Method and device for obtaining elastic mechanical parameters of hard rock under eccentric loading condition

Abstract

This application proposes a method and apparatus for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions, belonging to the technical fields of optical measurement and numerical simulation. The method includes: obtaining a first displacement through a uniaxial loading experiment; introducing an eccentric loading coefficient and calculating a second displacement in finite element software; establishing a multi-objective error function based on the first and second displacements; outputting the final elastic modulus, Poisson's ratio, and eccentric loading coefficient when the multi-objective error function reaches the convergence condition; and iteratively optimizing the mechanical parameters using a simulated annealing particle swarm optimization algorithm improved by a dynamic cooling strategy based on particle swarm diversity, incorporating the eccentric loading coefficient into the parameters to be inverted, using the method of this application. This method realizes the inversion analysis of rock elastic mechanical parameters and eccentric loading coefficient, and improves the inversion accuracy by using an improved simulated annealing algorithm.

Description

Technical Field

[0001] This invention belongs to the technical field of optical measurement and numerical simulation, specifically relating to a method and device for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions. Background Technology

[0002] Rock, as a common engineering material, is a major component of the surface rock mass of the Earth's crust. The accurate determination of its mechanical parameters is of great significance for the design, construction, operation and maintenance of various major national projects such as tunnel excavation, underground CO2 storage, underground urban space utilization projects and deep geothermal projects.

[0003] Due to the unique heterogeneity and discontinuity of rocks, obtaining rock mechanical parameters presents numerous challenges. Existing methods for obtaining mechanical parameters of hard rocks, such as conventional MTS presses, conventional triaxial and true triaxial laboratory experiments, often fail to capture the macroscopic mechanical parameters of the rock mass, resulting in highly discrete experimental data and unrepresentative results. Obtaining rock-related mechanical parameters through field monitoring methods, such as microseismic monitoring, is limited by engineering costs, experimental sites, and time constraints, leading to a limited amount of data. Compared to these methods, rock mechanical parameter inversion methods have gained popularity in recent years due to their low cost and relatively high accuracy. Numerous studies have incorporated digital image correlation (DIC), strain gauge measurements, and acoustic emission monitoring techniques, combined with intelligent optimization algorithms, to perform mechanical parameter inversion analysis. This avoids the need for repeated full-scale rock sample testing, achieving efficient acquisition of mechanical parameters.

[0004] However, the discreteness problem of indoor tests is significant. The natural non-uniformity inside the rock sample makes it easy for the defect concentration side to preferentially undergo local deformation, which in turn indirectly causes loading offset. Unavoidable end face unevenness defects during rock sample processing, as well as residual mineral particles left by the test head of the testing machine, may all lead to eccentric loading during the loading process. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this application proposes a method and apparatus for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions. The experimental displacement field of the rock at a specific loading moment is obtained through digital image correlation technology. A multi-objective error function is constructed between the experimental displacement field and the displacement field simulated by finite element software. The simulated annealing particle swarm optimization algorithm is improved based on a dynamic cooling strategy with particle swarm diversity, thereby achieving the convergence condition of the multi-objective error function and obtaining the relevant elastic mechanical parameters of the rock sample.

[0006] On one hand, the present invention provides a method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions, including:

[0007] Step S1: Obtain the rock sample to be tested;

[0008] Step S2: Perform a uniaxial loading experiment on the rock sample to be tested, and obtain the first displacement of the specified displacement marker point through digital image method;

[0009] Step S3: Introduce the eccentric loading coefficient, define the simulation loading conditions, initialize the elastic modulus and Poisson's ratio, establish the same numerical calculation model as the uniaxial loading experiment in the finite element software, and calculate the second displacement of the specified displacement marker point.

[0010] Step S4: Establish a multi-objective error function based on the first displacement and the second displacement;

[0011] Step S5: If the multi-objective error function reaches the convergence condition, output the final elastic modulus, Poisson's ratio, and eccentric loading coefficient.

[0012] Step S6: If the multi-objective error function does not reach the convergence condition, the mechanical parameters are used as individuals in the particle swarm. An improved simulated annealing algorithm is used to optimize the mechanical parameters. Then, return to step S3 and recalculate in the finite element software using the optimized mechanical parameters. The mechanical parameters include: elastic modulus, Poisson's ratio, and eccentric loading coefficient. The improved simulated annealing algorithm includes: a dynamic temperature adjustment strategy based on particle swarm diversity, which enables the temperature decay rate in the simulated annealing algorithm to adaptively match the particle swarm state.

