Hydrodynamic and morphodynamic response to pipe soil interaction

Recent developments of the petrochemical industry in the last two decades, helped the rapid growth of pipeline installations and the related research. The costs associated with a pipeline failure or damage, in terms of reparation at deep water depth and loss of production, are so high that it is fundamental to evaluate all the physical conditions and the extreme events that a pipeline have to resist during its life. In the past, the main idea was to totally prevent the pipeline instability, blocking the buildup of axial stresses (with the introduction of a number of expanding axial joints) or to restrain the vertical or lateral displacements of the pipeline (with an appropriate burying). This type of approaches, being more and more unfeasible and expensive, is becoming obsolete so that the design of offshore pipelines is to have them placed directly on the seabed. In detail, when a pipeline is installed on the seabed it disturbs the local environment. As a result, vortices are formed in the neighborhood of the pipeline and a pressure gradient may occur between the upstream and downstream sides of the pipeline. Piping and stagnation eddy may combine, generating a scour hole under the structures. A two-dimensional scour,induced by the waves and currents, may develop into a three-dimensional scour hole along the axis of the pipeline. If the pipeline is stiff enough and the span length is not very large,the mid-span may be suspended above the scour hole, or, when the span length is longer,the pipeline may start to sag. The pipeline continues its sagging process during the development of the scour hole, until the mid-span comes into contact with the scour hole bottom. The research concerning the pipe-soil interaction is of fundamental interest for the offshore engineering; the scour hole and the scour development are very important design parameters for the safety of most structures. The scour around an offshore structures is one of the classical topics in the ocean engineering, while one classical problem of the hydraulic engineering is the prediction of the scour hole around bridge piers. The scouring problem is not theoretically completely resolved in a satisfactory way as yet. One of the main reasons is the highly complex three-dimensional turbulence flow pattern generated around the structures, thus the only studies available in the literature concern the equilibrium condition of the scouring and the time development of the scour hole. Mao (1986) was the first who described the role of the small vortices that are formed in the upstream and downstream sides of the pipeline. They were thought of being responsible to carry sand particles away from the footing area of the pipeline until a small opening is formed underneath the pipeline which leads to the tunnel scour. Sumer et al., (2001) found that the pressure difference between the upstream and downstream sides of a pipeline drives a seepage flow underneath the pipe. When this seepage flow becomes excessive, piping occurs; a mixture of water and sand breaks through underneath the pipe, resulting in the onset of scour. The pressure difference together with other effects (such as vortices forming in front of and at the lee-wake of the pipe) are the agitating forces for the piping process. Once the scour breaks out, it will propagate along the length of the pipeline. A complementary way to evaluate and understand the process of local scour around pipelines is offered by numerical models. Over the last two decades, two main types of numerical models for scouring prediction have been developed. One first type of numerical algorithms was based on potential flow theory (Hansen et al 1986; Li & Cheng 1999). However, such a theory cannot adequately describe the flow below the pipeline subjected to scouring conditions and is unable to predict the downstream side of the bed profile and the vortex shedding generated downstream the body of interest. More recently, turbulenceaveraged Navies-Stokes solvers (both RANS and LES) coupled with a suitable sediment transport equation were introduced (Brørs 1999; Li & Cheng, 2001; Liang & Cheng, 2005). The main limits of these algorithms is in the capturing of the inception of the scouring. The aim of this research is to investigate the mechanics of scouring both numerically and experimentally and to promote the understanding of the pipe-soil interaction by means of an analysis of the local flow-sediment dynamics. A two-dimensional turbulent flow is investigated through an experimental test using a non-intrusive technique for the particle motion (Particle Tracking Velocimetry, PTV). The basic image processing for the PTV was performed by means of the software “YATS” (Miozzi, 2004). Such a software implements a tracking technique based on the correlation between interrogation windows of consecutive images. Eleven monochromatic waves were tested both in a rigid and an erodible seabed,the former is made of steel plates above wood platforms and it was useful to analyze the vorticity and turbulence generated around the pipe, for the latter it was used a granular sand, with a median diameter D50= 0.6 mm, in order to investigate the maximum scour depth and the scour development. Further, an innovative numerical model, based on the Level Set technique for a two-phase flow, has been implemented to evaluate the transitional and equilibrium stages of the scour development. The scouring of the sand bed is modeled by coupling the solution of the flow in the fluid domain with a simplified model used to describe the erosion of a granular sand layer. The domain is divided into three parts: i) a pure-water domain, ii) a solid domain with the consolidated sand and iii) a water-sand mixture. The fluid regions are modeled as a single-fluid domain with variable properties of mass and viscosity and are governed by the mass-conservation and the Navier-Stokes equation. The scour model uses a bulk approximation of a conservation of mass and advection scheme to predict the transport of