Experimental Estimation of Material and Support Properties for Flexible Dolphin Structures

Present work describes the inverse problem for identification of material and support type properties of flexible dolphin structure. Most liquid bulk terminals are equipped with a jetty as berthing facility. The ship mostly berths to dedicated breasting dolphin structures, which can be single-pile flexible/rigid dolphins or multi-pile flexible/rigid dolphins. This work considers dolphin motion as massspring damped system where cantilever approximation mimics dolphin pile. Few measurements have been made for the dolphin structure, which is approximately 30 m long, 15 m immersed in the bottom and placed about 2-3 m above the sea level. The elastic material properties and pile support were identified via inverse method combined with displacement measurements of dolphin head.


INTRODUCTION / Uvod
The contemporary increase of ship dimensions and capacity require reengineering of some current harbour facilities.Among them are e.g.mooring and breasting flexible pile dolphins [1].Their lifetimes heavily depends on the material used in the construction and proper usage.The directions on dolphin design are given in Schmid report [2], Tomlinson and Woodward book [3], and British standard [4].Detailed studies of dolphin structures and their interactions with support can be found in the additional literature.For example in the work of Zhang with co-authors [5,6] and Xu with co-authors [7] they study complex nonlinear effects of laterally loaded rigid piles in cohesive soil.Fan and Yuan [8] use high-resolution finite element models of the ship-structure-soil interactions to analyse the plasticity effects on the flexible dolphin structure and its support.Farag with co-authors [9,10] propose an advanced reliability evaluation procedure for analysis and design of mooring dolphin with the use of hybrid response surface and secondorder reliability method approach.
In this paper an inverse procedure to estimate the stiffness and support of dolphin structure based on the beam theory will be presented.Simplified models are derived from the beam theory [11] identifying the material and support properties of a flexible dolphin.Identification of the material properties and mounting support of flexible pile has been done by using the inverse procedure, which was calibrated with measurements data.The main goal is to formulate a simple procedure that will enable the estimation of operating capabilities of the existing structure in a fast and reliable way before a new design, research or a possible redesign of dolphin structure.The very similar approach was developed in [12] where they established a continuous monitoring and instant data acquisition.In our work an advanced model is proposed based on the beam theory [11].

MODEL / Model
In the British Standard [4] (and many other standards) the maximum berthing energy is calculated with the kinetic energy approach, based on the work by Saurin [13].The basic assumption in the kinetic energy approach is that the kinetic energy of the ship at the moment of the first contact with the berthing structure is to be absorbed by the berthing structure (fender and structure itself ).The influence of the motions of the ship (the ship's position relative to the berthing structure and the surrounding water) on the loads acting on the berthing structure results in additional factors to be applied in the design of the structures.The dolphin should absorb all the energy of impact by lateral deflection of the piles [4].The pile should operate so that the absorption energy is a function of the square of the bending stress.The pile section should be selected to operate at 0.8 yield stress under abnormal energy conditions.For the recommended ratio between abnormal and normal energies of 2.0, this gives the normal energy bending stress as 0.57 yield stress.
The main assumption on the ship-dolphin impact interaction uses simple mass-spring damped model (Figure 1) of the impact of a mass with spring.At impact, by the conservation of linear momentum and total inelastic impact, the initial speed of the dolphin head after an impact ( where 0 V is the ship approaching speed, M is the ship mass and m is the dolphin mass.Motion after impact is governed by the energy conservation.In particular the maximal dolphin deformation ∆ (Figure 2) can be obtained from the balance of kinetic energy and the elastic energy where k is stiffness coefficient of dolphin structure.From the Eq.
(2) the maximal deflection is ( ) Always is the case m M � and from Eq. ( 3) it follows where are now 0 V and M design parameters.If k is known ∆ can be calculated, but in our case the task is inverse and ∆ is known and k can be estimated by Let us assume that the cantilever models the flexible dolphin structure and its deflection is where is cantilever bending stiffness (E-elastic modulus, I-beam cross section moment of inertia), F is the force applied at the end of a cantilever, L is its length and α is a parameter that depends on a type of dolphin mount on the seabed.In this problem, three typical situations (Figure 1) are considered for the parameter α.If fender on the top of the pile is clamped (Figure 1 When it is assumed that the deformation is small then only linear isotropic elasticity effect is present.By the linear elastic theory the relation between the force and the deformation is and the Eq. ( 6) can be rewritten in a form defining the dolphin structure stiffness.From Eq. ( 8) it can be seen that the dolphin structure stiffness constant depends on the three variables ) Since in our test only k is indirectly measured we can from Eq. ( 8) calculate only one parameter.Since κ and L are at least approximately known we can estimate i.e. approximate type of dolphin mounting.To justify this approach let us look at the sensitivity of the dolphin structure stiffness.From Eq. ( 8) and ( 9) we derive the total differential for stiffness coefficient of dolphin structure and it immediately follows In Table 1 the estimated values of each term in Eq. ( 11) from our study problem show the relation of similar order on the structural stiffness k.For our problem it was observed that the support coefficient α is an order of magnitude bigger than the other two parameters ( , L κ ).The support coefficient α has the most relevant influence on dolphin structural stiffness.In Table 2 the relations for the maximal dolphin head deflection ∆ and the dolphin structure bending energy U are derived.If it is supposed that the kinetic energy is completely transformed into the bending energy than we can find the bending stiffness coefficient κ with the help of formulas in Table 2. Bending energy also depends on the number of piles in dolphin structure and the kinetic energy is redistributed to each pile.

