Numerical Simulation Method for End-Anchored Rock Mass Engineering Based on DDDA

Abstract

This invention relates to the fields of computational mechanics and rock engineering, and particularly to a numerical simulation method for end-anchored rock mass engineering based on DDDA (Digital Directed Amplification and Analysis). The method includes: constructing a circular element discontinuous deformation analysis numerical model according to actual engineering conditions; performing discontinuous deformation analysis numerical calculations; analyzing the calculation results of the unanchored model to preliminarily determine the anchoring scheme; performing discontinuous deformation analysis numerical calculations again; determining whether the model contains unstable blocks, adjusting the anchoring scheme, and repeating the aforementioned steps until the model stabilizes, thus completing the design of the rock mass engineering anchoring scheme. This invention establishes a numerical simulation method capable of accurately simulating the interaction between anchor bolts (anchor cables) and rock mass, and integrating anchoring scheme design, stability assessment, and dynamic parameter optimization functions. It achieves accurate prediction of the deformation and failure behavior of anchored rock mass and optimizes anchoring design, featuring high simulation accuracy and strong practicality.

Description

Technical Field

[0001] This invention relates to the fields of computational mechanics and rock engineering, and in particular to a numerical simulation method for end-anchored rock engineering based on DDDA. Background Technology

[0002] In rock engineering projects such as tunnels, slopes, underground chambers, and dam foundations, rock masses are typically cut by complex joints, fissures, bedding planes, and other structural surfaces, exhibiting significant discontinuities, heterogeneity, and anisotropy. Under the influence of external forces (such as in-situ stress, excavation disturbance, and groundwater), they are prone to sliding, opening, rotation, and even block instability failure along these structural surfaces. End-anchored anchor bolts (anchor cables), as an effective and economical reinforcement method, significantly improve the integrity and bearing capacity of the rock mass by providing tensile constraints and are widely used in engineering practice.

[0003] However, accurately predicting the deformation and failure behavior of rock masses and optimizing anchorage design has always been a challenge in the field of rock engineering. Traditional numerical methods for continuous media (such as the finite element method (FEM) and the finite difference method (FDM) face significant challenges when dealing with rock masses containing a large number of discontinuities, making it difficult to effectively simulate discontinuous deformation and failure processes such as block movement, separation, and rotation controlled by structural surfaces. While the discrete element method (DEM) excels at simulating interactions between blocks, its computational efficiency and accuracy are often low for systems with complex fracture networks and a large number of blocks.

[0004] Discontinuous Deformation Analysis (DDA) is a numerical method specifically developed for discontinuous media. It can effectively simulate the rigid body motion (translation and rotation) of block systems and the deformation of bonded blocks themselves, and is particularly suitable for simulating large deformation and instability failure processes of rock masses along structural planes. Among them, Circular Element DDA (DDDA) shows potential in simulating rock mass failure processes due to its relatively simple and efficient contact detection algorithm, good adaptability to complex shapes (approximated by combining circular elements), and high computational stability. Therefore, there is an urgent need for a numerical simulation method based on DDDA that can accurately simulate the interaction between anchor bolts (anchor cables) and rock mass, and integrate anchoring scheme design, stability assessment, and dynamic parameter optimization functions, to provide more scientific, efficient, and reliable decision support for anchoring design in complex rock mass engineering. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the aforementioned background technology by providing a numerical simulation method for end-anchored rock mass engineering based on DDDA, in order to support the anchoring design of complex rock mass engineering projects.

[0006] To achieve the above objectives, this invention provides a numerical simulation method for end-anchored rock mass engineering based on DDDA, comprising the following steps:

[0007] S1. Based on the topographic conditions of real rock mass engineering, construct a complete DDDA numerical model. Based on the geological conditions of real rock mass engineering, set the parameters of the numerical model, carry out discontinuous deformation analysis, and simulate the progressive failure process of rock mass engineering under anchor support conditions until stability is achieved.

