CN111709148B - Discrete element numerical simulation method for hydraulic erosion damage of cohesive sand - Google Patents

Discrete element numerical simulation method for hydraulic erosion damage of cohesive sand Download PDF

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CN111709148B
CN111709148B CN202010575284.2A CN202010575284A CN111709148B CN 111709148 B CN111709148 B CN 111709148B CN 202010575284 A CN202010575284 A CN 202010575284A CN 111709148 B CN111709148 B CN 111709148B
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黄达
黄文波
裴向军
宋宜祥
岑夺丰
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Hebei University of Technology
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Abstract

The invention discloses a discrete element numerical simulation method for hydraulic erosion damage of cohesive sandy soil, which comprises the steps of establishing an initial calculation space area and a cohesive sandy soil numerical model; initializing a numerical model and balancing stress; compiling a time effect-based strength degradation criterion linear bonding contact model for simulating a clay phase among aggregate particles in the cohesive sand; selecting a contact model as a mesoscopic mechanical model for contact between aggregate particles, and then taking values of mesoscopic parameters of the contact model; calibrating the numerical model through a direct shear strength test; establishing a flow field to simulate the hydraulic erosion damage process of the viscous sandy soil; and obtaining a numerical simulation result of the hydraulic erosion damage test. The invention simulates the cohesive sandy soil hydraulic erosion damage through the discrete elements, simplifies the thought, can simulate the cohesive sandy soil hydraulic erosion damage process relatively truly on a microscopical level under the conditions of reducing the calculated amount as much as possible and improving the calculation efficiency, observes and records the migration condition of soil particles, and has accurate result.

Description

Discrete element numerical simulation method for hydraulic erosion damage of cohesive sand
Technical Field
The invention relates to the field of geotechnical engineering soil body hydraulic erosion damage numerical simulation, in particular to a discrete element numerical simulation method for hydraulic erosion damage of cohesive sand soil.
Background
Human beings live in water by choice from ancient times, rivers breed civilizations of human beings, but human beings are benefited by rivers and are also troubled by disasters brought by the rivers. In order to resist the attack of river flooding, the flow path of human along river and river building embankment engineering is restricted in a set range. However, the potential problem of osmotic damage of the dikes and dams has a great safety hazard while benefiting mankind. In addition, China is also an area deeply affected by geological disasters such as landslides, and rainfall and reservoir water have the greatest influence on the landslides. Therefore, the research on the hydraulic erosion damage is of great significance in the aspects of bank and dam engineering or in the aspects of soil erosion, slope stability and other scientific problems.
When the hydraulic erosion damage of rock and soil mass is researched, the research cannot be completed by using an analytical method, and an experimental method and a numerical simulation calculation method are often adopted. Although the experimental research of seepage erosion can provide a large amount of precious research data, a large amount of manpower and material resources are needed, the experimental period is often quite long, the research efficiency is low, meanwhile, the variables are not easy to control, and errors are easily generated, so the obtained experimental result is often limited, and the relevant parameters for analyzing the seepage erosion damage can be obtained only by processing. In addition, the hydraulic erosion damage of the soil body often occurs in the soil body, the discovery and real-time observation and recording during experiments are not easy, the development process of the erosion damage and related parameters in the erosion process can be observed and recorded at any time through the numerical simulation method, and meanwhile, the numerical simulation method has good reproducibility, so that the numerical simulation method has great advantages in researching the hydraulic erosion damage.
As a complex bulk material, the soil body cannot be simply considered as a continuous medium due to the anisotropy on a microscopic structure and the randomness of a pore structure. The discrete element program can consider the structural randomness of the microscopic category, well consider the interaction among the microscopic particles, and truly reflect the migration and loss of the soil particles, so that the problem of infiltration erosion damage of the soil can be better simulated.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to solve the technical problem of providing a discrete element numerical simulation method for hydraulic erosion damage of cohesive sandy soil.
