Simulation method for dynamic behavior of high-pressure water jet scouring mud cake based on spf-fem coupling

Abstract

The application discloses a high-pressure water jet scouring mud cake dynamic behavior simulation method based on SPH-FEM coupling, which comprises the following steps: constructing a water jet impact mud cake calculation model, setting a soil body and a scouring opening based on FEM theory, and setting fluid particles based on smooth particle hydrodynamics; based on the flow-solid coupling theory, the meshless method and the grid method are combined to perform water jet impact mud cake form prediction calculation. Through the secondary development based on the SPH-FEM coupling, the numerical simulation of the foundation scouring flow-solid-soil coupling can be realized, the high-speed scouring behavior in the water jet impact process is clearly shown, and therefore, the further research on the mud cake disposal of the shield cutter head is facilitated.

Description

Technical Field

[0001] This invention relates to the field of tunnel engineering, and in particular to a simulation method for the dynamic behavior of high-pressure water jet scouring mud cake based on SPH-FEM coupling. Background Technology

[0002] With the expanding application and scope of tunnel boring machine (TBM) construction, the difficulties faced by TBMs in challenging geological formations are increasing daily. For example, TBMs tunneling in hard rock formations face severe cutterhead and tool wear; in plastic clay formations, cutterhead mud cake formation and attitude control are significant challenges; and in coarse-grained soil formations (such as sand and gravel), severe equipment wear, muck removal difficulties, and blowouts are common construction risks. When tunneling through alternating layers of hard and soft strata, special geological features such as irregular lenses, boulders, spheroidal weathered bodies, and bedrock protrusions cause more frequent issues like tool breakage, segment floating, cutterhead mud cake formation, and muck blockage. Encountering these engineering problems often requires significant time and money to resolve, greatly limiting construction efficiency and increasing costs.

[0003] To address the issue of mud cake formation during shield tunneling in viscous strata, a common method for mud cake removal is water jet flushing. However, there is currently limited research both domestically and internationally on mud cake flushing from the cutterhead. Mud cake removal methods primarily rely on indoor experiments, adjustments to cutterhead equipment, and on-site engineering parameter adjustments. Simulation studies on mud cake flushing using smooth particle hydrodynamics numerical simulation methods are still lacking. Summary of the Invention

[0004] To address the limited research on cutterhead mud cake scouring during tunnel boring machine (TBM) construction, which leads to low efficiency and high costs, this invention provides a simulation method for the dynamic behavior of high-pressure water jet scouring mud cake based on SPH-FEM coupling. This method accurately simulates the impact of water jets on the mud cake, thereby obtaining precise information about the impact and providing a structural improvement scheme for the TBM nozzle.

[0005] To achieve the above-mentioned technical objectives, the technical solution of the present invention is as follows:

[0006] A simulation method for the dynamic behavior of high-pressure water jet flushing of mud cake based on SPH-FEM coupling includes the following steps:

[0007] Step 1: Based on the structure of the high-pressure water jet flushing port of the shield cutterhead, establish the geometric model of the nozzle of the flushing port, the water jet ejected from the nozzle, and the mud cake attached to the cutterhead.

[0008] Step 2: Mesh the geometric models of the nozzle, water jet, and mud cake to obtain the three-dimensional finite element (FEM) mesh models of the nozzle, water jet, and mud cake, respectively.

[0009] Step 3: Based on the FEM mesh model of water jet, SPH particles are generated at each mesh node to form a discretized SPH particle flow model.

[0010] Step 4: Combine the FEM mesh model of the nozzle and mud cake with the SPH particle flow model of the water jet to form an SPH-FEM coupled model in which the SPH particle flow model and the FEM mesh model are in contact with each other.

[0011] Step 5: Set the initial calculation material properties of the coupled model, and define the physical parameters and equation of state of the SPH particle flow based on the physical parameters of water.

[0012] Step 6: Set the SPH particle flow model and the FEM mesh model to point-to-surface contact, and the FEM mesh models to surface-to-surface contact. Set the boundary conditions, the total number of time steps, and the duration of one time step.

[0013] Step 7: Solve the SPH-FEM coupled model at each time step, obtaining a solution result after each time step. At the end of each time step, check if the total number of continuous time steps has been reached. If not, continue solving; otherwise, terminate the calculation and save all solution results.

[0014] In the method described above, step 2 involves meshing the geometric model of the nozzle using a shell element meshing method to generate several wall shell elements of the nozzle, thereby forming the FEM mesh model of the nozzle.

[0015] In the method described above, step 2 involves meshing the geometric model of the water jet and the mud cake using a solid element meshing method to generate several water area meshes and several mud cake meshes, thereby generating an FEM mesh model of the water jet and the mud cake.