[0013] The acquisition of the rock sample to be tested includes:

[0014] The rock sample to be tested is cut and polished to ensure that the surface smoothness of the rock sample reaches the smoothness threshold and the perpendicularity of the adjacent surfaces of the rock sample to be tested reaches the perpendicularity threshold.

[0015] High-pressure water jets were used to cut a tunnel chamber in the center of the rock sample after cutting and polishing, and black and white matte paint was used to pre-create a speckle field on the surface of the rock sample after cutting and polishing.

[0016] The introduction of an eccentric loading coefficient and the definition of simulation loading conditions include: adding an eccentric load above the finite element model at a specified loading rate; defining the addition of a first eccentric load at the leftmost Z1 point above the finite element model with an eccentric load coefficient of 1.0; adding a second eccentric load at Z2 point adjacent to Z1 with an eccentric load coefficient of λ; the eccentric load coefficient increases linearly from point Z1 to point Z2 until the nth eccentric load is added at the rightmost point above the finite element model.

[0017] The eccentric loading coefficient is calculated as follows:

[0018] ;

[0019] in, Let x be the eccentric load factor when the lateral coordinate of the finite element model is x. Let Z2 be the eccentric load factor at point Z2, and x be the transverse coordinate of the finite element model.

[0020] The specified loading rate is calculated as follows:

[0021] ;

[0022] in, This is the specified loading rate for the finite element model when the horizontal coordinate is x. Let Z2 be the eccentric load factor at point Z2, and x be the transverse coordinate of the finite element model.

[0023] The multi-objective error function is calculated as follows:

[0024] ;

[0025] in, The number of markers participating in the inversion. For the i-th displacement marker point, Let i be the first displacement of the i-th displacement marker. It represents the second displacement of the i-th displacement marker point.

[0026] The dynamic temperature adjustment strategy based on particle swarm diversity enables adaptive matching between the temperature decay rate and the particle swarm state in the simulated annealing algorithm, including:

[0027] The average distance between all particles in the particle swarm is calculated using the following formula:

[0028] ;

[0029] in, This represents the average distance between the particles. For the i-th particle, Let N be the j-th particle, and N be the total number of particles;

[0030] Set threshold The temperature in the simulated annealing algorithm is adjusted in stages, and the calculation formula is as follows:

[0031] ;

[0032] in, , As the first parameter, For the second parameter, To set a threshold, Let be the temperature in the simulated annealing algorithm of generation t. The temperature is the simulated annealing temperature in the (t+1)th generation.

[0033] On the other hand, the present invention also provides a device for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions, comprising:

[0034] The sample acquisition module is used to acquire rock samples to be tested;

[0035] The first displacement acquisition module is used to perform uniaxial loading experiments on the rock sample to be tested and obtain the first displacement of the specified displacement marker point through digital image methods.

[0036] The second displacement acquisition module is used to introduce the eccentric loading coefficient, define the simulation loading conditions, initialize the elastic modulus and Poisson's ratio, establish the same numerical calculation model as the uniaxial loading experiment in the finite element software, and calculate the second displacement of the specified displacement marker point.

[0037] The error function calculation module is used to establish a multi-objective error function based on the first displacement and the second displacement.

[0038] The mechanical parameter output module outputs the final elastic modulus, Poisson's ratio, and eccentric loading coefficient when the multi-objective error function reaches convergence. If the multi-objective error function does not reach convergence, the mechanical parameters are treated as individuals within the particle swarm, and an improved simulated annealing algorithm is used to optimize the mechanical parameters. The module then returns to the second displacement acquisition module, where the optimized mechanical parameters are recalculated in the finite element software. The mechanical parameters include the elastic modulus, Poisson's ratio, and eccentric loading coefficient. The improved simulated annealing algorithm includes a dynamic temperature adjustment strategy based on particle swarm diversity, enabling adaptive matching between the temperature decay rate and the particle swarm state.

[0039] Thirdly, this application proposes an electronic device, comprising: one or more processors, and a memory for storing instructions, which, when executed by the one or more processors, cause the one or more processors to perform the method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions.

[0040] Fourthly, this application proposes a computer-readable storage medium storing executable instructions that, when executed, cause a processor to perform the method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions.