The technical scheme for solving the technical problem is to provide a discrete element numerical simulation method for hydraulic erosion damage of cohesive sandy soil, which is characterized by comprising the following steps of:
step 1, establishing an initial calculation space area and a cohesive sand numerical model;
step 2, initializing a numerical model and balancing stress;
step 3, compiling a time effect-based strength degradation criterion linear bonding contact model for simulating a clay phase among aggregate particles in the cohesive sand soil; the process of hydraulic erosion of the clay phase can be seen as a reduction in the cohesive strength of the contact pattern;
step 4, selecting a contact model as a mesoscopic mechanical model for contact between aggregate particles, and then taking values of mesoscopic parameters of the contact model;
step 5, calibrating the numerical model through a direct shear strength test;
step 6, establishing a flow field to simulate the hydraulic erosion damage process of the viscous sand;
and 7, obtaining a numerical simulation result of the hydraulic erosion damage test.
Compared with the prior art, the invention has the beneficial effects that: the invention simulates the cohesive sandy soil hydraulic erosion damage through the discrete elements, simplifies the thought, can simulate the cohesive sandy soil hydraulic erosion damage process relatively truly on a microscopical level under the conditions of reducing the calculated amount as much as possible and improving the calculation efficiency, observes and records the migration condition of soil particles, and has accurate result.
Drawings
FIG. 1 is a graph of the clay loss process of a true percolation attack in a prior art system;
FIG. 2 is a diagram of the cohesive sand hydraulic erosion damage process in the discrete element numerical model of the present invention;
FIG. 3 is a schematic view of an aggregate particle and its contact according to the present invention;
FIG. 4 is a diagram showing the actual dimensions of a test piece in example 1 of the present invention;
FIG. 5 is a graph of particle grading in accordance with example 1 of the present invention;
FIG. 6 is a schematic diagram of a numerical model of cohesive sand produced from three particle grading curves according to example 1 of the present invention;
FIG. 7 is a graph showing the results of the direct shear strength test in example 1 of the present invention;
FIG. 8 is a plot of the particle size distribution of the soil particles lost during the hydraulic erosion simulation of example 1 of the present invention:
FIG. 9 is a diagram illustrating the hole erosion process in example 1 of the present invention;
FIG. 10 is a hydraulic gradient-erosion rate graph of example 1 of the present invention.
Detailed Description
The present invention will be further described with reference to the following examples and accompanying drawings. The specific examples are only intended to illustrate the invention in further detail and do not limit the scope of protection of the claims of the present application.
The invention provides a discrete element numerical simulation method (short method) for hydraulic erosion damage of cohesive sand, which is characterized by comprising the following steps:
step 1, establishing an initial calculation space area and a cohesive sand numerical model (numerical model for short): generating a corresponding initial calculation space region based on PFC3D software; then, in the initial calculation space region, according to the gradation of the cohesive sandy soil aggregate phase to be simulated, spherical particles representing the aggregate phase are generated according to the sequence of the size range from large to small, so that the generation of the aggregate particles is realized, and the generation position is randomly selected, thereby obtaining a cohesive sandy soil numerical model;
the viscous sandy soil consists of sandy soil aggregate and clay phase wrapped around the aggregate; the aggregate particles and the clay phase are uniformly distributed in the numerical model, and the aggregate particles are wrapped by the clay phase;
step 2, initialization and stress balance of the numerical model: setting a gravity field and calculating and solving corresponding unbalanced force until the stress balance or average unbalanced force in the numerical model meets the set requirement;
step 3, compiling a time effect-based strength degradation criterion linear bonding contact model (contact model for short) by utilizing a Python language or a C + + language to simulate a clay phase among aggregate particles in the cohesive sand;
step 4, selecting a contact model in PFC3D software as a mesoscopic mechanical model for contact between aggregate particles, and then taking values of mesoscopic parameters of the contact model;
the mesoscopic parameters comprise strength degradation criterion based on time effect, linear bonding rigidity ratio, linear bonding modulus, linear bonding normal strength, linear bonding cohesion and the like;
step 5, calibrating the numerical model through a direct shear strength test: performing a direct shear strength test on the cohesive sand test piece indoors by adopting a direct shear apparatus, and acquiring a stress-strain curve and corresponding macroscopic mechanical parameters of the cohesive sand test piece for calibration of numerical simulation; when the shear strength of the numerical model and the error between the stress-strain curve and the indoor test result are within a set range, the obtained microscopic parameters are considered to be reasonable, and the constructed numerical model can truly reflect the actual macroscopic mechanical property of the numerical model;
step 6, establishing a flow field to simulate the hydraulic erosion damage process of the viscous sand: establishing a corresponding flow field through a CFD module coupled in the PFC3D, carrying out grid division, calculating the interaction force of fluid-aggregate particles, and simulating the hydraulic erosion damage process of the viscous sandy soil;
step 7, obtaining a numerical simulation result of the hydraulic erosion damage test: arranging a measuring ball to measure corresponding porosity; and obtaining the soil mass lost in the hydraulic erosion damage process, the particle size distribution of the aggregate particles, the erosion rate, the hydraulic tangential shear force among the aggregate particles and the like by traversing the aggregate particles in the numerical model.