[0008] S2. After the progressive failure process simulated in S1 reaches stability, based on the final simulated displacement cloud map, analyze whether the displacement of each particle block after bedding and joint cutting is greater than the preset maximum safe displacement value. If it is greater than the maximum safe displacement value, then anchor the particle block. After anchoring all unstable particle blocks, determine the preliminary anchor design scheme and determine the mechanical parameters of the anchor selected in the actual project, thereby determining the anchor setting distribution and numerical mechanical parameters in the DDDA numerical model.

[0009] S3. Conduct discontinuous deformation analysis. After the DDDA numerical model with anchor bolt support is stabilized, analyze each particle block to determine the stability of each particle block in the model.

[0010] S4. Adjust the anchor bolts of the unstable particle blocks identified in S3, add the new anchor bolt design scheme to the DDDA numerical model constructed in S1, and repeat the loop from S2 to S4. When all particle blocks in the new DDDA numerical model with anchor bolt support reach stability, it is determined that the anchoring scheme can stabilize the rock mass project, the loop operation ends, and the rock mass project anchoring scheme design is completed.

[0011] Furthermore, the topographic conditions of the actual rock mass engineering in S1 include the outer contour of the engineering terrain, bedding, and joint occurrence; the geological conditions include the rock mass mechanical parameters after calibration, the initial geostress distribution, and the external load distribution.

[0012] Furthermore, in S2, line segments are used to represent anchor elements under the DDDA framework, establishing the interaction between the line segments representing anchors and the circular element assembly.

[0013] Furthermore, in S2, the interaction between the line segment representing the anchor and the circular unit assembly is established for each anchor, including:

[0014] The anchor is segmented into a series of short line segments connected end to end using the anchor segmentation algorithm. These short line segments are called sub-anchors, and the two ends of each sub-anchor fall on two circles respectively. In each time step, for each combination of sub-anchor and two circles, the sub-anchor is regarded as a constraint spring. The sub-matrix of the constraint spring is obtained through the principle of minimum potential energy and superimposed into the simultaneous equilibrium equations of the entire calculation, reflecting the constraint effect of the sub-anchor on the circular elements at both ends. At the end of each time step, the length of the sub-anchor is accumulated to obtain the length of the anchor at the end of the time step. The force on the anchor is calculated according to the elongation-force relationship of the anchor, and it is determined whether the anchor has broken. If the anchor has not broken, the above process is repeated in the next time step to realize the effect of the anchor on the circular element assembly.

[0015] Furthermore, the anchor segmentation algorithm used in S2 is as follows: the anchor rod as a whole is a line segment, which is divided into several segments; particles with an effective embedding amount greater than or equal to a preset value are selected based on the start and end points of the anchor rod; the selected particles are sorted from the start to the end point according to the projection point of their center on the anchor rod; sub-anchor rods are generated sequentially with the anchoring points of adjacent particles as endpoints, and the parameters of the original anchor rod are assigned to each sub-anchor rod; if the endpoint of the anchor rod is not inside the particle, it is adjusted to the nearest intersection point between the anchor rod and the particle; for adjacent anchoring points with a distance less than the minimum particle radius, the anchoring points with smaller embedding rates are discarded.

[0016] Furthermore, when calculating the contribution of the anchor rod to the overall stiffness matrix in S2, the constraint effect of the anchor rod on the circular elements at its two ends is reflected in the circular elements at each time step. On point Harmony circle unit On point Anchored by anchor bolts, point and The coordinates are respectively and Let the time step be the point and The displacements are respectively and The change in the elongation of the anchor bolt caused by the displacement of these two points is: ,in For point , The unit vector, let the initial anchor elongation be... Then the elongation of the anchor rod within the time step is The sub-matrix of the constraint spring is obtained through the principle of minimum potential energy, and the formula for calculating the potential energy of the sub-anchor is:

[0017]

[0018]

[0019]

[0020] in, This refers to the stiffness of the anchor bolt, measured in N / m. , Let be the unknown quantum matrix of the circular element, denoted as ,in For circular elements in Displacement in direction, For circular elements in Displacement in direction, The angle of rotation of a circular element around its center. For point The displacement interpolation matrix, For point The displacement interpolation matrix;

[0021] right beg and The partial derivatives of are used to obtain the submatrix superimposed on the simultaneous equilibrium equations:

[0022]

[0023] in, , circular unit With circular unit The interaction stiffness submatrix is matrix, , circular unit and Its own stiffness submatrix is matrix, , A generalized force quantum array of circular units, denoted as ,in For circular elements in Generalized force of direction For circular elements in Generalized force of direction.