[0041] Beneficial effects:

[0042] This application proposes a method and apparatus for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions. The eccentric loading coefficient is included in the parameters to be inverted, realizing the inversion analysis of rock elastic mechanical parameters and eccentric loading coefficient, providing a new path for improving the accuracy of parameter inversion. This application adopts a dynamic cooling strategy based on particle swarm diversity to improve the simulated annealing particle swarm optimization algorithm, overcoming the shortcomings of traditional particle swarm algorithms that are prone to getting trapped in local extrema. Attached Figure Description

[0043] Figure 1 Flowchart of a method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions according to an embodiment of the present invention;

[0044] Figure 2 A schematic flowchart of a method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions according to an embodiment of the present invention;

[0045] Figure 3 A schematic diagram of the dimensions of the rock sample to be tested according to an embodiment of the present invention;

[0046] Figure 4 A schematic diagram of the stress-strain curve under experimental loading according to an embodiment of the present invention;

[0047] Figure 5 A schematic diagram showing the specific locations of the markers in this embodiment of the invention;

[0048] Figure 6 A schematic diagram of a device for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions according to an embodiment of the present invention. Detailed Implementation

[0049] The specific implementation methods of this application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0050] Example 1:

[0051] This embodiment of the invention proposes a method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions, such as... Figure 1 As shown, it includes:

[0052] Step S1: Obtain the rock sample to be tested;

[0053] In this embodiment, the rock sample to be tested is cut and polished to ensure that the surface smoothness of the rock sample to be tested reaches the smoothness threshold and the perpendicularity of the adjacent surfaces of the rock sample to be tested reaches the perpendicularity threshold.

[0054] High-pressure water jets were used to cut a tunnel chamber in the center of the rock sample after cutting and polishing, and black and white matte paint was used to pre-create a speckle field on the surface of the rock sample after cutting and polishing.

[0055] Step S2: Perform a uniaxial loading experiment on the rock sample to be tested, and obtain the first displacement of the specified displacement marker point through digital image method;

[0056] In this embodiment, the boundary conditions of the uniaxial loading experiment loading process are determined, and the rock sample to be tested is loaded according to the design scheme. At the same time as the experiment, the experimental displacement field of the rock sample to be tested at a specific loading moment is obtained through digital image correlation technology, and the displacement data of a specific displacement marker point is extracted. In this embodiment, the displacement of the specified displacement marker point obtained by the digital image method is called the first displacement.

[0057] Digital imaging methods are a mature approach capable of obtaining displacement and strain results across the entire field. They also allow for real-time calculation and display of strain across the entire field, and can directly measure data such as strain and displacement. Due to their high accuracy and wide measurement range, they have been widely applied in professional scientific and engineering fields such as materials mechanics, mechanical engineering, strain analysis, and finite element verification. Their basic principle is to track the movement of the same point in the image before and after deformation to obtain deformation information for the entire field.

[0058] Step S3: Introduce the eccentric loading coefficient, define the simulation loading conditions, initialize the elastic modulus and Poisson's ratio, establish the same numerical calculation model as the uniaxial loading experiment in the finite element software, and calculate the second displacement of the specified displacement marker point.

[0059] In this embodiment, the SA-PSO (Simulated Annealing-Particle Swarm Optimization) algorithm is used to optimize the elastic modulus, Poisson's ratio, and eccentric loading coefficient. In each calculation iteration, dozens of particles (each particle represents a computational example) are calculated in parallel simultaneously. After each iteration, the magnitude of the eccentric loading coefficient of each particle in the next step is affected by three factors: the eccentric loading coefficient of the previous iteration, the individual's own learning status (i.e., if the eccentric loading coefficient of the previous iteration increases, the calculation error increases, and the eccentric loading coefficient of the next step will decrease, which is the particle's own learning status), and the information exchange and learning between the group (if the error between the eccentric loading coefficient of other particles and the experimental results is small, then the eccentric loading coefficient of other particles is learned).