Further, in the step 3, the aggregate is represented by spherical particles in the PFC3D, and the clay phase is represented by a contact model of the absence of solids among the aggregate particles; the process of hydraulic erosion of the clay phase can be regarded as a process of degradation of the cohesive strength between the aggregate particles, i.e. the hydraulic erosion process can be equivalently replaced by a reduction of the cohesive strength of the contact pattern (as shown in fig. 2).
In step 3, the adhesive strength of the contact model is determined by the following steps:
(1) determining the mass of the clay phase:
Mclay＝Mgrain*ξ (2)
in formula 2), MclayAnd MgrainRespectively representing the quality of a clay phase and an aggregate phase in the numerical model, and xi representing the proportion of the clay phase and the aggregate phase;
the clay phase surrounding each aggregate particle is proportional to the surface area of the aggregate particle, i.e.
Figure BDA0002551121980000031
In formula 3), mj_clayIs the mass of the clay phase around the aggregate particle j; r isjThe radius of the aggregate particles j is shown, and N is the total number of the aggregate particles in the numerical model;
(2) the introduction parameter λ represents the bond strength, which has the physical meaning of the bond strength provided per unit mass of clay, so that the total bond strength around the aggregate particle j is:
Figure BDA0002551121980000041
in formula 4), shear _ sjShear force between aggregate particles, tensile _ sjIs the tension between aggregate particles, lambdacohIs a cohesive strength coefficient, λtenIs the tensile strength coefficient; lambda, lambdacohAnd λtenThe value of (2) is obtained by the direct shear strength test in the step (5), so that the numerical model can reflect the macroscopic mechanical properties of the real viscous sand, such as the bonding strength, the internal friction angle and the like;
(3) there are several contacts around aggregate particle j that together make up the overall bond strength of the clay phase around aggregate particle j, where the bond strength of a single contact is expressed as:
Figure BDA0002551121980000042
in formula 5), CiAnd TiThe bonding strength of the contact i (shown in FIG. 3) between the aggregate particles j and kThe strength and the tensile strength of the steel,
Figure BDA0002551121980000043
and
Figure BDA0002551121980000044
the aggregate particles j and k, respectively.
The erosion rate of the cohesive sandy soil hydraulic erosion damage is approximately linear in relation to the hydraulic tangential shear force of the aggregate particle surface, and the correlation can be expressed as follows:
Figure BDA0002551121980000045
in the formula 1), a is an erosion rate per unit surface area (kg/m)2/s)；kerSurface erosion coefficient (s/m); tau is the hydraulic tangential shear force on the surface of the aggregate particles; tau iscCritical hydraulic tangential shear force; b is an empirical coefficient (usually taken approximately 1);
after the flow field of step 6 is applied to the numerical model, the degradation rate of the bonding strength of the contact model of step 3 can be obtained by the following formula:
Figure BDA0002551121980000051
in formula 6), rkIs the radius, τ, of the aggregate particle kjAnd τkThe hydraulic tangential shear force of the particle j and the particle k in the flow field is respectively.
