Microcrack connection force inference method based on graph neural network

Abstract

The invention discloses a microcrack connection force inference method based on a graph neural network, and provides a crack contact model considering connection substances in cracks by splitting crack contact into an unconnected part and a connected part for calculation based on a parallel bonding model and a flat joint model. On the basis that a new contact model provides certain tensile strength and shear strength for a unit, a high compression-tension ratio is obtained by limiting the damage of cementation to be only controlled by contact force and torque of a connecting part, and the invention relates to the technical field of engineering rock monitoring and analysis. According to the microcrack connection force inference method based on the graph neural network, a contact model is constructed and verified through a contact surface force-displacement test and a crack-containing model loading and unloading test. And finally, testing the contact model by simulating a rock mechanical test. Results show that the contact model can effectively simulate the axial and radial strain rules of the rock at the same time.

Description

Technical Field

[0001] This invention relates to the field of engineering rock monitoring and analysis technology, specifically a method for inferring microcrack connection force based on graph neural networks. Background Technology

[0002] In the extraction of energy resources such as coal and oil and gas, and in the construction of engineering projects such as tunnels and subways, rock materials are a major and indispensable component. The mechanical properties of rock materials determine both the construction plan and the safety of the construction process. However, unlike other engineering materials, most rocks contain abundant microcracks, resulting in complex mechanical characteristics under loading. Understanding and reconstructing the mechanism of crack action in rocks in engineering analysis, calculation, and simulation helps to further ensure the safe implementation and use of projects. Among these methods, particle flow simulation, through granular materials and contact models, can effectively simulate the heterogeneous material characteristics of rocks. This method helps researchers understand the failure mechanism of rock materials from a microscopic perspective, and it has been well applied in engineering simulations. However, existing contact models lack consideration for rock cracks, limiting their ability to simulate the effect of microcracks on rocks. Therefore, to further understand and reconstruct the impact of microcracks on the integrity of rock's mechanical behavior through particle flow simulation, it is necessary to further construct a particle contact model that incorporates the characteristics of microcracks in rocks.

[0003] Numerical simulation methods for particle flow can effectively simulate the heterogeneous material characteristics and failure behavior of rocks. However, existing contact models lack consideration for rock cracks, and various simulation methods proposed by researchers that take cracks into account also have certain limitations. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] To address the shortcomings of existing technologies, this invention provides a method for inferring microcrack connection force based on graph neural networks. It constructs a rock model containing microcracks by using a crack contact model with connecting materials, and effectively simulates the complete mechanical behavior of the rock during uniaxial loading.

[0006] (II) Technical Solution

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for inferring the connection force of microcracks based on graph neural networks, specifically comprising the following steps:

[0008] S1. Two conceptual planes of length 2R are used to simulate the two sides of the crack surface. The size and position of the connecting material in the crack are randomly distributed, and the force exerted by a single connecting material on the crack surface is... Where the subscripts n and s represent the normal and tangential directions of the crack surface, respectively, the resultant force on the crack surface is:

[0009]

[0010] Where N represents the amount of bonding material, the subscript l represents the bonding material, and the distance from the bonding material to the crack center is set to L. i Then the resultant torque exerted by all the connecting materials on the crack surface is:

[0011]

[0012] in, Therefore:

[0013]

[0014] S2. Let the effective modulus of the connecting material be E. i The stiffness of the connecting material is:

[0015]

[0016] Among them, A i To connect the effective area of ​​the matter, L i For the effective length of the connecting material, The normal force acting on the connecting matter, To address the normal deformation of materials due to forces, but for the sake of simplifying calculations, referring to the parallel bonding model, a special stiffness concept is defined that does not consider the element area: Then we have:

[0017]

[0018] in, For tangential stiffness, k * Given the stiffness ratio, the force exerted by the i-th connecting material on the crack surface is:

[0019]

[0020] In the formula, The tangential force acting on the connecting material. This represents the relative displacement of the crack surface at the bonding material;

[0021] S3. Assume the stiffness of the bonded surface is... The bonding force is then:

[0022]

[0023] In the formula, This represents the relative displacement of the bonded surface at the center.

[0024] Therefore, we have:

[0025]

[0026] Solving for the given information yields:

[0027]

[0028] Similarly:

[0029]

[0030] S4. When the crack surface angle is θ b At that time, the relationship between the relative displacement at each connecting material and the relative displacement at the crack center is as follows:

[0031]

[0032] in, The distance from the material to the center of the crack surface;

[0033] Similarly, due to the included angle θ b Smaller, crack surface due to θ b The resulting tangential displacement is approximately zero; therefore, the relative tangential displacement at any point on the crack surface can be replaced by the relative tangential displacement at the center of the crack surface.

