Critical Skirt Spacing for Shallow Foundations under General Loading

TLDR: In this paper, the critical internal skirt spacing for the undrained failure of shallow skirted foundations under conditions of plane strain based on the criterion that the confined soil plug should ideally displace as a rigid block, such that optimal bearing capacity is realized.

Abstract: Finite-element limit analysis is used to identify the critical internal skirt spacing for the undrained failure of shallow skirted foundations under conditions of plane strain based on the criterion that the confined soil plug should ideally displace as a rigid block, such that optimal bearing capacity is realized. General loading (vertical, horizontal, and moment) is considered for foundations with skirt embedments ranging from 5 to 50% of the foundation breadth in soil having either uniform strength or strength proportional to depth. The results explicitly identify the number of internal skirts required to ensure soil plug rigidity under arbitrary combinations of horizontal and moment loading expressed as a function of the normalized skirt embedment and the maximum expected level of vertical loading as a fraction of the ultimate vertical bearing capacity. It is shown that fewer internal skirts are required with increasing normalized foundation embedment, but more internal skirts are required wit...

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Published in ASCE Journal of Geotechnical and Geoenvironmental Engineering,
139(9):1554-1566. http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0000882
1
Critical skirt spacing for shallow foundations under general loading 1
2
Divya S.K. MANA 3
Centre for Offshore Foundation Systems (M053) and ARC Centre of Excellence for 4
Geotechnical Science and Engineering 5
University of Western Australia 6
Email: 20674905@student.uwa.edu.au 7
8
Susan GOURVENEC (corresponding author) 9
Centre for Offshore Foundation Systems (M053) and ARC Centre of Excellence for 10
Geotechnical Science and Engineering 11
University of Western Australia 12
35 Stirling Highway, Crawley 13
Perth, WA 6009 14
Australia 15
Tel: +61 8 6488 3995 16
Fax: +61 8 6488 1044 17
Email: susan.gourvenec@uwa.edu,au 18
Christopher M. MARTIN 19
Department of Engineering Science 20
University of Oxford 21
Email: chris.martin@eng.ox.ac.uk 22
23
No. of words: 5607 (without abstract, acknowledgements and references) 24
No. of tables: 0 25
No. of figures: 23 26
27

Published in ASCE Journal of Geotechnical and Geoenvironmental Engineering,
139(9):1554-1566. http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0000882
2
Abstract 28
Finite element limit analysis is used to identify the critical internal skirt spacing for 29
undrained failure of shallow skirted foundations under conditions of plane strain, based 30
on the criterion that the confined soil plug should ideally displace as a rigid block, such 31
that optimal bearing capacity is realized. General loading (vertical, horizontal and 32
moment) is considered for foundations with skirt embedments ranging from 5% to 50% 33
of the foundation breadth, in soil having either uniform strength or strength proportional 34
to depth. The results explicitly identify the number of internal skirts required to ensure 35
soil plug rigidity under arbitrary combinations of horizontal and moment loading, 36
expressed as a function of the normalized skirt embedment and the maximum expected 37
level of vertical loading (as a fraction of the ultimate vertical bearing capacity). It is 38
shown that fewer internal skirts are required with increasing normalized foundation 39
embedment, but more internal skirts are required if the soil strength increases with 40
depth. The results also indicate the potential for a significant reduction in capacity if 41
insufficient skirts are provided, such that plastic deformation is permitted to occur 42
within the soil plug. 43
44
Key words: Offshore structures; Limit analysis; Shallow foundations; Failure loads 45
46