In step 6, simulating the hydraulic erosion damage process of the viscous sandy soil as follows:
(1) initializing a CFD module of PFC3D, reading initial conditions, fluid parameters and CFD meshes, and calculating porosity and drag force;
(2) the PFC3D sends data to a CFD solver, the CFD solver calculates data such as fluid speed, pressure gradient, dynamic viscosity, density and porosity, and then the PFC3D solver reads corresponding data to the PFC 3D;
(3) calculating the hydraulic tangential shear force borne by each aggregate particle according to a control equation, and judging whether the hydraulic tangential shear force is greater than a critical hydraulic tangential shear force; if the hydraulic tangential shear force is larger than the critical hydraulic tangential shear force, the hydraulic erosion damage occurs, and the step 4) is carried out; if the hydraulic tangential shear force is less than or equal to the critical hydraulic tangential shear force, the time step is increased by one step, and the step 2) is returned for recalculation;
(4) judging whether particle loss exists in the numerical model, if the particle loss exists, increasing the time step by one step, and returning to the step 2) to continue calculation; if no particle loss or hydraulic erosion has not occurred, the procedure is ended.
In step 6, in order to improve the calculation efficiency, shorten the calculation time, and ensure the simulation accuracy, the selection criteria of the time step in the numerical simulation process are as follows:
Figure BDA0002551121980000052
in formula 7), Δ tmin、Δtmid、ΔtmaxAnd Δ t represents a minimum time step, an intermediate time step, a maximum time step, and an actual time step, respectively; rlow、RhighAnd RuRespectively representing the ratio of the low-level unbalanced force, the high-level unbalanced force and the actual maximum unbalanced force in the numerical model.
Example 1
In this embodiment, the size of the sample for the cavitation erosion test is 112mm × 224mmm × 112mm (as shown in FIG. 4), and a cavity with a diameter of 20mm is present in the middle.
In step 1, respective cohesive sand numerical models are generated according to the aggregate phase grading curve shown in fig. 5, and as shown in fig. 6, three cohesive sand numerical models are generated from left to right for grading curves with fractal dimensions D of 1.7, 2.0 and 2.5, respectively;
in step 4, the mesoscopic parameters comprise strength degradation criterion based on time effect, linear bonding rigidity ratio, linear bonding modulus, linear bonding normal strength and linear bonding normal strengthCohesion and the like, and the specific parameters are as follows: the density of aggregate particles is 2500kg/m3Contact modulus of aggregate particles Ec＝1.0×107Pa, linear bond modulus Eb＝1.0×107Pa, linear bond stiffness ratio kn/ksWhen the ratio of the clay to the specific surface area is 1.0, the ratio ζ of the clay phase is 0.3, the coefficient b of the bonding radius range is 1.0, and the coefficient l of the linear bonding strength iscoh、lten＝2.0×104N/kg, fluid density 1000kg/m3Hydrodynamic viscosity μf＝0.001Pa·s；
In step 5, the direct shear strength test result is shown in fig. 7, the shear strength of the numerical model and the error between the stress-strain curve and the indoor test result are within the set range, the obtained microscopic parameters are reasonable, and the constructed numerical model can truly reflect the actual macroscopic mechanical property of the numerical model.
In step 7, taking the particle size distribution with fractal dimension D of 1.7 as an example, the soil mass lost in the hydraulic erosion damage process and the particle size distribution of aggregate particles obtained by traversing the aggregate particles in the numerical model are shown in fig. 8, the pore erosion development process is shown in fig. 9, and the erosion rate is shown in fig. 10.
In this embodiment, Δ tmin＝1.0×10-3s，Δtmid＝1s，Δtmax＝500s，Rlow＝5×10-4，Rhigh＝5×10-3。
Nothing in this specification is said to apply to the prior art.