[0024] Furthermore, the stress update and failure criterion for anchor bolts in S2 is as follows: Different anchor bolt materials result in different elongation-force relationship curves. A three-segment curve representing the elastic stage, plastic hardening stage, and failure-failure stage is selected. When the anchor bolt has prestress... When, assuming the length of the anchor rod under stress is... Then we have:

[0025]

[0026] in, This represents the initial length of the anchor bolt;

[0027] From yield strength Calculate the length of the anchor bolt when it reaches the yield point. :

[0028]

[0029] Calculate the length of the anchor bolt at break using the ultimate elongation. :

[0030]

[0031] According to tensile strength Calculate the tensile force when the anchor bolt breaks. :

[0032]

[0033] When the anchor bolt is subjected to stress before reaching its yield strength, it is in the elastic deformation stage, and its elastic modulus is... Calculate using the following formula:

[0034]

[0035] After the stress on the anchor bolt exceeds the yield limit, it enters the plastic deformation stage, during which plastic hardening occurs. The plastic hardening coefficient... Calculate using the following formula:

[0036]

[0037] Based on the selected elongation-force relationship curve, during the calculation process, after obtaining the length of the anchor bolt at the end of the corresponding time step, the tension of the anchor bolt is updated according to the following formula:

[0038]

[0039] During the calculation, at the end of each time step, when the anchor bolt tension... It broke at times; among them, This represents the length of the anchor bolt at the end of each time step.

[0040] Furthermore, in S3, the stability of each particle block is determined using strength and displacement criteria. If a particle block satisfies one of the two criteria, it is determined to be unstable. If there is an unstable block in the model, the model is also unstable. The strength criterion is that the tensile force on the anchor rod in the particle block reaches the tensile strength. The displacement criterion is that the displacement of the particle block is greater than the maximum safe displacement value.

[0041] Furthermore, anchor bolt adjustment methods include increasing the tensile strength of the anchor bolt, increasing the cross-sectional area of ​​the anchor bolt, reducing the anchor bolt spacing, and changing the number of anchor bolts.

[0042] The above-described solution of the present invention has the following beneficial effects:

[0043] The numerical simulation method for end-anchored rock mass engineering based on DDDA provided by this invention offers effective principles, algorithms, and processes for studying anchoring schemes in rock mass engineering. It establishes a numerical simulation method that can accurately simulate the interaction between anchor bolts (anchor cables) and rock mass, and integrates anchoring scheme design, stability assessment, and dynamic parameter optimization functions. It utilizes the advantages of DDDA, such as its relative simplicity and efficiency, good adaptability to complex shapes (approximated by circular element combination), and high computational stability, to accurately predict the deformation and failure behavior of anchored rock mass and optimize anchoring design. It features high simulation accuracy and strong practicality, and can provide more scientific, efficient, and reliable decision support for anchoring design in complex rock mass engineering.

[0044] Other beneficial effects of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0045] Figure 1 This is a flowchart of the steps of the present invention;

[0046] Figure 2 This is a schematic diagram of the anchor bolt segmentation algorithm of the present invention;

[0047] Figure 3 This is a typical three-segment elongation-force relationship curve of the present invention;

[0048] Figure 4 The diagram shows the typical slope modeling, excavation, and failure modes of the present invention, where (a) is before excavation, (b) is after excavation, and (c) is the final failure mode of the unsupported slope.

[0049] Figure 5 The present invention provides a single constant resistance large deformation energy-absorbing anchor bolt support slope model and failure diagram, wherein (a) is a single anchor bolt support slope model and (b) is the final failure mode of the single anchor bolt support slope.

