Kjell Herfjord

Application of response surfaces for reliability analysis of marine structures

Abstract Marine structures subjected to multiple environmental loads (i.e. waves, current, wind) are considered. These loads are characterized by a set of corresponding parameters. The structural fatigue damage and long-term response are expressed in terms of these environmental parameters based on application of polynomial response surfaces. For both types of analysis, an integration across the range of variation for all the environmental parameters is required. The location of the intervals which give rise to the dominant contribution for these integrals depends on the relative magnitude of the coefficients defining the polynomials. The required degree of numerical subdivision in order to obtain accurate results is also of interest. These issues are studied on a non-dimensional form. The loss of accuracy which results when applying response surfaces of too low order is also investigated. Response surfaces with cut-off limits at specific lower-bound values for the environmental parameters are further investigated. Having obtained general expressions on non-dimensional form, examples which correspond to specific response quantities for marine structures are considered. Typical values for the polynomial coefficients, and for the statistical distributions representing the environmental parameters, are applied. Convergence studies are subsequently performed for the particular example response quantities in order to make comparison with the general formulation. For the extreme response, the application of ‘extreme contours’ obtained from the statistical distributions of the environmental parameters is explored.

Computation of Interaction Between Deepwater Risers: Collision Statistics and Stress Analysis

A methodology for computing the dynamics of interacting risers is presented. During the time simulations, riser impacts (if any) are recorded. The relative velocity and angle between the axes of the risers are recorded at each hit, so that the actual stress and accumulated fatigue damage may be computed in a post-processing operation. Detailed material properties, such as properties of coating, the actual composite material properties, etc. are used in that process. The methodology is based on a pre-established database of forces acting on the cylinders. At each time step, all riser elements are loaded with a combination of in-line and transverse forces, depending on local relative distance to the neighbouring riser. This imply that the methodology is based on quasi-static assumptions. The paper presents a validation of the computed force database by comparison with measured results. Examples of results from simulation with top tensioned risers on a TLP are given.© 2002 ASME

Experimental Investigation of Dual Riser Interaction

Hydrodynamic interaction and clashing of two long flexible cylinders in uniform steady current have been studied. Model tests have been performed in the towing tank at Marintek in Trondheim. The riser models were free to move in vortex induced vibrations (VIV) and wake induced vibrations (WIO). The main objectives of the experimental campaign were to acquire high quality data that can be used to enhance the understanding of the mechanisms that drives riser clashing and to provide benchmark data for riser clashing code validation. Model tests were performed both for straked and naked risers, and for risers with and without bumper elements attached. Riser spacing, inflow angle, riser pretension and current velocity were systematically varied. The analysis of the recorded data has emphasized on assessing the spatial distribution of clashing, the relative impact velocities, WIO and VIV.Copyright

WAVE IMPACT ON DECKS OF FLOATING PLATFORMS

This paper presents two methods for predicting wave impact loads underneath decks of offshore platforms. These are a Wagner base method (WBM) and a non-linear boundary element method (BEM). Experiments of wave impact on a fixed idealized deck in 2-dimensional flow conditions have been performed to validate the theories. A procedure for accounting for 3-dimensional effects is also suggested. At present only the WBM can account for motions of the platform and compute the rigid body response due to impact. This method is used to study the loads on the deck and the rigid body responses of a semi-submersible due to regular incident waves. Stokes second order theory is used to describe the incident waves. It is shown that the impact can cause an important section force and resulting downward heave motion.

Deepwater Riser Interaction: Computational Method and Validation

A method for predicting interaction between risers is presented. The method is efficient and handles different riser systems exposed to complex environmental data. To achieve this, the method utilizes pre-established data for forces on risers in close proximity. Interaction effects concerning mean values as well as the dynamic forces at vortex shedding frequencies are stored. The interaction effects cause large wake induced oscillations (WIO), and the vortex induced vibrations (VIV) are influenced as well. The method uses the database of forces in a strip theory manner to obtain excitation forces on risers and other slender bodies exposed to current. The method is implemented in a non-linear dynamic finite element tool, HYBER. During the simulation, the clearance between the risers is followed up. If collisions occur, relevant data are recorded, and the simulation continues. Fatigue and possible single event damage are assessed. In the present paper, results from the method are compared with comprehensive measurements in model scale, and the computed results show good agreement with the measurements. Databases exist for bare cylinders with equal and unequal diameters as well as for two geometries of strakes.Copyright

Probabilistic Modeling and Analysis of Riser Collision

Analysis and design of deep-water riser arrays requires that both collision frequency and resulting stresses in the pipes are addressed. Within a probabilistic context, the joint modelling of the current magnitude and surface floater motions must be taken into account. The present paper gives an outline of the general analysis setup, and response statistics obtained as a result of time domain simulation are described. Utilization of the analysis is also discussed in relation to estimation of extreme response and fatigue lifetime. As an example of application, a specific Spar buoy riser configuration at a waterdepth of 900m is considered.

Estimation of Extreme Response and Fatigue Damage for Colliding Risers

For design of deep-water riser arrays, consideration must be made of the possibility for mechanical contact between the different riser pipes. Both the anticipated frequency of collision and the resulting stresses in the pipes need to be estimated. Such an assessment need to cover a certain range of conditions regarding environmental loading and surface floater motions. The present paper outlines a procedure which admits the most “critical” conditions to be identified based on an iterative approach. For each “load case”, which corresponds to a certain combination of environmental actions and surface floater motion, the corresponding contact stresses are computed. Furthermore, the accumulated damage for each load case (referred to a certain duration) is estimated. The numerical procedure for external load calculation is based on Computational Fluid Dynamics (CFD). For a given riser spacing, interpolation is performed during the response simulation in a pre-established data base. Contact between pipes is checked at each time step by looping through the nodal coordinates of the Finite Element Mesh which represents the pipe geometry. By assembling the response and accumulated damage which correspond to all the different load cases, the long-term probability distributions and weighted damage can be calculated. The procedure is applied to a particular example riser configuration. The effect of varying current direction (relative to the symmetry axis of the floater and riser configuration) on fatigue damage is focused upon in particular.© 2002 ASME

An Assessment of Response-Surfaces for Estimation of Fatigue Damage and Extreme Response Due to Environmental Loads

For marine structures subjected to environmental loads (i.e. waves, current, wind), the fatigue damage and long-term response characteristics can frequenlty expressed in terms of the environmental parameters by polynomial response surfaces. For both types of “response”, an integration across the range of variation for all the environmental parameters is required. The location of the intervals which give rise to the dominant contribution to these integrals is studied. Convergence studies are performed by applying response surfaces of increasing order, from linear to cubic expressions. In addition, response surfaces with lower cut-off limits at specific values for the environmental parameters are also investigated. Having obtained general expressions on non-dimensional form, various examples which correspond to specific response quantities for marine structures are considered. Typical values for the polynomial coefficients, and for the statistical distributions representing the environmental parameters, are applied. Convergence studies are subsequently performed for the particular example response quantities which are considered in order to make comparison with the general formulation. For the extreme response, the application of “extreme contours” obtained from the statistical distributions of the environmental parameters in combination with the response surface is explored.Copyright