Claims (7)

1. A discrete element numerical simulation method for hydraulic erosion damage of cohesive sandy soil is characterized by comprising the following steps:
step 1, generating an initial calculation space region in a hole erosion test; then in the initial calculation space area, according to the grading D of the cohesive sandy soil aggregate phase to be simulated, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.3, 2.5 and 2.7, spherical particles representing the aggregate phase are generated according to the sequence of the particle size range from large to small, and the generation positions are randomly selected, so that three numerical models of the cohesive sandy soil generated by grading curves with the fractal dimensions D of 1.7, 2.0 and 2.5 are obtained;
step 2, initializing a numerical model and balancing stress;
step 3, compiling a time effect-based strength degradation criterion linear bonding contact model for simulating a clay phase among aggregate particles in the cohesive sand soil; the process of hydraulic erosion of the clay phase can be seen as a reduction in the cohesive strength of the contact pattern;
step 4, selecting a contact model as a mesoscopic mechanical model for contact between aggregate particles, and then taking values of mesoscopic parameters of the contact model;
the mesoscopic parameters include strength degradation criterion based on time effect, linear bond stiffness ratio, linear bond modulus, linear bond normal strength, and linear bond cohesion; the density of aggregate particles is 2500kg/m3Contact modulus of aggregate particles Ec＝1.0×107Pa, linear bond modulus Eb＝1.0×107Pa, linear bond stiffness ratio kn/ksWhen the ratio of the clay to the specific surface area is 1.0, the ratio ζ of the clay phase is 0.3, the coefficient b of the bonding radius range is 1.0, and the coefficient l of the linear bonding strength iscoh、lten＝2.0×104N/kg, fluid density 1000kg/m3Hydrodynamic viscosity μf＝0.001Pa·s；
Step 5, calibrating the numerical model through a direct shear strength test;
step 6, establishing a flow field to simulate the hydraulic erosion damage process of the viscous sand;
the selection criteria for time steps are as follows:
Figure FDA0002943960870000011
in formula 7), Δ tmin、Δtmid、ΔtmaxAnd Δ t represents a minimum time step, an intermediate time step, a maximum time step, and an actual time step, respectively; rlow、RhighAnd RuRespectively representing the ratio of the low-level unbalanced force, the ratio of the high-level unbalanced force and the actual maximum unbalanced force in the numerical model; Δ tmin＝1.0×10-3s，Δtmid＝1s，Δtmax＝500s，Rlow＝5×10-4，Rhigh＝5×10-3；
Step 7, obtaining a numerical simulation result of the hydraulic erosion damage test; in the grain gradation with fractal dimension D equal to 1.7, arranging measuring balls to measure corresponding porosity; obtaining the soil mass lost in the hydraulic erosion damage process, the particle size distribution of the aggregate particles, the erosion rate and the hydraulic tangential shear force among the particles by traversing the aggregate particles in the numerical model; average erosion Rate q 1.8424 × 103.2106i6.3297, wherein i is a hydraulic gradient.
2. The method for discrete element numerical simulation of hydraulic erosion damage of cohesive sandy soil according to claim 1, wherein the step 2 is specifically: and (4) solving the corresponding unbalanced force by setting a gravity field and calculating until the stress balance or the average unbalanced force in the numerical model meets the setting requirement.
3. The method for discrete element numerical simulation of hydraulic erosion damage to cohesive sandy soil of claim 1 wherein in step 3, the bond strength of the contact model is determined by:
(1) determining the mass of the clay phase:
Mclay＝Mgrain*ξ (2)
in formula 2), MclayAnd MgrainRespectively representing the quality of a clay phase and an aggregate phase in the numerical model, and xi representing the proportion of the clay phase and the aggregate phase;
the clay phase surrounding each aggregate particle is proportional to the surface area of the aggregate particle, i.e.
