Pile are being increasingly used as permanent anchors for single point mooring systems, and to achieved the high resistances required in weak soils, it is invariably necessary to position the chain connection to the pile at some depth below the seabed. The chain, therefore has to cut down through the seabed soils to achieve an equilibrium configuration under the action of the applied tension.
Published information on this aspect of chain geometry is restricted to an analytical treatment of the problem and no comparison with measured values has so far been reported.
The experimental work presented in this chapter coupled to a comprehensive investigation of the effects of variation in soil resistance normal to the chain, will enable a more complete analysis of the anchor chain to be undertaken.
Laboratory tests were carried out to measure the profile of both a chain and cable, anchored at a fixed point below the soil surface, subjected to a horizontal tension at the surface. These tests were performed in a small rectangular water channel, equipped with horizontally graduated top rails supporting a mobile depth probe. This enabled direct measurement of the horizontal and vertical coordinates of the chain. To determine contact between the probe and chain, an electrical circuit was made, thus causing a buzzer to sound. Measurements were carried out in soft clay and loose dry sand of depth 310 mm, with a uniform cohesion of 24 kPa and angle of friction 30°, respectively.
Reese (ref 1) discussed the equilibrium of a chain which is tangential to the seabed and considered resistance to movement of the chain normal to the chain path only Gault and Cox (ref 2) have extended this work to include the effects of chain weight and tangential resistance to movement of the chain. They develop their equations by considering equilibrium of forces about two rectangular exes and assume the cable geometry as a circular arc. By so doing, however, they ignore moment equilibrium of the system and this equilibrium can only be achieved for the assumed circular geometry when both the tangential resistance and cable weight are zero, thereby reducing the system that considered by Reese.
The moment equilibrium equation for Gault and Cox's assumptions is derived in the appendix, and use of this enables moments to be calculated for any point along the cable profile. Figure 1 shows the effects of layer thickness on the value of this moment on an example with uniform soil strength and shows the need to keep to suitably thin soil layers to achieve the true momentless geometry that a chain must assume.
Fig 1 Theoretical moment in chain v soil layer thickness (available in full paper)
The well recognized formula for shallow strip foundations due to Casman et al (ref 3) is (Formula available in full paper)
The exact formulas for Nq and Nc were given by Prandtl (ref 4), and Brinch Hansen (ref 5).