Canadian Geotechnical Journal
Centrifuge modelling of uplift response of suction caisson groups in soft clay
Journal: Canadian Geotechnical Journal
Manuscript ID cgj-2018-0838.R2
Manuscript Type: Article
Date Submitted by the 12-Oct-2019 Author:
Complete List of Authors: Zhu, Bin; Zhejiang University, College of Civil Engineering and Architecture Dai, Jialin; Zhejiang University, College of Civil Engineering and Architecture Kong, Deqiong;Draft Zhejiang University, College of Civil Engineering and Architecture Feng, Lingyun; Zhejiang University, College of Civil Engineering and Architecture Chen, Yun Min; Zhejiang University, College of Civil Engineering and Architecture
Keyword: suction caisson, soft clay, shadowing effect, cyclic loading
Is the invited manuscript for consideration in a Special Not applicable (regular submission) Issue? :
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Centrifuge modelling of uplift response of suction caisson groups in soft clay
Bin Zhu
Professor, College of Civil Engineering and Architecture, Zhejiang University, China
Jia-lin Dai
PhD student, College of Civil Engineering and Architecture, Zhejiang University, China Draft De-qiong Kong (corresponding author)
Professor, College of Civil Engineering and Architecture, Zhejiang University, China
Ling-yun Feng
PhD student, College of Civil Engineering and Architecture, Zhejiang University, China
Yun-min Chen
Professor, College of Civil Engineering and Architecture, Zhejiang University, China
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ABSTRACT
This paper describes a programme of centrifuge model tests on the uplift behaviour of suction caisson foundations. The parameters considered were the loading rate, caisson diameter (D), soil strength profile and type of footing (i.e. mono-caisson and tetra-caissons group). The loading responses were examined in terms of total uplift resistance, suction beneath the caisson lid and the vertical displacements of the caisson and at the soil surface. There exists a critical uplift displacement, approximately 0.02D and 0.01D for the mono-caisson and the tetra-caissons group respectively, at which a turning point can be identified in the load-displacement curve. This was found to be attributed to the adhesion on the caisson-soil interface reaching a peak response and then dropping. Of interest is that the tetra-caissonsDraft group exhibits much greater normalised uplift resistance than the mono-caisson before reaching an uplift displacement of about 0.02D, suggesting superiority of the former in term of serviceability. However, a reversed trend was observed at greater displacement, and accordingly an empirical model was derived to quantify the shadowing effect of caisson groups. Regarding the cyclic response, several cycles of large- amplitude loading are sufficient to reduce the ultimate bearing capacity of caisson(s) to below the self-weight of the inner soil plug(s), indicating a transition of failure mechanism.
Keywords: suction caisson; soft clay; shadowing effect; cyclic loading
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INTRODUCTION
In the past few decades, suction caissons have been widely used in offshore engineering as
foundations of wind turbines, oil and gas platforms, etc., due to the low cost in construction and the
possibility of reuse (Bye et al. 1995; Byrne and Houlsby, 2002). Recently, they have also been
considered as an alternative for large-diameter pile foundations in swamp regions that are
associated with river networks and their range of application has been widened to include power
transmission towers (henceforth as PTTs) built there (Kai et al. 2002; Qin et al. 2014). In the
context of Zhejiang Province, China, a large number of PTTs locate in swamp regions where the
transmission lines account for 45% of the total line mileage. Tetrapod jacket foundations, with each footing being built on a monopod suctionDraft caisson or a group of caissons, have shown very promising potential to be applied to these PTTs (STDZP, 2014; ZEPDI and IGEZU, 2015). Similar
to offshore wind turbines, PTTs are typically very tall structures and are vulnerable to overturning
moments induced by extreme wind loads (Richards, 2010).
The overturning moment on a jacket structure is primarily sustained by the “tension-compression”
response of its upwind and downwind footings (Houlsby et al. 2005), and proper understanding of
the uplift response of the upwind footing is of particular importance in the design (Rattley et al.
2008; Senders 2008; Kim et al. 2014b). A number of small-scale laboratory tests have been carried
out to look into this issue in soft soil (e.g. Finn and Byrne 1972; Wang et al. 1977; Fuglsang and
Steensen 1991). Deng and Carter (2002) assumed three different failure modes for fully drained,
partially drained and fully undrained conditions, and proposed a model to assess the uplift bearing
capacity of caissons, considering the influences of aspect ratio, loading rates and over-
consolidation ratios. Following that, the uplift bearing capacity of a caisson under undrained 3
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conditions was commonly determined as the sum of the resistance on its outer skirt and the reverse end bearing capacity at its bottom, with the caisson and the inner soil plug being treated as a monolithic unit (Byrne and Cassidy 2002; Yun and Bransby 2007; Zhan and Liu 2010). Centrifuge tests have been carried out as well (e.g. Lehane et al. 2014; Du et al. 2016). In particular, Mana et al. (2013) proposed an empirical model to assess the relationship between the reverse end bearing capacity coefficient and the aspect ratio of caisson, and pointed out that the gap between the outer skirt and the soil that developed during uplifting would result in a significant decrease in the suction mobilised beneath the caisson lid.