[0050] Figure 6 The present invention provides a slope model and failure diagram of a slope supported by multiple and constant resistance large deformation energy-absorbing anchor bolts, wherein (a) is a slope model supported by four anchor bolts, (b) is the final failure mode of a slope supported by four anchor bolts, (c) is a slope model supported by nine anchor bolts, and (d) is the final failure mode of a slope supported by nine anchor bolts. Detailed Implementation

[0051] The following specific examples illustrate the implementation of this disclosure. Those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0052] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0053] It should also be noted that the illustrations provided in the following embodiments are merely schematic representations of the basic concept of this disclosure. The illustrations only show components relevant to this disclosure and are not drawn according to the actual number, shape, and size of components in implementation. In actual implementation, the type, quantity, and proportion of each component can be arbitrarily changed, and the component layout may be more complex. Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0054] like Figure 1 As shown, an embodiment of the present invention provides a numerical simulation method for end-anchored rock mass engineering based on DDDA, comprising the following steps:

[0055] S1. Based on the topographic conditions of the real rock mass project, construct a complete DDDA numerical model, and set the numerical model parameters according to the geological conditions of the project. Complete the construction of the DDDA numerical model, conduct discontinuous deformation analysis, and simulate the progressive failure process of the rock mass project under the support of anchor bolts (anchor cables).

[0056] It should be noted that the topographic conditions of a real rock mass engineering project include the outer contour of the engineering terrain, bedding and joint occurrence, etc., and the geological conditions include parameters such as rock mass mechanical parameters, initial geostress distribution and external load distribution after calibration.

[0057] S2. After the progressive failure process simulated in S1 reaches stability, based on the final simulated displacement cloud map, analyze whether the displacement of each particle block after bedding and joint cutting is greater than the preset maximum safe displacement value. If it is greater than the maximum safe displacement value, the particle block needs to be anchored. After anchoring all unstable particle blocks, determine the preliminary anchor bolt (anchor cable) design scheme and determine the mechanical parameters of the anchor bolt (anchor cable) selected in the actual project. In this way, determine the distribution of anchor bolt (anchor cable) settings and numerical mechanical parameters in the DDDA numerical model, and complete the construction of the DDDA numerical model with anchor bolt (anchor cable) support.

[0058] It should be noted that the original DDDA numerical model is a circular unit assembly. In this embodiment, line segments are used to represent anchor units under the DDDA framework. The purpose of constructing this model is to establish the interaction between the line segments representing the anchors and the circular unit assembly. In order to realize this interaction, each anchor is subjected to the following sub-steps to reflect its effect on the circular unit assembly: (1) The anchor is divided into a series of short line segments connected end to end according to the anchor segmentation algorithm. The short line segments are called sub-anchors. The two ends of each sub-anchor fall on two circles respectively; (2) In each time step, for each "sub-anchor + two circles" combination, the sub-anchor is regarded as a constraint spring. The sub-matrix of the constraint spring is obtained through the principle of minimum potential energy and superimposed on the entire set of simultaneous equilibrium equations to reflect the constraint effect of the sub-anchor on the circular units at its two ends; (3) At the end of each time step, the length of the sub-anchor is accumulated to obtain the length of the anchor at the end of the time step. The force on the anchor is calculated according to the elongation-force relationship of the anchor and it is determined whether the anchor is broken. If the anchor bolt is not broken, the anchor bolt's effect on the circular unit assembly will be implemented in the next time step according to the above sub-steps.

[0059] For example, the anchor bolt segmentation algorithm used is as follows: Figure 2 As shown, line segment AB represents an anchor rod, which is then segmented. Specifically, if points A and B are both inside the particle, anchor rod AB is divided into 9 segments: ab, bc, cd, de, ef, fg, gh, hi, and ij, where point j coincides with point B. Using the start and end points of the anchor rod as the range, segments with an effective embedment depth greater than or equal to 10e are selected. -8The particles are sorted from the start point to the end point according to the projection of their center onto the anchor rod. Sub-anchor rods are generated sequentially with the anchor points of adjacent particles as endpoints, and the parameters of the original anchor rod are assigned to each sub-anchor rod. If the endpoint of the anchor rod is not inside the particle, it is adjusted to the nearest intersection point between the anchor rod and the particle. For adjacent anchor points with a distance less than the minimum particle radius, the anchor points with a smaller embedding rate are discarded.

