Calculation method for frictional loss of slurry shield circulation system along the way in sandy soil stratum considering wall slip and rheological properties

Abstract

The present invention proposes a calculation method for the frictional loss along the way of the slurry shield circulation system in sandy soil strata considering wall slip and rheological characteristics, belonging to the fields of civil engineering and tunnel engineering. Based on a rheological model with a higher fitting degree for slurry rheology and considering the wall slip effect and rheological characteristics, a new calculation method is proposed, which is consistent with the pipeline transportation characteristics of the actual circulation system, thereby reducing errors, being convenient to calculate and having a higher accuracy. First, the present invention selects the pipeline of the circulation system according to the actual slurry shield project, and then, according to the characteristics of pipeline flow, divides the pipeline into the mainstream area and the slip area. Based on the shear rate and the basic formula of pipe flow, the basic flow equation considering the wall slip effect of the pipeline used at the construction site is obtained. Next, the rheological model is substituted, and the frictional pressure loss along the way of the slurry balance shield circulation system in sandy soil strata considering the volume fraction of sand is considered, and the Matlab mathematical software is used to solve the frictional pressure loss along the pipeline.

Description

Technical Field

[0001] The present invention relates to the fields of civil engineering and tunnel engineering, and particularly to a method for calculating the frictional head loss of the circulating system of a slurry shield in sandy soil considering wall slip and rheological characteristics. Background Art

[0002] In recent years, with the rapid progress of infrastructure construction in China, slurry shield tunneling machines have been widely used in the construction of highway tunnels and subway tunnels due to their construction safety and high efficiency, especially in river-crossing projects and water conveyance projects. During the tunneling process of a slurry shield, fresh bentonite slurry is pumped through the slurry inlet pipeline in the circulating system into the excavation chamber (slurry chamber) to balance the water and soil pressures in front of the working face. After the soil cut from the working face is mixed with the slurry in the slurry chamber, it is pumped out of the tunnel through the slurry discharge pipeline to the slurry separation plant for screening, hydrocyclone separation, and pressure filtration treatment, so that the bentonite slurry can be recycled. Therefore, the effective operation of the circulating system of a slurry shield is very important.

[0003] In sandy soil, the slurry in the slurry discharge pipeline of the circulating system of a slurry shield is composed of bentonite slurry and excavated sand, and the slurry is considered a non-Newtonian fluid. Wall slip usually occurs during the pipeline pumping process, and the wall slip phenomenon has a positive effect on reducing resistance and saving energy in pipeline transportation. Most current studies focus on slurry transportation without slip, which brings errors to the estimation of pipeline pressure loss. Moreover, the slurry is assumed to be a Bingham non-Newtonian fluid, but through rheological tests, the rheological behavior of the slurry is more in line with the H-B rheological model. To sum up, there are always large errors between the existing calculation methods and the actual situation. Summary of the Invention

[0004] In order to overcome the deficiency of the low calculation accuracy of the existing method for calculating the pressure loss of the circulating system of a slurry shield, the present invention designs a method for calculating the frictional head loss of the circulating system of a slurry shield in sandy soil considering wall slip and rheological characteristics. Based on a rheological model with a higher fitting degree of slurry rheology and considering the wall slip effect and rheological characteristics, a new calculation method is proposed, which is consistent with the pipeline transportation characteristics of the actual circulating system, thereby reducing errors, being convenient to calculate, and having high accuracy.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0006] A method for calculating the frictional head loss of the circulating system of a slurry shield in sandy soil considering wall slip and rheological characteristics, comprising the following steps:

[0007] Step 1: Select the pipeline of the circulating system according to the requirements of the actual slurry shield project;

[0008] Step 2: Construct the basic flow equation of the pipeline considering the wall slip effect;

[0009] Step 3: Introduce the rheological model and substitute it into the basic flow equation of the pipeline considering the wall slip effect to obtain the pipeline flow equation based on the rheological model and considering the wall slip;

