CN104021277B - Numerical analysis method for piping phenomenon - Google Patents

Abstract

The invention discloses a numerical analysis method for piping phenomena, comprising the steps of: obtaining the similarity criterion of seepage deformation based on the fluid dynamics similarity criterion combined with the interphase force action item of the medium on the fluid; Particle model; the model satisfies that the gravity level is consistent with the prototype, and the particle gradation is scaled and the porosity is kept at the same condition, and the skeleton and filling particles are randomly generated; the model is simulated for the piping process, and the filling particles in the model reach equilibrium or skeleton particles When damage occurs, the internal parameter information of the model is output; the actual value is obtained by combining the seepage deformation similarity criterion with the internal parameter information of the model, and fed back to the prototype to analyze the piping phenomenon. The invention complies with Darcy's and non-Darcy's laws, and the model can describe the prototype truly when there are two flow states at the same time, overcomes the problem that the conventional model or centrifugal test cannot realize the proportional scaling of the particle size and the model, and the analysis is accurate.

Description

A Numerical Analysis Method of Piping Phenomenon

technical field

The invention relates to a numerical analysis method for piping phenomena, belonging to the technical field of civil engineering.

Background technique

China is one of the countries most severely affected by floods in the world, and floods in the middle and lower reaches of the Yangtze River are particularly frequent and severe. Damage to embankments includes various forms such as piping, flooding, bank collapse, and overall instability. A large number of flood disaster data show that embankment foundation piping is the most harmful. When piping damage occurs in embankments, the seepage field has strong spatial characteristics. There are few studies on the spatial characteristics of the seepage field. The reason is that, on the one hand, the current understanding of the mechanism of piping is not deep enough; on the other hand, due to the complexity of the hydraulic conditions of the project, the analysis of the seepage field is relatively difficult.

At present, the research on piping problems in the engineering and theoretical circles mostly focuses on the anti-seepage performance of soil. However, with the development of piping research work, a consensus has been gradually reached on the strong temporal and spatial characteristics of the seepage field. If the complex changes of geometric and hydraulic properties of materials in the seepage process can be described, and the dynamic changes of water head, hydraulic gradient, particle displacement field and porosity can be obtained, it will provide strong support for the study of piping process.

Before the present invention, the research on piping was divided into theoretical research, laboratory test and numerical test research, and in the seepage deformation test, it was generally assumed that the seepage process conformed to Darcy's law. There is a certain deviation between the conclusion and the prototype. In the centrifuge test, if a reduced particle size is used for the test, there will be a problem: the diameter range of the prototype particle is in the range of sandy soil, and after the ratio of particle size to model length is reduced year-on-year, the particle size may already be in the range of clay, while When seepage occurs in clay and sandy soil, the force between soil and water faces a large difference. There may be strong and weak binding water on the surface of clay, but this situation does not exist in sandy soil, that is, using Although the method of year-on-year reduction of particle size achieves similarity in mechanism, the influence of physical and chemical effects in the mesoscopic category is likely to make the results different from expectations; at the same time, the selection of scale relationship is used to ensure that the model and the prototype At the same time, the difference in mechanical properties between the prototype soil and the model cannot be eliminated; it is especially difficult to select fluids that meet specific conditions. Numerical analysis of piping mostly uses finite element simulation to simulate the seepage field. The continuity method is feasible for the simulation of the relatively stable seepage stage before the piping occurs. When the critical state is reached, the interaction between the geometric properties of the soil and the hydraulic properties caused by particle loss cannot be considered. This complex water-soil interaction cannot fully explain the mechanism of piping. The complex water-soil interaction in the process of piping determines that the development of piping is a nonlinear dynamic process, and there is no recognized most suitable research method and theory at present. Scholars have begun to try to track and record the entire process of sand piping by using microscopic camera visualization tracking technology combined with digital image recognition and analysis methods, and reveal that water-soil interaction runs through the entire process of piping development from the microscopic level. However, this technology only It is limited to the laboratory test level, and it is not yet adaptable to the analysis of the actual piping seepage damage process.