[0060] When calculating the contribution of the anchor bolt to the overall stiffness matrix, at each time step, the constraint effect of the anchor bolt on the circular elements at its two ends is manifested as a circular element. On point Harmony circle unit On point Anchored by anchor bolts. Point and The coordinates are respectively and Let the point within the time step be... and The displacements are respectively and The change in the elongation of the anchor bolt caused by the displacement of these two points is: ,in For point , The unit vector. Let the initial anchor elongation at time step be... Then the elongation of the anchor rod within the time step is The sub-matrix of the constraint spring is obtained through the principle of minimum potential energy, and the formula for calculating the potential energy of the sub-anchor is:

[0061]

[0062]

[0063]

[0064] in, This refers to the stiffness of the anchor bolt, measured in N / m. , Let be the unknown quantum matrix of the circular element, denoted as ,in For circular elements in Displacement in direction, For circular elements in Displacement in direction, Let be the angle of rotation of a circular element around its center. For point The displacement interpolation matrix, For point The displacement interpolation matrix.

[0065] right beg and The partial derivatives of are used to obtain the submatrix superimposed on the simultaneous equilibrium equations:

[0066]

[0067] in, , circular unit With circular unit The interaction stiffness submatrix is matrix, , circular unit and Its own stiffness submatrix is matrix, , A generalized force quantum array of circular units, denoted as ,in For circular elements in Generalized force of direction For circular elements in Generalized force of direction.

[0068] The anchor bolt stress update and failure criterion are as follows: Different anchor bolt materials result in different elongation-force relationship curves. This embodiment selects a typical three-segment curve representing the elastic stage, plastic hardening stage, and failure-failure stage. However, it is not limited to this typical three-segment elongation-force relationship curve; in other embodiments, more types of relationship curves can be selected as needed. A typical three-segment curve is shown below. Figure 3 As shown, it includes three segments: AB, BC, and CD. Segment AB is the elastic stage, BC is the plastic hardening stage, and CD is the failure and fracture stage.

[0069] When the anchor bolt is prestressed When, assuming the length of the anchor rod under stress is... Then we have:

[0070]

[0071] in, This represents the initial length of the anchor bolt.

[0072] From yield strength Calculate the length of the anchor bolt when it reaches the yield point. :

[0073]

[0074] Calculate the length of the anchor bolt at break using the ultimate elongation. :

[0075]

[0076] According to tensile strength Calculate the tensile force when the anchor bolt breaks. :

[0077]

[0078] When the anchor bolt is subjected to stress before reaching its yield strength, it is in the elastic deformation stage, and its elastic modulus is... Calculate using the following formula:

[0079]

[0080] After the stress on the anchor bolt exceeds the yield limit, it enters the plastic deformation stage, during which plastic hardening occurs. The plastic hardening coefficient... Calculate using the following formula:

[0081]

[0082] Based on the selected elongation-force relationship curve, during the calculation process, after obtaining the length of the anchor bolt at the end of the corresponding time step, the tension of the anchor bolt is updated according to the following formula:

[0083]

[0084] During the calculation, at the end of each time step, when the anchor bolt tension... It broke at times; among them, This represents the length of the anchor bolt at the end of each time step.

[0085] S3. Conduct discontinuous deformation analysis. After the DDDA numerical model containing anchor bolts (anchor cables) support has been calculated to be stable, analyze each particle block to determine the stability of each particle block in the model.

[0086] In this embodiment, the stability of each particle block in the model is determined using two criteria: a strength criterion (the tensile force on the anchor bolts (anchor cables) in the particle block reaches the tensile strength) and a displacement criterion (the displacement of the particle block is greater than the maximum safe displacement value). If a particle block satisfies either criterion, it is considered unstable; if there is one unstable block in the model, the model itself is also unstable. It should be noted that the two criteria, based on the two most fundamental dimensions of geotechnical mechanics—"force" and "shape"—jointly construct a double-insurance stability evaluation system. The strength criterion ensures the mechanical reliability of the support system, while the displacement criterion ensures the functional and long-term safety of the project. Using both criteria simultaneously in numerical analysis allows for a more comprehensive and reliable assessment of the stability of anchored rock mass engineering projects.

