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Australian Geomechanics Vol 49 No 4 December 2014 81

FRONTIERS IN DEEPWATER GEOTECHNICS: OPTIMISING GEOTECHNICAL DESIGN OF SUBSEA FOUNDATIONS

Susan Gourvenec and Xiaowei Feng1ARC Centre of Excellence for Geotechnical Science and Engineering, The University of Western Australia, Crawley, WA, Australia

ABSTRACT This paper outlines a toolbox of methods for optimising the geotechnical design of subsea foundations. Subsea foundations are becoming increasingly widespread as offshore development moves away from the conventional template of a fixed platform over a set of wells to subsea development of multiple wells and fields tied back to a single facility. Subsea developments comprise a network of infield flowlines and assorted pipeline and wellhead infrastructure, which is typically supported on shallow, mat foundations. The optimisation methods presented cover (i) capacity assessment methodology, (ii) foundation configuration, (iii) geotechnical input and (iv) mode of operation. The research results derive from a combination of physical model testing in a geotechnical centrifuge, numerical analysis and theoretical modelling. Many of the research results have been immediately adopted in engineering practice in Australia and overseas, demonstrating the relevance of the methods to the national and international offshore hydrocarbon industries.

1 INTRODUCTIONMost offshore development in Australia is relatively close to shore, in shallow water and the architecture generally conforms to a standard template of a fixed bottom platform over a cluster of wells. Current and planned offshore developments are located further from shore, in previously undeveloped areas, and rely on subsea architecture. This trend mirrors the evolution of other oil and gas development regions worldwide.

Figure 1 shows the location of the main existing offshore developments and associated submarine pipelines to shore on the North West Shelf (NWS) of Australia (shown in red). Planned offshore developments and those under construction are shown on the same figure (in white). The future gas developments that are not associated with an export pipeline indicate adoption of the new floating liquefied natural gas (FLNG) technology, for which all processing is carried out offshore, mirroring the FPSO (Floating Production Storage and Offloading) approach for oil fields.

Figure 1: Location of exisiting (red) and future (white) facilities on the North West Shelf of Australia.

The new generation of developments (as shown in white in Figure 1) tend to serve a distributed network of wells, connected by infield flowlines. In some cases the wells are tied back to a floating host, such as the Prelude FLNG facility (as shown in Figure 2) or a semi-submersible as at Ichthys. In other cases the infield flowlines lead to a fixed bottom platform in shallower water, such as at Pluto, or directly back to shore, such as at Gorgon. The subsea architecture is essentially common to each type of development and involves a network of infield flowlines connected

FRONTIERS IN DEEPWATER GEOTECHNICS: OPTIMISING GEOTECHNICAL DESIGN OF SUBSEA FOUNDATIONS GOURVENEC & FENG


through various pieces of infrastructure, such as pipeline end terminations (PLETs), pipeline end manifolds (PLEMs) and in-line structures (ILS). These structures are typically supported on shallow foundations or ‘mudmats’. An example of a mudmat and pipeline structure is shown in Figure 3. Mudmat foundations for pipeline infrastructure are ideally installed by the pipe-laying vessel concurrently with the pipelines. Pipe-laying vessels have limitations on the size and weight of mudmats that can be handled. Increasingly the requirements of the mudmats are exceeding those limitations when designed using conventional methods.

Figure 2: Example of subsea architecture (foreground) © Shell.

Figure 3: Example of subsea mudmat and pipeline end termination (Subsea7 2012).

The required size of a foundation is a function of the loads it is required to resist and the strength of the deposit on which it will be founded. Loads on a subsea mudmat for pipeline infrastructure are derived from the self-weight of the foundation and the supported infrastructure and loads derived from the weight and thermal expansion of the attached pipelines and other connected equipment. Eccentricities of the pipe attachment points lead to biaxial moments about the axes of the mudmat. Loading on a subsea mudmat is illustrated schematically in Figure 4. Dead loads and operational loads on subsea mudmats are increasing as subsea infrastructure takes on more functions and as developments target deeper reservoirs and pipeline temperatures increase. Deepwater seabed sediments also typically comprise soft, normally consolidated deposits with low shear strength close to the mudline.

The geotechnical design challenge is therefore to design subsea mudmats to withstand greater dead and operational loads on softer seabeds without increasing the footprint size or weight. The motivation is to reduce costs associated with



installation – for example eliminating the need for a heavy-lift vessel to place the mudmats alone if handling limits of pipe-laying vessels are exceeded – whilst providing acceptable in-service reliability.

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Figure 4: Loading on a subsea mudmat.

The research presented in this paper provides a toolbox of solutions for optimising the geotechnical design of subsea foundations, with the aim of reducing the size of mudmat foundations – for the same operational conditions – compared with designs based on conventional practice. The optimisation methods represent enabling technologies, in that they may improve the viability of projects, contributing to the unlocking of Australia’s valuable but currently ‘stranded’ hydrocarbon reserves.

The optimisation tools presented here include:

Optimisation of the capacity assessment methodology – by adopting a failure envelope approach as an alternative to classical bearing capacity theory.

