Mooring Systems for Very Large Floating Structures

Abstract

Owing to scarcity of land, very large floating structures (VLFS) are now being designed to cater for the increase in population and growth of coastal areas. The applications of VLFS include floating piers, floating airports, floating bridges, floating fuel storage facilities and even floating cities. One of the key design aspects of VLFS is the mooring design. Mooring design of VLFS is a challenge due to huge size of the structures, environmental loads, shallow water depths, space constraint for mooring lines and anchor installation. There are additional challenges pertaining to transportation of blocks, integration onsite and design allowance for possible future expansion of the VLFS. This paper examines the hydrodynamic and mooring design of a typical VLFS. The relevant concepts, motion response, mooring design and design criteria will be presented. The mooring design will incorporate sensitivity studies on different material choices for mooring lines. Chains, wire ropes and polyester (Dyneema) will be considered for the mooring design. The chain mooring system is compared with piles mooring system. Additional issues pertaining to installation and future expansion of VLFS will be discussed.

Appendices

Appendix 1: Detailed Results for Mooring Analysis

Case	Wave (deg)	Wind (deg)	Current (deg)	L01 (MT)	L02 (MT)	L03 (MT)	L04 (MT)	L05 (MT)	L06 (MT)	L07 (MT)	L08 (MT)	Offset (m)
1	0	0	0	51.7	43.8	17.5	18.1	18.1	17.5	43.8	51.7	3.9
2	0	45	0	46.9	40.0	42.0	31.5	8.1	7.9	32.1	35.4	4.3
3	0	−45	0	38.5	33.9	23.5	25.3	25.3	23.5	33.9	38.5	3.2
4	0	0	45	67.3	96.4	58.8	69.4	25.6	23.1	6.1	6.4	5.4
5	0	45	45	78.3	110.6	77.4	89.2	22.2	20.0	5.9	6.3	5.7
6	0	−45	45	61.7	102.1	68.3	85.4	38.1	33.6	4.8	4.9	5.9
7	0	0	90	47.7	42.0	37.2	31.1	13.6	13.1	31.0	34.0	4.1
8	0	45	90	63.2	54.0	66.9	48.7	9.1	8.6	28.5	31.6	5.0
9	0	−45	90	33.7	33.8	37.7	40.0	23.3	21.8	21.0	22.2	3.4
10	45	45	0	117.1	91.3	136.8	73.3	7.8	7.5	74.6	84.6	6.5
11	45	90	0	125.1	94.4	144.3	77.6	7.5	7.1	78.3	90.7	6.7
12	45	0	0	86.0	70.7	85.9	56.7	14.3	15.0	74.9	81.0	5.4
13	45	45	45	134.5	171.0	137.6	132.9	35.0	30.4	36.4	42.8	6.7
14	45	90	45	142.1	177.4	158.9	154.0	39.1	33.4	34.3	40.0	6.8
15	45	0	45	111.0	150.4	110.9	118.0	42.0	36.5	28.6	32.9	6.4
16	45	45	90	166.3	124.9	164.4	100.1	16.5	14.9	101.3	121.1	7.3
17	45	90	90	158.0	117.7	177.2	107.7	15.1	13.8	102.6	121.9	7.3
18	45	0	90	150.3	113.6	140.3	82.2	20.1	18.9	104.0	121.5	6.9
19	90	90	0	94.0	93.7	115.2	75.0	6.6	6.6	35.9	37.1	5.3
20	90	135	0	56.2	58.9	70.6	53.3	43.1	56.6	33.3	33.7	4.1
21	90	45	0	87.4	88.3	108.7	72.6	10.0	10.3	45.7	48.2	5.1
22	90	90	45	118.4	180.0	151.2	138.9	10.9	10.3	4.6	4.7	5.8
23	90	135	45	95.4	159.5	115.9	121.2	27.3	25.8	4.2	4.3	5.9
24	90	45	45	117.7	176.3	142.4	130.7	11.8	11.2	4.7	4.8	5.8
25	90	90	90	118.9	127.2	144.2	95.8	5.6	5.5	19.8	20.4	5.5
26	90	135	90	73.6	89.5	90.6	73.0	13.1	13.1	15.9	15.6	4.6
27	90	45	90	101.7	106.9	126.1	84.3	6.0	5.9	20.7	21.4	5.3

Appendix 2: Environmental Forces on Pile

Here a theoretical method for calculation of wave and current forces on pile have been presented. The linear wave theory was used for calculation of wave components. In the end, comparison was made with Orcaflex results where irregular wave (as per Table 9) was used for analysis for head and beam directions.