Contents of the invention

The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide an accurate and convenient numerical analysis method for a piping phenomenon that can truly reflect the actual piping seepage damage process. Based on the existing fluid dynamics similarity criterion, consider The interphase force between the medium and the fluid in the Darcy-non-Darcy state, based on the complete fluid dynamics equation of porous media, the similarity criterion of seepage failure is derived, and the similarity criterion followed when the sand seepage deformation occurs, so that when the calculation area The model can truly describe the prototype when Darcy, non-Darcy seepage occurs, or the two flow regimes exist simultaneously in the domain.

The present invention specifically adopts the following technical solutions to solve the above technical problems:

A numerical analysis method for piping phenomenon, comprising the following steps:

Step (1), based on the fluid dynamics similarity criterion combined with the interphase force term of the medium on the fluid, by introducing the extended D-B-F equation to consider the Darcy-non-Darcy effect of seepage, and obtaining the similarity criterion followed when seepage deformation occurs in sandy soil;

Step (2), establish a mesoscopic particle model similar to the prototype based on the seepage deformation similarity criterion combined with the particle flow method; the mesoscopic particle model meets the gravity level consistent with the prototype, and in the mesoscopic particle model according to The grading curve scales the prototype soil particles according to the similarity criterion of seepage deformation and randomly generates skeleton and filling particles under the condition of maintaining the same porosity;

Step (3), simulating the piping process on the mesoscopic particle model, and outputting the internal parameter information of the model when the filled particles in the model reach equilibrium or the skeleton particles are damaged;

Step (4), combining the seepage deformation similarity criterion with the internal parameter information of the model to obtain an actual value, and feeding the actual value back to the prototype to analyze the piping phenomenon.

Further, as a preferred technical solution of the present invention: the similar criteria to be followed when the sand seepage deformation occurs in the step (1) is:

where α _n , α _σ , α _γ , α _t , α _v , α _l , α _g , α _ρf , α _μ , α _k , α _d respectively represent: porosity, stress, gravity, time, velocity, length, acceleration, fluid density, kinematic viscosity coefficient, permeability coefficient similarity constant, equivalent permeability coefficient similarity constant, particle size scaling factor; (a) formula The porosity in the model and the prototype must be consistent; formula (b) indicates that the stress state of the model is consistent with that of the prototype, including the corresponding consistency of effective stress and total stress; formulas (c)~(f) represent the time-harmonic criterion, Gravity similarity criterion, pressure similarity criterion, and viscous force similarity criterion; (g) and (h) represent the influence of the dynamic exchange coefficient between phases on the fluid dynamic similarity in porous media when the pore fluid is in laminar flow and turbulent flow state.

Further, as a preferred technical solution of the present invention: in the step (2), the mesoscopic particle model is scaled according to the seepage deformation similarity criterion to meet: the particle size and the model scale proportionally and the fluid density scale proportionally to the model size, viscous The coefficient scale is the square of the model scale.

Further, as a preferred technical solution of the present invention: in the step (3), the model internal parameter change data includes particle velocity, stress distribution, flow rate, flow velocity, and pressure data in the model.

Further, as a preferred technical solution of the present invention: the step (4) combines the seepage deformation similarity criterion with the model internal parameter change data to obtain the critical hydraulic gradient consistent with the prototype, and refer to the seepage deformation similarity criterion The obtained time scale consistent with the inertial time is used to analyze the piping process.

The present invention adopts above-mentioned technical scheme, can produce following technical effect:

The advantage and effect of the numerical analysis method of piping phenomenon of the present invention are:

(1) The conventional model and centrifugal model are used to study seepage problems based on Darcy's law, and it is inappropriate to use relevant conclusions based on Darcy's law when non-Darcy seepage occurs in the model. The invention overcomes the limitations faced when using conventional model tests or centrifugal model tests to study the seepage deformation of sandy soil.

(2) Based on the existing fluid dynamics similarity criterion of porous media, considering the interphase force action term of the medium on the fluid, the similarity criterion followed when seepage deformation occurs in sandy soil is given. The core idea is to ensure that the particle size scales with the model , and ensure that the viscosity coefficient scale is consistent with the length scale, the seepage model established on this premise is similar to the prototype. When Darcy and non-Darcy seepage appear in the calculation area, or the two flow states exist in the domain at the same time, the model can describe the prototype. Therefore, when the flow state in the prototype changes from Darcy to non-Darcy, based on the seepage deformation The model established by the criterion can also accurately describe the process.

(3) The particle flow method uses particles as the basic calculation unit. The scaling of simulated particles has unique advantages. Combined with its advantages in the study of seepage deformation, it overcomes the problem that conventional model tests or centrifuge tests cannot achieve the same scaling of particle size and model.

