To simulate filling a moving funnel, a model area with a large length and a relatively small height is required. The results of the static simulations can be considered reliable, because the 2DV model remains well within the limits in these simulations.
General development
Covering of pipelines
Relevance of this research
Problem definition
Aims and objectives
Structure of the thesis
A subsea pipeline is susceptible to flotation during excavation-based backfilling if its density is lower than the density of the surrounding soil-water mixture. Sedimentation is the tendency for suspended particles to settle out of the soil-water mixture.
Inlet zone
The density of the soil-water mixture (ρm) is affected by the fraction of solids in the transporting fluid. The volumetric concentration determines the part of the mixture volume that is occupied by soil particles.
Sedimentation zone
- Grain size
- Specific density
- Grain size distribution
- Fall velocity of individual sphere in still water
- Non spherical particles
- Effect of sediment concentration
- Effect of grain size distribution
- Kynch’s sedimentation theory
- Sedimentation length
- Porosity
- Permeability
- Erosion
This separation is due to the different fall speeds of the smaller and larger grains. The length by which a turbulent soil-water mixture can extend is determined by the degree of turbulence and the fall velocity of the soil particles.
Settled bed
Structural density
All the work reported so far has been limited to solving vertical deposition problems. Nevertheless, the study of a backfilled trench should not be limited to modeling only sedimentation and strength development.
Transition from sand like to clay like behaviour
The boundaries for the transition between cohesive and network structures are shown in the sand-silt-clay triangle (see Figure 10). The dashed lines in the left corner indicate the boundary of the sand-dominated grid structure for different water volume fractions.
Consolidation
This can be predicted even in a simple model, so it is not necessary to model this type of sand with a 2DV model. However, this type of material is not relevant for modeling with the 2DV model, as backfilling with this type of material using the deepening method is not recommended.
Overview of the 2DV model
Mixing velocities are used in the momentum equations, while the sediment transport equations use grain velocities. The horizontal component of the mixing velocity is substituted directly into the sediment transport equations.
Boundary conditions
The total mixture concentration consists of the mixture concentrations of all fractions added together. The velocity of the grains in the horizontal direction is equal to the velocity of the suspension mixture. The effect of bottom shear stress on sedimentation is modeled by the reduction factor R(θ).
The critical value of the Shields parameter was found to be independent of the grain size of the tested sand (d50 < 300 μm).
Numerical procedure
These equations are solved using a pressure correction method, using the mixture density and the eddy viscosity of the old time step (tn). This is done using the flow field of tn+1 and the mixture velocity of tn. Update of the concentrations for all fractions and the total mixture density to time tn+1.
This is done by using the flow field and eddy viscosity of tn+1 to calculate the grain velocities for the next time step.
Validation of the 2DV model
This chapter describes the implementation of the 2DV sedimentation model with respect to pipeline flooding during excavation-based backfilling. This can lead to the pipeline flowing if the density of the pipeline is lower than the density of the surrounding soil-water mixture. The 90% sedimentation length is defined as the horizontal distance that the sand-water mixture flow covers before 90% of the sand from the mixture has settled (Mastbergen, 1988).
These fines can have a major impact on the total length of sedimentation, although they represent only a small fraction of the material.
The Europipe II flotation occurred in this section of the pipeline between the 1999 and 2000 surveys. The exposure of the Europipe II pipeline cannot be directly attributed to the pipeline jetting operation. In addition to the previously treated cases, another reference case is also used in this thesis.
In this way it is possible to compare the general behavior of coarse and fine material.
One dimensional tests
Model setup
Soil particles have already settled out of suspension and have formed a bed at the bottom of the column. The bed material is marked with a red-brown color and the bed height is marked with a thin white line. The dark blue color at the top of the column indicates clear water without suspended particles.
Results
The empirical formula, derived from the results of the 2DV sedimentation tests, is only valid for an initial mixture density of 20%. This relationship can be converted to a more generally applicable term if cruise velocity, initial mixture velocity, mixture density and the trench profile are taken into account. It was not possible to perform a complete sedimentation test of the Kuwaiti soil-water mixture.
The large fraction of fine material and the low average grain size (23 μm) resulted in a very long sedimentation time.