[0060] In finite element software, an eccentric load factor λ is introduced as an inversion factor during the inversion process. For example... Figure 3 as well as Figure 5As shown, the finite element model is subjected to an eccentric load from above. The eccentric load coefficient at the left end Z1 is defined as 1.0, while at the right end Z2, it is denoted as λ. An x-λ coordinate system is established with the direction of increasing eccentric load as the positive x-axis and the opposite direction of the applied eccentric load as the positive λ-axis. In the x-λ coordinate system, the coordinates of point Z1 are (-0.075, 1.0), and the coordinates of point Z2 are (0.075, λ). The eccentric load coefficient increases linearly from point Z1 to point Z2.

[0061] The introduction of an eccentric loading coefficient and the definition of simulation loading conditions include: adding an eccentric load above the finite element model at a specified loading rate; defining the addition of a first eccentric load at the leftmost Z1 point above the finite element model with an eccentric load coefficient of 1.0; adding a second eccentric load at Z2 point adjacent to Z1 with an eccentric load coefficient of λ; the eccentric load coefficient increases linearly from point Z1 to point Z2 until the nth eccentric load is added at the rightmost point above the finite element model.

[0062] The eccentric loading coefficient is calculated as follows:

[0063] ;

[0064] in, Let x be the eccentric load factor when the lateral coordinate of the finite element model is x. Let Z2 be the eccentric load factor at point Z2, and x be the transverse coordinate of the finite element model.

[0065] The constant loading rate in the indoor test was 0.002 mm / s. The eccentric loading coefficient at point Z1 was 1, meaning the loading rate at point Z1 was 0.002 m / s. The eccentric loading coefficient at point Z2 was... That is, the constant loading rate at point Z2 is 0.002. mm / s, therefore in x- In the coordinate system, the loading rate at each position above the finite element model is calculated as follows:

[0066] ;

[0067] in, This is the specified loading rate for the finite element model when the horizontal coordinate is x. Let Z2 be the eccentric load factor at point Z2, and x be the transverse coordinate of the finite element model.

[0068] In this embodiment, the observation of the experimental displacement cloud map revealed the eccentric loading phenomenon commonly seen in indoor uniaxial compression experiments. By introducing an eccentric loading coefficient and redefining the simulation loading conditions, the same numerical calculation model was established in the finite element software, and a C++ program was written to initialize the elastic modulus of each element. Compared to Poisson ,in The element number is used to calculate the finite element model in the software.

[0069] In this embodiment, if a uniaxial loading test is performed on a rock sample containing fissures or pores in an indoor test, it is usually necessary to conduct a uniaxial loading test on the intact rock sample. If no eccentric loading phenomenon occurs, a normal inversion can be performed, inverting only the elastic modulus and Poisson's ratio, as the uniaxial loading test of the intact sample aims to obtain these two mechanical parameters. However, in actual engineering sites, some rock masses face numerous obstacles in core extraction and sample preparation due to high weathering, well-developed joints and fissures. Furthermore, core transportation costs are high, and the test itself has significant dispersion. If an indoor uniaxial compression test is performed on a rock sample containing pores and fissures, the test results cannot reflect the mechanical properties of the intact rock mass. In this case, using this real-time inversion method eliminates the need for a separate indoor uniaxial compression test on the intact rock, thus saving rock samples, especially in engineering sites where core extraction and sample preparation are difficult.

[0070] During real-time inversion, displacement contour maps of the rock sample loading experiment can be exported in real time using digital image correlation methods. By observing the displacement contour maps, it can be determined whether eccentric loading has occurred. If eccentric loading is detected, the eccentric loading coefficient is also considered as a parameter to be inverted. At this point, the total parameters to be inverted are the elastic modulus, Poisson's ratio, and eccentric loading coefficient. If the eccentric loading coefficient is not taken into account, the inverted elastic modulus and Poisson's ratio will have large errors. Therefore, the method in this embodiment improves the accuracy of elastic parameter measurement and provides valuable guidance for indoor tests and engineering sites with limited measurement points and complex conditions.

[0071] Step S4: Establish a multi-objective error function based on the first displacement and the second displacement;

[0072] The multi-objective error function is calculated as follows:

[0073] ;

[0074] in, The number of markers participating in the inversion. For the i-th displacement marker point, Let i be the first displacement of the i-th displacement marker. It represents the second displacement of the i-th displacement marker point.

[0075] Step S5: If the multi-objective error function reaches the convergence condition, output the final elastic modulus, Poisson's ratio, and eccentric loading coefficient.