Figure FDA0002943960870000021
In formula 3), mj_clayIs the mass of the clay phase around the aggregate particle j; r isjIs the radius of the aggregate particle j, and N is the aggregate particle in the numerical modelThe total number of grains;
(2) the introduction parameter λ represents the bond strength, which has the physical meaning of the bond strength provided per unit mass of clay, so that the total bond strength around the aggregate particle j is:
Figure FDA0002943960870000022
in formula 4), shear _ sjShear force between aggregate particles, tensile _ sjIs the tension between aggregate particles, lambdacohIs a cohesive strength coefficient, λtenIs the tensile strength coefficient; lambda, lambdacohAnd λtenObtained by the direct shear strength test in step 5;
(3) there are several contacts around aggregate particle j that together make up the overall bond strength of the clay phase around aggregate particle j, where the bond strength of a single contact is expressed as:
Figure FDA0002943960870000023
in formula 5), CiAnd TiThe bonding strength and the tensile strength of the contact i between the aggregate particles j and the aggregate particles k,
Figure FDA0002943960870000031
and
Figure FDA0002943960870000032
the aggregate particles j and k, respectively.
4. The discrete element numerical simulation method for hydraulic erosion damage of cohesive sandy soil according to claim 3, wherein the erosion rate of the hydraulic erosion damage of the cohesive sandy soil is related to the hydraulic tangential shear force of the surface of the aggregate particles as follows:
Figure FDA0002943960870000033
in formula 1), a is the erosion rate per unit surface area; k is a radical oferIs the surface erosion coefficient; tau is the hydraulic tangential shear force on the surface of the aggregate particles; tau iscCritical hydraulic tangential shear force; b is an empirical coefficient;
after the flow field of step 6 is applied to the numerical model, the degradation rate of the bonding strength of the contact model of step 3 can be obtained by the following formula:
Figure FDA0002943960870000034
in formula 6), rkIs the radius, τ, of the aggregate particle kjAnd τkThe aggregate particles j and the aggregate particles k are subjected to hydraulic tangential shear force in the flow field respectively.
5. The method for discrete element numerical simulation of hydraulic erosion damage of cohesive sandy soil according to claim 1, wherein the step 5 is specifically: performing a direct shear strength test on the cohesive sandy soil test piece indoors, and acquiring a stress-strain curve and corresponding macroscopic mechanical parameters of the cohesive sandy soil test piece; when the shear strength of the numerical model and the error between the stress-strain curve and the indoor test result are within the set range, the obtained microscopic parameters are reasonable, and the constructed numerical model can truly reflect the actual macroscopic mechanical property of the numerical model.
6. The method for discrete element numerical simulation of hydraulic erosion damage of cohesive sandy soil according to claim 1, wherein the step 6 is specifically: and establishing a corresponding flow field, carrying out grid division, calculating the interaction force of the fluid and aggregate particles, and simulating the hydraulic erosion damage process of the viscous sand.
7. The discrete element numerical simulation method for hydraulic erosion damage of cohesive sandy soil according to claim 1 or 6, wherein in the step 6, the hydraulic erosion damage process of the cohesive sandy soil is simulated as follows:
(1) initializing a CFD module of PFC3D, reading initial conditions, fluid parameters and CFD meshes, and calculating porosity and drag force;
(2) the PFC3D sends data to a CFD solver, the CFD solver calculates data such as fluid speed, pressure gradient, dynamic viscosity, density and porosity, and then the PFC3D solver reads corresponding data to the PFC 3D;
(3) calculating the hydraulic tangential shear force borne by each aggregate particle according to a control equation, and judging whether the hydraulic tangential shear force is greater than a critical hydraulic tangential shear force; if the hydraulic tangential shear force is larger than the critical hydraulic tangential shear force, the hydraulic erosion damage occurs, and the step 4) is carried out; if the hydraulic tangential shear force is less than or equal to the critical hydraulic tangential shear force, the time step is increased by one step, and the step 2) is returned for recalculation;
(4) judging whether particle loss exists in the numerical model, if the particle loss exists, increasing the time step by one step, and returning to the step 2) to continue calculation; if no particle loss or hydraulic erosion has not occurred, the procedure is ended.
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