The total force (wave and current) exerted on a vertical cylindrical pile [7] is given by

$$dF = \mathop \int \limits_{ - h}^{0} \frac{1}{2}C_{D} \rho Du\left| u \right|dz + \mathop \int \limits_{ - h}^{0} C_{M} \rho \pi \frac{{D^{2} }}{4}\,\frac{Du}{Dt}dz$$

(6)

The wave induced velocity and current velocity are combined together [8] and the total force acting on pile is given by

$$\begin{aligned}dF &= \mathop \int \limits_{ - h}^{0} \frac{1}{2}C_{D} \rho D\left( {v_{c} + \frac{H\omega }{2}\frac{{\cosh \left( {k\left( {h + z} \right)} \right)}}{{\sinh \left( {kh} \right)}}} \right)^{2} \cos \left( {kx - \omega t} \right)|{ \cos }(kx - \omega t|dz \\ & \quad + \mathop \int \limits_{ - h}^{0} C_{M} \rho \pi \frac{{D^{2} }}{4}\,\frac{{H\omega^{2} }}{2}\frac{{\cosh \left( {k\left( {h + z} \right)} \right)}}{{\sinh \left( {kh} \right)}}\sin \left( {kx - \omega t} \right)dz \end{aligned}$$

(7)

The drag force F_DC and inertia force F_IC constant terms are defined by

$$Let,\quad F_{DC} = \mathop \int \limits_{ - h}^{0} \frac{1}{2}C_{D} \rho D\left( {v_{c} + \frac{H\omega }{2}\frac{{\cosh \left( {k\left( {h + z} \right)} \right)}}{{\sinh \left( {kh} \right)}}} \right)^{2} dz$$

(8)

$$Let,\quad F_{IC} = \mathop \int \limits_{ - h}^{0} C_{M} \rho \pi \frac{{D^{2} }}{4}\,\frac{{H\omega^{2} }}{2}\frac{{\cosh \left( {k\left( {h + z} \right)} \right)}}{{\sinh \left( {kh} \right)}}dz$$

(9)

F_DC is calculated from

$$\begin{aligned}dF_{DC} &= \mathop \int \limits_{ - h}^{0} \frac{1}{2}C_{D} \rho D\left( {v_{c}^{2} + 2v_{c} \frac{H\omega }{2}\frac{{\cosh \left( {k\left( {h + z} \right)} \right)}}{{\sinh \left( {kh} \right)}} + \frac{{H^{2} \omega^{2} }}{4}\frac{{\cosh^{2} \left( {k\left( {h + z} \right)} \right)}}{{\sinh^{2} \left( {kh} \right)}}} \right)dz \\ & = \frac{1}{2}C_{D} \rho D\left( {v_{c}^{2} h + v_{c} H\omega \frac{{\sinh \left( {kh} \right)}}{{k\sinh \left( {kh} \right)}} + \frac{{H^{2} \omega^{2} }}{{4\sinh^{2} \left( {kh} \right)}}\frac{{\left( {2kh + \sinh \left( {2kh} \right)} \right)}}{4k}} \right) \\ & = \frac{1}{2}C_{D} \rho D\left( {v_{c}^{2} h + \frac{{v_{c} H\omega }}{k} + \frac{{H^{2} gktanh\left( {kh} \right)}}{{4\sinh^{2} \left( {kh} \right)}}\frac{{\left( {2kh + \sinh \left( {2kh} \right)} \right)}}{4k}} \right) \\ & = \frac{1}{2}C_{D} \rho D\left( {v_{c}^{2} h + \frac{{v_{c} H\omega }}{k} + \frac{{H^{2} g}}{{2\sinh \left( {2kh} \right)}}\frac{{\left( {2kh + \sinh \left( {2kh} \right)} \right)}}{4}} \right) \end{aligned}$$

(10)

F_IC is calculated from

$$F_{IC} = \mathop \int \limits_{ - h}^{0} C_{M} \rho \pi \frac{{D^{2} }}{4}\,\frac{{H\omega^{2} }}{2}\frac{{\cosh \left( {k\left( {h + z} \right)} \right)}}{{\sinh \left( {kh} \right)}}dz = C_{M} \rho \pi \frac{{D^{2} }}{4}\frac{{H\omega^{2} }}{2k}$$

(11)

The total force F as a function of F_DC and F_IC is given by

$$F = F_{DC} \cos \left( {kx - \omega t} \right)\left| {\cos \left( {kx - \omega t} \right)} \right| + F_{IC} \sin \left( {kx - \omega t} \right)$$

(12)

The maxima of F is calculated from the following equations

$$\frac{dF}{dt} = 0$$

(13)

$$F_{DC} \left( { - 2\omega } \right)\cos\left( {kx - \omega t} \right)( - \sin \left( {kx - \omega t} \right)) + F_{IC} ( - \omega )\cos\left( {kx - \omega t} \right) = 0$$

(14)

$$2F_{DC} \sin \left( {kx - \omega t} \right) - F_{IC} = 0$$

(15)

$$\sin \left( {kx - \omega t} \right) = \frac{{F_{IC} }}{{2F_{DC} }}$$

(16)

The substitution of the value of sin(kx − ωt) in Eq. (12) furnishes the maximum value of F, i.e.

$$F = F_{DC} + \frac{{F_{IC}^{2} }}{{4F_{DC} }}$$

(17)

The environment parameters used for pile force calculation are shown in Table 20. The wave parameters were derived from Hs and Tp (Table 9) as per formulations in [9].

Table 20 Environment parameters

The summary of environment forces on the Pile is shown in Table 21. Comparison was also made with irregular wave analysis on a pile model in Orcaflex software. The Linear theory provided higher results and have been considered in the pile design.

Table 21 Pile forces