Optimisation of the configuration of the mudmat – illustrated through provision of internal shear keys and corner pinpiles or caissons.

Optimisation of the geotechnical input – by acquiring the best available site investigation data and by relying on consolidation strength gains following placement of the foundation and prior to operational loading.

Optimisation of the mode of operation – by challenging the conventional but conservative paradigm that foundations should remain stationary, and adopting the alternative solution of ‘mobile’ foundations.

2 OPTIMISATION OF CAPACITY ASSESSMENT METHODOLOGY

2.1 CURRENT CAPACITY ASSESSMENT METHODOLOGY AND SHORTCOMINGS Classical bearing capacity theory is recommended by most industry guidelines and is typically used to design subsea mudmats. Classical bearing capacity theory is based on uniaxial vertical failure of a plane strain rigid surface punch in uniform plastic material - far from the conditions encountered for a subsea mudmat. The basic bearing capacity equation is modified by a raft of factors to account for foundation shape, foundation embedment, load inclination and soil strength heterogeneity together with the effective width method to account for load eccentricity. The superposition of the various modification factors implies simple superposition of the effects of the variables with no account of interaction, which has been shown to poorly represent the actual response for a range of conditions, particularly horizontal load and moment (HM) interaction (e.g. Ukritchon et al., 1998; Gourvenec and Randolph, 2003; Gourvenec 2007; Taiebat & Carter, 2010). The effective width method, which is conventionally used to capture moment loading, implicitly implies a zero-tension interface between the underside of a shallow foundation and the soil, so that a foundation will lift-off the soil under applied moment in conjunction with low vertical loads. This compounds the conservatism of the classical bearing capacity approach for subsea foundations as offshore ‘skirted’ shallow foundations can mobilise transient tension, providing moment resistance at low vertical load mobilisation (Clukey & Morrison, 1993; Watson et al., 2000; Acosta-Martinez et al., 2008; Gourvenec et al., 2009; Mana et al., 2013). Significantly, classical bearing capacity provides a single equivalent allowable vertical bearing pressure, qult, with no indication on how variations in individual load components affect the factor of safety. These conservatisms are becoming increasingly unacceptable as efficiency of design is becoming increasingly important.

2.2 FAILURE ENVELOPE APPROACH The failure envelope approach allows ultimate limit states to be defined in terms of individual load components and explicit definition of the boundary conditions, such as foundation geometry and soil strength characteristics. The result is a failure envelope or surface defining ultimate limit states in combined load space, so that the effect on factor of safety of a variation in any independent component of load can be assessed. A failure envelope approach for predicting capacity of shallow foundations is attractive over classical bearing capacity theory as the methodology enables insights



into how individual variables affect the design outcome and, through the principle of normality, can provide an indication of displacements at failure. The failure envelope approach is not in itself new (Roscoe and Schofield, 1957; Butterfield and Ticof, 1979; Nova and Montrasio, 1991; Butterfield and Gottardi, 1994; Martin, 1994) but development of a failure envelope-based framework for prediction of capacity under six degrees of freedom, as described in the following section, is a powerful advance (Feng et al., 2014a).

2.3 SIX DOF FAILURE ENVELOPE FRAMEWORK A new framework has been developed to predict undrained ultimate limit states of subsea mudmats under loading in six degrees of freedom. The methodology involves deriving a failure envelope in two-dimensional load space of resultant horizontal load and moment (at any angle to the orthogonal axes of the foundation), adjusted for varying levels of vertical and torsional load mobilisation. Although the approach may be applied more generally, the particular formulation developed is restricted to the conditions shown in Figure 5, of a rectangular skirted foundation resting on a deep clay layer where the strength may be idealised as linearly increasing with depth. The foundation is acted on by fully three-dimensional loading, involving vertical dead load (self-weight) V, biaxial live horizontal loads, Hx, Hy, biaxial moments, My, Mx, and torsion T, referred to as V-H2-M2-T loading. The foundation geometry is focussed on those typically adopted for subsea systems with aspect ratio, B/L = 0.5 and skirt depth ratios, d/B up to 0.2. The load reference point is taken at mudline level. The mudmat is assumed to be able to mobilise transient tensile resistance across the mudmat baseplate (an established phenomenon for sealed offshore foundations, e.g. Dyvik et al., 1993; Clukey and Morrison, 1993; Bye et al., 1995; Watson et al., 2000; Acosta-Martinez et al., 2008; Mana et al., 2013).

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Figure 5: Schematic of mudmat geometry, loading and soil conditions for six degree-of-freedom investigation (Feng et al., 2014a).

The resulting normalised failure envelope, shown in Figure 6 can be described by a relatively simple algebraic approximating expression:

112

max

2

maxmaxmax HH

HH

MM

HH

MM

MM

q

(1)

where Hmax and Mmax are respectively the maximum available horizontal and moment capacity, accounting for mobilised vertical resistance, V/Vult, and mobilised torsional resistance T/Tult. M* is a transformed moment to skirt tip level, M* = M + Hd (which reduces the asymmetry of the failure envelope). The power, q, and the coefficients and are functions of the direction of the resultant horizontal loading, expressed as an angle from the x-axis, and of the soil strength heterogeneity su = kB/su0.

su

22su

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09.0

sin2cos10

33.0

1013q

(2)

The normalised failure envelopes can be transformed to absolute load space by multiplying the apex points by the pure horizontal and moment ultimate limit states for given foundation and soil conditions. A full set of equations for using the methodology is presented by Feng et al. (2014a). The method has been extended to incorporate seabeds with a surficial crust (Feng et al., 2014b) and corner pin piles (see Section 3.1).