There are, however, fewer studies on the cyclic response. Among them, Byrne et al. (2006) investigated the influence of ambient pressureDraft and loading rate and found that the former has significantly less impact than the latter on the uplift behaviour. Chen and Randolph (2007a) carried out centrifuge tests under both sustained and cyclic vertical loadings and found that the cyclic bearing capacity was 72%-86% of the monotonic one. Wallace and Rutherford (2016) reported that the uplift resistance was not reduced under small-amplitude cyclic loading and, for a caisson with an aspect ratio of one, the uplift resistance significantly reduces if the cyclic amplitude was greater than 0.25% of caisson diameter.
The research described above is all confined to mono-caissons, and that on caisson groups is still limited. Andersen et al. (1993) reported field trials on a group of 2 × 2 adjacent caissons with spacing of zero under monotonic and cyclic loading in a lightly over-consolidated soft soil, and found that the ultimate bearing capacity can be reduced by 18%-34% under several dozens of loading cycles. Gourvenec and Jensen (2009) analysed the ultimate uplift capacity of double-
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caisson groups with spacing varying from 0 to 7 caisson diameters in ABAQUS. The results showed
negligible shadowing effect for caisson groups with spacing greater than one caisson diameter.
Similar work was carried out by Kim et al. (2014a) on a tripod-caissons group with spacing 0.3 to 4
caisson diameters and found that the shadowing effect was greater than 0.95 for spacing beyond
0.3 times caisson diameter. This effect was reported by Kim et al. (2015) to be independent of the
aspect ratio of caissons through centrifuge and numerical modelling.
In summary, studies on the uplift response of caisson groups with small spacing are still limited,
and thus are insufficient to guide the design of caisson groups used as a leg of jacket foundations.
This paper presents a series of centrifuge tests to shed some light on this issue. The uplift response
of both mono-caissons and tetra-caissonsDraft groups is examined in terms of the total uplift resistance,
the suction beneath caisson lid and the vertical displacements of the caisson and the surficial soil.
The primary parameters considered are the loading rate, the caisson diameter, the skirt thickness
and the over-consolidation ratio of soil.
CENTRIFUGE MODEL TESTS
The centrifuge model tests were carried out in a beam geotechnical centrifuge at Zhejiang
University, which has a maximum payload of 400 g·ton and an effective arm radius of 4.5 m. The
strong box used for the presented tests is 1.2 m in length, 0.95 m in width and 1.0 m in depth. More
details of this facility can be referred to Chen et al. (2010).
Soil sample
The soil used for all tests was kaolin clay and its properties are listed in Table 1. More details of
this soil can be referred to Hu et al. (2011) and Xie et al. (2012). For the soil preparation, dry kaolin
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powder was mixed in a vacuum mixer at a water content of 160%, two times its liquid limit, to obtain
the slurry. The slurry was then poured into the strongbox, on the bottom of which a 50 mm thick
coarse sand layer was laid in advance. The water level was kept 0.2 m above the sand surface
before the slurry was poured in order to guarantee full saturation.
Three boxes of over-consolidated clay were prepared. The preparation process consists of four
steps: (1) consolidate the slurry under 100g for 8 hours and then stop the centrifuge; (2) spread
geotextiles upon the clay and add a 0.15 m thick Fujian standard sand on them; (3) consolidate the
clay again through gradually increasing the acceleration to 100g and last for 8 hours; (4) remove
the geotextiles and sand layer prior to the tests.
Model caisson and loading device Draft
All caissons had a diameter (D) of 0.1 m and a skirt length (H) of 0.1 as well, giving an aspect ratio
of one. This value of aspect ratio was mostly adopted in previous studies (e.g. Dyvik et al. 1993;
Du et al. 2016; Kim et al. 2014) especially when the caisson was used a footing of a jacket structure,
whilst caissons with low aspect ratio are also very common, typically more suited for mono-caisson
foundations. Two different values of skirt thickness t were chosen, namely 0.02D and 0.1D, to investigate the loading behaviour of different caisson wall thicknesses. As shown in Fig. 1, there are two vents in the lid of each caisson, and the skirt tip was sharpened to reduce the disturbance to the clay during installation. Two tetra-caissons group foundations with wall spacing (s) of 0.5D and 0.1D were designed, each with four corner caissons fixed to a rigid structure consisting of a 10 mm thick plate and four triangular rib plates (see Fig. 1). Two accelerations, 40g and100g, were applied so that caissons with differing geometries in prototype scale can be modelled. More details are summarised in Table 2. 6
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The loading device is a servo hydraulic cylinder with loading rate ranging from 0.01 to 3 mm/s.
The maximum travel distance and payload are 500 mm and 30 kN respectively. The long strip hole
on the vertical active connection between this loading device and the caisson foundation (see Fig.1
and Fig. 2(b) allows the connecting bolt to travel within a range of 25 mm. As a result, the caisson
can disengage from the servo hydraulic cylinder and settle freely during the compression phase in
cyclic loading tests.