[0010] Step 4: Conduct rheological tests on the slurry and sand mixture with different sand volume fractions respectively, solve the rheological parameters of the slurry at different volume fractions, and finally fit the expressions between each rheological parameter and the volume fraction respectively, and substitute them into the pipeline flow equation based on the rheological model and considering the wall slip to obtain the pipeline flow equation based on the rheological model and considering the wall slip and rheological characteristics;

[0011] Step 5: Consider the slurry balance shield in the sandy soil layer to obtain the implicit expression of the frictional pressure loss along the pipeline of the slurry balance shield circulation system in the sandy soil layer based on the rheological model, wall slip effect and considering the sand volume fraction;

[0012] Step 6: Input the numerical values of each parameter into the implicit expression of the frictional pressure loss along the pipeline of the slurry balance shield circulation system in the sandy soil layer based on the rheological model, wall slip effect and considering the sand volume fraction, and use the Matlab mathematical software to solve the frictional pressure loss along the pipeline.

[0013] Furthermore, Step 2 includes the following steps:

[0014] Step 2.1: Divide the pipeline into the main flow area and the slip area, then:

[0015] V = V slip + V c

[0016] where V is the pipeline flow velocity, V slip is the flow velocity in the slip area, and V c is the flow velocity in the main flow area;

[0017] Step 2.2: Establish the calculation formulas for V slip and V c respectively, which are:

[0018]

[0019]

[0020] where δ is the thickness of the slip layer, τ w is the wall shear stress, τ is the shear stress, f(τ) represents the rheological function, μ slip is the viscosity of the slip layer, D is the pipeline diameter,

[0021] Step 2.3: Establish the shear rate equation in the pipe flow based on the pipeline flow velocity and the pipeline diameter:

[0022]

[0023] Among them, is the shear rate;

[0024] Then the basic flow equation of the pipeline considering the wall slip effect is:

[0025]

[0026] Preferably, μ slip is replaced by the viscosity of water.

[0027] Furthermore, the rheological model is:

[0028]

[0029] Among them, k represents the plastic viscosity, τ 0 represents the yield stress, and n represents the power-law index.

[0030] Furthermore, after integral transformation, the pipeline flow equation based on the rheological model and considering the wall slip effect is:

[0031]

[0032] Furthermore, the rheological parameters in step 4 are k, τ 0 and n.

[0033] Preferably, the pipeline flow equation based on the rheological model and considering the wall slip and rheological characteristics is:

[0034]

[0035] Among them, f 1 () represents the functional relationship between the yield stress and the sand volume fraction, f 2 () represents the functional relationship between the plastic viscosity and the sand volume fraction, f 3 () represents the functional relationship between the power-law index and the sand volume fraction, C v represents the sand volume fraction in the slurry.

[0036] Furthermore, the specific steps of step 5 are as follows:

[0037] Step 5.1: Take a slurry microelement with a radius of r and a length of L in the pipeline for force analysis:

[0038] ΔP·πr 2 =2πr·L·τ

[0039] Among them, ΔP is the pressure difference at both ends of the microelement,

[0040] Step 5.2: According to Step 5.1, when the radius r of the micro - element body is equal to the radius R of the pipeline, τ = τ w , the wall shear stress τ w and the relationship with the frictional pressure loss ΔP / L along the way is:

[0041]

[0042] where R is the radius of the pipeline,

[0043] Step 5.3: Substitute the formula in Step 5.2 into the equation in Step 4 to obtain the implicit expression of the frictional pressure loss along the way of the slurry - balanced shield circulation system in sandy soil stratum considering the rheological model, wall slip effect and sand volume fraction, which is:

[0044]

[0045] Preferably, δ = 2mm.

