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The 12 th International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG) 1-6 October, 2008 Goa, India Assessment of Bearing Capacity and Settlement of Irregular- Shaped Mat Supported Oil Drilling Rigs Using Finite Element Analysis Mahanta. R, Prakasha, K. S, Deshpande.A.R and Dholey H.S, Institute of Engineering and Ocean Technology, ONGC, Panvel, Navi Mumbai, India. Keywords: mat, finite element, bearing, drilling rig ABSTRACT: Mobile drilling rigs are used for drilling offshore wells by the oil and gas industry. Many rigs have legs connected at the bottom by a large sized and irregular shaped mat for bearing the loads. Design of its shape is dictated by the loads arising out of the gravitational as well as lateral forces and moments. The mats are generally ‘A’ shaped which makes it a somewhat complicated task for exact evaluation of its bearing capacity and settlement. The complicated geometry makes adoption of usual limit equilibrium method for calculation of bearing capacity un-amenable, unless simplifying assumptions are made. The inaccuracies arising out of such assumptions are difficult to estimate/predict. Hence, it is desirable to find the ‘exact’ solution adopting finite element method for calculation of bearing capacity. The solution so obtained has been compared with those obtained from the limit equilibrium approach. The other important consideration in such foundations is settlements which occur during the operation period.The paper presents the results of analysis and discusses the inaccuracies associated with making different assumptions. Based on the study, the most suitable limit equilibrium approach is suggested. 1 Introduction One of the two main types of jack up rigs used for offshore drilling is mat supported rig. These rigs have large area of foundation and they can be used in areas where the soil is soft up to a significant depth below the mudline and where independent leg jack up rigs would require large penetration of their footing (spudcan) which becomes risky and sometimes infeasible from operational point of view. The large area of the mat in the mat supported leg ensures that penetration of the mat is small in the seabed. The bearing stress is less and even soft soil can support it. The analysis for penetration into the seabed soil and to know the stability during operation requires the calculation of bearing capacity. The irregular shape makes it difficult to follow the limit equilibrium method in the same way as for a rectangular footing. Therefore, attempts have been made to assess it through finite element method and compare it with the limit equilibrium method to come out with the comparison and recommend a practice to reduce uncertainty in the calculation of bearing capacity. The main issues that concern the mat supported rig foundation are- The penetration under the preload or due to consolidation and differential settlement later should not exceed the depth of the mat There should be an adequate factor of safety against failure due to effect of environmental load while in operation The differential settlement due to environmental loading should be within the acceptable limit These issues are discussed in the paper. 2 Foundation detail The type of the mat supported rig foundation is of ‘A’ type as shown in the Fig.1. The depth of the mat box is 3.1m. These foundations should not sink completely into the soil during preloading and operation. Load is transferred to the mat through 3 legs of tubular shape having external diameter of 3.1m. The area of the mat is 1925 sqm. Maximum preload is 110MN and operational load is 72MN. The foundation has been assumed as rigid and rough for the analysis. Skirts which are located in the periphery of the footing have not been considered. Also, sliding stability has not been discussed in this paper. 3127

Mat Rig Mat Reactions

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The 12th International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG) 1-6 October, 2008 Goa, India

Assessment of Bearing Capacity and Settlement of Irregular-Shaped Mat Supported Oil Drilling Rigs Using Finite Element Analysis

Mahanta. R, Prakasha, K. S, Deshpande.A.R and Dholey H.S, Institute of Engineering and Ocean Technology, ONGC, Panvel, Navi Mumbai, India.

Keywords: mat, finite element, bearing, drilling rig

ABSTRACT: Mobile drilling rigs are used for drilling offshore wells by the oil and gas industry. Many rigs have legs connected at the bottom by a large sized and irregular shaped mat for bearing the loads. Design of its shape is dictated by the loads arising out of the gravitational as well as lateral forces and moments. The mats are generally ‘A’ shaped which makes it a somewhat complicated task for exact evaluation of its bearing capacity and settlement. The complicated geometry makes adoption of usual limit equilibrium method for calculation of bearing capacity un-amenable, unless simplifying assumptions are made. The inaccuracies arising out of such assumptions are difficult to estimate/predict. Hence, it is desirable to find the ‘exact’ solution adopting finite element method for calculation of bearing capacity. The solution so obtained has been compared with those obtained from the limit equilibrium approach. The other important consideration in such foundations is settlements which occur during the operation period.The paper presents the results of analysis and discusses the inaccuracies associated with making different assumptions. Based on the study, the most suitable limit equilibrium approach is suggested.