Instrumentation
A pore pressure transducer (PPT) with a measuring range of 300 kPa was fixed under the caisson
lid (see Fig. 1) to measure the pore pressure beneath it. For the tetra-caissons groups, two corner caissons at the diagonal position were equippedDraft with PPTs, and the average of their readings are plotted later for interpretation. Laser displacement transducers (LDTs) with a measuring range and
precision of 50 mm and 0.05 mm respectively were used to monitor the vertical displacement of
the caisson and at the mudline. The latter were installed Ls (2D by default) away from the caisson
skirt (see Fig. 2). Two axial load transducers, with range of 5 kN and 15 kN for tests on the mono-
caisson and the tetra-caissons group respectively, were used to measure the vertical load applied
(see Figs. 2(a) and (b)).
Testing programme
The model caissons were all pushed into the clay vertically by jacking at 1g with the vents open to
exclude the air inside, which were sealed after installation. This push-in installation approach,
though differing from the suction installation in the field, was widely adopted in centrifuge modelling
on suction caissons (e.g. Kim et al. 2014b; Gourvenec et al. 2015). All loading tests were conducted
two hours after the target acceleration had been achieved so that the soil can fully settle.
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Disengagement is allowed between the servo hydraulic cylinder and the suction caisson and the caissons can settle together with the clay within this time period. Three series of uplift tests were carried out, one at 100g and two at 40g, to mimic the response of caissons with different diameters
(i.e. 10 m and 4 m respectively). Since all soils were previously over-consolidated under 100g, this would produce a lightly over-consolidated (at 100g) and two highly over-consolidated (at 40g) samples, denoted hereafter by LOC and HOC respectively. The over-consolidation ratios of the
LOC and HOC estimated at the depth equaling the caisson skirt length were 2.4 and 6.0 respectively.
Figure 3 shows the undrained shear strength profiles measured via T-bar penetration tests, using a resistance factor of 10.5 (Stewart and RandolphDraft 1991). The HOC soil clearly show higher strength
than the LOC and all three curves can reasonably be fitted by a linear formula su = kz + sum, where
sum is the strength intercept at mudline, k is the strength gradient and z is the depth. The fitted values of each curve are also provided in this figure. For the analysis of test results in HOC, the average of the two strength profiles is used.
Four main monotonic tests, denoted by HSM-1, HSM-2, HTM-1 and HTM-2, were conducted in
HOC to examine the influence of loading rate and compare the uplift responses of mono-caisson and tetra-caissons group, and two complementary monotonic tests, denoted by LSM and LTM, were carried out in LOC to extend the findings from tests in HOC. Two cyclic tests were conducted to investigate the degradation of the ultimate bearing capacity of mono-caisson and tetra-caissons group with loading cycles and reveal the deformation mode of the surrounding soil.
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All loadings were applied in a displacement-control mode unless stated otherwise when the
results are discussed. Two displacement rates of loading v, namely 0.3 mm/s and 2 mm/s, were
adopted, giving non-dimensional displacement rates vD/cv of 23.7 and 158 respectively, where cv
is the consolidation coefficient. A vD/cv above 30 is believed to yield undrained-dominant soil
behaviour and that below 0.01 indicates drained behaviour (Finnie and Randolph 1994). As a result,
all tests except HSM-1 and HTM-1 in this paper were conducted under fully undrained conditions.
Comparison is made between the undrained and partially drained response and only the undrained
cases were considered for back-calculation. More details of the test programme are tabulated in
Table 2.
MONOTONIC TEST RESULTS Draft
This section presents the results of the monotonic tests. All variables relating to resistance were
normalised by nDLsu,b (e.g. Figs. 4(a) and 5(c)), where su,b is the soil strength at the caisson tip and
n is the number of caissons, taking values of one for the mono-caisson and four for the caisson
group, to enable comparison of results. The suction beneath the caisson lid is normalised by the
atmosphere pressure pa. Note that the dead weight of caisson(s) has been subtracted from the
uplift load.
In highly over-consolidated clay (HOC)
Figure 4 shows the results of Tests HSM-1, HSM-2, HTM-1 and HTM-2. Due to the distinct uplift
rates (i.e. vD/cv = 23.7 and 158) and thus differing drained conditions, the normalised resistance
corresponding to Tests HSM-1 and HTM-1 is significantly lower than that of Tests HSM-2 and HTM-
2. The jaggedness in the curve "HTM-1" in Figs. 4(a) and (b) is owing to the high sampling
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frequency (100Hz) in test HTM-1. Lower frequency (10Hz) was used in the other tests to avoid
such fluctuations in the results. There is strong rate dependency from the very beginning of loading
(see Fig. 4(a)), which differs from the observations made in sand (Byrne and Houlsby 2002).
However, upon reaching a upward displacement of approximately 0.02D, both slow and fast loading
curves of the mono-caisson start to show a turning point, similar to the observations made in sand
(Byrne and Houlsby. 2002; Villalobos et al. 2010). This critical displacement is about 0.01D in the
caisson group case. In general, the fast loading cases can achieve an ultimate bearing capacity
about 170% greater than the slow cases for both mono-caisson and caisson group, mostly due to
the greater suction mobilised under the caisson lid. Of interest is that the caisson group shows stronger uplift resistance than the mono-caissonDraft before w = 0.01D and then becomes slightly softer, for both fast and slow loadings, suggesting that the “shadowing effect” may enhance the uplift
response of caissons at small-amplitude displacement.
