A PARAMETRIC STUDY ON THE PULL-OUT . . . JOURNAL of MARINE ENGINEERING
A PARAMETRIC STUDY ON THE PULL-OUT RESPONSE OF SUCTION CAISSONS
M. Zeinoddini 1 , M. Nabipour 2
1- Associate professor, Faculty of Civil Eng. , KNToosi University of Technology 2- MSc in Offshore Structures, Faculty of Civil Eng., KNToosi University of Technology
Abstract Suction caisson foundation systems have been successfully used in the past two decades in numerous occasions on a variety of offshore structures in a wide range of environments. The pull-out capacity of suction caissons remains a critical issue in their applications, and reliable methods of predicting the capacity are required in order to produce effective designs. In the current study a numerical approach has been chosen to investigate the behavior of suction caissons under pull-out loads. The model has first been calibrated against available experimental data and also been verified against other test data. The verified model has then been used to study the influence of a number of parameters on the pull-out behavior of suction caissons. Variations in the soil type, soil cohesion, internal friction angle, dilatancy angle, Poisson’s ratio and the aspect ratio of the caisson have been studied. Soil nonlinearities, soil/caisson interactions, drainage conditions and suction effects have also been taken into consideration. Simple approximations have been put forward to express the effects from above mentioned different parameters on the pull-out capacity. These approximations have also been compared with some analytical and simplified relationships proposed by other researchers. Keywords: Suction Caisson, Pull-Out Capacity, Offshore Structures, Sand, Clay, Drained, Undrained, Aspect Ratio
Nomenclature 1.Introduction c: Soil cohesion Suction caissons are hollow steel (or φ: Friction angle ψ: Dilatancy angle concrete) cylinders which are open at Su: Undrained shear strength bottom but capped on their top (Fig.1).
Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 D: Caisson diameter They are allowed to penetrate the L: Caisson length seafloor under their own weight and then L/D: Aspect ratio pushed to the required depth with R : Soil/caisson strength reduction factor int. differential pressure applied by pumping Pu: Ultimate pull-out load pu(net): Net ultimate pull-out stress under water out of the caisson.
undrained conditions Pu(net): Net ultimate pull-out load Pud: Ultimate pull-out load under drained conditions Puu: Ultimate pull-out load under undrained conditions q: Pull-out stress capacity qu(net): Net ultimate pull-out stress under drained conditions ' σ v : Effective vertical stress
δud: Displacement at ultimate load under drained conditions Fig.1- Schematic view of a suction anchor δ : Displacement at ultimate load under uu pile [1] undrained conditions
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Iranian Association of Naval Architecture & Marine Engineering JOURNAL of MARINE ENGINEERING Suction caissons have been employed to It should be noticed that suction caissons a greater extent as foundations for deep- are relatively new as compared to piled water offshore structures and anchors for foundations, which benefit from more mooring lines. Depending on their than a century of experimental, applications and dimensions, they are analytical and computational also called suction cans, suction piles, investigation on their behavior. Reliable bucket foundations, suction anchors or rules for describing the behavior of skirted foundations. Their incipient goes suction caissons are yet subject to back to late sixties, but investigations on development and investigation. The their behavior virtually commenced late effects from different parameters such as eighties. They are considered as a the caisson geometry, soil solution for marine shallow foundations characteristics, soil/caisson interaction and are an attractive option with regard nature on the load bearing capacities of to providing anchorage for floating suction caissons still need further structures in deep water as they offer a attentions. The current numerical study number of advantages in that mainly deals with effects from a number environment. Suction caissons are easier of above mentioned parameters into the to install than impact driven piles and behavior of suction caissons subjected to can be used in water depths well beyond vertical pull-out loads. It has been tried where pile driving becomes infeasible. to make a distinction between different Suction caissons have higher load types of the pull-out responses and the capacities than drag embedment anchors tendency each parameter affects the pull- and can be inserted reliably at pre- out capacity. These aspects appear to selected locations and depths with have been overlooked in previous minimum disturbance to the seafloor numerical studies (for example [12 to environment and adjacent facilities [2]. 16]). One crucial aspect for a suction caisson is its capacity to resist pull-out loads 2.Numerical models of the caisson which commonly arise under harsh Modeling of nonlinear and time environments to which they are usually dependent responses of soils requires exposed. This has been investigated by advanced numerical programs. The two
Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 some researchers using experimental and dimensional finite element program analytical approaches [3, 4, 5, 6, 7, 8, 9, PLAXIS [17] has been used to model the 10, 11]. Suction caisson’s pull-out pull-out behaviour of suction caissons. behavior has also been studied by means The saturated soil has been modeled as a of numerical simulations, involving two-phase medium composed of solid extensive axisymmetric and three- (soil skeleton) and pore-fluid (water) dimensional models. For example phases. Nonlinear behavior of the solid Sukumaran et al. [12], Erbrich and Tjelta phase is described by means of a Mohr- [13], El-Gharbawy and Olson [14], Deng Coulomb elasto-plastic model. This and Carter [15] and Maniar et al. [16] involves five input parameters, i.e. carried out studies to determine suction Young’s modulus (E) and Poisson's ratio caissons capacity under different loading (ν) for soil elasticity, internal friction and drainage conditions. The angle (φ) and cohesion value (c) for soil commercial finite element codes plasticity and angle of dilatancy (ψ). The ABAQUS, PLAXIS, CRISP3D and Mohr-Coulomb yield condition is an other codes such as AFENA have been extension of Coulomb friction law to used by these researchers. general states of stress. In fact, this