1 Introduction One of the two main types of jack up rigs used for offshore drilling is mat supported rig. These rigs have large area of foundation and they can be used in areas where the soil is soft up to a significant depth below the mudline and where independent leg jack up rigs would require large penetration of their footing (spudcan) which becomes risky and sometimes infeasible from operational point of view. The large area of the mat in the mat supported leg ensures that penetration of the mat is small in the seabed. The bearing stress is less and even soft soil can support it. The analysis for penetration into the seabed soil and to know the stability during operation requires the calculation of bearing capacity. The irregular shape makes it difficult to follow the limit equilibrium method in the same way as for a rectangular footing. Therefore, attempts have been made to assess it through finite element method and compare it with the limit equilibrium method to come out with the comparison and recommend a practice to reduce uncertainty in the calculation of bearing capacity. The main issues that concern the mat supported rig foundation are-

• The penetration under the preload or due to consolidation and differential settlement later should not exceed the depth of the mat

• There should be an adequate factor of safety against failure due to effect of environmental load while in operation

• The differential settlement due to environmental loading should be within the acceptable limit

These issues are discussed in the paper.

2 Foundation detail The type of the mat supported rig foundation is of ‘A’ type as shown in the Fig.1. The depth of the mat box is 3.1m. These foundations should not sink completely into the soil during preloading and operation. Load is transferred to the mat through 3 legs of tubular shape having external diameter of 3.1m. The area of the mat is 1925 sqm. Maximum preload is 110MN and operational load is 72MN. The foundation has been assumed as rigid and rough for the analysis. Skirts which are located in the periphery of the footing have not been considered. Also, sliding stability has not been discussed in this paper.

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3 Soil profile The soil profile has been chosen from a typical site of Indian offshore, where the mat supported rig deployment is suitable. The profile contains clay in very soft condition near the seabed gradually increasing in strength up to 15.0m depth and overlying a dense sand layer. The mudline shear strength is 5 kPa with increment of 1kPa/m depth. In the model the mat is considered as sitting at the mudline without penetration. Normally penetration of about 1-1.5m is commonly seen. Therefore, the soil has been modeled with undrained shear strength of 7 kPa at the mudline(instead of 5 kPa) with an increment of 1 kPa/m depth downward. The soil parameters used in the finite element analysis and for settlement calculation are considered as listed in table1.

Table 1. Soil parameters

Soil property Value Undrained shear strength at surface 7.0 kPa

Rate of undrained Shear strength increase with depth 1.0 kPa/m Poisson’s ratio (Undrained) 0.49 Young’s modulus at surface 2000 KN/m2 Young’s modulus increment 400 KN/ m2/m

Friction angle 0 Dilatancy angle 0

Submerged unit weight 6.0 KN/m3 Average water content 50%

Liquid limit 70% Compression index, Cc 0.54

Coefficient of consolidation 3 m2/year

50.0

59.5

28.0

11.0

20.5

11.011.0

17.0

11.0

All dimensions are in metre (Figure not to scale)

Opening

Legs

20.5

centroid

X X

Y

Y

Figure 1. Plan of the Mat

11.0

27.0

28.0

LEGS

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3 Bearing Capacity

3.1 Limit equilibrium method For soil profile where the soil is very soft to soft clay to a significant depth below the mudline, the bearing capacity calculation by Davis and Booker (1973) method is reported to have given good results from the field data. Therefore this method was adopted for comparison with the finite element result.

3.2 Finite Element Method 2 D version of the finite element package PLAXIS was used for the analysis. The elastic perfectly plastic Mohr Coulomb model was used. The analysis was carried out as a plain strain case. The discretisation of the soil was done with 6-noded triangular elements and the footing was modeled with 3-noded beam elements. The boundary conditions of horizontal fixity at the two vertical boundaries and total fixity at the bottom boundary was assumed. Undrained analysis was selected for the clay soil. The horizontal boundary was extended in such a way that the result was not affected by its extent. The model for the central portion of the mat is shown in Fig.2, where two strips are connected rigidly and mesh generation is shown in Fig.3.

Figure 2. Finite element model of two longitudinal strips rigidly connected

Figure 3. Generation of finite element mesh

4 Settlement There are two types of settlements- elastic and consolidation. Consolidation settlement was calculated with one dimensional consolidation theory by dividing the 15m thick clay layer into 7 sub layers. Average stress increment in the mid of the sub layers due to the applied operational load was then calculated with elastic theory. A maximum period of two years was assumed conservatively to estimate the consolidation settlement over the period of operation. Elastic settlement was computed from the finite element analysis. Elastic differential settlement was computed from the finite element analysis applying operational and environmental loads. The tilt of the hull due to total differential settlement was compared with the allowable degree of tilt during operation.

