NUMERICAL STUDY OF OFFSHORE SKIRTED FOUNDATIONS SUBJECTED TO COMBINED LOADING

NUMERICAL STUDY OF OFFSHORE SKIRTED FOUNDATIONS SUBJECTED TO COMBINED LOADING S.K. NAIK 1, S.M. DASAKA 2, and V.B. CHAUHAN 3 1 Former Post Graduate Student, Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai, India 2 Associate Professor, Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai, India 3 Research Scholar, Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai, India Skirted foundations are one of the offshore shallow foundations, which are used in offshore oil and gas industries. In offshore environment, foundations are subjected to large components of combined horizontal (H), moment (M), torsion (T) loading as compared to vertical loading (V) due to water waves, wind loading etc. These loads change frequently so it is important to analyze foundations subjected to combined loading conditions. The foundations are subjected to three-dimensional loading condition. Failure envelopes are particularly relevant to offshore shallow foundations, which provide useful information on bearing capacity, ultimate limit states and proximity to failure of foundations under 3d general loading. In the present study numerical analysis of a typical mudmat skirted foundation of size 20m 8m rested on clayey seabed is analyzed using three-dimensional finite-element code i.e. PLAXIS 3D. The foundation is assumed to be rigid and placed on soft normally consolidated seabed. The undrained shear strength and Youngs modulus of soil are assumed to vary linearly with depth, maintaining constant rigidity index and modeled as per linearly elastic-perfectly plastic constitutive law. Here mudmat foundation subjected to V-H-T loading condition is analyzed. Failure envelopes and bearing capacity subjected to different combination of loads i.e. V-T, V-H, H-T and V-H-T are evaluated and compared by providing both outer skirts and inner skirts, which can be used to provide a safe design of mudmat skirted foundations in offshore environment. The responses of failure envelopes for both normalized load space and dimensional load space are evaluated and reported. Keywords: Skirted foundation, Failure envelope, Mudmat, Heterogeneity factors, Strength gradient, PLAXIS. 1. Introduction The offshore industry requires sustainable development of novel techniques in order to extract oil and gas in those regions, which are inaccessible to extract the natural resources with the existing technologies. The continuous increase of energy consumption by mankind has led to depletion of resources in many parts of the world. Over 30% of total hydrocarbon resource is present in offshore regions and only 10% has been explored. Exploration of these resources requires effort from both geologists and engineers. As a result of this, most of the developments in offshore engineering is directed towards the recovery of these resources (K.S. Chakrabarti 2005). Geotechnical engineers are in phase of developing an alternative method for improving the bearing capacity and reducing the settlement of footing resting on soil. Advances in Soft Ground Engineering. Edited by C. F. Leung, T. Ku and S. C. Chian Copyright c 2015 by ICSGE15 Organizers. Published by Research Publishing ISBN: 978-981-09-7520-3 :: doi: 10.3850/978-981-09-7520-3 137 537

