Foundation scour fluid-solid-soil coupling simulation method based on sph-dem coupling and multiphase flow theory

A foundation scour fluid-solid-soil coupling simulation method based on SPH-DEM coupling and a multiphase flow theory, comprising following steps:

• step 1:
• constructing a particle model, setting fluid particles and bed material particles based on the multiphase flow theory, and setting rigid particles based on a DEM theory, specific steps comprising as below:
• step 1.1:
• respectively constructing a fluid particle model and a soil particle model based on a multiphase flow basic principle, setting the fluid particle model as Newtonian fluid, setting the soil particle model as non-Newtonian fluid, and determining a soil viscosity μHBP based on an HBP model,
• μ
• HBP
• =
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• τ
• c
• ❘
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• II
• D
• [
• 1
• -
• e
• m
• ⁢
• II
• D
• ]
• +
• 2
• ⁢
• μ
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• 4
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• n
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• 1
• 2
• wherein τc denotes yield stress of a model material, IID denotes a second invariant of a fluid strain rate tensor, m denotes a stress exponent growth coefficient, μ denotes a water viscosity, and n denotes an exponent associated with shear stress;
• step 1.2:
• introducing a DP yield criterion to calculate specific material yield stress τy;
• step 1.3:
• substituting the specific material yield stress τy obtained in step 1.2 into the calculation formula of the soil viscosity μHBP in step 1.1 to replace the model material yield stress τc, and establishing a soil viscosity calculation model;
• step 1.4:
• setting the rigid particles based on the DEM theory, and determining a normal contact rigidity Kn, normal contact damping γn, a tangential contact rigidity Kt and tangential contact damping γt among the rigid particles;
• and
• step 1.5:
• calculating normal contact force F, and tangential contact force F, based on the normal contact rigidity Kn, the normal contact damping γn, the tangential contact rigidity Kt and the tangential contact damping γt among the rigid particles obtained in step 1.4;
• step 2:
• introducing a fluid-solid coupling theory based on the particle model obtained in step 1 to correct a fluid control equation, and performing controlled solving of the fluid particles, specific steps comprising as below:
• step 2.1:
• introducing particle fluid-solid coupling force Ffs, and correcting a fluid momentum conservation equation;
• and
• step 2.2:
• giving a discrete form of the fluid momentum conservation equation obtained in step 2.1, based on a kernel function theory of an SPH algorithm;
• step 3:
• based on the particle model obtained in step 1, correcting and solving the rigid particle control equation by combining the Newton's second law and considering the particle fluid-solid coupling force Ffs obtained in step 2;
• step 4:
• based on the particle model obtained in step 1, introducing a sediment particle Shield criterion, correcting a sediment incipient motion model in combination with the fluid-soil coupling force obtained in step 1 and the solid-soil coupling force obtained in step 2, and performing foundation scour controlled solving, specific steps comprising as below:
• step 4.1:
• based on the fluid particle velocity μ obtained based on the momentum equation in step 2, introducing an Einstein logarithmic flow velocity distribution formula to calculate fluid shear stress τb exerted on soil particles;
• step 4.2:
• based on the soil particle viscosity μHBP model obtained in step 1.1, introducing the sediment particle Shield criterion to calculate sediment incipient motion critical stress τcr,0;
• step 4.3:
• based on the sediment incipient motion critical stress τcr,0 obtained in step 4.2, introducing the fluid-solid coupling force Ffs of the sediment particles and the rigid particles obtained in step 2 to calculate corrected sediment incipient motion critical stress τcr considering an external load and a side slope effect;
• step 4.4:
• judging the incipient motion state of the sediment particles based on the fluid shear stress τb obtained in step 4.1 and the corrected sediment incipient motion critical stress τcr obtained in step 4.3, wherein if τcr<TD is satisfied, τcr is substituted into the formula in step 1.1 to replace the yield stress τc, a bed material particle viscosity μHBP is updated to make the bed material particle into a bed load particle, and if the condition is not satisfied, processing is performed according to step 1.2 and step 1.3;
• step 4.5:
• according to the bed load particles obtained in step 4.4, introducing a Mastbergen formula to calculate a critical flow velocity μlift at which a bed load is converted into a suspended load, wherein if a flow velocity μ≥μlift of the fluid particles is satisfied, the fluid particles are converted into suspended load particles, and an equivalent viscosity μlift is calculated to replace the bed material particle viscosity μHBP, and if the condition is not satisfied, no processing is performed;
• and
• step 4.6:
• according to the suspended load particles obtained in step 4.5, introducing the Mastbergen formula to calculate a critical flow velocity μset at which the suspended load is converted into the bed load, wherein if the actual flow velocity us μset of the particles is satisfied, the particles are converted into the bed load particles and processed according to step 4.4, and if the condition is not satisfied, no processing is performed;
• and
• step 5:
• repeating step 1 to step 4 until solving is completed.