Annex - An Example of Alternative Intact Stability Criteria for Twin-Pontoon Column-Stabilized Semisubmersible Units

1.1 The criteria hereunder constitute alternative intact stability criteria for column-stabilized units under the provisions of section 3.3.3 of the Code for the Construction and Equipment of Mobile Offshore Drilling Units, 1989 (1989 MODU Code). These criteria apply only to twin-pontoon column-stabilized semisubmersible units in severe storm conditions which fall within the following range of parameters:

	V_p/V_t		is between 0.48 and 0.58
	A_wp/(V_c)^2/3		is between 0.72 and 1.00
	l_wp/[V_c× (L_ptn/2)]		is between 0.40 and 0.70

The parameters used in the above equations are defined in paragraph 1.3.

1.2 Intact stability criteria

The stability of a unit in the survival mode of operation should meet the following criteria:

.1 Capsize criteria

These criteria are based on the wind heeling moment and righting moment curves calculated as shown in section 3.2 of the 1989 MODU Code at the survival draught. The reserve energy area 'B' must be greater than 10% of the dynamic response area 'A' as shown in figure 1.1.

Area 'B'/Area 'A' ≥ 0.10
where
- Area 'A' is the area under the righting arm curve measured from θ₁ to (θ₁ + 1.15 θ_dyn)
- Area 'B' is the area under the righting arm curve measured from (θ₁ + 1.15 θ_dyn) to θ₂
- θ₁ is the first intercept with the 100 knot wind moment curve
- θ₂ is the second intercept with the 100 knot wind moment curve
- θ_dyn is the dynamic response angle due to waves and fluctuating wind
- θ_dyn = (10.3 + 17.8C)/(1 + GM/(1.46 + + 0.28BM))
- C = (L_ptn ^5/3 * VCP_w1 * A_w * V_p * V_c ^1/3)/(l _wp ^5/3 * V_t)
Parameters used in the above equations are defined in paragraph 1.3.
.2 Down flooding criteria

These criteria are based on the physical dimensions of the unit and the relative motion of the unit about a static inclination due to a 75 knot wind measured at the survival draught. The initial downflooding distance (DFD_o) must be greater than the reduction in downflooding distance at the survival draught as shown in figure 1.2.

DFDo - RDFD > 0.0
Where:
- DFD_o = initial downflooding distance to D_m in metres
- RDFD = reduction in downflooding distance in metres
- = SF (k * QSD₁ + RMW)
- SF = 1.10, which is a safety factor to account for uncertainties in the analysis, such as non-linear effects.
- k (correlation factor) = 0.55 + 0.08 (a - 4.0) + 0.056 (1.52 - GM)
- a = (FBD_o/D_m)(S_ptn * L_ccc)/A_wp
  (a cannot be taken to be less than 4.0)
  
  (GM cannot be taken to be greater than 2.44 m)
- QSD₁ = DFD_o - Quasi-static downflooding distance at θ₁ in metres, but not to be taken less than 3.0 m.
- RMW = Relative motion due to waves about 0₁ in metres
- = 9.3+0.11(X-12.19)
- X = D_m(V_t/V_p)(A_wp ²/l _wp)( L_ccc/L_ptn)
- (X cannot be taken to be less than 12.19 m)
The parameters used in the above equations are defined in paragraph 1.3.