(4) The research is carried out on the analysis platform, with few constraints and a wide range of applications. It avoids cumbersome processes such as indoor sample preparation and instrument operation, improves test efficiency, and saves research costs.

The process of the invention is simple, on the basis of particle flow theory, based on the porous medium fluid dynamics similarity criterion, considering the action item of the medium on the fluid, the similarity criterion followed when the sand seepage deformation occurs is given, and the establishment of the model is easy to operate and easy to calculate. Simple, cost-effective, and more accurate analysis.

Description of drawings

Fig. 1 is a schematic diagram of establishing a mesoscopic particle model in the numerical analysis method of the piping phenomenon of the present invention.

Fig. 2 is a schematic diagram of the boundary conditions of the mesoscopic particle model of the present invention.

Fig. 3 is a flow chart of the numerical analysis method of the piping phenomenon of the present invention.

Fig. 4A is a comparison calculation result diagram of the critical hydraulic gradient when piping occurs at orifice A in the mesoscopic particle model and the laboratory test.

Fig. 4B is a graph comparing the calculation results of the critical hydraulic gradient when piping occurs at orifice B in the mesoscopic particle model and the laboratory test.

Fig. 4C is a diagram comparing the calculation results of the critical hydraulic gradient when piping occurs at orifice C in the mesoscopic particle model and the laboratory test.

Fig. 5A is a schematic diagram of the initial moment of osmotic damage of sample I-1 of the present invention when orifice C is opened.

Fig. 5B is a schematic diagram of the time when the sample I-1 of the present invention is osmotically damaged and the fine particles are lost when orifice C is opened.

Fig. 5C is a schematic diagram of the moment when the sample I-1 of the present invention undergoes osmotic damage and the loss of coarse particles when the No. C orifice is opened.

Fig. 5D is a schematic diagram of the moment when the model of the sample I-1 of the present invention is destroyed when the opening C is opened.

detailed description

Embodiments of the present invention will be described below in conjunction with the accompanying drawings.

The present invention has designed a kind of numerical analysis method of piping phenomenon, and the concrete steps of implementing are as shown in Figure 3, comprise:

Step (1), based on the fluid dynamics similarity criterion combined with the action item of the medium on the fluid, deduce the similarity criterion followed when the sand seepage deformation occurs. details as follows:

(1.1) Based on the similarity criterion of the existing fluid dynamics of porous media, the extended D-B-F equation is introduced by considering the interphase dynamic action term of the medium on the fluid;

(1.2) Considering the Darcy-non-Darcy effect of seepage, according to the similarity of geometry, movement and dynamics, the similarity criterion followed when seepage deformation occurs in sandy soil is deduced. The specific derivation is as follows:

In fluid dynamics, assuming that the change of the temperature field is not considered, for incompressible fluids, the mass conservation equation must be obeyed when solving the flow field and pressure field in a porous medium composed of granular particles:

In formula (1), n is the porosity of porous media, is the fluid velocity,

The average momentum conservation equation is:

Different from the N-S equation, the present invention considers the action term of the medium on the fluid, see the last item on the right side of the equation for details.

The present invention refers to formula (2) as the Darcy-Brinkman-Forchheimer equation of expansion, and the first item on the left end represents the local inertial force, and the second item represents the displacement inertial force, and the sum of the two terms represents the inertial force, that is, the acceleration item; The terms on the right represent the contribution of body force, pressure, viscous force and solid-liquid interphase force to acceleration respectively.

In formula (2), n is the porosity of porous media, is the fluid velocity, is the average velocity of particles, τ is the viscous force tensor, g is the acceleration of gravity, ρf is the fluid density, p is the pressure, and β is the dynamic exchange coefficient between phases, determined according to the Ergun equation and the formula proposed by Wen and Yu (1966), specifically The expression is as follows:

In the formula (3), μ _f is the fluid viscosity coefficient, is the particle equivalent particle size.

The corresponding pressure gradient and superficial flow velocity can be expressed as:

In formula (4), dp/dx represents the pressure gradient.