[0087] S4. Adjust the anchor bolts (anchor cables) that were determined to be unstable particle blocks in S3. Add the new anchor bolt (anchor cable) design scheme to the DDDA numerical model constructed in S1. Repeat steps S2 to S4. When all particle blocks in the DDDA numerical model containing anchor bolt (anchor cable) support reach stability, it is determined that the anchoring scheme can stabilize the rock mass project. End the cycle operation and the rock mass project anchoring scheme design is completed.

[0088] In this embodiment, the anchor bolt (anchor cable) adjustment methods include increasing the tensile strength of the anchor bolt, increasing the cross-sectional area of ​​the anchor bolt (anchor cable), reducing the spacing between anchor bolts (anchor cables), and changing the number of anchor bolts (anchor cables). These adjustment methods can all affect the anchoring strength, and therefore can all be adjusted to form a new anchor bolt (anchor cable) design scheme.

[0089] The following specific example further illustrates the effectiveness of the invention. Based on the geometric parameters and calibrated material parameters of a certain inclined bedding slope, a complete DDDA numerical model of the slope is constructed. The model contains 49,704 rigid circular elements, and discontinuous deformation analysis calculations are performed to simulate the stress equilibrium. After the stress equilibrium is achieved, the numerical model is excavated, resulting in 35,750 rigid circular elements. Discontinuous deformation analysis calculations are then performed to simulate the progressive failure process of the slope engineering under unsupported conditions. Figure 4 It is a diagram of the final failure mode of a slope from a complete model to excavation and then to an unsupported state.

[0090] Based on the final failure mode of the slope under unsupported conditions, a preliminary support scheme is set. In this slope engineering case, a support scheme with the addition of a constant resistance large deformation energy-absorbing anchor is first adopted. Discontinuous deformation analysis and calculation are performed to simulate the progressive failure process under this support scheme. Figure 5 It shows a model diagram of a slope supported by a single constant-resistance, large-deformation energy-absorbing anchor and a diagram of the final failure mode.

[0091] Based on the final failure mode of the slope under the previous support scheme, a new support scheme was designed and calculated until the slope anchoring project achieved the expected results. In this slope engineering case, when four equal-length, constant-resistance, large-deformation energy-absorbing anchors were installed, large displacement of the slope was achieved without large-area collapse; when nine long, constant-resistance, large-deformation energy-absorbing anchors were installed, displacement control of the slope project was achieved, such as... Figure 6 As shown, a reasonable rock mass engineering anchoring scheme was thus obtained.

[0092] Based on the same inventive concept, this embodiment also provides an apparatus, including: a memory for storing a computer program; and a processor for executing the computer program to implement the software method-related steps of the numerical simulation method for end-anchored rock mass engineering based on DDDA as described above.

[0093] The processor may include one or more processing cores, such as a quad-core processor or an octa-core processor. The processor can be implemented using at least one hardware form of Digital Signal Processing (DSP), Field-Programmable Gate Array (FPGA), or Programmable Logic Array (PLA). The processor may also include a main processor and coprocessors. The main processor, also known as the Central Processing Unit (CPU), is used to process data in the wake-up state; the coprocessors are low-power processors used to process data in the standby state. In some embodiments, the processor may integrate a Graphics Processing Unit (GPU), which is responsible for rendering and drawing the content to be displayed on the screen. In some embodiments, the processor may also include an Artificial Intelligence (AI) processor, which handles computational operations related to machine learning.

[0094] The memory may include one or more computer-readable storage media, which may be non-transitory. The memory may also include high-speed random access memory and non-volatile memory, such as one or more disk storage devices or flash memory devices. In this embodiment, the memory is used to store at least the following computer program, which, after being loaded and executed by the processor, is capable of implementing the aforementioned software method steps. In addition, the resources stored in the memory may also include operating systems and data, and the storage method may be temporary or permanent storage. The operating system may include Windows, Unix, Linux, etc.

[0095] This embodiment also provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the software method-related steps in the numerical simulation method for end-anchored rock mass engineering based on DDDA as described above.