Figure 4(b) shows the development of normalised suction pressure △U/pa with uplift displacement, where △U was determined as the difference in the pore pressures measured under the caisson lid and the corresponding hydrostatic pressure. Even the slow loading cases witness considerable suction, which increases throughout the whole displacement range of 0.25D, though significantly lower than that in the fast loading cases. The suction in the fast loading cases exhibit very high degree of vacuum inside the caisson, considering an only 0.05 m high (i.e. 2 m in prototype scale) water above the mudline. In general, the maximum suction level measured for the mono-caisson is approximately 30% higher than that for the caisson group. Note that at the end of loading all curves still show an upward trend, suggesting great capability of suction caisson
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foundations to sustain uplifting load even at very large displacement. However, the serviceability
limit has been greatly exceeded (Villalobos 2006; James 2014).
3 Taking a saturated unit weight γsat of 16.3 kN/m , it can be found that a suction pressure of
approximately 67.7 kPa is sufficient to pullout the inner soil plug even without accounting for the
adhesion / friction between the soil plug and the caisson, if a localised failure mode applies.
Accordingly, a suction level beyond this value (see the two fast loading curves) suggests a global
failure mode, with more soils been pulled together with the caisson than that corresponding to a
localised one. In general, shearing occurs on the caisson side in a local failure mode while happens
in the surrounding soil far away from the caisson in a global failure mode. The definition of a global
or localised failure mode are in accordanceDraft with that in Zeinoddini and Nabipour (2006).
Figure 4(c) shows the uplifting resistance contributed by the adhesion between the soil and
2 caisson skirt, determined as V' = V – △UπDi /4. All curves show a clear peak response and then
degrade, owing to the disturbance of soil at large caisson displacement (cracks were also observed
at the soil surface) and the reduction in contact area (i.e. part of the caisson was pulled out of the
soil). The displacements at which these peaks take place are in accordance with that shown in Fig.
4(a), i.e., approximately 0.02D and 0.01D for the mono-caisson and tetra-caissons respectively.
Figure 4(d) plots the vertical displacements of the surficial soil (ws). All measurements were
obtained at a distance (Ls) of 2D away from the caisson skirt (see Fig. 2(a)). ws in both mono-
caisson tests is almost negligible, and that of the tetra-caissons cases is larger, owing to the latter
having an equivalent diameter double that of the former and hence greater influential range. For
the tetra-caissons cases, the development of ws is highly rate-dependent due to the distinct
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deformation modes and the fast loading test even shows a vertical soil displacement of more than
0.01D.
In lightly over-consolidated clay (LOC)
Figure 5 compares the uplift responses from tests conducted in HOC and LOC, all obtained at fast loading at 2 mm/s. There are consistent results (see Fig. 5(a)), considering different caisson diameters of 4 m and 10 m. Consistent with the findings in HOC, the tetra-caissons in LOC show stronger uplift resistance than the mono-caisson at very small-amplitude displacement of 0.01D, beyond which the contrary can be observed. A slight difference is that the tests in LOC shows significantly more decrease in uplift resistance caused by shadowing effect than those in HOC. It is, however, difficult to determine if this phenomenonDraft results from the difference in the degrees of over-consolidation or in the caisson spacing (i.e. the spacing is 0.5D and 0.1D for the HOC and
LOC cases respectively).
As shown in Fig. 5(b), the suction pressures in the HOC cases are initially higher than those in the LOC cases but reach lower ultimate values after w = 0.1D. Moreover, it can also be seen that the HOC curves show clear reduction in stiffness when reaching a displacement of about 0.01-
0.02D, which is less clear in the LOC cases. An interesting finding evidenced in Fig. 5(d) is that ws in LTM-f is one-order smaller than that in HTM-1, indicating the pronounced impact of the degree of over-consolidation on the deformation mode of the surrounding soil. In general, the
measurements of ws suggest that the zone strongly influenced by the uplift of caisson foundations is beyond one equivalent diameter and below two.
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Ultimate bearing capacity and shadowing effect
Figure 6 shows the deformation of soil after loading in Tests HTM-2. It is emphasized that the
suction measurements presented above are sufficient to pull out the inner soil plug. There is clear
evidence of isolated soil plugs being pulled out and a global circular crack being developed,
approximately 0.5D away from the caisson group.
Figure 7(a) illustrates the force equilibrium of the caisson-soil interaction system assuming fully
undrained conditions. The caisson and the inner soil plug are treated as a monolithic unit (Iskander
et al., 2002) and the uplift resistance can be expressed as
2 V = W + απDoH0su,o + Nsu,bπDo /4 (1)
in which W is submerged weight of the innerDraft soil plug, α is the adhesion factor assumed to be equal
on the inner and outer skirt wall, similar to that used in Chen and Randolph (2007b) and Mana et
al. (2013), Ho is the effective skirt length (i.e. Ho = H - w), su,o is the average undrained shear
strength along Ho, and N is the coefficient of reverse end resistance at the caisson bottom. Note
that only the resistance relating to soil strength and suction is considered here and in practice the
uplift resistance should also include the submerged caisson weight. It is also noteworthy that
assuming equal α on the inner and outer walls is certainly a compromise considering the limited
testing data for back-calculation, as the measurements provided by Jeanjean et al. (2006) indicated
otherwise. Figure 7(b) shows the force equilibrium of the inner soil plug, which can be expressed
as
2 2 Nsu,bπDi /4 + W = απDiHsu,i +△UπDi /4 (2)
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where su,i is the average undrained strength along the plug. The two unknowns N and α can be
obtained by Equations (1) and (2) based on the measurements previously presented.