[0046] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0047] In order to overcome the deficiency of the low calculation accuracy of the existing calculation method for the pressure loss of the slurry - balanced shield circulation system, the present invention designs a calculation method for the frictional loss along the way of the slurry - balanced shield circulation system in sandy soil stratum considering wall slip and rheological characteristics. Based on a rheological model with a higher fitting degree of slurry rheology and considering the wall slip effect and rheological characteristics, a new calculation method is proposed, which is consistent with the pipeline transportation characteristics of the actual circulation system, thereby reducing errors, being convenient to calculate and having a higher accuracy.

[0048] 1. Based on the rheological model, replacing the Bingham rheological model, the slurry rheology has a higher fitting degree with the H - B rheological model, being more consistent with the actual situation and improving the calculation accuracy.

[0049] 2. The slip effect between the slurry and the pipe wall is considered in the calculation method. Compared with the existing research that does not consider the slip phenomenon, it is more consistent with the actual pipeline flow and improves the calculation accuracy.

[0050] 3. The influence of the rheological characteristics of the slag slurry on the pressure loss considered in the calculation method provides convenience for the calculation of the pressure loss in actual engineering.

[0051] 4. Based on the Matlab calculation software, in subsequent actual construction, physical quantities such as the volume fraction of sand and the pipe size can be input into the calculation method proposed in this study, and solved by the Matlab calculation software, which is convenient to calculate. Description of the Drawings

[0052] Figure 1 is the flow chart of the determination method of the present invention;

[0053] Figure 2 It is a schematic diagram of the pipe flow in the pipeline of the present invention. Specific embodiments

[0054] The following further details the method for calculating the frictional loss along the way of the slurry shield circulation system in sandy soil considering wall slip and rheological characteristics of the present invention in combination with the accompanying drawings and specific implementation methods.

[0055] As Figure 1 shown, the present invention provides a method for calculating the frictional loss along the way of the slurry shield circulation system in sandy soil considering wall slip and rheological characteristics, including the following steps: Step 1: Select the pipeline of the slurry shield circulation system; Step 2: According to the definition of shear rate in pipe flow and the basic pipe flow formula, obtain the basic pipe flow equation considering the wall slip effect for the pipeline with diameter D used at the construction site; Step 3: Substitute the rheological equation of the Herschel-Bulkley (H-B) rheological model into the basic pipe flow equation considering the wall slip effect, and after integral transformation, obtain the pipe flow equation based on the H-B rheological model and wall slip effect; Step 4: Conduct rheological tests on slurries and sandy soil mixtures (slurry-sand mixtures) with different sand volume fractions respectively, solve the numerical values of the H-B rheological parameters of the slurry-sand mixtures at different volume fractions, and finally fit the expressions between each rheological parameter and the volume fraction respectively, and substitute them into the pipe flow equation based on the H-B rheological model and wall slip effect to obtain the pipe flow equation based on the H-B rheological model and wall slip effect and considering the proportion of sand volume; Step 5: Take a slurry-sand microelement with radius r and length L in the pipeline for analysis. According to the force balance, obtain the relationship between the wall shear stress τw and the frictional pressure loss ΔP / L along the way, and substitute it into the pipe flow equation based on the H-B rheological model and wall slip effect to obtain the implicit expression of the frictional pressure loss along the way of the slurry balance shield circulation system in sandy soil based on the Herschel-Bulkley rheological model and wall slip effect and considering the sand volume fraction; Step 6: Input the numerical values of each parameter in the implicit expression, and use Matlab mathematical software to solve the frictional pressure loss along the pipeline. The present invention provides a method for calculating the frictional pressure loss along the way of the slurry balance shield circulation system in sandy soil based on the Herschel-Bulkley rheological model and wall slip effect and considering the sand volume fraction, which is convenient to calculate and has high accuracy.