[0016] The method described, specifically step 3, includes: generating SPH particles at each node of the water area grid, and then deleting the original FEM model grid, thereby representing the water area using SPH particles that have mass and occupy independent space. Furthermore, the SPH particles do not need any connections and their arrangement is unrestricted; that is, the water jet is discretized to obtain the SPH particle flow model.

[0017] The method described above, in step 5, includes setting the initial calculation material properties of the coupled model, which includes:

[0018] The mud cake and nozzle were modeled using the PLASTIC_KINEMATIC kinematic hardening material model. The formula for calculating the yield strength of the model is as follows:

[0019]

[0020] Where, σ y E is the yield strength, σ0 is the initial yield strength, and E p For plastic hardening modulus, For effective plastic strain, p and c are input constants, ε is the strain rate, and β is the hardening parameter, taking values ​​between 0 and 1 to describe different hardening models. When β = 0, it is kinematic hardening, where the yield surface size remains constant but moves along the direction of plastic strain. When β = 1, it is isotropic hardening, where the yield surface position remains constant but its size changes with strain. When β is between 0 and 1, it belongs to the mixed hardening model, where both the position and size of the yield surface change.

[0021] The method described above, plastic hardening modulus E p The calculation formula is:

[0022]

[0023] Where E is the elastic modulus, E t It is the tangent modulus.

[0024] In the method described above, step 5, defining the physical parameters and equation of state for the SPH particle flow based on the physical parameters of water includes:

[0025] The physical parameters of water are defined using a NULL material model, and the Grüneisen equation of state is assigned to water. The Grüneisen equation of state is as follows:

[0026]

[0027] Where P is pressure, ρ w Let C be the density of water, and C be the shock wave velocity-particle velocity relationship. s -v p The intercept of the curve, v s For the shock wave velocity, v p Let v be the particle velocity, and S1, S2, and S3 be v. s -v p The slope of the curve, γ0 is the Grünesen constant, a is the first-order volume correction with respect to the Grünesen coefficient γ0 and μ = ρ / ρ0-1, ρ is the current volume density, ρ0 is the initial volume density, and E a Let be the internal energy per unit volume, and μ be the rate of change of volume.

[0028] In the method described above, step 6 involves point-to-surface contact calculations between the SPH particle flow model and the FEM mesh model, specifically between the water jet and the nozzle, and between the water jet and the mud cake. The formula for calculating the contact stiffness k is:

[0029] k=max(SLSFAC×SFS×k0,SOFSCL×k1)

[0030] Where SLSFAC is the sliding interface penalty function scaling factor, SFS is the default contact surface penalty function factor, SOFSCL is the constraint force scaling factor for the soft constraint option, and k0 and k1 are material- and node-related stiffnesses.

[0031] Between the FEM mesh models, i.e., between the nozzle and the mud cake, surface-to-surface contact is used for calculation. The formula for calculating the contact stiffness k is:

[0032] k=max(SLSFAC×SFM×k0,SOFSCL×k1)

[0033] SFM is the default primary penalty stiffness ratio coefficient.

[0034] In the method described above, step 6 involves fixing the boundary conditions for the mesh nodes at the bottom surface of the mud cake FEM mesh model and all mesh nodes of the nozzle FEM mesh model.

[0035] The technical advantage of this invention is that it can clearly obtain the morphology of the mud cake impact pit, obtain different impact ranges by changing different initial flow velocities of the water jet, and display the impact behavior of water jet scouring in real time, thereby helping to study the mechanism of water jet removal of mud cake on the cutter head. Attached Figure Description

[0036] Figure 1 This is a flowchart of the calculation process of the present invention;

[0037] Figure 2 This is a model diagram of the water jet scouring of mud cake simulated in this invention;

[0038] Figure 3 These are simulation results from embodiments of the present invention. Detailed Implementation

[0039] The present invention will be further described below with reference to the accompanying drawings and embodiments. However, the scope of protection of the present invention is not limited to the specific embodiments.

[0040] See Figure 1 The water jet scouring cake morphology prediction and simulation method based on the SPH-FEM coupling algorithm provided in this embodiment includes the following steps:

[0041] Step 1: Based on the structure of the high-pressure water jet flushing port of the shield cutterhead, establish the geometric model of the nozzle of the flushing port, the water jet ejected from the nozzle, and the mud cake attached to the cutterhead.

[0042] Step 2 involves meshing the geometric models of the nozzle, water jet, and mud cake to obtain their respective three-dimensional finite element (FEM) mesh models. The nozzle's geometric model is meshed using a shell element method to generate several wall shell elements for the nozzle, thus forming the nozzle's FEM mesh model. The water jet and mud cake's geometric models are meshed using a solid element method to generate several water area meshes and several mud cake meshes, thus creating the water jet and mud cake's FEM mesh models.