Figure 8 compares the back-calculated N of the present study and the most pertinent studies
(Villalobos 2010; Wallace 2016). An almost constant value is eventually achieved by these studies
but this trend cannot be seen for the present back-calculated curves. However, the ultimate values
of approximately 7 in the latter, is almost identical to that in Villalobos et al. (2010) and Wallace and
Rutherford (2016), which is taken as the reverse end bearing capacity coefficient Nc. A more
extensive comparison of Nc with previous studies is shown in Table 3 and the value in the present study is within the given range. This parameter is affected by a number of factors such as caisson geometries, soil properties and loading rateDraft (Cao 2003), and more detailed examination of these factors is not pursued in this paper. The curves corresponding to tetra-caissons are largely lower than that of mono-caisson, and maximum values of 5.2 and 4.2 can be achieved for caisson groups with spacing of 0.5D and 0.1D, respectively.
Figure 9 shows development of adhesion factor during the loading, where all curves reach a peak, at vertical displacement of 0.02D and 0.01D for mono-caisson and tetra-caissons respectively. The two mono-caisson cases, HSM-2 and LSM, achieve peak values of 0.7 and 0.9 respectively and then both degrade to approximately 0.5 at large displacement. The tetra-caissons clearly have lower α, which, furthermore, exhibit more pronounced degradation compared to the mono-caisson cases. The low α values of tetra-caisson could be possibly attributed to the fact that the soil among the tetrapod caissons experienced more disturbance than a monopod caisson and had not fully recovered before the loading test, thus having lower strength than that of the soil in
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the outer zone. The stabilized value of α calculated here is slightly below those in Chen and
Randolph (2007a) and Mana et al. (2013), namely 0.67-0.75 and 0.6 respectively, in which this
parameter was reported to be strongly dependent on caisson wall roughness and soil properties.
Significantly wider range of 0.64-0.99 can be found in Cao (2003) and the maximum was achieved
by allowing a very large time interval between the installation and the pullout loading, showing
heavy dependency on the reconsolidation of soil.
Figure 10 plots the coefficient of shadowing effect (K) of the caisson group, which is determined
as the ratio of normalised uplift resistance of the tetra-caissons to that of the mono-caisson.
Comparing the HTM-1 and HTM-2 curves shows that, for the parameters investigated here, the
loading rate appears to have little effect onDraft the shadowing effect. All curves show a K greater than
one during the initial uplift stage before degrading rapidly to below one at approximately w = 0.02D.
These curves get stablised at wc/D = 0.1, and residual constant values (Ku) of 0.89 and 0.72 are
achieved by the s = 0.5D and s = 0.1D cases respectively. Dyvik et al (1993) reported a field trial
on the uplift response of a tetra-caissons group with s = 0 in over-consolidated clay and the
caissons had geometry (H/D = 0.9; t/D = 0.02) similar with that adopted in this study. Though
corresponding tests on a mono-caisson were not conducted in that study, its bearing capacity can
be estimated using N and α described above, taking values of 7 and 0.5 respectively and
accordingly Ku in that study can be determined as 0.55. The relationship between Ku and s can
thus be fitted as
-4s/D Ku = 1 – 0.45e (7)
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The above equation shows that the shadowing effect of caisson-groups can be considered to be negligible when the caisson spacing surpasses one caisson diameter, which agrees with the numerical results reported by Gourvenec and Jensen (2009). It should be noted that the present model is developed based on test data obtained in over-consolidated clay and its applicability to caissons in other soil types remains unverified. It may also has certain limitations when the caissons to be analysed have distinctly different aspect ratio from those used in the present study (i.e. L/D
=1).
CYCLIC TEST RESULTS
Mono-caisson
Figure 11 shows the cyclic vertical loadingDraft response of the mono-caisson in HOC. The caisson was uplifted to wc/D = 0.3 in each cycle, and then settled freely under its self-weight (469 kN) after detaching from the servo hydraulic cylinder. No additional compressive load was applied and the test was designed to mimic the behaviour of the upwind caissons of a jacket structure undergoing one-way cyclic loading. The present study focuses on the loading response of caisson foundations subjected to extreme loads rather than the accumulative displacement under long-term cyclic loading, and as a result large-amplitude cycling was chosen. In general, the peak uplift resistance experiences a significant reduction of about 15% after the first loading cycle and then degrades approximately 2% after each subsequent cycle, as shown in Fig. 11(a). It is noteworthy that the load corresponding to the turning point eventually decreases to even below the self-weight of the inner plug, demonstrating severe soil degradation and may imply a transition of failure mechanism.
Fig. 11(b) shows the development of suction under the caisson lid where no turning point can be seen for all loading cycles during the uplift stage. On the contrary, a pronounced peak is observed 16
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in V' (see Fig. 11(c)) during the virgin pullout, which agrees with the parallel monotonic tests. This
observation, however, cannot be made for the subsequent cycles.