5 Result

5.1 Validation The finite element model was validated by comparing the result with the limit equilibrium method. The limit equilibrium calculation was performed by dividing the mat into strips with pure vertical load. For the areas common between the strips, bearing capacity was evaluated for a strip equal to the width of the mat (50m). Finally unit bearing capacities were multiplied by the relevant areas to find the total load capacity. Finite element analysis was performed along both x and y axis with the vertical load placed at the centre of the two strips (Fig.2). Rigid connection has been assigned between the two strips for analysis of the parts separated by the central opening. For the common areas between rectangular parts of the mat, strips of width equal to the width of the mat (50m) has been considered by applying same settlement as computed for the strips in x-x direction at failure. Ultimately the relevant capacities were multiplied with the corresponding areas and total load capacity of the rig was derived. The results for different soil profiles are compared in Table 2. When centric load is considered, the bearing capacity calculation by limit equilibrium method shows a good agreement with the finite element method with minor differences. Thus the model is validated and applied for further calculation with eccentricity and inclination of the load.

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Table 2. Comparison of results from limit equilibrium method and FEM for centric load

Result of unit Bearing capacity Davis and Booker

method (kPa)

Result of unit Bearing capacity by Finite Element method (kPa)

Load Capacity by Davis and Booker (MN)

Load Capacity by Finite

element (MN)

Comparative ratio

Strip

Common area (25% of total area)

Along Y axis

Along X axis

Common area (25% of total area) ‘A’ ‘B’ A/B

Su = 5 kPa at surface, gradient =0 26 26 27 27 30 50 53 0.94

Su = 5 kPa at surface, gradient= 0.4 kPa/m 32 46 34 34 47 68 72 0.94

Su = 5 kPa at surface, gradient =0.7 kPa/m 36 55 38 38 57 78 82 0.95

Su = 5 kPa at surface, gradient = 1 kPa/m 39 64 41 41 65 87 90 0.97

Su = 7 kPa at surface, gradient = 1 kPa/m 50 78 53 53 79 110 115 0.96 Note: Mat area = 1925 m2

The effect of the presence of the skirts in the actual rig was not considered in the analysis. It can be seen that the separated strips have hardly any influence on each other so far as the ultimate bearing capacity is concerned Fig.4. it may be safely assumed that the strips are acting individually. The equilibrium is established for soil undrained strength of 7 kPa at the surface and an increment of 1 kPa/metre depth which gives the ultimate capacity equal to the preload of the rig i.e. 110MN. Now, with this soil strength stability is assessed under environmental loading.

Figure 4. Plastic points after failure under centric loading

5.2 Eccentric and Inclined Loading The mat is subjected to vertical & horizontal loads and moment for which the stability assessment is essential to ensure adequate safety during operation. In case of such eccentric and inclined load, the capacity and stability assessment are more complicated compared with the centric load. The maximum lateral load and moment were calculated considering a wave height of 18.0m with a period of 14 seconds. Water depth of 40m was assumed. Contribution of wind load was assumed to be 33% of the total lateral load. Current force was neglected to be a small component. Moment due to gravitational load from permanent and variable loads in the rig if any, are neglected. The analysis is carried out in 2 D by considering the mat into two parts during analysis of each load case. It is customary to assume that the rig is placed in the orientation where it can resist the maximum environmental load i.e. along the longitudinal axis. However, stability has been examined by applying the wave and wind forces from the aft side (bottom of Fig.1) as well as from forward side in the longitudinal direction. The transverse direction is symmetrical from both sides. Analysis was carried out by applying loads in the transverse direction assuming the horizontal load to be 75% of corresponding load in the longitudinal direction. Soil resistance to the horizontal load was assumed to be uniformly distributed in the mat area of contact with the soil. The effect of the presence of the skirts in the actual rig was not considered in the analysis. The result is shown in Table 3 below:

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Table 3. Comparison of results from limit equilibrium method and FEM for eccentric and inclined load

Extreme wave from direction

Forces (MN) Moment (MN.m)

Bearing capacity FEM (MN)

Bearing capacity conventional (MN) Remarks

Horizontal 5.4 Long strips 62.6 Vertical 72 Short strips 28.4

moment 243 Total 91 Total 92.1 South (Aft of rig facing

south) eccentricity 3.4 F.O.S. 1.26 F.O.S. 1.28

For conventional calculation:

Correction factor = 1.08 Effective area = 1705

sqm Unit bearing capacity =50kpa for 11m strip

Horizontal 5.4 Long strips 67.2 Vertical 72 Short strips 21.5

moment 243 Total 88.7 Total 92.1 South (Aft of rig facing

North) eccentricity 3.4 F.O.S. 1.23 F.O.S. 1.28

For conventional calculation:

Correction factor = 1.08 Effective area = 1705

sqm Unit bearing capacity =50kpa for 11m strip

Horizontal 4 Long strips 61.6 Vertical 72 Short strips 28

moment 187.4 Total 89.6 Total 92.2 East- West (geometry

symmetrical) eccentricity 2.6 F.O.S 1.24 F.O.S. 1.28

For conventional calculation:

Correction factor = 1.07 Effective area = 1724

sqm Unit bearing capacity =50kpa for 11m strip

Figure 5. Failure under eccentric and inclined load(displacement scaled up 2 times)

5.3 Settlement The results of settlement calculations are presented in Table 4. Average bearing stress on soil due to operating load is calculated as 37.4 kPa.