[0043] Step 3: Generate SPH particles at each node of the water area mesh, then delete the original FEM model mesh, thus representing the water area using SPH particles that have mass and occupy independent space. Furthermore, the SPH particles do not need any connections and their arrangement is unrestricted; in other words, the water jet is discretized to obtain the SPH particle flow model.

[0044] Step 4: Combine the FEM mesh model of the nozzle and mud cake with the SPH particle flow model of the water jet to form an SPH-FEM coupled model where the SPH particle flow model and the FEM mesh model are in contact, and where the FEM mesh models are in contact with each other. That is, as shown... Figure 2 As shown, 1 is the FEM mesh model of the mud cake, 2 is the FEM mesh model of the nozzle, and 3 is the SPH particle flow model of the water jet.

[0045] Step 5, set the initial calculation material properties for the coupled model:

[0046] The mud cake and nozzle were modeled using the PLASTIC_KINEMATIC kinematic hardening material model. The formula for calculating the yield strength of the model is as follows:

[0047]

[0048] In the above formula, σ y E is the yield strength, σ0 is the initial yield strength, and E p For plastic hardening modulus, For effective plastic strain, p and c are input constants, ε is the strain rate, and β is the hardening parameter, ranging from 0 to 1, used to describe different hardening models. When β = 0, it is kinematic hardening, the yield surface size remains unchanged, but moves along the direction of plastic strain. When β = 1, it is isotropic hardening, the yield surface position remains unchanged, but its size changes with strain. β between 0 and 1 belongs to the mixed hardening model, where both the position and size of the yield surface change. The plastic hardening modulus E... pThe calculation formula is:

[0049]

[0050] Where E is the elastic modulus, E t This is the tangent modulus.

[0051] The material parameters in this embodiment are shown in the table below:

[0052] Table 1 SPH Material Model Parameters

[0053]

[0054] Table 2. Parameters of Mud Cake Material Model

[0055]

[0056] Table 3 Nozzle material model parameters

[0057]

[0058] Then, based on the physical parameters of water, the physical parameters and equation of state for SPH particle flow are defined:

[0059] The physical parameters of water are defined using a NULL material model, and the Grüneisen equation of state is assigned to water. The Grüneisen equation of state is as follows:

[0060]

[0061] Where P is pressure, ρ w Let C be the density of water, and C be the shock wave velocity-particle velocity relationship. s -v p The intercept of the curve, v s For the shock wave velocity, v p Let v be the particle velocity, and S1, S2, and S3 be v. s -v p The slope of the curve, γ0 is the Grünesen constant, a is the first-order volume correction with respect to the Grünesen coefficient γ0 and μ = ρ / ρ0-1, ρ is the current volume density, ρ0 is the initial volume density, and E a Let be the internal energy per unit volume, and μ be the rate of change of volume.

[0062] Step 6: Set the SPH particle flow model and the FEM mesh model to point-to-surface contact, and the FEM mesh models to surface-to-surface contact. Specifically, the contact between the SPH particle flow model and the FEM mesh model, i.e., between the water jet and the nozzle, and between the water jet and the mud cake, is calculated using point-to-surface contact. The formula for calculating the contact stiffness k is:

[0063] k=max(SLSFAC×SFS×k0,SOFSCL×k1)

[0064] Where SLSFAC is the sliding interface penalty function scaling factor, SFS is the default contact surface penalty function factor, SOFSCL is the constraint force scaling factor for the soft constraint option, and k0 and k1 are material- and node-related stiffnesses.

[0065] In the FEM mesh model, surface-to-surface contact is used for calculation, i.e., between the nozzle and the mud cake. The formula for calculating the contact stiffness k is:

[0066] k=max(SLSFAC×SFM×k0,SOFSCL×k1)

[0067] SFM is the default primary penalty stiffness ratio coefficient.

[0068] Then, boundary conditions are set, namely, the mesh nodes at the bottom surface of the mud cake FEM mesh model and all mesh nodes of the nozzle FEM mesh model are fixed and constrained. Next, the total number of time steps and the duration of each time step are set.

[0069] Step 7: Solve the SPH-FEM coupled model at each time step, obtaining a solution result after each time step. At the end of each time step, check if the total number of continuous time steps has been reached. If not, continue solving; otherwise, terminate the calculation and save all solution results. The calculation results are as follows: Figure 3 As shown.

[0070] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that some local modifications or changes can still be made without departing from the spirit or essential characteristics of the invention; all of these fall within the scope of protection of the present invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is determined by the appended claims.

[0071] The parts not covered in this invention are the same as or can be implemented using existing technologies.