2 Fig. 11(d) shows the vertical displacements of the caisson and the surficial soil against cvt/D .
2 The incremental cvt/D during each cycle is below 0.002, giving consolidation degree less than 5%
according to the Terzaghi one-dimensional consolidation theory and thus suggesting undrained
conditions. Limited accumulation of ws is seen at the positions 2D and 3D away from the caisson
skirt, which is about 3 orders smaller than wc. Of interest is that, as w varies during each cycle, ws
at Ls = 2D varies in the opposite direction while that at Ls = 3D varies in the same. This somewhat
suggests a deforming mode that upon uplift a large block of soil tends to form a global mechanism
and be pulled out with the caisson, whileDraft the soil nearby also exhibits a trend of flowing into the
caisson due to large suction force.
Tetra-caissons group
Figure 12 shows the cyclic loading response of the tetra-caissons in HOC, where the ultimate pull-
out and push-in displacements are 0.4D and 0 respectively. Nonetheless, it should be noted that
this case corresponds to a two-way loading scenario in the field because of the application of extra
compressive force to push the caisson back. Observations similar to that in Fig. 11(a) can be made
here, except that the inflection point of the initial uplift curve takes place much earlier in this cases
(0.01D compared to 0.02D), as previously discussed. In this particular case, the maximum
compressive load is of similar magnitude of the maximum uplift load. There is an abrupt drop of
uplift resistance at w = 0.35D due to the sudden loss of suction pressure (Fig. 12(b)), which cannot
be observed in the previous tests where the ultimate upward displacement is not sufficient to
develop such a response. This observation can also be made in the following loading cycles. The 17
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peak of V' taking place at approximately 0.01D during the initial uplift, cannot be achieved during
the subsequent uplift phases (Fig. 12(c)). The soil displacement measured at Ls = 2D is shown in
Fig. 12(c) and the variation trend is the same as that found in Fig. 11(d) (i.e. ws and wc varies in the
opposite directions). However, the magnitude of ws in this figure is about 20 times that in Fig. 11(d).
It can thus be concluded that the soil within the range 1D to 2D radially away from the caisson tends to flow into the caisson upon uplift.
CONCLUSIONS
A series of centrifuge model tests on the monotonic and cyclic uplift response of suction caissons were described. The main findings can be summarised as follows. Draft 1. Under undrained conditions, the total uplift resistance of a mono-caisson and a tetra-caissons group shows a turning point at upward displacements of approximately 0.01D and 0.02D respectively, regardless of the caisson diameter or the over-consolidation ratio of soil. The uplift resistance excluding the contribution from suction force was found to reach a pronounced peak at these displacements for both mono- and tetra-caissons.
2. The tetra-caissons groups with spacing of 0.5D and 0.1D both exhibit moderately stronger response (e.g. 12% and 28% respectively at w/D = 0.005) than the mono-caisson, in terms of
V/nDLsu,b, before reaching a upward displacement of about 0.02D, illustrating superiority of caisson groups over mono-caissons under small-amplitude loading. This trend was then reversed with further upward displacement.
3. A power law equation was derived to assess the shadowing effect of caisson groups regarding uplift bearing capacity, taking into account the influence of caisson spacing, and a spacing of 1D 18
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was found to be sufficient to eliminate the shadowing effect. It should be noted that the present
model was developed based on test data obtained in over-consolidated clay for caissons with L/D
= 1, and its applicability to other conditions (i.e. normally consolidated clay or caissons with
significantly lower aspect ratio) should be treated with caution.
4. During cyclic loading, the soil at 3D away from the caisson displaces synchronously with it
while that within the range between 1D and 2D shows a contrast trend, suggesting flow of adjacent
soil into the caisson upon uplifting. After several cycles of loading, the bearing capacity of both
mono- and tetra-caissons falls below the self-weight of the soil plug inside the caisson(s), which is
most probably attributed to a transition of failure mechanism.
ACKNOWLEDGEMENT Draft
The funds provided by the National Natural Science Foundation of China (Grant 51679211,
51890912 and 51809232) are highly appreciated. We also acknowledge the financial support from
the project Key Technology of Suction Bucket Foundation for Large Transmission Lines in River
Network Area funded by Zhejiang Electric Power Company (ZB12-043B-020).