1.3 Geometric parameters

A_wp	is the waterplane area at the survival draught including the effects of bracing members as applicable (in square metres).
A_w	is the effective wind area with the unit in the upright position (i.e. the product of projected area, shape coefficient and height coefficient) (in square metres).
BM	is the vertical distance from the metacentre to the centre of buoyancy with the unit in the upright position (in metres).
D_m	is the initial survival draught (in metres).
FBD_o	is the vertical distance from D_m to the top of the upper exposed weathertight deck at the side (in metres).
GM	for paragraph 1.2.1.1 , GM is the metacentric height measured about the roll or diagonal axis, whichever gives the minimum restoring energy ratio, 'B'/'A'. This axis is usually the diagonal axis as it possesses a characteristically larger projected wind area which influences the three characteristic angles mentioned above.
GM	for paragraph 1.2.1.2, GM is the metacentric height measured about the axis which gives the minimum downflooding distance margin (i.e. generally the direction that gives the largest QSD₁) (in metres).
l _wp	is the waterplane second moment of inertia at the survival draught including the effects of bracing members as applicable (in metres to the power of 4).
L_ccc	is the longitudinal distance between centres of the corner columns (in metres).
L_ptn	is the length of each pontoon (in metres)
S_ptn	is the transverse distance between the centreline of the pontoons (in metres).
V_c	is the total volume of all columns from the top of the pontoons to the top of the column structure, except for any volume included in the upper deck (in cubic metres).
V_p	is the total combined volume of both pontoons (in cubic metres).
V_t	is the total volume of the structures (pontoons, columns and bracings) contributing to the buoyancy of the unit, from its baseline to the top of the column structure, except for any volume included in the upper deck (in cubic metres).
VCP_w1	is the vertical centre of wind pressure above D_m, (in metres).

Figure 1.1 Righting moment and heeling moment curves

Figure 1.2 Definition of downflooding distance and relative motion

1.4 Capesize criteria assessment form

Input data
GM	__________________________________________ = ________	m
BM	__________________________________________ = ________	m
VCP_w1	__________________________________________ = ________	m
A_w	__________________________________________ = ________	m²
V_t	__________________________________________ = ________	m³
V_c	__________________________________________ = ________	m³
V_p	__________________________________________ = ________	m³
l _wp	__________________________________________ = ________	m⁴
L_ptn	__________________________________________ = ________	m
Determine
θ₁	__________________________________________ = ________	deg
θ₂	__________________________________________ = ________	deg
C=(L_ptn ^5/3 * VCP_w1 * A_w * V_p * V_c ^1/3)/l _wp ^5/3 * V_t)		m^-1
θ_dyn	(10.3+17.8C)/(1.0+GM/(1.46+0.28BM)) __________ = ________	deg
Area 'A'	__________________________________________ = ________	m-deg
Area 'B'	__________________________________________ = ________	m-deg
Results
	Reserve energy ration:
'B'/'A' = _____________ (min=0.10)
GM = __________ m (KG=__________ m)

Note:

The minimum GM is that which produces a 'B'/'A' ratio = 0.10

1.5 Downflooding criteria assessment form

DFD_o	_________________________________________	= _______	m
FBD_o	_________________________________________	= _______	m
GM	_________________________________________	= _______	m
D_m	_________________________________________	= _______	m
V_t	_________________________________________	= _______	m³
V_p	_________________________________________	= _______	m³
A_wp	_________________________________________	= _______	m²
l _wp	_________________________________________	= _______	m⁴
L_ccc	_________________________________________	= _______	m
L_ptn	_________________________________________	= _______	m
S_ptn	_________________________________________	= _______	m
SF	_________________________________________	= _______	1.10
Determine
θ₁	____________________________________________________		deg
DFD₁	____________________________________________________		m
QSD₁	____________________________________________________		m
a=(FBD_o/DM)(S_ptn * L_ccc)/A_wp = ____ (A_MIN=4.0)
k=0.55+0.08(a-4.0)+0.056(1.52–GM)= ____ (GM_MAX=2.44 m)
X=D_m(V_t/V_p)(A_wp ²/l _wp)(L_ccc/L_ptn)= ____ m
	= (X_MIN=12.19 m)
RMW=9.3+0.11(X-12.19)		= _______	m
RDFD=SF (k * QSD₁+RMW)		= _______	m
Results	downflooding margin:
	DFD_o-RDFD= __________ (min=0.0 m)
	GM= ____ m (KG= ____ m)

Note:

The minimum GM is that which produces a downflooding margin = 0.0 m.