Claims

1. A simulation method for the dynamic behavior of high-pressure water jet scouring of mud cake based on SPH-FEM coupling, characterized in that, Includes the following steps: Step 1: Based on the structure of the high-pressure water jet flushing port of the shield cutterhead, establish the geometric model of the nozzle of the flushing port, the water jet ejected from the nozzle, and the mud cake attached to the cutterhead. Step 2: Mesh the geometric models of the nozzle, water jet, and mud cake to obtain the three-dimensional finite element (FEM) mesh models of the nozzle, water jet, and mud cake, respectively. Step 3: Based on the FEM mesh model of water jet, SPH particles are generated at each mesh node to form a discretized SPH particle flow model. Step 4: Combine the FEM mesh model of the nozzle and mud cake with the SPH particle flow model of the water jet to form an SPH-FEM coupled model in which the SPH particle flow model and the FEM mesh model are in contact with each other. Step 5: Set the initial calculation material properties of the coupled model, and define the physical parameters and equation of state of the SPH particle flow based on the physical parameters of water. Step 6: Set the SPH particle flow model and the FEM mesh model to point-to-surface contact, and the FEM mesh models to surface-to-surface contact. Set the boundary conditions, the total number of time steps, and the duration of one time step. Step 7: Solve the SPH-FEM coupled model at each time step to obtain a solution result after each time step; and at the end of each time step, determine whether the total number of continuous time steps has been reached. If not, continue solving; otherwise, terminate the calculation and save all solution results. In step 5, the physical parameters and equation of state for the SPH particle flow are defined based on the physical parameters of water, including: The physical parameters of water are defined using a NULL material model, and the Grüneisen equation of state is assigned to water. The Grüneisen equation of state is as follows: . in, P For pressure, ρ w For the density of water, C The relationship between shock wave velocity and particle velocity v s - v p The intercept of the curve, v s For the shock wave velocity, v p For particle velocity, S 1. S 2. S 3 is v s - v p The slope of the curve, γ 0 is the Grünesen constant. a For Grünesen coefficients γ 0 and μ=ρ / ρ The first-order volume correction factor of 0-1 ρ For the current volume density, ρ 0 represents the initial volume density. E a Internal energy per unit volume μ This represents the rate of change in volume.

2. The method according to claim 1, characterized in that, In step 2, the geometric model of the nozzle is meshed using a shell element meshing method to generate several wall shell elements of the nozzle, thereby forming the FEM mesh model of the nozzle.

3. The method according to claim 1, characterized in that, In step 2, the geometric model of the water jet and mud cake is meshed using a solid element meshing method to generate several water area meshes and several mud cake meshes, thereby generating the FEM mesh model of the water jet and mud cake.

4. The method according to claim 3, characterized in that, Step 3 includes: generating SPH particles at the nodes of each water area grid, and then deleting the original FEM model grid, thereby representing the water area with SPH particles that have mass and occupy independent space; and the SPH particles do not need to be connected to each other and their arrangement is not restricted, that is, discretizing the water jet to obtain the SPH particle flow model.

5. The method according to claim 1, characterized in that, Step 5, setting the initial calculation material properties of the coupled model, includes: The mud cake and nozzle were modeled using the PLASTIC_KINEMATIC kinematic hardening material model. The formula for calculating the yield strength of the model is as follows: in, σ y For yield strength, σ 0 represents the initial yield strength. E p For plastic hardening modulus, For effective plastic strain, p , c For input constants, ε For strain rate, β These are hardening parameters, with values ​​between 0 and 1, used to describe different hardening models. β When the yield strength is 0, it is kinematic hardening, the size of the yield surface remains unchanged, and it moves along the direction of plastic strain; β When = 1, it is isotropic hardening, the position of the yield surface remains unchanged, and its magnitude changes with strain; β Between 0 and 1, it belongs to the mixed hardening model, where the position and size of the yield surface change.

6. The method according to claim 5, characterized in that, plastic hardening modulus E p The calculation formula is: in E For elastic modulus, E t This is the tangent modulus.

7. The method according to claim 1, characterized in that, In step 6, point-to-surface contact calculations are used between the SPH particle flow model and the FEM mesh model, i.e., between the water jet and the nozzle and between the water jet and the mud cake; contact stiffness... k The calculation formula is: Where SLSFAC is the scaling factor of the sliding interface penalty function, SFS is the default penalty function factor from the contact surface, and SOFSCL is the constraint force scaling factor of the soft constraint option. k 0、 k 1 represents the material and node-related stiffness; The FEM mesh model is used for surface-to-surface contact calculations, i.e., between the nozzle and the mud cake, to determine the contact stiffness. k The calculation formula is: SFM is the default primary penalty stiffness ratio coefficient.

8. The method according to claim 1, characterized in that, In step 6, the boundary conditions are to fix the mesh nodes at the bottom surface of the mud cake FEM mesh model and all the mesh nodes of the nozzle FEM mesh model.

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