[0076] Step S6: If the multi-objective error function does not reach the convergence condition, the mechanical parameters are used as individuals in the particle swarm. An improved simulated annealing algorithm is used to optimize the mechanical parameters. Then, return to step S3 and recalculate in the finite element software using the optimized mechanical parameters. The mechanical parameters include: elastic modulus, Poisson's ratio, and eccentric loading coefficient. The improved simulated annealing algorithm includes: a dynamic temperature adjustment strategy based on particle swarm diversity, which enables the temperature decay rate in the simulated annealing algorithm to adaptively match the particle swarm state.

[0077] In this embodiment, the traditional particle swarm optimization (PSO) algorithm is updated by introducing the Metropolis criterion and roulette wheel selection method from the simulated annealing algorithm. This probabilistic acceptance of differential solutions overcomes the traditional PSO algorithm's tendency to get trapped in local optima. The simulated annealing algorithm is written into a C++ program, and iterative optimization of elasticity parameters is achieved through simulated annealing PSO, thereby minimizing the multi-objective error function. Given convergence conditions, if the iteration satisfies the convergence condition, the elastic modulus, Poisson's ratio, and eccentric loading coefficient of the finite element software model at this point are output. If the iteration does not satisfy the convergence condition, the elastic modulus, Poisson's ratio, and eccentric loading coefficient of each element in the finite element software model are updated using the simulated annealing PSO algorithm, replacing the elastic modulus, Poisson's ratio, and eccentric loading coefficient of the previous iteration, and then substituted into the finite element software model for calculation.

[0078] The improved simulated annealing algorithm has the following specific steps:

[0079] Assuming in In the target search space of dimension, there are A community is formed by 3 particles, where the 1st particle is the 2nd particle. Each particle is represented as one A 3D vector is calculated as follows:

[0080] ;

[0081] in, For the i-th particle, Let be the D-dimensional vector of the i-th particle, and N be the total number of particles;

[0082] No. The "flight" speed of each particle is also A 3D vector is calculated as follows:

[0083] ;

[0084] in, Let be the velocity of the i-th particle. Let be the D-dimensional vector of the velocity of the i-th particle.

[0085] when The first generation Individual particles evolved to In time, its motion is influenced by three factors: the inheritance of previous velocities, individual learning, and information exchange and learning between groups. The particle's next position is determined by the sum of the products of the previous position and the next velocity, with time considered as 1. The calculation formula is as follows:

[0086] ;

[0087] ;

[0088] in, This indicates the inheritance of the velocity from the previous particle iteration. This is the inertia factor coefficient. Let be the j-th dimension vector of the velocity of the i-th particle in the t-th generation. Represents the individual's own learning. Represents information exchange and learning between groups. For the t-th generation individual learning factor, Let be the learning factor for the t-th generation group, here... = =1.49, (t) is the first random number between [0, 1] in the t-th generation. (t) is the second random number between [0, 1] in the t-th generation. This represents the optimal position currently discovered for an individual particle. It is the optimal position for the entire group.

[0089] The particle's velocity is limited by the maximum velocity limit in each spatial dimension. The constraints ensure that the speed is controlled within [...]. , Within the range of ], this determines the intensity of the problem space search. If If it's too large, particles might fly past the optimal region without an effective search. Conversely, if... If the velocity is too small, the particle may not be able to detect areas outside the local optimum. This could cause the particle to get trapped in a local optimum, unable to move far enough to escape and find a better position in space. Therefore, it is necessary to reasonably constrain the particle's flight speed according to the problem in order to find the global optimum.

[0090] Inertia factor coefficient, used This indicates the influence of the velocity of the previous generation of particles on the velocity of the current particle, reflecting the particle's confidence in its own motion. Particles move inertial motion based on their own velocity, and the inertial weight... The inertial weight is the key factor determining whether a particle maintains its inertial motion and expands the search space. When the inertial weight is large, the particle has a greater ability to explore new regions and perform global optimization, thus avoiding getting trapped in local optima. Conversely, when the inertial weight is small, the particle is more inclined to local search, which is beneficial for quickly converging to the optimal solution. To achieve a balance between search speed and search accuracy, the inertial weight is usually adjusted at different stages of the algorithm. Initially, it has a strong global search capability, which helps find the global optimum. Later, it enhances the local search capability and improves convergence accuracy to achieve better optimization results. This dynamic weight adjustment method helps to address the characteristics of the problem space and improve the algorithm's performance. The equation is shown below:

[0091] ;

[0092] in, This is the maximum value of the inertia factor. To be the minimum value of the inertia factor, in this embodiment, we take... =0.9, =0.4, =150, This is the current iteration number.