Static analysis
Model setup
Therefore, it is necessary to ensure that the wall of the model is open so that the pressure can leave the model. It is enough to model the distance from the bottom of the suction pipe to the bottom of the trench. It is also necessary to maintain the velocity of the mixture above the critical value of 3.5 – 4 m/s to prevent clogging of the TSHD pipe.
The simulations of the 2DV model are performed with an initial mixture velocity of 4 m/s.
Results
The build-up height is the maximum height of the sand body at a given moment, which is visualized in Figure 23. This graph makes it clear that the build-up height of the sand body of a particular soil-water mixture remains constant in time. This interferes with the build-up rate of these soil-water mixtures as the maximum height of the sand body is measured.
This graph shows the results of four simulations of the same soil-water mixture ('250 µm') with four different initial concentrations.
Moving hopper
- Models setup
- Multiple fixed inflow points
- Moving boundary
- Comparison of the Moving boundary and the Multiple fixed inflow points
The trailing speed of the TSHD (the speed at which the input point moves) is set to 1 m/s. The results of the 'moving boundary' method are different from the results of the 'multiple fixed input points' method. In the "moving boundary" method, soil particles remain on top of the modeled area.
Although the grid size and inflow point size are the same as in the 'multiple fixed inflow point' method.
Beam on elastic foundation
At places where the deflection acts upwards, there will be no contact with the underlay. The driving force is determined by the density of the displaced liquid and the dimensions of the pipeline.
Beam-model
Overview of the model
This implies that any upward movement of an element is not impeded by the associated spring. The displacement of a single element is influenced by the properties of the pipeline, the soil-water mixture density, the bed constant and the displacement of nearby elements. Furthermore, the soil-water mixture density is distributed as a function of the length of the pipeline x(i) and the displaced height w(i).
The density of the mix can vary depending on the length and height of the modeled area.
Model setup
Since there is no element of time in the model, this distribution is static and does not change. The upper layer of the seabed is affected by a combined load of waves and currents. To obtain a realistic evaluation of pipeline displacement due to dredging-based backfill, more parameters are required.
Variation in fluid density
Results
The weight of this soil-water mixture is slightly lower than the weight of the pipe. The weight of the pipeline is also included in the graph and is indicated by the dotted line. The weight of the displaced groundwater mixture is also shown at the top of the graph.
The weight of the displaced mixture of soil and water is shown at the top of the graph.
Fluidised length
Results
A greater concentration of solids gives a greater weight to the mixture, which will make the pipeline more prone to flow. The bending stiffness of the pipeline is in this case faster insufficient to prevent flow compared to lighter mixes. Using only the properties of the pipeline, there are two related approaches to making pipelines less prone to pipeline flow during excavation-based backfilling.
The bending stiffness is related to the modulus of elasticity of the material used to construct the pipeline and the moment of inertia.
Backfilling offshore pipeline
Model setup
If the pipe is heavier than the surrounding soil-water mixture, there is no risk of floating up.
Results
Before using the ray model, information on the distribution and development of the soil-water mixture must be obtained. The beam model cannot be used as a tool to predict pipeline flooding if the history of the pipeline is not included. In order to achieve this, the density of the slurry, the gradation of the soil, the initial speed of the mixture and the pulling speed of the floating suction hopper dredger (TSHD) must be known.
The characteristics of the pipeline in combination with the three points above will provide an estimate of whether the pipeline will remain stable during backfilling.
Conclusions
The density evolution of a soil-water mixture depends mostly on the grain size distribution of the considered soil. These plots can be used to simulate TSL and the density of the soil-water mixture. The results of the 2DV model may become inaccurate as the model space becomes larger.
The strength development of the soil-water mixture is not included in the model and already sedimented soil cannot be used to strengthen the pipe.
Recommendations
The plots on the left show the contour of the concentration when the mixture inflow point is placed at the top of the model. The width of the discharge pipe is the same as the width of the inflow point: one meter. The method of the multiple fixed inflow points defines a maximum of fifty inflow points next to each other.
The trailing speed is simulated using the fifty inlet points one by one. The setup of the moving boundary model is basically the same as the setup of the multiple inlet method. It is believed that this method provides a smoother moving inflow point compared to the more uneven method with the multiple inflow points.