The first term of the equation is the Kozeny-Carman formula in the state of laminar flow, and the second term indicates that the pressure gradient is proportional to the square term of the velocity. When the two phases are not dominant, the relationship between the pressure gradient and the velocity is between 1 and 2, which is why the ratio of the permeability coefficient is the xth power of the gravity scale. If only the velocity square term is considered and the first term is ignored when the flow is completely in a turbulent state, formula (5) can be expressed as:

For the convenience of elaboration, in the formula (5) It is defined as the equivalent permeability coefficient, i is the hydraulic gradient, g is the acceleration of gravity, combined with the Darcy's law expression v=k·i in the state of laminar flow, and k is the permeability coefficient. Let β ₁ and β ₂ represent the two terms on the right side of formula (3), respectively, and β ₁ and β ₂ are the interphase force coefficients under the condition of complete laminar flow and complete turbulent flow respectively, then formula (2) can be expressed as:

Define time, velocity, length, acceleration, fluid density, kinematic viscosity coefficient, and interphase dynamic exchange similarity constants as: α _t , α _v , α _l , α _g , α _ρf , α _μ , α _β , and substitute the similarity constants into The momentum conservation equation (2) gets:

In formula (7), α _d is the particle size scaling factor, and τ is defined as the fluid shear stress. α _n is the porosity similarity constant.

Following the basic requirement of similarity in fluid dynamics, the ratio of isomorphic forces acting at corresponding points should be equal in unit volume, and the combined formula (6) is:

In formula (8) are the similarity constants of the interphase force coefficients under fully laminar flow and fully turbulent flow conditions, respectively.

Substituting formula (6) into formula (8), combined with similar gravity and similar porosity, we finally get:

In formula (9), α _k is the similar constant of permeability coefficient, is a similar constant for the equivalent permeability coefficient.

In formula (9), the representation model of formula (a) must be consistent with the porosity in the prototype; the representation model of formula (b) is consistent with the stress state of the prototype, including the corresponding correspondence between effective stress and total stress; formulas (c)~(f) respectively represent The time-harmonic criterion, gravity similarity criterion, pressure similarity criterion, and viscous force similarity criterion in fluid dynamics similarity; (g) and (h) represent the effect of dynamic exchange coefficient between phases in porous media when the pore fluid is in laminar flow and turbulent flow state Similar effects to fluid dynamics.

In step (2), a mesoscopic particle model similar to the prototype is established based on the seepage deformation similarity criterion combined with the particle flow method. details as follows:

(2.1) Establish an indoor mesoscopic particle model, as shown in Figure 1, the upstream boundary coincides with the plane of x=0, the water head is applied on the upstream boundary, the other surfaces are set as impermeable boundaries, and A, B, and C are reserved on the upper surface No. orifice (covered by the wall at the beginning), the size follows the model scale to simulate different outlets, the center position of the orifice is set as the zero pressure boundary, and the wall unit at the corresponding position is deleted when simulating the outflow of different orifices , the schematic diagram of the boundary conditions of the model is shown in Figure 2. The left side of the model is the hydraulic head boundary, the orifice is the zero pressure boundary, and the other boundaries are set as rigid impervious and non-slip boundaries.

The specific parameters are shown in Table 1;

(2.2) According to the penetration deformation similarity criterion obtained in step 1, combined with the particle gradation in the prototype, the particle size range in the mesoscopic particle model is determined;

(2.3) Then, in the model, the prototype soil sample particles are scaled according to the similarity criterion according to the same particle grading curve as the prototype. The scaling includes the scaling of the particle size and the model, the fluid density and the model size, and the viscosity coefficient scale. is the square of the model scale. In order to avoid the phenomenon of contact erosion, the upper boundary friction coefficient of the model is set to a larger value. After the boundary model is generated, the PFC3D particle random generator is used to generate coarse particles first, and then fine particles. During the generation process, the porosity is kept consistent with the prototype. The skeleton and filling particles are randomly generated under the condition of maintaining the same porosity.

(2.4) The mesoscopic particle model can perfectly satisfy the similarity criterion of seepage deformation. The model must meet the gravity level consistent with the prototype, and the effect of model scaling can be offset by increasing the gravity level. Ensure that the mesoscopic particle model reaches the initial stress balance state, and simulate the initial state under the condition of no seepage. After the model reaches the initial stable state, the model is first placed in hydrostatic pressure.