538 S.K. Naik et al. Though a variety of methods of soil stabilization are known and well-developed, they can be prohibitively expensive and restricted by the site conditions. In some situations they are difficult to apply to existing foundations. In this case, structural skirts hold good as an alternative method of improving the bearing capacity and reducing the settlement of footing resting on soil. Structural skirts have been used for a considerable period to increase the effective depth of the foundations in marine and other situations where water scour is a major problem (E.T.R. Dean 2008). This method of bearing capacity improvement does not require any excavation of the soil and is also not restricted by the presence of a high ground water table. Skirts provided with foundations, form an arena, in which soil is strictly confined and act as a soil plug to transfer super-structure load to soil (Hu et al. 1999). Skirted foundations have been extensively used for offshore structures like wind turbine due to easy installation compared to deep foundation (Gourvenec et.al. 2011). Shallow skirted foundations have been used to support structures in gas industry. It is believed that the vertical skirts improve the foundation capacity by trapping the soil beneath the raft and between the skirts so that applied load is transferred to the soil at the skirt tips. Skirt foundations have a wide variety of functions, such as control of settlement during service life and lesser impact to environments during operation at installation site. Skirted foundations are used to satisfy bearing capacity requirement, and to minimize the embedment depth and dimensions of the foundation (Eid 2012). Vertical loading due to the self weight of installation (i.e. Jacket structure, Wind turbine) is improved, as soft surface soils are confined within the skirts and the foundation loads are transferred down to harder underlying soil layers. Inclusion of skirts in foundation improves the horizontal load carrying capacity by resisting lateral sliding. In the present study, numerical analysis of skirted foundation is performed in various loading conditions using multiple skirts to know the bearing capacities of foundations and failure envelopes are derived in different loading space. 2. Numerical Modelling Mohr-coulomb model is the first order approximation of soil behavior and due to its simplicity. It is adopted extensively in geotechnical analyses. In the present study Mohr-coulomb model is adopted to model the soil (Yun and Bransby 2007). The combination of Mohr failure envelope and the Coulomb strength parameters is referred as Mohr-Coulomb failure criterion. It states that a material fails not due to their maximum normal stress or shear stress but due to the critical combination of normal and shear stress. This is the only failure criterion that predicts the stresses on failure plane. In PLAXIS, the Mohr-Coulomb criterion uses an elastic perfectly plastic constitutive model for three dimensional state of stress. The use of effective strength parameters in undrained analysis in this model may overestimate the shear strength of material in undrained conditions. To avoid that problem total stress analysis is preferred in present case, where the cohesion parameter is used to model the actual undrained shear parameter (C u ) and the friction angle (ϕ) is set to be zero (Yun and Bransby 2007). In the present analysis, a rectangular mudmat skirted footing having dimensions, length (L) = 21m, breadth (B) = 9m, area (A) = 189m 2 and depth of skirt (D s )=1m is adopted for actual simulation. It is assumed that seabed consists of soft clay and its shear strength varies linearly from foundation level as shown in Fig. 1.

Numerical Study of Offshore Skirted Foundations Subjected to Combined Loading 539 Fig. 1. Linear variation of shear strength with depth. Here S u is the undrained shear strength at the skirt tip level. Undrained shear strength at any depth is determined by using the linear equation as follows: S u = S u0 + kz (1) Where, the undrained shear strength gradient, k is about 1.0 to1.3kpa/m from the mud line (Yun and Bransby 2007). A conservative value of undrained shear strength gradient, k equals to 1.3 kpa/m is assumed for the analysis. Boundary conditions corresponding to model are applied. Horizontal boundary (u x = 0) conditions are maintained at 3B from the edge of the foundation in both directions of length and width. Bottom of the mesh is fixed in x and y direction (u x = 0andu y = 0) and maintained at 3B from the top which is shown in Fig. 2. Properties of skirts and soil considered in this analysis are listed below. Poisson s ratio (υ) of clay is considered as 0.49 instead of 0.5 to avoid error in numerical computation. It is assumed that both skirts and baseplate of mudmat are weightless to avoid any difficulty in calculation. After assigning the properties to soil and plate elements, mesh is generated. A refinement of mesh is done near the mudmat foundation for precise results as shown in Fig. 2. Load combinations in offshore environment are selected based on the previous studies carried out by Poulos (1988) and Kellezi (2008). In these studies, failure envelopes are evaluated in different loading spaces i.e. V-H, V-T, H-T and V-H-T. The application of loadings on the mudmat foundation is based on the component loading systems according to Kellezi et al. (2008). So, in the present study, different combination of loads are applied and the corresponding failure loads are evaluated (with internal skirts and without internal skirts). In this case, the reference point for calculation of failure load is chosen at the middle of the foundation (mudmat). Table 1. Material properties (soil and skirts). Unit weight of soil 16.5 kn/m 3 Thickness of base plate 0.2 m Poissons ratio (ν) 0.49 Thickness of skirts 0.02 m Rigidity index 500 Youngs modulus (E) 2 10 8 kn/m 2 Interface factor 0.6 Poissons ratio (ν) 0.27