[0034]

[0035] S5. Assuming that the mechanical properties of the connecting materials in the same crack are similar, the stiffness of any connecting material i can take the same value k, thus simplifying to:

[0036]

[0037] Simultaneously, the normal force of the binding material on the crack surface The stress σ, which is linearly distributed on the bonded surface, can be determined by... l Equivalent substitution:

[0038]

[0039] in, This represents the equivalent area of ​​the bonding material on the cementing surface, and It is related to the proportion of the i-th connecting substance in the total amount of connecting substances;

[0040] Similarly, the tangential force exerted by the bonding material on the crack surface is equivalent to the tangential stress at the center of the cemented surface:

[0041]

[0042] S6. When the bonding materials in the same crack are considered as materials with similar mechanical properties, the tensile strength and bond strength of any bonding material i can also be taken as the same value. and c l Therefore, with σ l and τ l Similarly, the tensile strength σ of the bonding material in the cemented surface is also... c Equivalent calculations were performed with the bond strength c:

[0043]

[0044] Correspondingly, the criteria for judging the failure of the cemented surface are:

[0045]

[0046] in,

[0047] S7. If the unconnected portion of the crack surface is equivalently replaced by two conceptual planes, then when the crack surface closes, we have:

[0048]

[0049] in, The equivalent stiffness of the crack in the unconnected portion is given by ΔU, where g0 is the initial crack gap and ΔU is the stiffness of the crack in the unconnected portion. s Let be the tangential displacement within time Δt after the crack closes. And when... Slippage occurs on the crack surface, eventually

[0050] At the same time, when there is an included angle θ between the crack surfaces b When there is no connection, the crack surface of the crack can be closed in three ways: no contact, partial contact, and complete contact. Therefore, the normal contact force and moment of this part need to be calculated in three cases.

[0051] Preferably, in step S2, the effective length L of the connecting material is... i The associated portion of the bonding material in the matrix on both sides of the crack should be considered, therefore it is not equal to the inter-crack gap.

[0052] Preferably, in step S3, it is assumed that the various bonding materials are relatively uniformly distributed in the crack surface, and the N bonding materials are equivalently calculated from a single cementing surface.

[0053] Preferably, in step S4, assuming that the various connecting materials are relatively uniformly distributed in the crack surface, the crack surface is centrally symmetrical.

[0054] Preferably, the crack is located at the contact point between the particles, and the resultant force and resultant torque of the two parts at the contact point are:

[0055] F = F l +F c M = M l +M c .

[0056] Preferably, the conceptual surface and the cemented surface are calculated in parallel. The displacement and rotation of both the conceptual surface and the cemented surface are converted and recorded in the interparticle contact plane. When the new contact model is installed at the contact point, the position of the unconnected portion of the conceptual surface is initialized according to the crack spacing g0.

[0057] Preferably, when the bonding of the bonded part is broken, the contact mode of the bonded part will change. The broken connecting material is simulated by setting a conceptual surface parallel to the conceptual surface of the unconnected part, wherein the distance between the conceptual surface of the connecting material part and the conceptual surface of the unconnected part is g0 / 2.

[0058] Preferably, the magnitude of the residual shear stress is determined by the tangential stiffness and total tangential displacement of the connecting surface, and the maximum value of the shear stress is determined by the normal stress and the friction coefficient. and M l Calculated based on the degree of overlap of the transformed conceptual surfaces.

[0059] (III) Beneficial Effects

[0060] This invention provides a method for inferring microcrack connectivity force based on graph neural networks. Compared with existing technologies, it has the following advantages: This graph neural network-based method for inferring microcrack connectivity force, based on parallel bonding and planar joint models, proposes a crack contact model that considers the connecting material in the crack by calculating the crack contact by splitting it into unconnected and connected parts. The new contact model provides the elements with certain tensile and shear strengths while considering the influence of pore closure on the contact force-displacement law. Furthermore, by limiting the failure of cementation to be controlled only by the contact force and torque of the connected part, a high compressive-tensile ratio is obtained. Then, using the Fish Model tool in Particle Flow Software (PFC2D), the contact model was constructed and verified through contact surface force-displacement tests and loading / unloading tests with a cracked model. Finally, the contact model was tested through simulated rock mechanics experiments. The results show that the contact model can effectively simulate the axial and radial strain laws of rocks simultaneously and also has a good reproduction of the dual-mode nature of rocks. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of the connecting material in the crack of the present invention;