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condition ensures that Coulomb's friction PLAXIS characterizes the elastic-plastic law is followed in any plane within a modeling of soil/structure interactions. material element. The full Mohr- A standard fixity boundary condition has Coulomb yield condition can be defined been considered on the soil boundaries by three yield functions when formulated of the model. The pull-out load has been in terms of principal stresses [18]. The introduced on top of the caisson and yield functions together represent a above its walls to avoid possible flexural hexagonal cone in principal stresses. In deformations from structural elements addition to the yield functions, three used for the caisson cap. In the vicinity plastic potential functions are also of the caisson a relatively fine meshing defined for the Mohr-Coulomb model. has been used for the soil body while, The employed soil plastic model is coarser meshes have been utilized versatile but relatively simple. As will be elsewhere to reduce computational reported later, this plastic criterion has efforts (Fig.2). A load advancement proved to yield to an acceptable level of number of steps option, which better correspondence between the numerical suits those cases where a failure load is results and experiments available on expected during the analysis, has been suction caissons. The program offers used. The water level has been some complicated plastic models but considered to be around 1-3L above the they require more detailed soil data soil surface. It should be mentioned that which was not made available with those the results have not been found to be experiments used for the affected by the water level height. verifications/calibrations of the numerical models. A two dimensional axisymmetric finite A element model has been used. Six-node triangular elements which provide a second order interpolation for displacement have been considered. The element stiffness matrix is evaluated by numerical integration using a total of
Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 three Gauss points (stress points). The caisson itself has been modeled by non- porous linear elastic materials with elastic modulus which correspond to their material properties. A key feature with geotechnical models
containing structural elements is the type and formulations used for the interaction Fig.2- A view from one of the numerical between the soil and structural elements. models (left), magnified view of the caisson and the pull-out load (right)
Special interface elements in PLAXIS take care of soil/structure interactions. In the current investigation, the suction Interface elements with three pairs of caisson is assumed being already nodes have been employed to simulate installed in soils and that it has regained the soil/structure interaction. They are its original intact strengths which was consistent with the six-node soil prevailing in the soils prior to the elements for the soil body. An interface installation of the caisson. In other strength reduction factor (Rint) in words, the soil properties are primarily
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assumed to be unaffected by the caisson L = 194 mm D = 110 mm t = 5 mm installation. This assumption, however, remains to be verified by experiments. In Fig.3 experimental results from El- With drained conditions no excess pore Gharbawy and Olson [6], as an example, pressure is generated. This is obviously have been compared with corresponding the case where free drainage has been numerical results from the current study. allowed through the top cap of the The figure depicts load-displacement caisson. An undrained condition allows response for a caisson model in clay with for full development of excess pore aspect ratios of 6 under drained pressure and is used when, during the conditions. Relatively good agreement pull-out, the top cap remains closed. can be noticed between numerical and Numerical models, employed in the experimental responses. In general, the current study, have been initially examined numerical models have shown validated against experimental records an acceptable level of correspondence available in the literature. The laboratory with test results from above referenced data used for the calibration/verification experiments for other soil types and drainage conditions. of numerical models are those from Rao
et al. [19], El-Gharbawy and Olson [6] 750 and Iskander et al. [10]. Rao et al. [19] carried out a series of 600 tests on suction caissons with different aspect ratios (L/D) to get an estimate of 450 (N)
their pull-out capacity in soft clays Test Data [6] Load (similar to those in the Indian waters). 300 FEM results (Plaxis) The caisson dimensions in their Kaolinite Clay- Drained test 2 150 Cohesion= 0.0001 N/mm experiments were: Friction Angle=27.8°
L=600 mm D=100 mm
0 D = 75 mm t = 3 mm L/D=1.0, 1.5 and 2.0 0 10203040
Displacement (mm)
El-Gharbawy and Olson [6] conducted pull-out tests on caisson models with Fig.3- Comparison between the experimental (from El-Gharbawy and Olson; [6]) and
Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 different aspect ratios (2 to 12) in kaolin numerical (current study) results for suction clays under drained and undrained caissons, diameter of 100mm in soft marine conditions. They tried to evaluate the clay under drained conditions. response of suction caisson foundations for TLPs in the Gulf of Mexico in deep Based on the mentioned verification waters of 2000 to 3000m. The caisson attempts, it has been concluded that dimensions in their tests were: employed numerical models are
convincingly able to predict the response D = 100 mm t = 3.125 mm L/D = 4 and 6 of suction caissons in different soil types
and drainage conditions with acceptable Iskander et al. [10] performed tests in accuracies. sands to investigate the variation of the pore pressure during the penetration and 3.Effect of different soil/ caisson subsequent pull-out of the suction parameters on the pull-out capacity caisson models. Oklahoma sand, which Effects from different is quite fine and of round corners, has caisson/soil/drainage conditions on the been used in their experiments. The pull-out behavior of suction caissons caisson dimensions in their tests were: have been investigated. The utilized
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numerical models in the current study • interface strength reduction factor are, in general, based on dimensions of (Rint) the experimental models used by El- • caisson’s aspect ratio (L/D), while D is Gharbawy and Olson [6] for clays and constant but L varies Iskander et al. [10] for sands • caisson’s aspect ratio (L/D), while L is respectively. As previously stated, these constant but D varies.