MxH ≤ Hmax

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Figure 6: Failure envelope for undrained capacity of a subsea mudmat under loading in six degrees of freedom (Feng et al., 2014a).

The failure envelope approach is conducive to implementation in an automated calculation tool, which can provide insight into how independent input parameters, e.g. foundation geometry, soil strength profile, loads and moments, affect the design output. The method then allows the mudmat size to be optimised for given required loading conditions, soil shear strength profile or design load and material factors. The alternative methodology is a significant advance on a classical bearing capacity approach to subsea mudmat design, but caution should be exercised to ensure the method is used within its limits and by geotechnical engineers. The choice of an appropriate undrained shear strength is central to the calculations and is based on assumptions of an undrained soil response and transient tensile resistance being mobilised. Work is currently underway looking at a zero-tension interface, i.e. as would be appropriate for a perforated foundation that cannot mobilise transient tension under the baseplate. Nonetheless, the method provides a convenient tool for preliminary sizing, can indicate the influence of design input independent variables on design output, demonstrates how improved site investigation data can have significant impact on design and can be augmented with more detailed analysis for detailed design.

The industry partner involved in this project reported that the new design methodology has led to the possibility of reducing the size of shallow foundations such as PLET mudmats by 20%, or alternatively increasing their ability to withstand larger jumper loads (Subsea 7, 2012).

3 OPTIMISATION OF FOUNDATION CONFIGURATIONOptimisation of capacity assessment methodology, as presented above, is one tool for enhancing subsea foundation design. Design outcomes can also be enhanced by optimising the configuration of the mudmat. Two examples of optimisation of mudmat configuration are presented here (i) a so-called ‘hybrid’ subsea foundation, coupling a mudmat with a deeper foundation system and (ii) provision of internal shear keys.

3.1 HYBRID SUBSEA FOUNDATIONA hybrid subsea foundation involves a mudmat and a deeper foundation system acting in consort to increase load carrying capacity above the mat alone. Two concepts for hybrid subsea foundations have been considered at COFS, one involving corner pinpiles as the deeper foundation solution (Dimmock et al., 2013; Gaudin et al., 2012), illustrated in Figure 7 and another using suction caissons (Fu et al., 2014; Bienen et al., 2012), illustrated in Figure 8. The purpose of the provision of the pinpiles or suction caissons is to increase the six degree-of-freedom load capacity over a mat alone, in particular enhancing lateral and torsional resistance, ultimately leading to smaller required footprint sizes.

Considering the pinpile hybrid foundation, in practice the mat would be laid on the seabed and the piles then jacked through a tapered slot in the mudmat, with a locking cap to restrain the pile head from vertical displacement while allowing pile rotation. Centrifuge modelling was carried out at COFS to assess the viability and potential gains in capacity of the hybrid subsea foundation (Gaudin et al., 2012). A simplified lower-bound approach has been developed



for predicting capacity of hybrid subsea foundations (Dimmock et al., 2013) whereby the mat carries the entire vertical design load and the pile group carries the entire sliding and torsional loading. The moment is shared between the mat and the piles through the effective width method and a push-pull mechanism respectively. Considering the two foundation systems independently – i.e. not relying on interaction between the mat and the piles – indicates considerable increase in capacity can be achieved over the mat alone (Figure 9). Research on pinpiled hybrid subseafoundations has continued at COFS refining the design methodology, looking at fully combined load response in six degrees of freedom (Randolph et al., 2012) and at the load-sharing of the mat and pile group when acting in consort. This work is not as yet in the public domain. The industry partner on this project has adopted this innovative foundation system on Esso’s Erha North project offshore Nigeria as a cost-effective mitigation solution against pipeline walking (Subsea 7, 2014). The suction caisson concept has yet to be adopted in the field.

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Figure 7: Hybrid subsea foundation with corner pinpiles (a) schematic (Dimmock et al., 2013) and (b) finite element mesh.

Figure 8: Hybrid subsea foundation with centrally aligned suction caissons (Fu et al., 2014).

The potential efficiency of a pinpiled hybrid subsea foundation in reducing the footprint area is illustrated here for a hypothetical but realistic field case. The example case considers a mudmat of aspect ratio B/L = 0.5, embedment ratio 0.05 with the optional provision of pinpiles with diameter ratio Dp/B = 0.12 and length ratio Lp/B = 1.15 installed in a soft normally consolidated clay. The example foundation geometry, soil shear strength profile and factored loads are summarised in Table 1. For given material factor, s = 1.5, the required footprint area of the unpiled mat is 172.8 m2, compared with 71.3 m2 for the hybrid mudmat foundation, a reduction of 60% - demonstrating the potential benefit from the pile group in improving mudmat load-carrying capacity.