[0062] Figure 2 This is a schematic diagram of the contact state of the crack surface in this invention. Detailed Implementation

[0063] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] Please see Figure 1-2 The present invention provides two technical solutions: a method for inferring microcrack connectivity force based on graph neural networks, specifically including the following embodiments:

[0065] Example 1: A method for inferring the connection force of microcracks based on graph neural networks, specifically including the following steps:

[0066] S1, through two lengths of The concept of the surface simulates the crack surfaces on both sides, such as Figure 1 As shown in (a), the size and location of the connecting material in the crack are randomly distributed, such as Figure 1 As shown in (b), the force exerted by a single connecting material on the crack surface is: Where the subscripts n and s represent the normal and tangential directions of the crack surface, respectively, the resultant force on the crack surface is:

[0067]

[0068] Where N is the number of connecting substances, and the subscript l represents the connecting substances. Also, as... Figure 1 As shown in (c), let L be the distance from the bonding material to the crack center. i Then the resultant torque exerted by all the connecting materials on the crack surface is:

[0069]

[0070] in, Therefore:

[0071]

[0072] S2. Let the effective modulus of the connecting material be E. i According to mechanics of materials, the stiffness of the connecting material is:

[0073]

[0074] Among them, A i To connect the effective area of ​​the matter, L i For the effective length of the connecting material, The normal force acting on the connecting matter, To address the normal deformation of materials due to forces, but for the sake of simplifying calculations, referring to the parallel bonding model, a special stiffness concept is defined that does not consider the element area: Then we have:

[0075]

[0076] in, For tangential stiffness, k * Given the stiffness ratio, the force exerted by the i-th connecting material on the crack surface can be obtained from equations (4) and (5):

[0077]

[0078] In the formula, The tangential force acting on the connecting material. This represents the relative displacement of the crack surface at the bonding material;

[0079] S3. Assume the stiffness of the bonded surface is... Referring to formula (6), the bonding force is:

[0080]

[0081] In the formula, This represents the relative displacement of the bonded surface at the center.

[0082] Therefore, the relationships (1), (6), and (7) are:

[0083]

[0084] Solving for the given information yields:

[0085]

[0086] Similarly:

[0087]

[0088] S4. When the crack surface angle is θ b At that time, the relationship between the relative displacement at each connecting material and the relative displacement at the crack center is as follows:

[0089]

[0090] in, The distance from the material to the center of the crack surface;

[0091] Similarly, due to the included angle θ b Smaller, crack surface due to θ bThe resulting tangential displacement is approximately zero; therefore, the relative tangential displacement at any point on the crack surface can be replaced by the relative tangential displacement at the center of the crack surface.

[0092]

[0093] S5. Assuming that the mechanical properties of the connecting materials in the same crack are similar, the stiffness of any connecting material i can take the same value k. Therefore, equations (9), (10), and (11) can be further simplified to:

[0094]

[0095] Meanwhile, from equations (6), (11), and (13), it can be seen that the normal force F of the connecting material on the crack surface is... n i The stress σ, which is linearly distributed on the bonded surface, can be determined by... l Equivalent substitution:

[0096]

[0097] in, This represents the equivalent area of ​​the bonding material on the cementing surface, and like Figure 1 As shown in (b) and equation (16), It is related to the proportion of the i-th connecting substance in the total amount of connecting substances;

[0098] Similarly, the tangential force exerted by the bonding material on the crack surface is equivalent to the tangential stress at the center of the cemented surface:

[0099]

[0100] S6. When the bonding materials in the same crack are considered as materials with similar mechanical properties, the tensile strength and bond strength of any bonding material i can also be taken as the same value. and c l Therefore, with σ l and τ l Similarly, the tensile strength σ of the bonding material in the cemented surface is also... c Equivalent calculations were performed with the bond strength c:

[0101]

[0102] Correspondingly, the criteria for judging the failure of the cemented surface are:

[0103]

[0104] From equation (15), we can obtain that...