test data have also been used for the verification of the FE models. P u1 3.1.Ultimate Pull-Out Capacity Pu2 In general, four distinctive pull-out load-displacement responses have been
identified. Fig.4 outlines how the pull- (N)
out capacity Pu has been defined with Load
suction caissons performing post- Pu=Min.{P u1, P u2} ultimate softening and or hardening, δu=Min.{ δu1, δu2} respectively. Displacement limits, as δu2 recommended by Rao et al. [19], have δu1
0.25L Displacement (mm) also been taken into consideration for determining the ultimate pull out capacity (Fig.4). Pu2
P 3.2.Basic Scenarios and Parameters u1 Studied
Parametric studies have been (N) performed in four basic scenarios each Load Load Pu=Min.{P u1, P u2}
relating to a specific δu=Min.{ δu1, δu2} caisson/soil/drainage configuration. They are suction caissons: 0.25L
δu2 - in clay under drained conditions δu1
Displacement (mm) - in clay under undrained conditions
Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 - in sand under drained conditions Fig.4- Pull-out capacity with suction caissons - in sand under undrained conditions performing post ultimate softening behavior (top) and post ultimate hardening behavior The numerical model, in each of above (bottom), as defined in the current study. scenarios, simulates in particular one test in the previously referenced 3.3. Soil Cohesion Effect
experiments. For each parametric study, 3.3.1. General Results all parameters in the numerical model Cohesion is the resistance due to the have been kept constant while one forces tending to hold the particles parameter in soil/caisson properties has together in a solid mass [20]. Cohesion been changed. Key parameters which has important effects on the behavior of their effects on the pull-out capacity structures embedded in the soil have been examined are: (particularly in clays). Soil cohesion also
• soil cohesion (c) appears to influence the pull-out • soil internal frication angle (φ) response of suction caissons. In numerical models identical to that of • soil dilatancy angle (ψ) experiments in clays [6], the cohesion • soil Poisson's ratio (ν) value (c) has been changed from 0.0001
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Iranian Association of Naval Architecture & Marine Engineering JOURNAL of MARINE ENGINEERING to 0.03 N/mm2, to verify its effect. Other Results obtained indicate that under both soil/caisson parameters in the model drained (scenario No. 1) and undrained have been kept constant. Both drained (scenario No. 2) conditions, the ultimate and undrained conditions have been pull-out load (Pu) almost linearly considered (scenarios No. 1 and 2). increases with the increase in (c) values Some of the results are given in Figs.5 to (for example see Fig.7). A linear trend 7. between ultimate pull-out load (Pu) and cohesion (c) is not far from anticipated. 6000 This is because the shear strength over Clay 5000 Drained Condition the caisson skin and in the soil body both L=600 mm D=100 c=0.03, 0.05, 0.1 are directly related to the soil cohesion. 4000 Linear semi-empirical relationships c=0.02 (N) 3000 between the soil undrained shear Load
2000 strength and the pull-out stress capacity c=0.01 was also proposed by other researchers 1000 c=0.005
c=0.002 [21]: c=0.001
0 0 5 10 15 20 25 30 Displacement (mm) −1 D (1) Fig.5- Soil cohesion effects on numerical pull- q = 6.42Su 1+ 0.18tan L out responses of suction caissons in clay under drained conditions. and under drained conditions [15]: 20000 −0.18 +0.82 c=0.1 L L (2) 15000 qu(net) = 9.48 + 3.792 Su(tip) D D
10000
c=0.05 Load (N) Load or under undrained conditions [15]:
5000 Clay c=0.02 Undrained Condition (3) c=0.01 L=600 mm D=100 c=0.005 0 pu(net) = 0 25 50 75 100 125 150 0.537 Displacement (mm) L sinφ′ 9.1 ()()1− sinφ′ OCR tanφ′σ v′(bottom) d Fig.6- Soil cohesion effects on numerical pull- Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 out responses of suction caissons in clay under undrained conditions 3.3.2. Review of the Results
6000 Under drained conditions, the pull-out
FEM results capacity Pu was noticed to increase by an Trend line increase in the soil cohesion. However, 4000 high values of soil cohesion did not have
Pu= 0.96 π D L c +263 extra improving effect on the pull-out (N) u P ClayKaolinite Clay capacity. Undrained Conditions 2000 Undrained Conditions L=600 mm D=100 mm Further review of the results indicated L=600 mm D=100 mm that, under drained conditions the failure was mostly local (developed either on 0 the caisson walls or in the soil plug). 0 0.01 0.02 0.03 Cohesion (N/mm2) Undrained conditions, however, mostly
Fig.7- Soil cohesion effects on pull-out resulted in a post failure hardening capacity of suction caissons in clay under response and their failure surfaces were undrained conditions. extended in the surrounding soils far from the caisson.