[0056] Specifically, it includes the following steps:

[0057] Step 1: Select the pipeline of the circulation system according to the actual slurry shield project;

[0058] Step 2: As Figure 2 shown, the pipeline is divided into the main flow area and the slip area. The definition of the shear rate in pipe flow is:

[0059]

[0060] The basic formula for pipe flow is:

[0061]

[0062] V = V slip + V c

[0063]

[0064] The basic flow equation considering the wall slip effect for the pipeline with diameter D used at the construction site is obtained as:

[0065]

[0066] Among them, δ is the thickness of the slip layer, V is the pipeline flow velocity, D is the pipeline diameter, τ is the shear stress, τ w is the wall shear stress, V c is the flow velocity in the mainstream area, V slip is the flow velocity in the slip area, δ is the thickness of the slip layer, approximately 2 mm; μ slip is the viscosity of the slip layer, approximately the viscosity of water.

[0067] Step 3: Substitute the rheological equation of the Herschel - Bulkley (H - B) rheological model into the basic pipeline flow equation considering the wall slip effect. The Herschel - Bulkley (H - B) rheological model is:

[0068]

[0069] After performing integral transformation, the pipeline flow equation based on the H - B rheological model and considering the wall slip effect is obtained as:

[0070]

[0071] Step 4: Conduct rheological tests on the slurry - sand mixtures (slurry) with different sand volume fractions respectively, and solve the rheological parameters of the slurry at different volume fractions: τ 0 yield stress, k plastic viscosity, n power - law index. Finally, fit the expressions between each rheological parameter and the volume fraction respectively, and substitute them into the pipeline flow equation based on the rheological model and considering the wall slip to obtain the pipeline flow equation based on the rheological model and considering the wall slip and rheological characteristics:

[0072]

[0073] Step 5: Take a slurry micro - element with radius r and length L in the pipeline for force analysis:

[0074] ΔP·πr 2 =2πr·L·τ

[0075] Wherein, ΔP is the pressure difference at both ends of the infinitesimal element,

[0076] When the radius r of the infinitesimal element takes the pipe radius R, τ = τ w , the wall shear stress τ is obtained w The relationship between the wall shear stress τ and the frictional pressure loss ΔP / L along the way is:

[0077]

[0078] Wherein, R is the pipe radius,

[0079] Wherein ΔP is the pressure difference at both ends of the infinitesimal element. The infinitesimal element is a concept of limit. For example, for a glass of water, taking a water droplet for analysis, the water droplet can be called an infinitesimal element. According to the force balance, the wall shear stress τ can be obtained w The relationship between the wall shear stress τ and the frictional pressure loss ΔP / L along the way is:

[0080]

[0081] And substituting it into the pipeline flow equation based on the rheological model and the wall slip effect, the implicit expression of the frictional pressure loss along the way of the slurry balance shield circulation system in sandy soil strata considering the rheological model, the wall slip effect and the sand volume fraction is obtained:

[0082]

[0083] Step 6: Input the numerical values of each parameter into the implicit expression of the frictional pressure loss along the way of the slurry balance shield circulation system in sandy soil strata considering the rheological model, the wall slip effect and the sand volume fraction, and use Matlab mathematical software to solve the frictional pressure loss along the pipeline.