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NOTATION
cv Coefficient of consolidation
D caisson diameter
Di internal caisson diameter g gravity acceleration
Gs soil specific gravity
H caisson skirt length
Ho effective skirt length, equaling H - w k undrained shear strength gradient Draft K coefficient of shadowing effect
Ku residual constant value of K
L caisson skirt length
Ls distance measuring the soil displacement away from the caisson skirt n number of caissons, taking values of one for mono-caisson and four for caisson-group
N coefficient of reverse end resistance
Nc reverse end bearing capacity coefficient
pa atmospheric pressure s caisson spacing
su undrained shear strength of soil
su,b soil strength at the caisson tip
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su,i average undrained strength along the plug
sum undrained shear strength at the mudline
su,o average undrained shear strength along Ho
t caisson thickness
z soil depth
△U suction pressure measured under the caisson lid, equaling the outside pore pressure
minus the inside at the caisson lid
v loading rate
V uplifting load
V' uplifting load excluding the contributionDraft of suction
wc caisson displacement
W submerged weight of the inner soil plug
ws soil displacement
α adhesion factor, treated to be the same on the inner and outer skirt wall
γsat Saturated unit weight of soil
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Table captions
Table 1. Properties of Malaysia kaolin clay
Table 2. Parameters in monotonic tests (prototype scale)
Table 3. Typical Nc of suction caissons
Draft
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Figure captions
Figure 1. Schematic of tetra-caisson group (showing cross-section)
Figure 2. Test layout: (a) sketch map (unit: m); (b) photo taken during testing
Figure 3. Undrained shear strength profile
Figure 4. Monotonic uplift response of caissons in HOC for slow and fast loading: (a) total
resistance; (b) suction pressure under caisson lid; (c) resistance excluding suction force; (d) vertical
displacement of surficial soil against that of caisson
Figure 5. Monotonic uplift response of the caissons in lightly and heavily over-consolidated clays:
(a) total resistance; (b) suction pressure underDraft caisson lid; (c) resistance excluding suction force;
(d) vertical displacement of surficial soil against that of caisson
Figure 6. Soil deformation after loading in HOC
Figure 7. Force equilibrium under undrained condition: (a) caisson with soil plug (b) isolated soil plug
Figure 8. Variation of reverse end resistance coefficient N with caisson displacement
Figure 9. Variation of adhesion factor α on caisson-soil interface with caisson displacement
Figure 10. Variation of shadowing effect coefficients K with caisson displacement
Figure 11. Cyclic vertical loading response of mono-caisson: (a) total resistance; (b) suction
pressure under caisson lid; (c) resistance excluding suction force; (d) vertical displacement of
surficial soil against that of caisson
29
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Figure 12. Cyclic vertical loading response of tetra-caisson group: (a) total resistance; (b) suction pressure under caisson lid; (c) resistance excluding suction force; (d) vertical displacement of surficial soil against that of caisson
Draft
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Table 1 Properties of Malaysia kaolin clay
Parameter value Liquid limit (%) 80 Plastic limit (%) 35
Specific gravity, Gs 2.6
2 Coefficient of consolidation, cv (m /year) 40
3 Saturated unit weight, γsat (kN/m ) 15.5–16.4
Table 2 Parameters in monotonic tests (prototype scale)
Tests in highly over-consolidated clay Tests in lightly over- Parameters (HOC) consolidated clay (LOC) HSM-1 HSM-2 HTM-1 HTM-2 LSM LTM Centrifugal acceleration, g 40Draft40 40 40 100 100 Diameter, D (m) 4 4 4 4 10 10 Length, H (m) 4 4 4 4 10 10 Thickness, t (m) 0.08 0.08 0.08 0.08 1 1 Normalised caisson spacing s/D – – 0.5 0.5 – 0.1
Normalised loading rate vD/cv 23.7 158 23.7 158 395 395 Note: ‘H’ and ‘L’ denote highly and lightly over-consolidated clay respectively; ‘S’ and ‘T’ denote single caisson and tetra-caissons respectively; ‘M’ for monotonic loading.
Table 3. Typical Nc of suction caissons
Fuglsang & Datta & Villalobos Wallace & Data Present Steensen- Kumar Cao (2003) et al. Rutherford Source study Back (1991) (1996) (2010) (2016)
Nc 4.7~11.3 3.5~7.5 6.5~10.8 6.9 7.2 6.7~6.9
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Side view Connecting bolt
Active connection Long strip hole
Triangular rib plates Connecting bolt Vents Draft Connecting plate PPT
t H
D s D
Figure 1: Schematic of tetra-caisson group (showing cross-section)
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Servo hydraulic cylinder
LDTs