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Generally speaking, Figs.5 and 6 show Values of α1 and B1 are 0.96 and 263 N that the pull-out capacities under respectively for studied undrained undrained conditions are considerably models and 0.82 and 147 N under higher than those from corresponding drained conditions. It should be models under drained conditions (Puu >> emphasized that this paper is mainly Pud). This difference is partially due to a aimed to evaluate the significance of change in the mode of failure for different soil/caisson parameters on the undrained suction caissons compared to pull-out capacity. Eq. 4 and similar that for drained caissons. Besides, the forthcoming equations just provide suction developed inside undrained indications on the order and the tendency caisson directly contributes to the load that a specific parameter influences the bearing capacity. The suction, moreover, pull-out capacity. Delivering a results in improvement of the soil comprehensive analytical solution for resistance characteristics in the vicinity the pull-out capacity of suction caissons of the caisson and indirectly augments is out of the scope of this paper. the pull-out capacity. In general, the pull-out capacity of a From Figs.5 and 6 it can also be suction caisson (Pu) comprises recognized that, under undrained components from the submerged weight conditions the caisson displacement at of the caisson, its surcharge, the failure point δu is notably higher than submerged weight of the soil plug, the that under the corresponding drained negative pressure (suction) developed conditions (δuu>>δud). This is also inside the caisson (just under undrained believed to be due to a shift in the failure conditions), frictional shear strength on mechanisms of the caisson (from weak the caisson outer and inner skins and the local modes under drained conditions reverse end bearing. towards demanding global modes under The constant part in Eq. 4 (B1) can be undrained conditions). These higher related to the submerged weight of the displacements required to achieve the caisson, the submerged weight of the soil ultimate capacity point out on wider plug, the negative pressure and other margins of safety for undrained caissons. parameters which remain typically It is necessary to mention that in here a unchanged with variations in soil Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 drained condition corresponds to pull- cohesion (such as the skin friction that is out cases when openings in the caisson originated from the soil internal friction top cap allow free drainage. An angle). Under drained conditions, undrained condition refers to pull-out suction effects are vanished and the cases when the top cap remains closed constant part (B1) grows smaller than and the pull-out has a high loading rate. that of undrained models. It has also A linear equation shown in Fig.7 relates been noticed that in weak soils under the pull-out capacity (Pu) to the soil drained conditions, the soil plug does not cohesion (c) and has been found to best accompany the caisson up to the failure fit the numerical results obtained in the point. It means that in these cases the current study. Similar relationships have weight of the soil plug will not been obtained under drained conditions. contribute to the constant part (B1). These equations are in the form of: The variable part in Eq. 4 (α1) is associated with the soil cohesion effect
Pu = α1 π D L c + B1 (4) on the pull-out capacity of the caisson. Interior and exterior skin area surfaces of the caisson contribute to α1. It was
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Iranian Association of Naval Architecture & Marine Engineering JOURNAL of MARINE ENGINEERING noticed that with some models failure
occurs just on the outer skin. With some 600 SandOklahoma Sand Undrained Conditions models it happens on both the inner and 2 UndrainedL=194 mm D=110Conditions mm c=0.01 N/mm L=194 mm D=110 mm the outer skins and in some on a conic 450
wedge around the caisson [22]. c=0.005 N/mm2 ) Coefficient α1 therefore has to represent c=0.002 N/mm 2 (N 300 the ratio between the actual failure c=0.001 N/mm 2 Load surfaces to the caisson wall skin surface. c=0.0005 N/mm2 c=0.0001 N/mm2 Coefficient α1 is also related to the ratio 150 of the soil/caisson interaction (Rint). Greater values for α1 have been obtained 0 under undrained conditions as compared 0 1020304050 Displacement (mm)
with those from corresponding drained conditions. This is most likely caused by Fig.9- Soil cohesion effects on numerical pull- the failure surface shifting from the out responses of suction caissons in sand caisson’s vicinity (under drained under undrained conditions. conditions) to more extended areas in the surrounding soil (under undrained For models in sand (scenarios No. 3 and conditions). In the latter case, 4) a more limited range has been development of suction ensures considered for the soil cohesion (from reductions in the positive pore pressure. almost zero to 0.01 N/mm2). Results It creates higher effective stresses in the from sand models are given in Figs8 and soil body and greater normal stresses on 9. They virtually demonstrate the same failure surfaces. Consequently higher linear trend observed with models in shear and frictional forces are clay, for the cohesion effects on the pull- accumulated over the failure surfaces. out capacity. Values of α1 and B1 are Negative pressures also prevent a 0.48 and 238 N respectively for premature tensile failure in the soil plug undrained models while they are 0.44 [22]. Therefore under undrained and 106 N for drained models. Therefore conditions, both α1 and B1 show higher α1 presents smaller values compared to values than their respective drained the clay models. This is somehow due to Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 models. lesser interface ratios (Rint) considered for sand models than that of clay models 400 (0.4 compared to 0.5 respectively). c=0.01 N/mm2 Sand Oklahoma Sand Smaller penetration of studied sand DrainedDrained Conditions Conditions c=0.005 N/mm2 300 L=194L=194 mm mm D=110 D=110 mm mm models, compared to that of clay models, have been noticed to generally result in
200 lesser pull-out capacities.
Load (N) 2 c=0.001 N/mm 3.4.Soil Internal Friction Angle Effect
100 2 c=0.0001 N/mm2 c=0.0005 N/mm c˜ 0 3.4.1.General Results The internal friction angle (φ) is the 0 0 15304560resistance due to interlocking of the Displacement (mm) particles [20]. It is another key factor
Fig.8- Soil cohesion effects on numerical pull- influencing the pull-out capacity of out responses of suction caissons in sand suction caissons. Effects from variations under drained conditions. of φ values on the pull-out capacity have
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been examined within the four already 500 mentioned basic scenarios. Numerical models employed in the study 400 F=35 F=30 are identical to that of experiments in F=27.8 F=25 300 clays (from El-Gharbawy and Olson ) F=20 (N [6]), and in sands (from Iskander et al. d oa [10]). All soil/caisson parameters in the L200 reference models have been kept Clay constant while φ values change in a 100 Undrained Conditions range of 10 to 35 degrees for clays and L=600 mm D=100 mm 0 20 to 41 degrees for sands. It is 02.557.510 acknowledged that some of these values Displacement (mm) are far from actual field conditions but have been introduced into the models to Fig.10- Soil friction angle effects on numerical pull-out responses of suction caissons in clay allow for a more extend range of under undrained conditions.
parameters.