Table 1: External loads for example applications.

Parameter Value Parameter Value Mudmat aspect ratio, B/L 0.5 Soil unit weight, ': kN/m3 5 Mudmat embedment ratio,d/B 0.05 Material factor, s 1.5 Pile diameter ratio, Dp/B 0.12 Vertical load, V: kN 480 Pile length ratio, Lp/B 1.15 Horizontal load, Hx: kN 66.7 Pile spacing: Bpiles/B 0.81 Horizontal load, Hy: kN 91.2 Pile spacing ratio: Lpiles/B 1.81 Moment, Mx: kNm 453 Mudline strength, sum: kPa 0.6 Moment, My: kNm 432 Strength gradient, k: kPa/m 1 Torsion, T: kNm 389

Figure 9: Biaxial moment capacity of a mudmat, pile group and hybrid subsea foundation with pinpiles (Dimmock et al., 2013).

3.2 INTERNAL SHEAR KEYS Provision of sufficient internal shear keys to prevent shearing within the confined soil plug of a skirted foundation is another method for enhancing mudmat capacity (Yun & Bransby, 2007; Mana et al. 2013; Feng et al., 2014c). Skirted foundations, or mudmats, comprise a base plate, which rests on the seabed and a peripheral and often internal ‘skirts’ that penetrate into the seabed beneath the base plate confining a soil plug. A schematic of a mudmat with internal skirts is shown in Figure 10. While internal skirts are provided to enhance structural stiffness, they provide a geotechnical function in pushing the failure mechanism to skirt tip level. This is illustrated in Figure 11 for the simple case of horizontal sliding. A mudmat with only a peripheral skirt exhibits an internal shear mechanism within the confined soil plug, resulting in a limited and near-surface zone of soil being mobilised. Provision of one internal skirt, or shear key, pushes the failure mechanism towards foundation level, mobilising deeper, stronger soil. Provision of sufficient internal shear keys pushes the failure mechanism to foundation level, leading to shearing at tip level, identical to the sliding mechanism of a rigid solid plug. The trend holds under general loading (Feng et al., 2014c), as illustrated in Figure 12 for a constant ratio load path M/HB = 1.5. The bold solid line represents the optimal capacity achieved when the soil plug displaces as a rigid body while the broken lines indicate the reduced capacity if insufficient shear keys are provided.

external skirts

internal skirts

L

B

Figure 10: Schematic of internal shear keys in a subsea mudmat (Feng et al., 2014c).



Figure 11: Effect of shear keys on failure mechanism of a mudmat under pure sliding.

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Figure 12: Effect of internal shear keys on mudmat capacity and accompanying kinematic failure mechanism under general loading (Feng et al., 2014c)

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d/B (d/L) = 0.1

d/B (d/L) = 0.2

a) Number of shear keys as f(shear strength heterogeneity, su) b) Shear key interval as f(local strength heterogeneity, d)

Figure 13: Design charts for optimal shear key spacing, example for 0.25 < V/Vult 0.5 (Feng et al., 2014c).

Results from a program of finite element analyses determined the optimal number of internal shear keys for rectangular mudmats under fully combined loading in six degrees of freedom for a range of embedment ratio, shear strength heterogeneity index and vertical load mobilisation (Feng et al., 2014c). The results are distilled into simple design charts defining the optimal number of internal shear keys as a function of equivalent embedment ratio for intervals of strength heterogeneity index and vertical load mobilisation, as illustrated in Figure 13a. It is seen that the commonly adopted shear key interval of s/d = 5 in engineering practice over-estimates the critical number of internal skirts for cases of low vertical load mobilisation, low soil heterogeneity index and low embedment ratio but becomes unconservative with increasing vertical load mobilisation, soil heterogeneity index and foundation embedment ratio.



The recommendation of s/d = 1 in the geotechnical handbook by Thompson et al. (2011), is shown to over-predict the required number of skirts for all conditions.

Alternatively, the optimal internal shear key spacing ratio, s/B = 1/(n + 1) (or equivalent for s/L), may be plotted as a function of the local soil heterogeneity index, d = kd/su0, focusing on the local shear strength gradient relative to the local strength within the skirt compartment. Figure 13b shows that the optimal skirt spacing varies from approximately 0.33 (though potentially as high as 0.5 at low vertical load) at low d down to around 0.2 at high d but with some dependence on vertical load level and embedment ratio.

4 OPTIMISATION OF GEOTECHNICAL INPUT The previous sections have addressed optimisation of subsea mudmat design by optimising the capacity assessment method and the configuration of the mudmat. In this section, opportunities for optimisation of the geotechnical input parameters are discussed.