[0096] In summary, the numerical simulation method, apparatus, memory, and computer-readable storage medium based on DDDA for end-anchored rock mass engineering provided in this embodiment offer effective principles, algorithms, processes, and program execution carriers for studying rock mass engineering anchoring schemes. It establishes a numerical simulation method capable of accurately simulating the interaction between anchor bolts (anchor cables) and rock mass, and integrating anchoring scheme design, stability assessment, and dynamic parameter optimization functions. Utilizing the advantages of DDDA, such as its relative simplicity and efficiency, good adaptability to complex shapes (approximated by circular element combination), and high computational stability, it accurately predicts the deformation and failure behavior of anchored rock masses and optimizes anchoring design. It features high simulation accuracy and strong practicality, providing more scientific, efficient, and reliable decision support for anchoring design in complex rock mass engineering.

[0097] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0098] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A numerical simulation method for end-anchored rock mass engineering based on DDDA, characterized in that, Includes the following steps: S1. Based on the topographic conditions of real rock mass engineering, construct a complete DDDA numerical model. Based on the geological conditions of real rock mass engineering, set the parameters of the numerical model, carry out discontinuous deformation analysis, and simulate the progressive failure process of rock mass engineering under anchor support conditions until stability is achieved. S2. After the progressive failure process simulated in S1 reaches stability, based on the final simulated displacement cloud map, analyze whether the displacement of each particle block after bedding and joint cutting is greater than the preset maximum safe displacement value. If it is greater than the maximum safe displacement value, then anchor the particle block. After anchoring all unstable particle blocks, determine the preliminary anchor design scheme and determine the mechanical parameters of the anchor selected in the actual project, thereby determining the anchor setting distribution and numerical mechanical parameters in the DDDA numerical model. S3. Conduct discontinuous deformation analysis. After the DDDA numerical model with anchor bolt support is stabilized, analyze each particle block to determine the stability of each particle block in the model. S4. Adjust the anchor bolts of the unstable particle blocks identified in S3, add the new anchor bolt design scheme to the DDDA numerical model constructed in S1, and repeat the loop from S2 to S4. When all particle blocks in the new DDDA numerical model with anchor bolt support reach stability, it is determined that the anchoring scheme can stabilize the rock mass project, the loop operation ends, and the rock mass project anchoring scheme design is completed.

2. The numerical simulation method for end-anchored rock mass engineering based on DDDA according to claim 1, characterized in that, The topographic conditions of the real rock mass engineering in S1 include the outer contour of the engineering terrain, bedding, and joint occurrence; the geological conditions include the rock mass mechanical parameters, initial geostress distribution, and external load distribution after calibration.

3. The numerical simulation method for end-anchored rock mass engineering based on DDDA according to claim 1, characterized in that, In S2, line segments are used to represent anchor elements under the DDDA framework, and the interaction between the line segments representing anchors and the circular element assembly is established.

4. The numerical simulation method for end-anchored rock mass engineering based on DDDA according to claim 3, characterized in that, In S2, the interaction between the line segment representing the anchor and the circular unit assembly is established for each anchor, including: The anchor is segmented into a series of short line segments connected end to end using the anchor segmentation algorithm. These short line segments are called sub-anchors, and the two ends of each sub-anchor fall on two circles respectively. In each time step, for each combination of sub-anchor and two circles, the sub-anchor is regarded as a constraint spring. The sub-matrix of the constraint spring is obtained through the principle of minimum potential energy and superimposed into the simultaneous equilibrium equations of the entire calculation, reflecting the constraint effect of the sub-anchor on the circular elements at both ends. At the end of each time step, the length of the sub-anchor is accumulated to obtain the length of the anchor at the end of the time step. The force on the anchor is calculated according to the elongation-force relationship of the anchor, and it is determined whether the anchor has broken. If the anchor has not broken, the above process is repeated in the next time step to realize the effect of the anchor on the circular element assembly.