In step (3), the water head boundary is applied to the mesoscopic particle model to carry out seepage deformation, the piping process is simulated, and the parameter change data in the model is recorded. Specifically:

(3.1) Apply the hydraulic head boundary to the mesoscopic particle model to conduct seepage deformation analysis, open different orifices (delete the overlying wall at the corresponding position), and set it as a free surface to simulate the seepage failure of different orifices. The monitoring means obtain the corresponding parameters in the model, such as the volume of particles flowing out of the orifice, the flow rate of the orifice, the porosity in the unit, the position of the particles, the velocity of the particles, the pressure, the flow rate, etc., and analyze the particle velocity, stress distribution and permeability characteristics in the model. Fluid velocity, pressure, and the coupling force between particles and fluid, so as to obtain the corresponding parameter information in the model in real time during the simulation process.

(3.2) Under each level of hydraulic gradient, when the orifice velocity reaches a steady state or cannot maintain a steady state, the permeation analysis under the hydraulic head of this level ends. If no damage occurs, apply the next level of water head, start the model under hydrostatic pressure, and restart the analysis to eliminate the influence of some particles that have migrated under the action of the previous level of water head until the simulated object cannot maintain stability or the orifice flows out It has stabilized, otherwise continue to apply the next level of water head slowly. Until the filling particles in the model reach an equilibrium state or the model skeleton particles are destroyed, the parameter data information in the model is output.

Step (4), combine the seepage deformation similarity criterion with the parameter change data in the model to obtain actual values, and feed back to the prototype according to the actual values to analyze the piping phenomenon. Specifically:

Using the seepage deformation similarity criterion derived in step (1), analyze the corresponding parameter data in the model obtained in step (3), such as particle velocity, stress distribution, flow rate, flow rate and other data, and obtain the actual value based on the derived similarity criterion, Analyze piping phenomena based on actual values. To obtain the actual value, obtain the corresponding parameter value according to the needs during the analysis process. In the present invention, the critical hydraulic gradient consistent with the prototype is preferably obtained, and referring to the time scale consistent with the inertial time obtained through the seepage deformation similarity criterion, according to the same time scale To characterize the actual piping process by analyzing the changes in the piping development process.

The seepage deformation similarity criterion is combined with the model internal parameter change data. Specifically, taking the orifice flow velocity in the model as an example, according to the gravity similarity criterion and viscous force similarity criterion in formula (9), the flow velocity in the model and the prototype can be obtained Consistent, so, the flow velocity in the model represents the actual flow velocity; at this time, if the relationship between flow and flow velocity continues, according to: Q=VAt, combined with the conclusion that the flow velocity of the model is consistent with the prototype, since the flow cross-sectional area ratio is 1/N ² , the time ratio The scale is 1/N, and the flow ratio between the model and the prototype can be obtained as 1/N ³ . From this, the actual value of the prototype flow can be obtained, and then analyzed.

Therefore, this method is based on the similarity criterion of fluid dynamics in porous media, and considers the interphase force term of the medium on the fluid, and gives the similarity criterion followed when seepage deformation occurs in sandy soil. The core idea is to ensure that the particle size scales with the model , the seepage model established on this premise is basically similar to the prototype. When Darcy and non-Darcy seepage appear in the calculation area, or the two flow states exist in the domain at the same time, the model can describe the prototype. Therefore, when the flow state in the prototype changes from Darcy to non-Darcy, based on the similarity criterion The established model can also accurately describe the process, and the numerical analysis method thus formed can solve the technical problem that the West and non-Darcy effects cannot be satisfied simultaneously in the existing piping analysis process, and overcome the failure of conventional model tests or centrifugal tests. The problem of particle size scaling with the model can be accurately applied to the actual piping analysis process.

In order to verify that the numerical analysis method of the piping phenomenon of the present invention can simulate the piping phenomenon and analyze the seepage deformation in the model, the following experimental data are specially used for verification.

First, according to the parameters shown in Table 1, the critical hydraulic gradients of six groups of soil samples at different orifices for seepage failure were obtained through laboratory tests. Then, according to the method of the present invention, the corresponding hydraulic gradient is obtained by establishing a microscopic particle model and analyzing it.