4.1 BEST AVAILABLE SITE INVESTIGATION DATA A sound understanding of near-surface soil strength is essential for the accurate prediction of the response of structures laid on or shallowly embedded in the seabed, such as subsea mudmats (and pipelines). However, characterisation of the uppermost region of the seabed, which is typically very soft and at a low-stress state, is extremely challenging. High quality in situ strength data is increasingly achieved with flow around penetrometers (Randolph et al., 2011). One drawback of flow around penetrometers for near-surface characterisation is the uncertainty in the assessed shear strength at very shallow penetrations and corrections must be made to the measured penetration resistance to account for near-surface effects brought about by soil buoyancy and the changing failure mechanism mobilised prior to the full flow of soil around the penetrating bar (White et al., 2010). These corrections are further complicated by the entrainment and mixing of water into the sediment as the penetrometer enters and exits the seabed during cyclic tests. A number of novel tools suited to near-surface strength characterisation are being developed, including the hemi-ball and toroid (Yan et al., 2010; 2011) and the pile penetrometer (Sahdi, 2012; Cocjin et al., 2014a), as shown in Figure 14.

(a) hemiball and toroid (Yan et al., 2010) (b) pile penetrometer (Cocjin et al., 2014a)

Figure 14: New-generation site investigation tools for near-surface characterisation.

The hemi-ball and toroid are shallowly penetrated into the seabed and following a period for equalisation, twisted. A measure of shear strength is provided by the penetration phase, the undrained or drained interface strength can be derived during the twist phase, and the coefficient of consolidation can be deduced from dissipation of excess pore pressure. Further penetration of the device after the dissipation stage allows the gain in strength due to consolidation to be assessed. The pile penetrometer assesses the mean shear strength of near-surface soils without necessitating progressively changing corrections to relieve near-surface effects. The device is a short rigid cylinder, and works by being dragged laterally through soil whilst the bending moment is measured at multiple locations above the soil surface. The pile penetrometer operates in a mode similar to a laterally loaded pile, thus is aptly called a pile penetrometer. The strength profile of the soil can be assessed by evaluating the lateral resistance along the embedded depth and the line of action of the resultant force (Figure 15).

A hypothetical but realistic subsea mudmat design problem is considered again to illustrate the importance of good quality geotechnical site investigation data on design outcomes. The same foundation geometry and loading conditions as set out for the example application in Section 3.2 are utilised (Table 1) and the design methodology presented in Section 2 is employed for evaluating the optimal mudmat footprint. Figure 16 shows the required footprint area of a subsea mudmat as a function of the design value of near-surface soil shear strength which is hypothetically increased from 0.6 to 3 kPa as a result of improved strength definition. It is seen that a small increase in shear strength close to the mudline realises significant benefits in terms of footprint area.



Figure 15: Pile penetrometer interpretation (Cocjin et al., 2014a).

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Hybrid foundation

Figure 16: Example showing required mudmat footprint area with varying near-surface soil shear strength.

4.2 CONSOLIDATED UNDRAINED STRENGTH In an offshore scenario, a mudmat and supported structure may be set down on the seabed several months in advance of operation of the attached pipelines, when the horizontal loads (and therefore moments and torsion) come in to play due to thermal expansion of the attached pipelines. Consolidation of the soil in the vicinity of the foundation will take place under the self-weight of the foundation and structure it is supporting in the period following set down and before operation. Further efficiencies in subsea foundation design can therefore be realised if the consolidation-induced strength gains can be banked, i.e. it may be possible to rely on a higher value of undrained shear strength than measured in situ. The time lapse between installation and operation may range from a few months to a year depending on the project, over which time considerable gains in shear strength may be achieved, depending on the consolidation properties of the sediment. Numerical simulations of the gain in shallow foundation capacity as a result of consolidation of the soil in the vicinity of the foundation have been reported by Bransby (2002), Zdravkovic et al. (2003) and Vulpe and Gourvenec, 2014). Experimental observations are reported by Watson et al., 2000, Randolph and Erbrich (2000), Lehane and Gaudin (2005) and Vulpe and White (2014) and results of field tests by Lehane and Jardine (2003).

Systematic numerical studies that have reached generalised conclusions are reported by (Gourvenec et al., 2014; Feng and Gourvenec, 2014; Vulpe et al., 2014) demonstrating the effects of OCR, relative preload and degree of consolidation for a range of shallow foundation geometry. Figure 17 shows gain in undrained vertical bearing capacity of surface strip and circular foundations resting on deposits of various OCR following full primary consolidation, plotted as a function of relative vertical preload. It is evident that greatest gains are achieved in normally consolidated deposits, where the soil skeleton has the greatest potential for volume change, which represents the condition of most deep water seabed deposits.



Figure 17: Gain in undrained vertical bearing capacity of shallow foundations on deposits of varying OCR following vertical preloading and consolidation (Gourvenec et al., 2014).

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Figure 18: Consolidated undrained gains in capacity of a rectangular mudmat on a normally consolidated deposit under loading in six degrees of freedom (Feng and Gourvenec, 2014).

HV M

Figure 19: Interaction between zone of improved shear strength (contours) and kinematic failure mechanisms (velocity vectors) under pure vertical, horizontal and moment load paths (Vulpe et al., 2014).