.40 Axial load transducer
0
Ls = 2D
0.45 Clay
Coarse sand
0.15
0.55 0.25 0.40
(a) Draft
Axial load Active transducer connection
LDTs
T-bar
PPTs' wires
(b)
Figure 2: Test layout: (a) sketch map (unit: m); (b) photo taken during testing
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s / kPa
u
0 5 10 15 20 25 30
0
3
6 m
9 Depth / / Depth Draft HOC, s = 3.41+2.78 z
u
12 HOC, s = 2.45+2.72 z
u
LOC, s = 4.2+1.61 z
u
15
Figure 3: Undrained shear strength profile
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0.25 0.25
HSM-1
HTM-1
0.20 0.20
HSM-2
HTM-2 W
0.15 0.15 / D / D c c w w
0.10 0.10
HSM-1
HTM-1
HSM-2
0.05 0.05
0.02 D
HTM-2
0.01 D
0.00 0.00
0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 2 4 6 8 10
V/nDLs U/p
u, b a (a) (b)
0.25 0.25
HSM-1
0.20 0.20 HTM-1Draft
HSM-2
HTM-2
0.15 0.15 / D c / D w c w
0.10 0.10
HSM-1, L /D = 2
s
HTM-1, L /2 D = 1
s
0.05 0.05 HSM-2, L /D = 2 0.02 D
s
HTM-2, L /2 D = 1
s
0.01 D
0.00 0.00
0 1 2 3 0.000 -0.005 -0.010 -0.015
V'/nDLs w /D
u, b s (c) (d)
Figure 4: Monotonic uplift response of caissons in HOC for slow and fast loading: (a) total resistance; (b) suction pressure under caisson lid; (c) resistance excluding suction force; (d) vertical displacement of surficial soil against that of caisson
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0.25 0.25
LSM
LTM
0.20 0.20
HSM-2
W (D = 10 m)
HTM-2
0.15 0.15 / D / D c c w w
LSM 0.10 0.10
LTM
HSM-2
HTM-2
0.05 0.05
0.02 D
0.01 D
0.00 0.00
0 2 4 6 8 10 0.0 0.4 0.8 1.2 1.6 2.0
V/nDL s U/p
u, b a (a) (b)
0.25 0.25
LSM
0.20 0.20
LTM
HSM-2Draft
HTM-2
0.15 0.15 / D / D c c w w
0.10 0.10
LSM, L /D = 1
s
LTM, L /2 D = 1
s
0.05 0.05
HSM-2, L /D = 2
s 0.02 D
HTM-2, L /2 D = 1
s
0.01 D
0.00 0.00
0 1 2 3 4 5 0.000 -0.005 -0.010 -0.015
V'/nDLs w /D
u, b s (c) (d)
Figure 5: Monotonic uplift response of the caissons in lightly and heavily over-consolidated clays: (a) total resis- tance; (b) suction pressure under caisson lid; (c) resistance excluding suction force; (d) vertical displacement of surficial soil against that of caisson
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Draft
Figure 6: Soil deformation after loading in HOC
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V
,
o
o u o W
πD H s
α
2 Nsu,bπDo /4 (a)
△UπDi /4
,
u
i i W
απD Hs Draft
2 Nsu,bπD i /4 (b)
Figure 7: Force equilibrium under undrained condition: (a) caisson with soil plug (b) isolated soil plug
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10
HSM-2 Villalobos et al. (2010)
LSM W allace et al. (2016)
HTM-2
8
LTM
6 N
4
2 Draft
0
0.00 0.05 0.10 0.15 0.20 0.25
w /D
c
Figure 8: Variation of reverse end resistance coefficient N with caisson displacement
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1.0
HSM-2
LSM
0.8
HTM-2
LTM
0.6
0.4
0.2 0.02DraftD
0.01 D
0.0
0.0 0.1 0.2 0.3
w /D
c
Figure 9: Variation of adhesion factor α on caisson-soil interface with caisson displacement
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1.5
1.2 K
u
0.9 K
0.6
HTM-1
HTM-2
0.3 Draft LTM Anderson et al. (1993), s/D = 0
Kim & Le et al. (2014), s/D = 1.3
0.0
0.0 0.1 0.2 0.3
w /D
c
Figure 10: Variation of shadowing effect coefficients K with caisson displacement
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0.4
0.4
Initial cycle
Initial cycle
Following cycles
W Following cycles
0.3
0.3 / D c / D c 0.2 w 0.2 w
Uplifting
Uplifting
0.1 0.1
0.0 0.0
-4 -2 0 2 4 6 8 -0.6 -0.3 0.0 0.3 0.6 0.9 1.2
V/DLs U/p
u, b a (a) (b)
-3
0.4 0.4 1.0x10
Initial cycle
Following cycles
-4
0.2 0.3 Draft 5.0x10 / D D c / D / s c 0.0 0.0 0.2 w w w
Uplifting
-4
-0.2 0.1 -5.0x10
w , L /D = 2
s s
w , L /D = 3
s s
w
c
-3
-0.4 0.0 -1.0x10
0.00 0.03 0.06 0.09 0.12 0.15 -3 -2 -1 0 1 2 3
2
V'/DLs T (c t/D )
u, b v (c) (d)
Figure 11: Cyclic vertical loading response of mono-caisson: (a) total resistance; (b) suction pressure under caisson lid; (c) resistance excluding suction force; (d) vertical displacement of surficial soil against that of caisson
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0.5 0.5
W
Initial cycle
Initial cycle
Following cycles
Following cycles
0.4 0.4
0.3 0.3 / D c / D c w w
0.2 0.2
Uplifting
Uplifting
Pushing
0.1 Pushing 0.1
0.0 0.0
-10 -5 0 5 10 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
V/nDL s U/p
u, b a (a) (b)
0.5 0.6 0.02
Initial cycle
Following cycles
0.4 0.4
Draft 0.01
0.3 0.2 / D c D / / D s w
c 0.00 w w
0.2 0.0
Uplifting
-0.01 Pushing
-0.2 0.1
w , L /2 D = 1
s s
w
c
-0.4 -0.02 0.0
0.00 0.03 0.06 0.09 0.12 0.15 -6 -3 0 3
2
V'/nDLs T (c t/D )
u, b v (c) (d)
Figure 12: Cyclic vertical loading response of tetra-caisson group: (a) total resistance; (b) suction pressure under caisson lid; (c) resistance excluding suction force; (d) vertical displacement of surficial soil against that of caisson
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