Some of the results are shown in Figs.10 100 to 12. These figures demonstrate that the F=41 F=35 ultimate pull-out capacity of suction 75
F=25 caisson models monotically increases F=30 with an increase in φ values. An ) F=20 (N50 ad exponential relationship has been o L presented which provide a good Sand correlation between φ values and the 25 Drained Conditions L=194 mm D=110 mm obtained numerical Pu values. They are in the form of: 0 0 1020304050
Displacement (mm) α 2ϕ Pu = Po′ e (5) Fig.11- Soil friction angle effects on numerical
Values obtained for Po′ and α2 are pull-out responses of suction caissons in sand under drained conditions. summarized in Table 1. P′ and α2 vary o Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 in different scenarios depending on the 450
0.0172F soil type and the drainage conditions. Pu = 214 e 2 Besides, a linear equation in terms of 400 R = 0.9898 tan(φ). which seems to be of better FEM results 350 physical meaning, fits the obtained Trend line (N)
numerical u P 300
2 π γ ′D L ClayKaolinite Clay Pu = α3 tan(ϕ) + Po′′ (6) 250 UndrainedUndrained ConditionsConditions 2 L=600L=600 mm mm D=100 mm
200 Values observed for α3 and Po′′ in basic 0 1020304050 Friction Angle (degrees)
scenarios are summarized in Table 1. Fig.12- Soil friction angle effects on pull-out capacity of suction caissons in clay under undrained conditions.
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Iranian Association of Naval Architecture & Marine Engineering JOURNAL of MARINE ENGINEERING Table 1- Variations of coefficients in Eqs. 5 with undrained models, even beyond and 6 in different analysis scenarios. failure, suction still keeps on its improving effects on the load bearing Scenario Condition P′(N) P′′ (N) No. α2 o α3 o characteristics of the system. Within post 1 Clay-drained 0.0213 195 0.83 186 failure region, as the pull-out advances 2 Clay-undrained 0.0172 214 0.68 209 up, yet extra suction is produced inside 3 Sand-drained 0.0178 44 0.80 43 the caisson. This directly augments the 4 Sand-undrained 0.0131 120 1.32 124 load bearing of the caisson. The suction also indirectly improves the 3.4.2.Review of the Results soil resistance on failure surfaces. Upon In general, models studied under development of a plastic state in undrained conditions achieve pull out elements and as the pull-out proceeds capacities greater than those from further, extra suctions are created. This corresponding drained models. This is results in an increase in effective stresses seemingly owing to development of in the soil body around the caisson and suction, negative pore pressures and in normal stresses acting on failure hydraulic gradients under undrained surfaces. Consequently the yield surfaces conditions. They bring about higher grow bigger. It means that although the effective stresses which magnifies the element stresses remain in a plastic state, soil friction angle effects. The drainage as the normal stresses increase, higher conditions become more pronounced shear strength are developed over the with models in sand. This is obviously a yield surfaces. Therefore with undrained result of higher permeability in sand models, beyond the ultimate load, the models which allows for further direct and indirect effects of the suction extension of the suction through the soil provide a mounting load bearing body. response or a hardening behavior (Fig.9). Drained responses in Fig.8 and 11 The slope of the load-displacement curve typically demonstrate a load drop ahead in the post failure region (the hardening of their ultimate pull-out load P (a post u rate) is generally less than the slope prior ultimate softening response). This to P (see for example Figs.4 and 9). The softening response is mostly believed to u reason is that in the post failure region,
Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 be caused by a local failure either in in contrary to the pre-failure zone, only shear on the caisson vertical skins or in the suction effect contributes to the load tension at the interface of the soil plug bearing of the soil. with the soil underneath the caisson tips It has been noticed that with clay models [22]. Subsequent to the drop, the pull- the post ultimate hardening rate, out load remains almost constant. This although still positive, is much lower residual strength emerges from the soil than that from sand models. This is plug and the caisson submerged weights likely because lower permeability in the and the plastic resistance on the caisson clay restricts the suction effect in skins. comparison to that from sand models. On the other hand, undrained models Failure modes observed in undrained (despite those of low penetration) do not clay models are closer to the caisson show the above mentioned load drop or body while they become more extended softening (see for example Fig.9). in the sand models. Beyond P (see Fig.4) the pull-out load u Under undrained conditions, failure keeps increasing with increase in the modes noticed to be global, in shear and displacement (a post ultimate hardening in the soil body surrounding the caisson. response). This is most likely because
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They are dissimilar to failure modes with higher ψ values, improved post failure drained models (and models of low behavior has been recognized for the penetration) where failure modes suction caissons under both drained and observed to be local and happening on undrained conditions. This is because in the caisson walls or in the soil plug [22]. the numerical program the dilatancy Yet again in undrained models the angle (ψ) introduced in the plastic caisson’s upward displacement at the potential functions besides the yielding failure point (δu) has been found to be Mohr-Coulomb functions. They are in notably higher than that of the the form of: corresponding drained model (δuu>>δud). 1 ′ ′ 1 ′ ′ Suction’s direct effects (negative g = σ −σ + σ + σ sinψ pressure) and indirect effects (seepage 1 2 2 3 2 2 3 1 ′ ′ 1 ′ ′ forces, change in the pore pressure in the g = σ −σ + σ + σ sinψ (7) soil and increase in the effective stress) 2 2 3 1 2 3 1 seem to postpone the caisson failure to 1 ′ ′ 1 ′ ′ g = σ −σ + σ + σ sinψ higher levels of deformations. Pertaining 3 2 1 2 2 1 2 to the caisson safety, high deformations at the limit point load and the hardening It means that the dilatancy angle type response in the post ultimate region, introduces its effects mostly in the both observed with the undrained plastic regions of the behavior. It was models, provide better load bearing previously discussed that with drained behaviors. models a post failure softening response (or in their best performance a residual 3.5.Dilatancy Angle Effect strength equal to their ultimate capacity) Dilatancy angle represent positive has been observed. It means that these plastic volumetric strain increments as caissons reach their ultimate capacity actually observed for dense soils. Its prior to when dilatancy angle starts to effect has only been examined with effectively function. This is most scenarios No. 3 and 4. Clays, apart from probably why drained models have not over consolidated ones, do not perform shown changes in their pull-out capacity dilatancy behavior [23]. Dilatancy angle (as a result of change in the dilatancy
Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 of sand depends on its relative density angle). Undrained models, on the other and degree of interlocking. For quartz hand, show post failure hardening sands it can be expressed by: responses. Consequently, both the pull-
D out capacity and the post failure ψ = φ − 30 responses can be affected by the
In most cases, where φ is less than 30o, variations in the dilatancy angle.