Figure 18 shows gains in capacity of a rectangular mudmat resting on a normally consolidated deposit under multi-directional operational loading, following vertical preloading and full primary consolidation. Greatest gains are achieved under horizontal loading and torsion with more moderate gains under vertical loading and moment. It is intuitive that the greatest gains in capacity can be achieved under load paths associated with near-surface kinematic mechanisms where gains in shear strength are greatest. The relative gain in capacity is a function of the extent of interaction between the zone of soil of enhanced shear strength and the zone of soil involved in the kinematic mechanism accompanying failure, as illustrated in Figure 19 and confirmed quantitatively in Figure 18. The gain in capacity is also a function of foundation flexibility and the distribution of the applied load. In the work conducted to date, a rigid foundation has been assumed, thus attracting stress concentrations around the edges of the foundation, resulting in large post-consolidation strength gain. Current work is underway at COFS addressing the effect of mudmat flexibility (i.e. preloading by a uniform pressure across the mudmat base) and non-uniform distribution of load across the mat.

Field situations often preclude full primary consolidation taking place prior to operational loading with only partial consolidation likely to take place. Finite element analyses have shown that the proportion of the fully consolidated gain in uniaxial multi-directional capacity of shallow foundations can be related to the degree of consolidation through simple power law functions (Feng and Gourvenec, 2014) or a lower-bound linear 1:1 relationship can be assumed for a lower limit prediction (Gourvenec et al., 2014), generalising earlier observations reported by Bransby (2002). Furthermore, the normalised failure envelope for undrained (unconsolidated) loading in six degrees of freedom has been shown to scale proportionally with both relative preload and degree of consolidation (Figure 20, Feng and Gourvenec, 2014).

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Vp/Vu = 0.3

Figure 20: Scaling combined load capacity as a function of (a) relative preload and (b) degree of consolidation (Feng and Gourvenec, 2014).

A theoretical method for predicting consolidated strength gains in capacity of shallow foundations under vertical preloading, based on a critical state framework, was presented by Gourvenec et al. (2014). The method relates the change in void ratio over a given stress increment to the change in shear strength at an element level. Elastic and plastic stress increments can be defined for an ‘operative’ preload pressure, defined as the applied preload, vp scaled by a constant ‘stress factor’, f , to account for the non-uniform distribution of stress in the zone of soil affected by the preload (and to account for the applied vertical stresses being considered, rather than the mean stresses). The operative shear strength, su,op, can then be defined from the change in void ratio, e, under the operative preload pressure, adjusted by a constant ‘shear strength factor’, fsu, to account for the non-uniform distribution of the increase in shear strength in the zone of soil that controls the consolidated bearing capacity. Figure 21 illustrates the change in stress and state for an ‘average’ soil element i.e. a notional element representing the average response of the soil within the preloaded zone and the consolidated bearing capacity mechanism.

The method treats the zone of soil beneath the foundation as a single element such that the resulting increase in strength of the affected soil can be calculated as elplsuu Rfs '' (3)

where fsu is a strength factor that scales the gain in strength of the ‘lumped’ soil to that mobilised during subsequent failure which is found to vary with foundation geometry, R is the normally-consolidated strength ratio of the soil, 'pl

and 'el are the elastic and plastic stress components, and and are the slopes of the elastic recompression and normally consolidated lines respectively.



For a pre-consolidation pressure and stress change for which the stress state remains on an elastic recompression line, i.e. f vp < 'vc, the elastic stress is given by

0'' vpel vf (4) and the plastic stress, 'pl = 0.

Figure 21: Representation of soil stress and state for theoretical prediction of consolidated undrained strength gains (Gourvenec et al., 2014).

If the stress state spans across an elastic recompression line to the normal compression line, i.e. f vp > 'vc, the elastic and plastic stresses are given by 0vvcel ''' and (5)

For a normally consolidated deposit the elastic stress, 'el = 0, and the plastic stress change is given by vcppl vf '' (6) where f is a stress factor to account for the non-uniform distribution of the stress in the affected zone of soil, which is found to vary with foundation geometry.

Stress and strength factors, f and fsu, can be uniquely defined for given foundation geometry and operational loading path following vertical preloading. The theoretical method has been applied to a range of foundation and pipeline problems under multi-directional loading (Gourvenec et al,. 2014; Chatterjee et al., 2014; Feng & Gourvenec, 2014; Vulpe et al., 2014), providing a quick and easy methodology for predicting consolidated undrained resistances. These solutions have been derived using the Modified Cam clay model, and the observed gains in strength agree with model testing observations from centrifuge modelling using kaolin clay. However, the influence of consolidation on the strength of a particular natural soil may differ from this experience, and detailed validation of this approach is required for unusual soils.

Potential relative gain in undrained capacity of mudmats under multi-directional loading is illustrated through a hypothetical field case. The design example considers a rectangular mudmat of aspect ratio B/L = 0.5 resting on the seabed (i.e. d/B = 0) with a smooth foundation-soil interface and assumes transient tension resistance can be mobilised. The foundation is assumed to rest on a normally consolidated fine grained seabed with operative coefficient of consolidation 2 m2/year, at a relative vertical load Vp/Vult = 0.5 (where Vult is the undrained, unconsolidated, vertical ultimate limit state) for a period of four months. The analytical method outlined above, programmed into a simple calculation tool, shows around 40% of full primary consolidation occurred over the specified time period, resulting in gains of up to 170% in the undrained consolidated horizontal capacity, 127% in moment capacity and up to 184% for torsional capacity. Input parameters and output in terms of the relative gain in capacity in all six degrees of freedom, Vult, Hxult, Hyult, Myult, Mxult, Tult, are summarised in Table 2.