MEASUREMENTS AND DATA PROCESSING / Mjerenja i obrada podataka
Laser speedometer was used in the conducted measurements of the dolphin head displacement.At Figure 3 (blue line) the typical displacement distribution shows the damping oscillations of the dolphin head.When the ship touches the structure ( 0 t = at Figure 3) the impact occurs.The dolphin starts to oscillate in a dumped mode.Data where fitted to the nonlinear model of the dumped oscillator ( ) In fitting procedure, only data in the yellow region (Figure 3) were used.Fitting model reveals that the oscillations are slowly damped (under damped mode) and the damped frequency of structure is already . The effect of damping can be neglected in the frequency calculations.Using natural frequency of the structure and mass of the system, dolphin structural stiffness can be immediately calculated ( ) Knowing dolphin structural stiffness the estimate of the parameter of support type reads .It is highly possible that the dolphin structure is double simple supported (Figure 2-c).
In Eq. ( 8) it was assumed that the relation between the force and deformation is linear.Let us analyse the situation if the relation is of non-linear type  6) and (15) we derive the nonlinear relation for dolphin structure stiffness Now, to determine the structural stiffness additional information of the maximal pile deflection must be provided with the knowledge of the nonlinear structural coefficient λ.Minimal three measurements are needed to calculate coefficient λ.For example, in nonlinear model structural stiffness is always smaller and pile maximal deflection will be larger compared to the linear stiffness model.In Figure 4 the simple Monte-Carlo experiment shows the difference in the linear and nonlinear model approach.The model difference can lead to the predication error of 10%-20%.

DISCUSSION AND CONCLUSIONS / Rasprava i zaključci
The proposed methodology can be a first step in the material support type examination of flexible dolphin structures.For example in the work of Metzger, Hutchinson, and Kwiatkowski [13] they have analysed the similar situation.In a similar fashion with continuous data assembly, it is possible to estimate, with a high confidence, different properties of flexible dolphin structures in a very simple, fast and non-invasive way.There was exposed a single experimental case showing the procedure with elementary calculations.Based on many experiments the model can be modified to the nonlinear response function 4), where it can be expected 1 λ < , resulting in a softer dolphin structure material.Nonlinear material response represents a real life situation and cannot be simplified.The combination of simple models discussed in this work and e.g. in [13] joint in a single toolbox can be a practical tool in the cheap and fast estimation of different parameters of flexible dolphin structures.
-a) then parameter 12 α = , else if support on top is simple (Figure 1-b) then parameter 3 α = and if double simple support is assumed (Figure 1-c) then parameter .

Figure 1 Figure 2
Figure 1 Situation of dolphin structure in the investigated problem.Above is a scheme of mass spring damped system as the approximation model for the structu re dynamics Slika 1. Stanje strukture priveznog stupa u istraženom problemu.Iznad je shema sustava masa -struna -prigušnik kao aproksimacija modela dinamike strukture