[0105] S7. In step S6, the bonding material in the crack has been equivalently replaced by the cementing surface. Considering the contact force and torque generated by the unbonded portion of the crack when the crack surface closes, this part needs to be calculated. Continuing to use two conceptual surfaces to equivalently replace the unbonded portion of the crack surface, we have the following when the crack surface closes:

[0106]

[0107] in, The equivalent stiffness of the crack in the unconnected portion is given by ΔU, where g0 is the initial crack gap and ΔU is the stiffness of the crack in the unconnected portion. s Let be the tangential displacement within time Δt after the crack closes. And when... Slippage occurs on the crack surface, eventually

[0108] At the same time, when there is an included angle θ between the crack surfaces b At this time, the crack surface of the unconnected part of the crack can have three closure states: no contact, partial contact, and complete contact (e.g., Figure 2 As shown in the figure, the normal contact force and torque of this part need to be calculated in three cases.

[0109] In this embodiment of the invention, the effective length L of the connecting material in step S2 i The associated portion of the bonding material in the matrix on both sides of the crack should be considered, therefore it is not equal to the inter-crack gap.

[0110] In this embodiment of the invention, step S3 assumes that the various bonding materials are relatively uniformly distributed in the crack surface, and then the N bonding materials are equivalently calculated from a single cementing surface.

[0111] In this embodiment of the invention, step S4 assumes that the various bonding materials are relatively uniformly distributed in the crack surface, and that the crack surface is centrally symmetrical.

[0112] Example 2: The technical difference between this example and Example 1 is that the crack is located at the contact point between the particles, and the resultant force and resultant torque of the two parts at the contact point are:

[0113] F = F l +F c M = M l +M c . (twenty one)

[0114] The conceptual surface and the cemented surface are calculated in parallel. The displacements and rotations of both are converted and recorded on the interparticle contact plane. When the new contact model is installed at the contact point, the position of the unconnected portion of the conceptual surface is initialized based on the crack spacing g0.

[0115] When the cementation in the bonded portion fails, the contact pattern of the bonded portion changes. However, unlike the parallel bonding model, we assume that the equivalent connecting material of the cementation is not lost after the cementation fails and can still provide stress to the crack surface. Therefore, we simulate the connecting material after failure by setting a conceptual plane parallel to the conceptual plane of the unconnected portion, where the distance between the conceptual plane of the connecting material portion and the conceptual plane of the unconnected portion is g0 / 2.

[0116] After the bond fails, the shear stress in the joint is not completely released. The magnitude of the residual shear stress is determined by the tangential stiffness and total tangential displacement of the joint's conceptual surface, and the maximum value of the shear stress is determined by the normal stress and the coefficient of friction. and M l Calculated based on the degree of overlap of the transformed conceptual surfaces.

[0117] In summary, this invention proposes a crack contact model that considers the bonding material within the crack, based on the parallel bond model and the flat joint model, by calculating the crack contact by splitting it into unconnected and connected parts. The new contact model provides the elements with sufficient tensile and shear strength while simultaneously considering the influence of pore closure on the contact force-displacement law. Furthermore, by limiting the failure of the cementation to be controlled only by the contact force and moment of the connected part, a high compressive-tensile ratio is achieved. Then, using the Fish Model tool in the Particle Flow software (PFC2D), the contact model was constructed and verified through contact surface force-displacement tests and loading / unloading tests with a cracked model. Finally, the contact model was tested through simulated rock mechanics experiments. The results show that the contact model can effectively simulate both axial and radial strain laws of rock simultaneously and also provides a good representation of the dual-mode nature of rock.

[0118] Furthermore, any content not described in detail in this specification is existing technology known to those skilled in the art.