Table 2: Input parameters and calculated gains in mudmat capacity for consolidated undrained ultimate limit state example.

Parameter Unconsolidated undrained capacity

Consolidated undrained capacity

Gain %

Width, B: m 5 Vertical, Vult: kN 756 Vertical, Vult: kN 1017 134 Length, L 10 Horizontal, Hxult: kN 72 Horizontal, Hxult: kN 121 170 Mudline strength, sum: kPa 1.41 Horizontal, Hyult: kN 72 Horizontal, Hyult: kN 121 170 Strength gradient, su: kPa/m 1.71 Moment, Mxult, kNm 1474 Moment, Mxult, kNm 1621 110 Coefficient of consolidation, cv: m2/yr 2 Moment, Myult, kNm 544 Moment, Myult, kNm 689 127

Preload, Vp/Vult 0.5 Torsion, Tult: kNm 212 Torsion, Tult: kNm 391 184 Consolidation period: yr 0.33

4.3 EFFECTS OF CYCLIC LOADING All offshore structures and hence the foundations that support those structures are subject to cyclic loading. Cyclic loading of subsea foundations may arise from environmental, installation or operational loading. Environmental cyclic loading of a subsea mudmat may derive from currents and internal waves (and surface waves in shallow water); installation cyclic loading of a subsea mudmat may derive from laying a pipeline around a buckle inducing structure; and operational cyclic loading of a subsea mudmat may derive from vibrations of attached components, slug flow in pipes or thermal expansion and contraction of attached pipelines during regular, scheduled start ups and shut downs. Cyclic loading of subsea structures, typically horizontal, may be one-way or two-way leading to accumulated residual strains or degradation of shear strength of the supporting seabed deposits.

Appropriate prediction of the degradation of cyclic strength and stiffness will ensure the most appropriate engineering parameters are defined. Unnecessary conservatism in parameter selection is required to account for uncertainty in the effect of cyclic loading on engineering parameters, which will lead to conservatism in design output. Current work at COFS is investigating a framework to predict cyclic degradation of soil properties, with particular attention to shallow foundations. Foundation capacity could then be assessed by accounting for consolidated gains in capacity, modified by a reduction factor to account for cyclic loading degradation.

Cyclic loading associated with degradation of the engineering properties of a soil refers to periods of loading in which excess pore pressure cannot dissipate, resulting in a reduction in effective stress and hence strength of the soil. Periods of cyclic loading of sufficient duration to allow dissipation of excess pore pressure, may lead to an increase in density of the soil and associated increase in shear strength, if the soil is initially contractile. This mode of so-called periodic monotonic loading is discussed further in the following section.

5 OPTIMISATION OF OPERATIONAL MODE The previous sections have demonstrated various methods, or tools, for enhancing geotechnical design of subsea foundations through optimising the capacity assessment method, the foundation configuration and the geotechnical input. A final method to be presented here is optimisation by challenging the traditional but conservative paradigm that a foundation should remain stationary – i.e. optimisation by adopting an alternative mode for operation of the foundation and the supported infrastructure.

5.1 MOBILE FOUNDATIONS The concept of mobile foundations is that they are designed to move tolerably across the seabed to absorb some of the load imposed by thermal expansion of the pipeline rather than being designed large enough to resist all the operational loads and remain stationary (Cathie et al., 2008; Cocjin et al., 2014b, 2015; Deeks et al., 2014; Gourvenec, 2014a, b). The concept of mobile foundations is radical. However, it is a logical progression from a parallel design trend which is the now widely-accepted practice of permitting subsea pipelines to buckle laterally either across the seabed or on engineered structures in response to thermally-induced expansion during operation. This approach is cost effective compared to the conventional technique of adopting expensive mitigation measures such as burial or anchoring to resist pipeline movement.

In contrast to a conventional static mudmat equipped with skirts to penetrate the seabed, mobile foundations rest on the surface of the seabed. A key aspect of the design concept of mobile foundations is a sliding response to pipeline expansion and contraction. Rotation of the foundation in any plane could overstress the pipeline connections with severe potential consequences in terms of loss of containment. In the investigation of mobile foundations being carried out at UWA, the mudmat is equipped with ‘skis’ to facilitate sliding. A schematic of a mobile foundation as part of a flowline network is illustrated in Figure 22.



Figure 22: Schematic of a ‘mobile’ subsea mudmat (Cocjin et al., 2014b).