Published in ASCE Journal of Geotechnical and Geoenvironmental Engineering,
139(9):1554-1566. http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0000882
3
1 Introduction 47
Skirted shallow foundations are comprised of a main foundation base plate with 48
relatively slender vertical plates (typically both peripheral and internal) protruding 49
below. These ‘skirts’ penetrate into the seabed, with the aim of confining a block of 50
surficial soil referred to as the soil plug. A cross-section through an idealized skirted 51
foundation is shown in Figure 1. In order to achieve maximum capacity, sufficient 52
internal skirts should be provided to ensure that the soil plug displaces as a rigid body 53
during plastic failure of the foundation. If too few internal skirts are provided, failure 54
mechanisms involving deformation within the soil plug may occur, leading to a 55
reduction in load-carrying capacity. Figure 2 illustrates some examples of these 56
potential ‘internal mechanisms’, as compared with the behavior of a corresponding solid 57
foundation, for the simplified cases of pure vertical and pure horizontal loading. In the 58
examples shown, deformation within the soil plug occurs when there are no internal 59
skirts and when a single internal skirt is provided, while the provision of two (or more) 60
internal skirts results in the same failure mechanism as that induced by the solid 61
foundation. 62
Previous research has shown that for foundations with peripheral skirts only, an internal 63
mechanism is unlikely to occur for deep skirts and a uniform profile of undrained 64
strength with depth, but the potential is increased for shallow skirts and a high degree 65
of strength heterogeneity (Yun and Bransby 2007, Bransby and Yun 2009, Mana et al. 66
2010). Although these previous works have identified the foundation configurations and 67
soil conditions most susceptible to the development of internal mechanisms, the 68
question of the number of internal skirts required to ensure rigid soil plug behavior – 69

Published in ASCE Journal of Geotechnical and Geoenvironmental Engineering,
139(9):1554-1566. http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0000882
4
whether for idealized cases of uniaxial loading or more realistic combinations of general 70
loading – has not been addressed to date. 71
Despite the potential for plastic deformation to occur within the soil plug, skirted 72
foundations are often treated as embedded solid foundations when assessing ultimate 73
capacity, on the basis that sufficient internal skirts have been provided to ensure that the 74
soil plug displaces rigidly. For example, the assumption of a solid, rigid foundation is 75
inherent in the classical bearing capacity calculation methods presented in current 76
recommended practices and industry guidelines (e.g. API 2000, ISO 2003). If, however, 77
the provision of internal skirts is insufficient, the critical collapse mechanism will 78
extend into the soil plug, resulting in a load-carrying capacity that is smaller than the 79
anticipated design value. 80
This paper presents results from a comprehensive numerical investigation of the critical 81
number of internal foundation skirts required to ensure that the soil plug confined within 82
a skirted foundation displaces as a rigid block, thus ensuring that the maximum load-83
carrying capacity of the foundation can be realized. 84
2 Scope of study 85
2.1 Foundation geometry 86
This study considers both solid and skirted shallow foundations with embedment to 87
breadth ratios, d/B, between 5% and 50%. The range of embedment ratio was selected 88
to represent a range encountered in the field, for example shallow foundations for 89
subsea systems typically lie in the range 0.05 ≤ d/B ≤ 0.2 while foundations for fixed-90
bottom or buoyant platforms typically lie in the range 0.2 ≤ d/B ≤ 0.5. For the skirted 91

Published in ASCE Journal of Geotechnical and Geoenvironmental Engineering,
139(9):1554-1566. http://dx.doi.org/10.1061/(ASCE)GT.1943-5606.0000882
5
foundations, the peripheral and internal skirts are modeled with a thickness to breadth 92
ratio t/B = 0.001 and are positioned with uniform spacing, s, across the foundation base 93
plate. The modeled skirt thickness ratio represents a value towards the lower end of the 94
range used in the field (e.g. Bye et al. 1995, Erbrich and Hefer 2002) and has been 95
selected to minimize the effect of the geometry of the skirts on the calculated bearing 96
capacities and failure mechanisms. A foundation with peripheral skirts only is referred 97
to as having ‘zero internal skirts’. Figure 3 shows the modeled geometry and the 98
nomenclature adopted in this paper. 99
In practice, skirted foundations and/or the distribution of internal skirts may often adopt 100
a three-dimensional arrangement. Skirted foundations for gravity base structures, 101
jackets or buoyant facilities are likely to be quasi-circular or rectangular with length to 102
breadth aspect ratio L/B between 1 and 2 while subsea foundations are likely to be 103
rectangular, also with L/B between 1 and 2. 104
However, plane strain modeling is considered adequate for the purpose of this study, 105
where the focus is identifying underlying mechanisms. Failure mechanisms dominated 106
by sliding and rotation are essentially in-plane and therefore shape effects of three-107
dimensional foundation geometry would not be expected to be significant. Failure 108
mechanisms with a significant axisymmetric component, such as vertical bearing 109
failure, would be expected to be more significantly affected by three dimensional 110
effects, although design situations with vertical load close to critical values are perhaps 111
unlikely. When considering foundations with a length to breadth aspect ratio greater 112
than 1, it should be borne in mind that the effective embedment ratio for loading acting 113
perpendicular to the long edge is defined by d/L rather than d/B, such that closer 114