5. The numerical simulation method for end-anchored rock mass engineering based on DDDA according to claim 4, characterized in that, The anchor segmentation algorithm used in S2 is as follows: the anchor rod as a whole is a line segment, which is divided into several segments; particles with an effective embedding amount greater than or equal to a preset value are selected based on the start and end points of the anchor rod; the selected particles are sorted from the start to the end point according to the projection point of their center on the anchor rod; sub-anchor rods are generated sequentially with the anchoring points of adjacent particles as endpoints, and the parameters of the original anchor rod are assigned to each sub-anchor rod; if the endpoint of the anchor rod is not inside the particle, it is adjusted to the nearest intersection point between the anchor rod and the particle; for adjacent anchoring points with a distance less than the minimum particle radius, the anchoring points with smaller embedding rates are discarded.

6. The numerical simulation method for end-anchored rock mass engineering based on DDDA according to claim 4, characterized in that, In S2, when calculating the contribution of the anchor to the overall stiffness matrix, at each time step, the constraint effect of the anchor on the circular elements at its two ends is manifested in the circular elements. On point Harmony circle unit On point Anchored by anchor bolts, point and The coordinates are respectively and Let the time step be the point and The displacements are respectively and The change in the elongation of the anchor bolt caused by the displacement of these two points is: ,in For point , The unit vector, let the initial anchor bolt elongation at time step be... Then the elongation of the anchor rod within the time step is The sub-matrix of the constraint spring is obtained through the principle of minimum potential energy, and the formula for calculating the potential energy of the sub-anchor is: in, This refers to the stiffness of the anchor bolt, measured in N / m. , Let be the unknown quantum matrix of the circular element, denoted as ,in For circular elements in Displacement in direction, For circular elements in Displacement in direction, The angle of rotation of a circular element around its center. For point The displacement interpolation matrix, For point The displacement interpolation matrix; right beg and The partial derivatives of are used to obtain the submatrix superimposed on the simultaneous equilibrium equations: in, , circular unit With circular unit The interaction stiffness submatrix is matrix, , circular unit and Its own stiffness submatrix is matrix, , A generalized force quantum array of circular units, denoted as ,in For circular elements in Generalized force of direction For circular elements in Generalized force of direction.

7. The numerical simulation method for end-anchored rock mass engineering based on DDDA according to claim 4, characterized in that, The stress update and failure criterion for anchor bolts in S2 is as follows: Different anchor bolt materials result in different elongation-force relationship curves. A three-segment curve is selected, representing the elastic stage, plastic hardening stage, and failure / breakage stage. This applies when the anchor bolt has prestress. When, assuming the length of the anchor rod under stress is... Then we have: in, This represents the initial length of the anchor bolt; From yield strength Calculate the length of the anchor bolt when it reaches the yield point. : Calculate the length of the anchor bolt at break using the ultimate elongation. : According to tensile strength Calculate the tensile force when the anchor bolt breaks. : When the anchor bolt is subjected to stress before reaching its yield strength, it is in the elastic deformation stage, and its elastic modulus is... Calculate using the following formula: After the stress on the anchor bolt exceeds the yield limit, it enters the plastic deformation stage, during which plastic hardening occurs. The plastic hardening coefficient... Calculate using the following formula: Based on the selected elongation-force relationship curve, during the calculation process, after obtaining the length of the anchor bolt at the end of the corresponding time step, the tension of the anchor bolt is updated according to the following formula: During the calculation, at the end of each time step, when the anchor bolt tension... It broke at times; among them, This represents the length of the anchor bolt at the end of each time step.

8. The numerical simulation method for end-anchored rock mass engineering based on DDDA according to claim 4, characterized in that, In S3, the stability of each particle block is determined by strength criteria and displacement criteria. If a particle block satisfies one of the two criteria, it is determined to be unstable. If there is an unstable block in the model, the model is also unstable. The strength criterion is that the tensile force on the anchor in the particle block reaches the tensile strength. The displacement criterion is that the displacement of the particle block is greater than the maximum safe displacement value.

9. The numerical simulation method for end-anchored rock mass engineering based on DDDA according to any one of claims 1-8, characterized in that, Anchor bolt adjustment methods include increasing the tensile strength of the anchor bolt, increasing the cross-sectional area of ​​the anchor bolt, reducing the spacing between anchor bolts, and changing the number of anchor bolts.

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