Jack-up foundation analysis

The initial embedment calculation as a function of the preload is verified for sand and clay models. A two-step single-element elastic analysis is performed with a given jack-up foundation preload for the different models. JOINT3D elements are used. In the first step the base node is fixed, and the tip node is subjected to concentrated forces and moments. The second step is a static perturbation analysis about the previous step. The analysis is done for the six models described below. It is verified that the embedment value is correct and that the elastic modulus has the correct dependence on embedment.

Force units are kN, and length units are meters.

1. Sand model, cylindrical spud can:

   Spud can diameter	10.9
   Spud can cone angle	180°
   Foundation preload	50600
   Foundation tensile capacity	0.0
   Soil submerged unit weight	10.0
   Soil friction angle	33°
   Soil Poisson's ratio	0.2
   Foundation elastic shear moduli, $G_{\nu \nu }$	5.14 × 104
   $G_{hh}$	3.87 × 103
   $G_{rr}$	2.04 × 104
   Constant coefficient, ${\mathrm{\Lambda }}_1$	1.0
   Constant coefficient, ${\mathrm{\Lambda }}_2$	0.5

2. Sand model, conical spud can—embedment greater than critical:

   The properties for the soil are the same as in Case a.

   Spud can diameter	10.9
   Spud can cone angle	150°
   Foundation preload	50,000
   Foundation tensile capacity	0

3. Sand model, conical spud can—embedment less than critical:

   The properties of the spud can and the soil are same as in Case b. The foundation preload is 15000 for this case.

4. Clay model, cylindrical spud can:

   Spud can diameter	20.0
   Spud can cone angle	180°
   Foundation preload	1.3 × 105
   Foundation tensile capacity	0.0
   Soil submerged unit weight	10.0
   Soil undrained shear strength	150.0
   Soil Poisson's ratio	0.5
   Foundation elastic shear moduli, $G_{\nu \nu }$	1.56 × 104
   $G_{hh}$	2.34 × 103
   $G_{rr}$	6.38 × 104
   Hardening parameter, a	7.204 × 104
   Hardening parameter, b	1.978 × 103

5. Clay model, conical spud can—embedment greater than critical:

   Spud can diameter	20.0
   Spud can cone angle	150°
   Foundation preload	8.5 × 105
   Foundation tensile capacity	0.0
   Soil submerged unit weight	10.0
   Soil undrained shear strength	50.0
   Soil Poisson's ratio	0.5
   Foundation elastic shear moduli, $G_{\nu \nu }$	1.56 × 104
   $G_{hh}$	2.34 × 103
   $G_{rr}$	6.38 × 104
   Hardening parameter, a	−2.395 × 10−5
   Hardening parameter, b	8.777 × 10−6
   Hardening parameter, c	2.9294

6. Clay model, conical spud can—embedment less than critical:

   The properties of the soil and the spud can are the same as in Case e. The foundation preload is 1.3 × 10⁵.

The structure tested is a four-leg square platform with a footing at each leg corner. The model can be reduced to two dimensions because of symmetry. The model is projected onto a vertical plane that cuts diagonally across the platform. The legs are modeled with B21 beam elements, and the foundation is modeled with JOINT2D elements. The platform is modeled as a two-dimensional portal frame, with one windward leg, one leeward leg, and two legs in the middle. The platform is considered rigid and is modeled with RB2D2 elements. Four push-over analyses with different foundation bearing capacities are performed.

Force units are kN, and length units are meters.

Leg length	59
Leg EI	1.0 × 1015
Leg AE	3.0 × 1015
Leg GA	2.0 × 1015
Horizontal distance from platform c.g. to leeward leg	29.33
Horizontal distance from platform c.g. to windward leg	29.33
Horizontal distance from platform c.g. to middle legs	0
Spud can diameter	14.0
Spud can cone angle	180°
Foundation preload, four cases	387500, 530000, 650000, 775000
Foundation tensile capacity	40000
Spud can initial vertical load	52250
Vertical distance from c.g. to load application point	0
Soil submerged unit weight	10.0
Soil friction angle	35°
Soil Poisson's ratio	0.2
Foundation elastic shear moduli, $G_{\nu \nu }$	1.63 × 105
$G_{hh}$	2.92 × 104
$G_{rr}$	2.10 × 104
Constant coefficient, ${\mathrm{\Lambda }}_1$	0.3
Constant coefficient, ${\mathrm{\Lambda }}_2$	0.3

The ultimate bearing capacity is determined by applying a load larger than the bearing capacity in a static step with a time period of 1. This load ramps up over the step, and the analysis fails to converge when the bearing capacity is reached. The capacity is determined by multiplying the reference load (in these cases 200000 kN) by the fraction of the time step completed.

For accurate results in a push-over analysis, experience shows that small time increments should be used to integrate the plasticity equations accurately. These analyses were each run with three different fixed time increments.

The test problem is a monotonic horizontal loading analysis of a triangular three-leg jack-up rig on clay. The rig is modeled as a frame composed of rigid elements, with two windward legs and one leeward leg. For the two-dimensional analysis the model is projected on a vertical plane of symmetry. Loading for both the two- and three-dimensional analyses is in this plane, so both analyses produce the same results. The loading consists of an applied horizontal load at a point below the rigid frame. The legs are modeled with B21 elements, and the joints are modeled with JOINT2D elements.

The properties of the soil and the spud can are as described in Case d of the initial embedment analysis.

Leg length	110.6
Leg EI	2.48 × 109
Leg AE	1.54 ×1015
Leg GA	3.61 × 1015
Horizontal distance from platform c.g. to leeward leg	37.0
Horizontal distance from platform c.g. to windward leg	18.0
Spud can initial vertical load	6.6 × 104
Vertical distance from c.g. to load application point	−55.0

The test structure is the same as that of Monotonic loading analysis: clay model. The soil plastic properties are different, and the spud can is conical. A conical spud can produces rather different results in this case, even in the elastic region, and the model verifies that the elastic properties depend correctly on the plastic properties through the embedment. The analysis consists of horizontal loading of the rig up to the value of 18000 kN.

The soil and spud can properties are as given in Case e of the initial embedment analysis. The rig dimensions are the same as that of the monotonic loading analysis.

The test structure is a half-model of a four-leg square rig, projected on the vertical, nondiagonal plane of symmetry. The horizontal and vertical loads are applied at the center of gravity of the platform. The shear stiffness of the legs is not included in the model; B23 elements are used. The spud cans are modeled as elastic-perfectly plastic in this case, using the “member”-type plasticity model. The vertical load is ramped up from 20 to 100 in the first step and then held constant until the end of the step. In the next step the horizontal load is ramped to 14.

The dimensions of the rig in the plane, the beam properties, and the elastic properties of the spud can are as given in the clay push-over analysis. The plastic properties of the member are given below:

Parabolic yield function parameters:
$V_c$	100
$V_t$	100
$M_u$	2400
$H_u$	1015