540 S.K. Naik et al. Fig. 2. Model geometry Mesh of mudmat foundation. 3. Validation and Results In this analysis vertical loading is kept constant to simulate offshore environment and both horizontal loading and torsional loading are varied from very low value to very high value to assess the behavior under combined loading conditions. The different combinations of loadings are applied on mudmat foundation. Non-dimensional failure envelopes are derived without provision of internal skirts and with provision of internal skirts which are shown in Fig. 3 and Fig. 3 respectively. Normalized failure envelopes are derived and validated with Randolph et al. (2014) which shows well agreement as shown in Fig. 4. Fig. 5 and Fig. 5 show non dimensional failure envelopes in V-T loading space. In this case vertical load and horizontal load with certain eccentricity is maintained to simulate torsional load. Figure 6 shows the normalized failure envelopes of foundation with the provision of internal skirts in V- T loading space. It showed well agreement with Randolph et al. (2014). Figure 7 (without internal skirts) and Fig. 7 (with internal skirts) show non dimensional failure envelopes in H-T loading space. In this case vertical load is kept constant. Fig. 3. Non-dimensional V-H failure envelopes without internal skirts with internal skirts.

Numerical Study of Offshore Skirted Foundations Subjected to Combined Loading 541 Fig. 4. Normalized V-H failure envelope with internal skirts. Fig. 5. skirts. Non-dimensional failure V-T failure envelopes without internal skirts with internal Both horizontal load and horizontal load with certain eccentricity are maintained. V- H-T failure envelopes with the provision of internal skirts are shown in Fig. 9. In this case vertical load is kept constant and both horizontal load and torsional load is varied from small value to large values. If any combinations of loads in field lie inside the failure envelopes then it is safe for the foundation and if it lies outside the failure envelopes then failure is imminent for the foundation. Factor of safety can be a determined using theses failure envelopes, which is the shortest distance between the loading point inside the failure envelopes and point on failure envelopes. The vertical bearing capacities of foundations do not have much effect due to installation of internal skirts. There is slight influence of internal skirts on vertical bearing capacity. The calculated bearing capacities are mentioned below. The horizontal bearing capacity is significantly influenced by the installation of internal skirts. It is increased up to 22.8%. The soil strength near skirts mobilized easily due to horizontal load. The failure mechanism of mudmat due to horizontal loading is shown below Also from the Fig. 9 it can be observed that the shape of the failure envelopes changes if torsional load is increased i.e. the area of failure envelope subjected to

542 S.K. Naik et al. Fig. 6. Normalized V-T failure envelopes with internal skirts. Fig. 7. Non-dimensional H-T failure envelopes without internal skirts with internal skirts. Fig. 8. Normalized H-T failure envelope. lower torsional load is less than the area of failure envelope with higher torsional load. It indicates that both vertical bearing capacity and horizontal bearing capacities reduce significantly. Because of torsional load, extra shear stress develops and it combines with the shear stress developed by horizontal loading. This combination of shear stress exceeds the shear capacity. So bearing capacity reduces. The effects of

Numerical Study of Offshore Skirted Foundations Subjected to Combined Loading 543 Fig. 9. Effect of increment of torsional load on failure envelopes. Table 2. Comparison of bearing capacities (with and without internal skirts). Foundation Details V ult H ult Mudmat without internal skirts 7520 kn 840 kn Mudmat with internal skirts 7370 kn 1088 kn Fig. 10. Failure mechanism due to horizontal loading. torsional loads are more in corner area of mudmat foundation and the soil close to corner area are more prone to failure of foundation as the soil close to corner area are easily mobilized. However, the central area of foundation doesn t show significant change in effect due to torsion load. Also when torsional loads increase the failure areas move to the corner, which is shown in Fig. 11. The same effect is studied for foundation with internal skirts and it envisages that the effect of internal skirts on mudmat foundation is significant. The area covered by failure envelope is more in comparison to that of foundation without internal skirts, which can be observed in Fig. 12. As failure envelopes are efficient tools for design and analysis of offshore foundation subjected to combined loading, an attempt is made to derive best fit equations for failure envelope in present analysis. Mudmat foundations are generally fabricated with both outer skirts and inner skirts. Here, ultimate limit state equations are derived