Frequently asked questions

Q1. What are the contributions in this paper?

In this paper, the critical number of internal skirts required to ensure rigid soil plug behavior was investigated for skirted shallow foundations. 

Q2. What is the effect of a foundation with very short skirts on the soil?

462• In reality, a foundation with very short skirts placed on soil with low mudline 463 strength will tend to settle until sufficient bearing capacity is achieved, resulting in a 464 higher effective embedment and thus a reduction in the required number of internal 465 skirts. 

Q3. How many internal skirts are required for a low embedment ratio?

In many cases, more than 411 twice as many internal skirts are required in soil with strength proportional to depth 412 (kB/sum = ∞) compared with uniform soil (kB/sum = 0) across the range of embedment 413 ratios considered in this study. 

Q4. What is the significance of the gapping between the foundation skirts and the adjacent soil?

It is 150 acknowledged that gapping between the foundation skirts and the adjacent soil may 151 occur, particularly when a foundation is subjected to predominantly horizontal loading 152 in soil with a low degree of strength heterogeneity. 

Q5. How many internal skirts are needed to achieve maximum H-M capacity?

441The efficiencies available from limiting the vertical load level are relatively modest, 442even when kB/sum = ∞, with one or at most two internal skirts being saved (although at 443 high embedment ratios this is a reduction by half). 

Q6. How many internal skirts are required to ensure soil plug rigidity?

337Figure 15 and 16 show that when the soil strength is proportional to depth (kB/sum = ∞), 338 more internal skirts are required, particularly when the skirt embedment ratio is low, as 339 in Figure 15. 

Q7. How many internal skirts are required to achieve maximum H-M capacity?

In the case of soil with strength proportional to depth, 434 Figure 23b, a reduction in the required number of internal skirts is achieved over the full 435 range of embedment ratios. 

Q8. how many internal skirts are required to ensure soil plug rigidity?

341 In fact, Figure 15 shows that six or more internal skirts are required to ensure soil plug 342 rigidity for a foundation with d/B = 0.1 in soil with strength proportional to depth – 343 twice as many as are required with the same embedment ratio in a deposit with uniform 344 strength (cf. Figure 13). 

Q9. How can the 122 variation of strength with depth be approximated?

In the field, the 122 variation of strength with depth can often be approximated with sufficient accuracy as a 123 linear function. 

Q10. What is the number of internal skirts required to ensure that the maximum load-carrying?

80This paper presents results from a comprehensive numerical investigation of the critical 81 number of internal foundation skirts required to ensure that the soil plug confined within 82 a skirted foundation displaces as a rigid block, thus ensuring that the maximum load-83 carrying capacity of the foundation can be realized. 

Q11. What is the effect of normalization on the bearing capacity factor of 256?

Also with respect to 256 Figure 8b, it should be noted that in the reduction in bearing capacity factor with 257 increasing embedment ratio is an effect of normalization by an ever-increasing strength 258 at skirt tip level; the actual bearing capacity Vult increases with d/B.