[0084] The above is only the preferred embodiment of the present invention. It should be pointed out that: for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for calculating the frictional loss of the circulating flow system of a slurry shield in sandy soil considering wall slip and rheological properties, characterized in that, it includes the following steps: Step 1: Select the pipeline of the circulating flow system according to the actual requirements of the slurry shield project; Step 2: Establish the basic flow equation of the pipeline considering the wall slip effect; Step 3: Introduce the rheological model and substitute it into the basic flow equation of the pipeline considering the wall slip effect to obtain the pipeline flow equation based on the rheological model and considering the wall slip; Step 4: Conduct rheological tests on the slurry and sandy soil mixtures with different sand volume fractions respectively, solve the rheological parameters of the slurry with different volume fractions, and finally fit the expressions between the rheological parameters and the volume fractions respectively, and substitute them into the pipeline flow equation based on the rheological model and considering the wall slip to obtain the pipeline flow equation based on the rheological model and considering the wall slip and rheological properties; Step 5: Considering the slurry balance shield in sandy soil, obtain the implicit expression of the frictional pressure loss along the circulating flow system of the slurry balance shield in sandy soil based on the rheological model and the wall slip effect and considering the sand volume fraction; wherein, Step 6: Input the numerical values of each parameter into the implicit expression of the frictional pressure loss along the circulating flow system of the slurry balance shield in sandy soil based on the rheological model and the wall slip effect and considering the sand volume fraction, and use Matlab mathematical software to solve the frictional pressure loss of the pipeline; Step 2 includes the following steps: Step 2.1: Divide the pipeline into the mainstream area and the slip area, then: V = V slip +V c Among them, V is the pipeline flow velocity, V slip is the flow velocity in the slip zone, V c is the flow velocity in the main flow zone; Step 2.2: Establish the calculation formulas for V slip and V c respectively, as follows: where δ is the thickness of the slip layer, τ w is the wall shear stress, τ is the shear stress, f(τ) represents the rheological function, μ slip is the viscosity of the slip layer, D is the pipe diameter, Step 2.3: Establish the shear rate equation in the pipe flow based on the pipe flow velocity and the pipe diameter: wherein, is the shear rate; Then the basic flow equation of the pipeline considering the wall slip effect is:

2. The method for calculating the frictional loss of the circulating flow system of a slurry shield in sandy soil considering wall slip and rheological properties according to claim 1, characterized in that: μ slip Replace with the viscosity of water.

3. The method for calculating the frictional loss of the circulating flow system of a slurry shield in sandy soil considering wall slip and rheological properties according to claim 1, characterized in that, the rheological model is: where k represents the plastic viscosity, τ 0 represents the yield stress, and n represents the power-law index.

4. The method for calculating the frictional loss of the circulating flow system of a slurry shield in sandy soil considering wall slip and rheological properties according to claim 3, characterized in that, after integral transformation, the pipeline flow equation based on the rheological model and considering the wall slip effect is:

5. The method for calculating the frictional loss of the circulating flow system of a slurry shield in sandy soil considering wall slip and rheological properties according to claim 4, characterized in that: In step 4, the rheological parameters are k, τ 0 and n.

6. The method for calculating the frictional loss of the circulating flow system of a slurry shield in sandy soil considering wall slip and rheological properties according to claim 5, characterized in that, the pipeline flow equation based on the rheological model and considering the wall slip and rheological properties is: Among them, f 1 () represents the functional relationship between the yield stress and the sand volume fraction, and f 2 () represents the functional relationship between the plastic viscosity and the sand volume fraction, and f 3 () represents the functional relationship between the power-law index and the sand volume fraction, and C v represents the sand volume fraction in the slurry.

7. The method for calculating the frictional loss of the circulating flow system of a slurry shield in sandy soil considering wall slip and rheological properties according to claim 6, characterized in that, the specific steps of Step 5 are as follows: Step 5.1: Take a slurry microelement with a radius of r and a length of L in the pipeline for force analysis: ΔP·πr 2 =2πr·L·τ wherein, ΔP is the pressure difference at both ends of the microelement, Step 5.2: According to Step 5.1, when the radius r of the microelement body takes the pipe radius R, τ = τ w , the wall shear stress τ w The relationship with the frictional pressure loss ΔP / L is: wherein, R is the pipeline radius, Step 5.3: Substitute the formula in Step 5.2 into the equation in Step 4 to obtain an implicit expression for the frictional pressure loss of the slurry balance shield circulation system in sandy soil stratum considering the rheological model, wall slip effect, and sand volume fraction, which is:

8. A method for calculating the frictional loss along the way of a slurry shield circulation system in sandy soil stratum considering wall slip and rheological characteristics according to claim 7, characterized in that: δ = 2 mm.

9. A method for calculating the frictional loss along the way of a slurry shield circulation system in sandy soil stratum considering wall slip and rheological characteristics according to claim 8, characterized in that: The rheological model is selected as the Herschel - Bulkley rheological model.

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