is such that the top helix is shallowly embedded (typically L_T < ∼1·5D).

The soil weight terms W_c and W_s can be obtained, respectively, as

The peak tensile capacity, Q_peak, can then be determined by substituting equations (7), (9), (13), (14) and (15) into equation (5)

A

helix bearing area

c_d

dilatational wave speed

c_h

coefficient of horizontal consolidation

c_v

coefficient of vertical consolidation

D

helix diameter

D_a

average pile diameter

d

shaft diameter

L_B

vertical position of bottom helix from mudline

L_c

length of cylinder

L_min

minimum element length

L_s

length of shaft above top helix

L_T

vertical distance from top helix to the mudline

N_cr

reverse end bearing capacity factor

N_cu

bearing capacity factor

p

helix pitch

Q

tensile force

Q_peak

peak tensile capacity

Q_sc

total shear force acting on the cylinder

Q_scd

shaft shear force over the soil cylinder

Q_sf

total shear resistance along slip plane

Q_sfv

vertical component of slip shear resistance

Q_ssd

shaft shear force above the top helix

r

geometric parameter

S

helix spacing

S_t

soil sensitivity

s_u

undrained shear strength

s_ua

average undrained shear strength

s_um

mudline undrained shear strength

T

installation torque

T_h

dimensionless time factor

t

consolidation time

V

dimensionless velocity

V_R

resultant velocity

v

penetration velocity

v_r

pile rotational velocity

v_v

pile vertical velocity

W_c

weight of soil cylinder

W_s

weight of soil in the cone frustum above top helix

z

depth beneath soil surface or position of pile tip beneath soil surface

γ′

effective unit weight

Δt

smallest transit time of a dilatational wave

Δz

vertical displacement

θ

slip plane inclination angle (measured to the vertical)

μ

frictional coefficient

ρ

undrained shear strength gradient with depth