ψ can be considered as zero. Small 3.6.Poisson’s Ratio Effect values of ψ are acceptable for loose With all four basic scenarios, variations sands with low relative densities [23]. of Poisson’s ratio show almost Results obtained indicate that under insignificant effects on the load bearing drained conditions, the pull-out capacity capacities of suction caissons. The of suction caissons virtually exhibits no reason is that the ultimate pull-out changes with variations in ψ angle. With capacity of suction caissons is usually undrained models, an almost linear achieved far away from their elastic upsurge in the pull-out capacity has been performance, where the Poisson ratio noticed in respect to ψ tangent. For may impose its foremost effects.
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Interface strength reduction factor or 1000
Rint indicates the portion of the cohesion ClayKaolinite Clay and friction strength from the soil (in the Undrained Conditions Conditions D=110 mm L/D=10 vicinity of caisson skins) that can be 750 D=100 mm
transferred to the caisson when subjected L/D=8
500 to the pull-out. Effects from variations in L/D=6
Rint have been examined in four Load (N) L/D=5 previously mentioned basic scenarios. 250 L/D=4
Results obtained indicate almost a linear L/D=3 L/D=2 relationship between the ultimate pull- L/D=1 L/D=0.5 out loads Pu and Rint. This relationship 0 05101520 can be expressed in the form of: Displacement (mm)
Pu = α4πDLRint + B4 (8) Fig.13- Aspect ratio effects (D remains constant) on numerical pull-out responses of It can be concluded that an increase in suction caissons in clay under undrained the interaction between the soil and the conditions. caisson, such as provisions proposed by
Dendani [24] for vertical inserts to the caisson wall, can most possibly result in 1000 improvement of the pull-out capacity. L/D=10
However this extra interaction will have 750 some negative impacts on the installation L/D=7 of the suction caisson. 500
Load (N) Oklahoma Sand 3.8.Aspect Ratio (L/D) Effects L/D=5 Sand 250 DrainedDrained Conditions Conditions D=110 mm This parameter has been studied in the L/D=3 D=110 mm
already mentioned four basic scenarios L/D=1 L/D=1.76 0 L/D=0.5 but in two different instances. In the first 0 50 100 150 200 instance, D is kept constant while the Displacement (mm)
aspect ratio varies and in the second Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 instance, L remains constant while the Fig.14- Aspect ratio effects (D remains aspect ratio changes. constant) on numerical pull-out responses of suction caissons in sand under drained 3.8.1.While (D) Remains Constant conditions. Figs.13 to 15 present some of the results obtained from four basic Higher values of P′′′ have been numerical scenarios. They reveal o considerable improvements in the pull- observed under undrained conditions out capacities by the increase in the compared to those of drained conditions, aspect ratios. Two types of trendlines but the power m shows a slight decrease. have been examined which both fit The changes have noticed to be more properly the numerical results. The first substantial in sand models in comparison series in the form of: to the clay models (Table 2).
m Pu = Po′′′ (L/D) (9)
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drainage path, boosts seepage forces and
900 improves the suction effect on the load FEM results The exponential trend line bearing of the caisson. 750 The second order trend line Another form of equation is proposed in P = 4.18(L/D)2 + 37(L/D) 600 u the current study, which relates the pull- R 2 = 0.9936 0.97 ) Pu = 64 (L/D) out capacity to the aspect ratios as 2 450 R = 0.9582 (N u
P follows:
300 KaoliniteClay Clay Undrained Conditions 2 Pu = A2 (L/D) + B2 (L/D) (12) 150 D=100D=100 mm
0 Values of A2 and B2 in four basic 024681012 scenarios are summarized in Table 2. Eq. Aspect Ratio 12 seems to be of better physical Fig.15- Aspect ratio effects (D remains interpretation. The pull-out resistance is constant) on pull-out capacity of suction caissons in clay under undrained conditions. partially originated from components being directly and linearly related to the caisson length (L) such as submerged Other researchers considered similar weights of the caisson wall, submerged trends between the caisson aspect ratio weight of the soil plug, soil cohesion and the net ultimate pull-out stress of the effects, etc. There are also components caisson. For example Rahman et al. [8] acting with the second orders of the presented these equations: caisson’s length such as soil internal friction angle effects. The latter can be • Under drained conditions: assumed as the product of the normal stresses acting on the caisson’s skins qu(net) = L −0.11833 L which are themselves depth dependant, −1 ′ 8Su(tip) 1+ 0.4 tan + γ L and the caisson’s wall surface areas. D D They are both directly related to the (10) caisson length and therefore justify a • Under undrained conditions: second order effect from the caisson’s depth.
Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 pu(net) = 0.5372 3.8.2.While (L) Remains Constant L 0.5 9.1 ()()1− sinφ′ OCR tanφ′σ v′(bottom) When the caisson length (L) remains d constant, a decrease in the caisson aspect (11) ratio (L/D), indicates a larger diameter (D), a bulkier and heavier caisson, a Lengthening of the caisson (increase in more stocky soil plug and increased the aspect ratio while D remains interface areas between the soil and the constant) leads to more voluminous caisson. As the aspect ratio decreases, caisson, heavier soil plug and the above mentioned parameters create accordingly higher weights. It also higher frictional and cohesive resistances increases the contact surface between the on the interface areas and consequently a soil and caisson and consequently higher total pull-out capacity is increases the friction forces developed achieved. over their interfaces. Lengthening of the With all four basic scenarios, the caisson also increases the average ultimate pull-out capacity has been normal forces acting on the caisson wall found to increase with the decrease in skins. In addition, it increases the the aspect ratio of the caisson. Some of
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the results are given in Figs.16 and 17. 1500
Sand With the studied cases some Oklahoma Sand Undrained Conditions relationships, between the pull-out 1200 Undrained Conditions LL=194=194 mm capacity and the aspect ratio, have been L/D=0.5 derived (see also Fig.18): 900
'''' -n Load (N) 600 Pu = Po (L/D) (13) L/D=1 Under both drainage conditions, Eq. 13 300 L/D=1.76 marks a general improvement of the L/D=3 L/D=5 0 pull-out capacity with decrease in the 0 1020304050 aspect ratio. However the changes Displacement (mm) become more pronounced when the Fig.17- Aspect ratio effects (L remains aspect ratio moves further below 1. With constant) on numerical pull-out responses of undrained models, P'''' and n demonstrate suction caissons in sand under undrained o conditions (models are based on test data higher values compared to those from from Iskander et al. [10]). drained models. It means that, in this
instance, undrained models show more sensitivity to the change in the aspect ratio as compared with that of the Coefficients obtained in Eqs. 9 and 12 drained models. (and 13) for studied models in different scenarios are summarized in Table 2.
4000 As it was already mentioned, presenting
KaoliniteClay Clay wide-ranging relationships for the pull- Drained Conditions Drained Conditions L=600 mm out capacity of suction caissons is out of 3000 L=600 mm
L/D=0.75 the scope of this paper. This paper mainly deals with the order and the trend 2000 L/D=1 that a specific parameter in Load(N)
L/D=1.5 soil/caisson/drainage condition 1000 L/D=2 influences the pull-out capacity.
L/D=5 However, and in general, the previously L/D=6 0 L/D=10 discussed relationships and parameters 02.557.510 Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 Displacement (mm) may be arranged in an overall form of:
Fig.16- Aspect ratio effects (L remains (14) constant) on numerical pull-out responses of 2 c D suction caissons in clay under drained Pu(net) = πDL Rint (αγ ′ tan(ϕ) + β + δγ ′( )) conditions (models are based on test data L L from El-Gharbawy and Olson [6])
where Pu(net) is the ultimate pull out load Table 2- Variations of coefficients of Eqs. 9, 12 of the caisson excluding its self weight. and 13 in different analysis scenarios. Coefficients α, β, and δ depend on soil/caisson/drainage conditions. Eq. 14, Scenario ''' A B '''' Condition P (N) m 2 2 P (N) n No. o (N) (N) o its range of validity, effects from Clay 1 49 1.21 0.77 55 2800 1.23 soil/caisson/drainage conditions on its drained parameters, its correlation with the Clay 2 64 0.97 4.18 37 10100 1.70 undrained experimental and numerical results and Sand other related issues will appear in a 3 47 1.25 5.63 40 140 1.25 drained separate paper. Sand 4 169 0.72 1.62 97 470 1.56 undrained
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1500 the effects of the studied parameters on
SandOklahoma Sand the pull-out capacities. The 1200 UndrainedUndrained Conditions approximations have also been LL=194=194 mm compared with some analytical and 900 simplified equations already been (N) u -1.56 proposed in the literature for evaluation P Pu = 470(L/D) FEM results 600 R2 = 0.9985 Trend line of the caisson pull-out capacities.