544 S.K. Naik et al. Fig. 11. Failure mechanism due to torsion without internal skirts small torsional load large torsional load. Fig. 12. Failure mechanism due to torsion with internal skirts small torsional load large torsional load. for foundation with inner skirts. The equation of ultimate limit states for horizontal and torsion loading according to Finnie and Morgan. (2003) is [( ) H n ( ) T m ] + = 1 (2) H ult An attempt is made to derive the approximate ultimate limit equations for V-T and V-H loading space from the data obtained from present analysis. These are mentioned below. So Ultimate limit state equation for V-T load space is found to be [( ) V n ( ) T m ] + = 1 (3) V ult Ultimate limit state equation for V-H load space is found to be [( ) H n ( ) V m ] + = 1 (4) H ult By using best fit technique for ultimate limit state equations, values of coefficient m is obtained which varies from 1.9 to 2.02 and that for n lies in between 0.95 to 1.84. It shows good agreement with the most of the loading paths of failure envelopes as shown in above failure envelopes plots. 4. Conclusions In the present study, numerical analysis of foundations is conducted in undrained condition to know the behaviour under combined loadings. In this analysis emphasis T ult T ult V ult

Numerical Study of Offshore Skirted Foundations Subjected to Combined Loading 545 is given more to horizontal and torsional loading. The effects of soil strength heterogeneity and effect of skirts on the bearing capacity of foundations are also determined. Deviations of present study results and from conventional methods are also evaluated. In the present study analysis of a typical rectangular mudmat foundation subjected to V-H-T loading is conducted. Bearing capacities are determined and validated with theoretical method. Also behaviour of this mudmat foundation with internal skirts is studied. Failure envelopes are derived which can be used for design and determination of factor of safety of foundations. From the present study it is observed that horizontal bearing capacity is increased by 22.8% approximately. The internal skirts shows more influence on the horizontal bearing capacity. Also twodimensional failure envelopes in normalized forms are derived in different loading spaces i.e. V-H, V-T, and V-H-T. Several numbers of loading paths are adopted for simulation of actual field conditions. With increase in torsional load, the size of the failure envelopes reduces. Also, due to torsional loading both vertical and horizontal bearing capacities are reduced. Attempt is made to find the best fit equations for those derived failure envelopes for easy analysis in combined loading conditions. Few well instrumented experimental tests may be conducted for analysis of offshore foundations in combined loading conditions and also serviceability responses may be assessed. References 1. Bransby, M.F. and Randolph, M.F. (1998). Combined loading of skirted foundations. Geotechnique 48(5), 637 655. 2. Chakrabarti, K.S. (2005). Handbook of offshore engineering, Offshore structure analysis, Inc, Plainfield, Illinois, USA. 3. Dean, E.T.R (2008). Offshore geotechnical engineering, Thomas Telford ltd, London, UK. 4. Eid, H.T. (2013). Bearing capacity and settlement of skirted shallow foundations on sand. International Journal of Geomechanics, ASCE Vol. 13, No. 15. 5. Finnie, I.M.S. and Morgan, N. (2004). Torsional loading of subsea structure. ISOPE conference, Toulon, 2004-JSC-346, pp. 326 333. 6. Gourvenec, S. (2007). Failure envelopes for offshore shallow foundations under general loading. Géotechnique 57(9), pp. 715 728. 7. Gourvenec and Barnett (2011). Undrained failure envelope for skirted foundations under general loading. Géotechnique 61(3), pp. 263 270. 8. Watson, P.G. (1999). Bearing response of skirted foundation on non-homogeneous soil. Journal of Geotechnical and Geo-environmental Engineering, ASCE, Vol. 125, No. 11, pp. 924 935. 9. Kellezi, L., Kudsk, G., Hofstede, H. (2008). Skirted Footings Capacity for Combined Loads and Layered Soil Conditions, Proceedings of the BGA International Conference on Foundations, Dundee, Scotland, 24 27 June 2008. IHS BRE Press. 10. Poulos, H.G., (1988). Marine Geotechnics, Unwin Hyman, UK. 11. Randolph, M.F. (2005), Cassidy M & Gourvenec S, (2005). Challenges of offshore geotechnical engineering, University of Western Australia. 12. Randolph, M.F., Gourvenec, S. and Wallerand, R. (2014). Design approach of rectangular mudmats under fully three dimensional loading. Geotechnique 64(1), pp. 51 63. 13. Yun, G., and Bransby, M.F. (2007). Undrained vertical bearing capacity of skirted foundations, Soils and foundations, Vol. 47, No. 493 498.