A mobile foundation would slide back and forth across the seabed 100s or 1000s of times over the operational life cycle of a field in response to thermal expansion and contraction of the attached pipelines during operation and subsequent scheduled and regular shutdowns. The mode of operation involves the mudmat translating from the shutdown position to an operational position sufficiently fast for an undrained soil response. The foundation then remains in the operating position for a period of time, a few months or more, before sliding back to the shutdown position. The period of shutdown is short relative to the period of operation (around 1 day) before the cycle is repeated. The operational modes of a mobile foundation are illustrated schematically in Figure 23). From a geotechnical perspective, the operational mode of a mobile foundation can be described as cycles of periodic monotonic shearing and reconsolidation. The sliding motion generates shear-induced excess pore pressures in the soil around the foundation, which then dissipate during the period of operation of the pipeline when the mudmat is stationary, allowing reconsolidation before a second cycle of shearing. The effect of these ongoing cycles of remoulding and reconsolidation during operation of a mobile foundation has been investigated through geotechnical centrifuge tests (Cocjin et al., 2014b).

pipelinefoundation

seabed

a) Set-down

b) Operation

uForward slide in response to thermal expansion of pipeline

c) Shut-down

Reverse slide in response to thermal contraction of pipeline-u

Figure 23: Schematic of operational mode of mobile foundation.

The centrifuge model is shown in Figure 24, attached to a purpose built in-house designed and constructed loading arm (O’Loughlin et al., 2014) that allows the foundation to be free to rotate in both planes and controls or measures the



vertical and horizontal loads and displacements. The raised discs seen at the corners of the foundation are laser targets for accurate measurement of foundation displacements throughout the tests. The tests involved whole-life modelling of the mobile foundation with multiple cycles of sliding and intervening periods of rest representing the operational and shutdown sequences of an offshore PLET mudmat. The longest test represented a prototype time of 70 years, carried out over 72 hours of non-stop flight. Figure 25 shows a photograph of the foundation footprint at the end of a test, after multiple cycles of sliding and rest periods, showing settlement of the mudmat and development of a soil berm at the ends of the footprint.

Loading arm

Model foundation

Actuator attachment

Horizontal load cell

Vertical load cell

Roller

Hinge

Figure 24: Geotechnical centriuge model of mobile subsea mudmat (Cocjin et al., 2014b).

Sliding direction

Soil berm

Figure 25: Post test image showing soil berm and settlement (Cocjin et al., 2014b).

Impact of the foundation against the berm can be clearly seen in Figure 26, showing sliding resistance of the foundation against sliding distance (highlighted for selected cycles). Towards the end of the forward and backward slide, the foundation impacts on the berm of soil created from the repeated sliding events and foundation settlement (points A and B in Figure 26). A peak in resistance is also observed on reversal of sliding (point C in Figure 26) – but in this case due to the increased shear strength of the underlying soil from reconsolidation, from dissipation of the shear-induced excess pore water pressure during the period while the foundation remained stationary, in the ‘operational’ position. The steady state sliding resistance also shows a consistent increase with increasing numbers of operational cycles (marked C in Figure 26), showing that the regain in shear strength due to consolidation between sliding events more than compensates for the reduction in strength caused by remoulding during the sliding event. The gain in sliding resistance against number of cycles of sliding and reconsolidation is plotted in Figure 27, showing up to a three-fold increase in sliding resistance as a result of the continuous process of remoulding and reconsolidation.

A theoretical framework is currently being developed to predict the observed foundation behaviour. Numerical simulations have also been performed that accurately predict the observed centrifuge test results and provide the springboard for wider parametric studies of other soil properties, foundation geometries and loading conditions.



Figure 26: Sliding resistance of mobile foundation (Cocjin et al., 2014b).

Figure 27: Cumulative gain in sliding resistance as result of remoulding and reconsolidation (Cocjin et al., 2014b).

6 CONCLUSIONS AND RECOMMENDATIONS This paper has presented some of the tools available to optimise the geotechnical aspects of subsea foundation design. These include an alternative failure envelope-based design method, extension of that method to incorporate corner pinpiles or central caissons, design charts for determining the optimal number of internal shear keys, a theoretical framework for predicting consolidated strength gains and reductions due to cyclic loading and, looking to the future, a design framework for tolerable foundation mobility. These various options can be described by an ‘optimisation class’ in terms of optimising the design methodology, optimising the configuration of the foundation, optimising the geotechnical input parameters and optimising the mode of operation. The techniques described in this paper are examples of some tools in each class, but the implication is not that the tool box is complete. Much scope exists for adding new tools in each class. Current research at COFS is investigating new tools for predicting cyclic load response



and settlements – tools that are simple enough to use but sophisticated enough to capture the necessary aspects of soil behaviour.

Many of the technologies described in this paper have been applied in practice by the CGSE partner Advanced Geomechanics, based in Perth, supporting projects offshore Australia and globally.

The key message in this paper is that the best way to address any geotechnical challenge is with a toolbox of solutions – so the most appropriate tool or a combination of tools can be employed to address a particular geotechnical challenge for the best design outcome. A bespoke approach is best for geotechnical design.

7 ACKNOWLEDGEMENTS The work presented here forms part of the activities of the Centre for Offshore Foundation Systems (COFS), supported as a node of the ARC Centre of Excellence for Geotechnical Science and Engineering (CGSE) and as a Centre of Excellence by the Lloyd’s Register Foundation (LRF). Lloyd’s Register Foundation helps to protect life and property by supporting engineering-related education, public engagement and the application of research. Parts of the research presented in this paper derive from a collaboration between COFS, Subsea 7 and BP and parts from ARC Discovery Project DP140100684. All sources of support are gratefully acknowledged.

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