[0119] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0120] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for inferring the connection force of microcracks based on graph neural networks, characterized in that: Specifically, the following steps are included: S1, through two lengths of The conceptual surface simulates two crack surfaces, with the size and location of the connecting material within the crack being randomly distributed. The force exerted by a single connecting material on the crack surface is... Where the subscripts n and s represent the normal and tangential directions of the crack surface, respectively, the resultant force on the crack surface is: Where N represents the amount of bonding material, the subscript l represents the bonding material, and the distance from the bonding material to the crack center is set to L. i Then the resultant torque exerted by all the connecting materials on the crack surface is: in, Therefore: S2. Let the effective modulus of the connecting material be E. i The stiffness of the connecting material is: Among them, A i To connect the effective area of ​​the matter, L i For the effective length of the connecting material, The normal force acting on the connecting matter, To address the normal deformation of materials due to forces, but for the sake of simplifying calculations, referring to the parallel bonding model, a special stiffness concept is defined that does not consider the element area: Then we have: in, For tangential stiffness, k * Given the stiffness ratio, the force exerted by the i-th connecting material on the crack surface is: In the formula, The tangential force acting on the connecting material. This represents the relative displacement of the crack surface at the bonding material; S3. Assume the stiffness of the bonded surface is... The bonding force is then: In the formula, This represents the relative displacement of the bonded surface at the center. Therefore, we have: Solving for the given information yields: Similarly: S4. When the crack surface angle is θ b At that time, the relationship between the relative displacement at each connecting material and the relative displacement at the crack center is as follows: in, The distance from the material to the center of the crack surface; Similarly, due to the included angle θ b Smaller, crack surface due to θ b The resulting tangential displacement is approximately zero; therefore, the relative tangential displacement at any point on the crack surface can be replaced by the relative tangential displacement at the center of the crack surface. S5. Assuming that the mechanical properties of the connecting materials in the same crack are similar, the stiffness of any connecting material i can take the same value k, thus simplifying to: Simultaneously, the normal force of the binding material on the crack surface The stress σ, which is linearly distributed on the bonded surface, can be determined by... l Equivalent substitution: in, This represents the equivalent area of ​​the bonding material on the cementing surface, and It is related to the proportion of the i-th connecting substance in the total amount of connecting substances; Similarly, the tangential force exerted by the bonding material on the crack surface is equivalent to the tangential stress at the center of the cemented surface: S6. When the bonding materials in the same crack are considered as materials with similar mechanical properties, the tensile strength and bond strength of any bonding material i can also be taken as the same value. and c l Therefore, with σ l and τ l Similarly, the tensile strength σ of the bonding material in the cemented surface is also... c Equivalent calculations were performed with the bond strength c: Correspondingly, the criteria for judging the failure of the cemented surface are: in, S7. If the unconnected portion of the crack surface is equivalently replaced by two conceptual planes, then when the crack surface closes, we have: in, The equivalent stiffness of the crack in the unconnected portion is given by ΔU, where g0 is the initial crack gap and ΔU is the stiffness of the crack in the unconnected portion. s Let be the tangential displacement within time Δt after the crack closes. And when... Slippage occurs on the crack surface, eventually At the same time, when there is an included angle θ between the crack surfaces b When there is no connection, the crack surface of the crack can be closed in three ways: no contact, partial contact, and complete contact. Therefore, the normal contact force and moment of this part need to be calculated in three cases.

2. The method for inferring microcrack connection force based on graph neural networks according to claim 1, characterized in that: The effective length L of the connecting material in step S2 i The associated portion of the bonding material in the matrix on both sides of the crack should be considered, therefore it is not equal to the inter-crack gap.

3. The method for inferring microcrack connection force based on graph neural networks according to claim 1, characterized in that: In step S3, it is assumed that the various bonding materials are relatively uniformly distributed in the crack surface, and the N bonding materials are equivalently calculated from a single cementing surface.

4. The method for inferring microcrack connection force based on graph neural networks according to claim 1, characterized in that: In step S4, it is assumed that the various connecting materials are relatively uniformly distributed in the crack surface, and the crack surface is centrally symmetrical.

5. The method for inferring microcrack connection force based on graph neural networks according to claim 1, characterized in that: The crack is located at the contact point between the particles. The resultant force and resultant moment of the two parts at the contact point are: F=F l +F c ,M=M l +M c 。 6. The method for inferring microcrack connection force based on graph neural networks according to claim 5, characterized in that: The conceptual surface and the cemented surface are calculated in parallel. The displacements and rotations of both are converted and recorded on the interparticle contact plane. When the new contact model is installed at the contact point, the position of the unconnected portion of the conceptual surface is initialized based on the crack spacing g0.

7. The method for inferring microcrack connection force based on graph neural networks according to claim 6, characterized in that: When the cementation of the cemented part is broken, the contact mode of the cemented part will change. The broken connecting material is simulated by setting a conceptual surface parallel to the conceptual surface of the unconnected part, wherein the distance between the conceptual surface of the connecting material part and the conceptual surface of the unconnected part is g0 / 2.

8. The method for inferring microcrack connection force based on graph neural networks according to claim 7, characterized in that: The magnitude of the residual shear stress is determined by the tangential stiffness and total tangential displacement of the connecting surface, and the maximum value of the shear stress is determined by the normal stress and the coefficient of friction. and M l Calculated based on the degree of overlap of the transformed conceptual surfaces.

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