300 5.References 1-Eltaher A., Rajapaksa Y. and Chang K. 0 01.534.56(2003) “Industry Trends for design of Aspect Ratio (L/D) anchoring systems for deepwater offshore structures”, Offshore Technology Fig.18- Aspect ratio effects (L remains Conference, Houston, Texas, U.S.A., 5–8 constant) on pull-out capacity of suction May 2003, OTC 15265. caissons in sand under undrained conditions. 2-Sparrevik, P. (2001) “Suction pile 4.Conclusions technology and installation in deep waters,” A numerical approach has been Proceedings, OTRC 2001 Intl. Conf., Geotech., Geol., and Geophy. Props. of chosen in the current study to investigate Deepwater Sediments, Houston, pp. 182- effects from different soil/caisson/ 197. drainage conditions and parameters on 3-Wang, M. C., Demares, K. R., and Nacci, the pull-out behavior of suction caissons. V. A. (1977) “Application of suction The numerical models have been found anchors in the offshore technology” to present an acceptable level of Proceedings, Offshore Technology correspondence to available Conference, OTC 3203, pp. 1311-1320. experimental data from other 4-Steensen-Bach, J. O. (1992) “Recent researchers. model tests with suction piles in clay and Based on the numerical results, a linear sand” Proceedings, Offshore Technology relationship has been observed between Conference, OTC 6844, pp. 323-330. 5-Zdravkovic, L.; Potts, D. M. and Jardine, soil cohesion values and the pull-out R. J. (1998) “Pull-out capacity of bucket capacity. The soil internal friction angle foundations in soft clay” Proceedings of the
Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 has been noticed to have an exponential International Conference on Offshore Site increasing effect on the pull-out Investigation and Foundation Behaviour - capacity. Poisson’s ratio and the New Frontiers, London, United Kingdom. dilatancy angles have been understood to 6-El-Gharbawy, S. and Olson, R. (1998) have no significant effects on the pull- “The pullout capacity of suction caissons for out strength. With constant values of the tension leg platforms” Proceedings of 8th caisson diameter, an increase in the International Offshore and Polar aspect ratio noticed to have a second Engineering Conference, Montreal. order effect on the friction originated 7-Deng, W. and Carter, P. J. (2000) “Uplift capacity of suction caissons in uniform soil” part and a linear influence on the Geo Eng. 2000, Melbourne, Australia paper cohesion originated part of the on CD. resistance. With constant values of the 8-Rahman, M. S.; Wang, J.; Deng, W. and caisson length, an increase in the aspect Carter, J. P. (2001) “A neural network ratio values has been found to result in model for the uplift capacity of suction an exponential decrease of the pull-out caissons” Elsevier com., Computers and capacity. Geotechnics 28, pp. 269-287. Simple formulations and approximations 9-Randolph, M. F; A. R. House. (2002) have been proposed in order to estimate “Analysis of suction caisson capacity in
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Iranian Association of Naval Architecture & Marine Engineering JOURNAL of MARINE ENGINEERING clay” 34th Offshore Technology 20-Capper, P. L. and Cassie W. F. (1976) Conference, Huston, Texas. OTC 14236 “The mechanics of engineering soils” 10-Iskander, M. El-Gharbawy, S. and Olson, McGraw-Hill, 6th edition R. (2002) “Performance of suction caissons 21-Clukey, E. C., Morrison, M. J., Gariner, in sand and clay” Canadian Geotechnical J., and Corté, J. F. (1995) “The response of Journal, 39, pp. 576-584. suction caissons in normally consolidated 11-Luke, A. M., Rauch, A. F. Olson, R. E. clays to cyclic TLP loading conditions” and Mecham, E. C. (2005) “Components of Proc., Offshore Tech. Conf., pp. 909-918. suction caisson capacity measured in axial 22-Zeinoddini, M., Nabipour, M. and Abdi, pullout tests” Ocean Engineering, 32, pp. M. (2006) “Modes of failure for suction 878-891. caissons under vertical pull-out loads” 25th 12-Sukumaran, B., McCarron, W.O., International Conference on Offshore Jeanjean, P., and Abouseeda, H. (1999) Mechanics and Arctic Engineering “Efficient finite element techniques for limit OMAE2006-92239, June 4-9, 2006, analysis of suction caissons under lateral Hamburg, Germany. loads” Comp. and Geotech, V. 24, pp. 89- 23-Bolton, M. D. (1986) “The strength and 107. dilatancy of sands” Geotechnique 36(1), pp 13-Erbrich, C.T., and Tjelta, T.I. (1999) 65-78. “Installation of bucket foundations and 24-Dendani, H. (2003) “Suction anchors: suction caissons in sand-Geotechnical some critical aspects for their design and performance” Proceedings, Offshore installations in clay” 35th Offshore Technology Conference, OTC 10990, pp. Technology Conference, Huston, Texas. 725-735. OTC 15376. 14-El-Gharbawy, S.L., and Olson, R.E. (2000) “Modeling of suction caisson foundations” Proceedings of the International Offshore and Polar Engineering Conference, Vol. 2, pp. 670- 677.
15-Deng, W., and Carter, J.P. (2002) “A theoretical study of the vertical uplift capacity of suction caissons,” International Journal of Offshore and Polar Engineering, Vol. 12, No. 2, pp. 89-97. Downloaded from marine-eng.ir at 13:24 +0330 on Wednesday October 6th 2021 16-Maniar, D.R., Vásquez, L.F.G and Tassoulas, J.L. (2005) “Suction caissons: finite element modeling” Proceedings of 5th GRACM International Congress on Computational Mechanics Limassol, 29 June – 1 July. 17-Brinkgreve R.B.J and Vermeer P.A. (2000) “PLAXIS finite element code for soil and rock analyses ver. 7.2, users manual” Delft University of Technology, Printed by A.A. Balkema Publishers. 18-Smith, I.M., Griffith, D.V., (1982) “Programming the finite element method”, Second Edition. John Wiley and Sons, Chisester, U.K. 19-Rao, S. N.; Ravi, R.; Prasad, B. S. (1997) “Pullout behavior of suction anchors in soft marine clays” Marine Georesources and Geotechnology, Vol. 15, pp. 95-114.
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