Table 4. Settlement of mat

Settlement Maximum total settlement (mm)

Maximum differential

settlement (mm)

Inclination of hull in worst condition

Type Quantity (mm) (a) Maximum consolidation 1034 (b) Consolidation in the period of operation (maximum two years assumed)

0.37x1034 = 383

(c) Elastic(operational load) 35 (d) maximum elastic in storm 48 (e) Differential settlement due to elastic compression 19

Differential settlement due to consolidation (0.5 x ‘b’) 191

383+48 =431

19+191 =210

tan-1 (210/50000) =0.25 degree

(Permissible limit =1 degree. Hence safe)

It is seen that the total maximum settlement is 431 mm after deployment. This will be in addition to the initial penetration under preload.

6 Conclusion Based on the above analysis for the given configuration of the mat, a simplified procedure has been recommended (Table 5) for the analysis of rig under different loading conditions and soil profiles where the soil is

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very soft up to a significant depth below the seafloor.

Table 5. Recommended procedure for evaluation of bearing capacity

Case Load condition Soil condition Recommendation 1 Vertical Constant strength profile with

soft soil to significant depth Calculate strip bearing capacity for constant strength condition (BCstr). Find area under strips (A). Correction Factor Fc = 1.06. Ultimate bearing capacity = Fc. BCstr. A

2 Vertical Increasing strength profile with soft soil to significant depth

Calculate strip bearing capacity for increasing strength condition (BCstr). Find total area under strips (A). Correction Factor Fc =1.15. Ultimate bearing capacity = Fc. BCstr. A

3 Extreme: Inclined and eccentric; horizontal load from forward direction

Increasing strength profile with soft soil to significant depth

Calculate strip bearing capacity for increasing strength condition (BCstr). Find total area under strips (A). Correction Factor Fc = 0.92. Ultimate bearing capacity = Fc. BCstr. A

4 Extreme: Inclined and eccentric; horizontal load from aft direction

Increasing strength profile with soft soil to significant depth

Calculate strip bearing capacity for increasing strength condition (BCstr). Find total area under strips (A). Correction Factor Fc = 0.94. Ultimate bearing capacity = Fc. BCstr. A

The bearing capacity of irregular shaped mats in soft soil may be evaluated based on bearing capacity of strips and applying correction in the range of -8% to +19% for different loading conditions. The load bearing capacity for pure vertical loading calculated by using finite element method for the soil profile is higher than strip bearing capacity of individual strips(11m width) calculated by using limit equilibrium method. For the soil profile considered in the case, it is about 19% greater. This is mainly because of the higher unit bearing capacity at the junctions. However, the capacity reduces on account of eccentricity and inclination of the load. These two factors compensate each other and the vertical capacity determined considering the mat as combination of strips provide a good approximation for the capacity under VHM loading. Most parts of the mat behave as individual strips and do not influence the capacity due to interference (Fig.3). Bearing capacity by finite element result is found to be in good agreement with bearing capacity of strip with vertical loading (Table 2). Conventional approach for stability assessment of the rig with VHM loading does not address the assymetry of the mat in the longitudinal direction. The factor of safety from the analysis is 1.0 with maximum preload and is nearly 1.3 with environmental load which are acceptable. Maximum possible settlement during operation is found to be about 14% of the mat depth for an operational period of 2 years which is within the recommended available mat depth after preload. Differential settlement is found to be within limit based on the allowable limit of tilt of the hull.

7 References American Petroleum Institute, 2000. Recommended practice for planning, designing and constructing fixed offshore platforms-

working stress design, API RP 2A, Twenty First Edition, December, 2000.

Davis E.H., Booker J.R. 1973. The effect of increasing strength with depth on the bearing capacity, Geotechnique, 23(4), 551-553.

Gaythwaite, John.1981. The marine environment and structural design Van Nostrand Reinhold Company, Van Nostrand Reinhold Company, New York (USA).

Lambe W., Whitman J., 2000. Soil Mechanics. John Wiley and Sons.

Pierre Le T., Christian P., 1993. Stability and operation of jackups, Editions Technip, Paris

PLAXIS, 1998. Finite Element Code for Soil and Rock Analyses, PLAXIS B.V., Netherlands.

The Society of Naval Architects and Marine Engineers, Technical & Research Bulletin 5-5A, Guidelines for Site Specific Assessment of Mobile Jack-Up Units, First Edition, 1994.

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