See Figure 4A, Figure 4B, and Figure 4C for the relationship between the apparent critical hydraulic gradient and the location of orifices A, B, and C. It can be seen that the two are basically consistent with the trend that the critical hydraulic gradient increases with the increase of fine material content and packing density, which is consistent with the engineering practice. Fig. 5A is a schematic diagram of sample I-1 at the initial moment of osmotic damage when orifice C is opened. In the initial stage, the particles in the model are initially balanced; then only a small amount of fine particles are lost in the sample, as shown in Fig. 5B. It is a schematic diagram of the loss time of fine particles in osmotic damage when orifice C is opened; as the fine particles gather towards the orifice area, after a certain period of time, individual coarse particles are carried out of the orifice by the fine particles. As time goes by, the coarse particles begin to lose gradually, as shown in Figure 5C, which is a schematic diagram of the time when the No. C orifice is opened and the penetration damage occurs when the coarse particles are lost; finally, a large pit appears in the orifice area, as shown in Figure 5D , which is a schematic diagram of the failure moment of the model, which is consistent with the engineering practice. At the same time, the entire numerical simulation process is performed by the computer, which avoids the tedious process of preparing samples and operating instruments in the laboratory test, improves the test efficiency, and saves research costs.

Table 1 Model parameters

Therefore, the experiment verifies that using the particle flow method to simulate piping failure can dynamically observe each parameter in the model, and can reflect the mesoscopic process of piping failure. It is proved that the invention can explain and analyze the piping phenomenon accurately and conveniently. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. After reading the present invention, those skilled in the art all fall into the appended claims of the present application to the amendments of various equivalent forms of the present invention limited range.

Claims (4)

1. a numerical analysis method of piping phenomenon, is characterized in that, comprises the following steps: Step (1), based on the fluid dynamics similarity criterion combined with the interphase force term of the medium on the fluid, by introducing the extended D-B-F equation to consider the Darcy-non-Darcy effect of seepage, and obtaining the similarity criterion followed when seepage deformation occurs in sandy soil; Step (2), establish a mesoscopic particle model similar to the prototype based on the seepage deformation similarity criterion combined with the particle flow method; the mesoscopic particle model meets the gravity level consistent with the prototype, and in the mesoscopic particle model according to The grading curve scales the prototype soil particles according to the similarity criterion of seepage deformation and randomly generates skeleton and filling particles under the condition of maintaining the same porosity; Step (3), simulating the piping process on the mesoscopic particle model, and outputting the internal parameter information of the model when the filled particles in the model reach equilibrium or the skeleton particles are damaged; Step (4), combining the seepage deformation similarity criterion with the internal parameter information of the model to obtain actual values, and feeding the actual values back to the prototype to analyze the piping phenomenon; Wherein, the similar criterion followed when the seepage deformation occurs in the step (1) sandy soil is: $\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; \&rho;</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; \&rho;</span>}\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$ where α _n , α _σ , α _γ , α _t , α _v , α _l , α _g , α _ρf , α _μ , α _k , α _d respectively represent: porosity, stress, gravity, time, velocity, length, acceleration, fluid density, kinematic viscosity coefficient, permeability coefficient similarity constant, equivalent permeability coefficient similarity constant, particle size scaling factor; (a) formula The porosity in the model and the prototype must be consistent; formula (b) indicates that the stress state of the model is consistent with that of the prototype, including the corresponding consistency of effective stress and total stress; formulas (c)~(f) represent the time-harmonic criterion, Gravity similarity criterion, pressure similarity criterion, and viscous force similarity criterion; (g) and (h) represent the influence of the dynamic exchange coefficient between phases on the fluid dynamic similarity in porous media when the pore fluid is in laminar flow and turbulent flow state. 2. according to the numerical analysis method of the described piping phenomenon of claim 1, it is characterized in that: in the described step (2), the mesoscopic particle model is scaled according to the seepage deformation similarity criterion and meets: the particle size and the model are scaled and the fluid density and the model The size is scaled year-on-year, and the viscosity coefficient scale is the square of the model scale. 3. The numerical analysis method of piping phenomenon according to claim 2, characterized in that: the model internal parameter change data in the step (3) includes particle velocity, stress distribution, flow, flow velocity, and pressure data in the model. 4. according to the numerical analysis method of the described piping phenomenon of claim 1, it is characterized in that: described step (4) obtains the critical hydraulic gradient consistent with prototype by combining described seepage deformation similarity criterion and model internal parameter change data, and refer to The piping process is analyzed on a time scale consistent with the inertial time obtained by the similarity criterion of seepage deformation.