the sediment. The model consists in two basic components one account for the sediment drifting and another for the sediment lifting (Mattioli et al., 2010). Drifting processes act on the suspended sediments, force the sand to pile up on the compact bottom considering that sand is composed of single grains that would fall on the bottom in the absence of a velocity field. Lifting processes only take place at the boundary between the solid and the fluid phase. Actually, the model is unable to reproduce the equilibrium stationary condition. Clearly the main problem with this sort of computations is related with the large difference in the time scales for the flow evolution and for the evolution of the seabed configuration: the morphological time scale is much larger than the hydrodynamic one. The vortex analysis performed for the rigid-bottom configuration, shows a good agreement with the experimental available results. The vortex motion is well reproduced for both KC=6 and KC=26. The simulations performed with an erodible sandy seabed made use of only 40 wave cycles, the model seems to not reproduce correctly the scouring under a pipeline. The erosion below the cylinder, is reached too far downstream of the cylinder, while it is expected to occur about 1D downstream of the pipe, the numerical result shows a scour hole about 3D far from the pipe. Regarding the maximum scour depth, the model seems to reproduce fairly well the experimental available results, this is mainly due to the value of β (lifting contribution) here used as a calibration parameter. The experimental study performed with the rigid-bottom configuration analyzes the boundary layer thickness, the streamwise vorticity dimension and the TKE equation. The boundary layer thickness δ increases with KC, following a logarithmic law (figure C.1 - Appendix C), while, the streamwise vortex dimension measured at the downstream side of the pipe, increases with KC following a linear law (figure C.2 - Appendix C). The TKE analysis, defines the contribute of each terms inside the equation (evolution + advection = production + transport + diffusion + dissipation). The results for the most energetic wave condition reproduced show that the evolution term, upstream of the pipe (x/D=-1) shows a peak for z/D=0.25 and z/D=1 at x/D=-0.5, it is almost negative over the pipe (x/D=0) and it decreases at the downstream side of the pipe for x/D=1 and x/D=1.5. The advection term is almost positive both upstream and downstream of the pipe. The production term is almost positive near the pipeline at the upstream end (x/D=1 and x/D=0.5), the profile exhibits a double peaks in correspondence of x/D=0. Far from the pipeline (x/D= -1.5 and x/D= 1.5), the production term decreases. The transport term increases rapidly reaching a maximum for x/D=0.5 showing a peak for z/D=0.6 on the top of the pipe. The dissipation term exhibits a peak near the bottom for all the sections studied, while the diffusion term is one order of magnitude smaller than all the other terms and seems not to give a fundamental contribution on the turbulence dynamics. An approximate balance between the evolution term and the production term upstream of the cylinder, a balance between evolution plus advection and the transport term above the cylinder and a balance between the advection and transport terms downstream of the pipeline were found. For the experimental analysis, to classify the scouring process, three distinctive regimes were recognized: i) no scour regime for KC<2, ii) scour with small ripples for 2< KC <12 and finally iii) scour with large ripples for 15< KC <26. The equilibrium scour depth was reached well within 60 minutes. The equilibrium scour shape seems to be symmetric with respect to the central section of the pipeline for KC<10, while an asymmetry of the scour hole is found for larger values of KC. The equilibrium scour depth for KC>15 acquired a shape similar to the surface of a non-linear wave. A hill was created at a distance of x/D=0.5 between two throughs with a gentle slope, due to the “jet” contribution of the tunnel erosion and the vortex developed downstream the pipe. The asymmetry of the scour hole is one aspect of the scouring mechanism not completely well explained as yet, further analysis will be performed in order to better understand the sediment dynamics and explain the physics of the phenomenon. An intuitive aspect found observing the experimental results is that, even if the piping and seepage flow do not occur, the sediment motion may create a scour hole around the cylinder. If the slope of the scour hole is sufficiently large,some sediment under the pipe may slide down, leading to the failure of the pipe foundation. This aspect is extremely relevant because it can give a new definition for the onset of scour. The empirical equation of Sumer and Fredsoe (1990) and Cevik and Yuksel (1999) on the measured S/D vs. KC, shows a good agreement with the experimental results. The measured scour widths in term of W/D, plotted against KC compared with the empirical equation of Catano-Lopera and Garcia (2007) and Sumer and Fredsoe (2002), shows a worse agreement. The Catano-Lopera formula overestimates the scour width for KC <15 and underestimates the experimental results for KC>15, while, the Sumer and Fredsoe fails for KC>15. In Chapter 1 a literature review concerning the mechanics of scour is presented. In Chapter 2 a numerical DNS solver of the Navier-Stokes equation is proposed. The scour conditions were simulated as forced by both currents and waves and some comparisons with the available experimental literature test were performed (Chapter 3). Chapter 4 illustrates a physical model on the pipe-soil interaction between a pipe and a rigid-erodible bed. Two different configurations were tested, in the former a PTV was applied to reconstruct the hydrodynamics around the pipeline, while the latter focuses on the influence of short and long waves on a pipe over a coarse sand bed. The results of the experimental tests are shown in Chapter 5. Chapter 6 closes the present research.