[0093] While the Proof-of-Stake (PSO) optimization algorithm boasts fast iterative convergence, its tendency for particles to get trapped in local optima prevents it from reaching the optimal solution. Simulated annealing, derived from the principle of solid-state annealing, is a probabilistic algorithm. Its core idea is similar to heating a solid to a very high temperature, causing particles within the solid to move randomly, and then gradually cooling it until it reaches a stable state. During heating, the particles move randomly, increasing energy and making the system unstable; while during slow cooling, the particles gradually become ordered, decreasing energy and stabilizing the system. Simulated annealing initially searches at a high temperature. As the temperature parameter gradually decreases, it uses the principle of probabilistically accepting different solutions to randomly search for the global optimum of the objective function within the solution space. By imbuing the search process with a time-varying probability of eventually approaching zero, simulated annealing effectively avoids getting trapped in local optima and ultimately achieves the global optimum. The algorithm consists of an outer loop and an inner loop. The outer loop, or annealing process, starts from a high initial temperature (T0) and decreases the temperature until the termination temperature or the maximum number of iterations is reached, completing the cooling process.

[0094] In particle cooling processes, traditional methods often employ a fixed temperature decay coefficient to achieve gradual cooling. However, if the decay coefficient is too large, the temperature decreases slowly, causing the algorithm to accept suboptimal solutions with a high probability in later iterations. This not only reduces search efficiency but also makes it difficult to converge to an exact solution. Conversely, if the decay coefficient is too small, the temperature drops rapidly, easily causing the algorithm to get trapped in local optima prematurely and fail to fully search the space. To address these issues, a dynamic temperature adjustment strategy based on population diversity is introduced, enabling adaptive matching between the temperature decay rate and the population state.

[0095] The dynamic temperature adjustment strategy based on particle swarm diversity enables adaptive matching between the temperature decay rate and the particle swarm state in the simulated annealing algorithm, including:

[0096] The average distance between all particles in the particle swarm is calculated using the following formula:

[0097] ;

[0098] in, This represents the average distance between the particles. For the i-th particle, Let N be the j-th particle, and N be the total number of particles;

[0099] Set threshold The temperature in the simulated annealing algorithm is adjusted in stages, and the calculation formula is as follows:

[0100] ;

[0101] in, , As the first parameter, For the second parameter, To set a threshold, Let be the temperature in the simulated annealing algorithm of generation t. The temperature is the simulated annealing temperature in the (t+1)th generation.

[0102] The inner loop uses the Metropolis algorithm, performing multiple iterations at each temperature to find the minimum energy at that temperature, i.e., the optimal solution. The Metropolis criterion allows the algorithm to accept poor solutions during the search process. This helps the algorithm avoid getting trapped in local optima and thus failing to find the global optimum. At higher temperatures, particles move more freely, which enhances its global search ability and makes it easier to find the global optimum. On the other hand, at lower temperatures, particles tend to be more stable, which enhances its local search ability and makes it easier to find local optima until the maximum number of iterations is reached or the termination criterion is met. Therefore, combining simulated annealing optimization algorithm with particle swarm optimization algorithm can effectively change the disadvantage of particle swarm optimization algorithm being prone to getting trapped in local optima. The equation is used to calculate the... The adaptive value for each particle:

[0103] ;

[0104] in, Indicates the first The probability value of a particle at the current temperature, where N is set to 10. This represents the local optimal fitness value of a particle at the current temperature. This represents the globally optimal fitness value of a particle at the current temperature. This is the current temperature.

[0105] Roulette wheel selection is a common and simple selection method, similar in principle to choosing numbers on a roulette wheel. Each individual has a corresponding sector on the wheel whose size is proportional to its fitness. Specifically, first, the fitness ratio of each individual is calculated. Then, the entire wheel is divided into several sectors proportionally, with the size of each sector corresponding to the fitness ratio of the individuals. Next, a rotation angle is randomly selected, and individuals from the sector corresponding to that angle are chosen. Roulette wheel selection effectively retains individuals with high fitness and increases their probability of being selected during the selection process by adjusting their fitness ratio, thus promoting the retention and optimization of excellent individuals. In this method, the selection probability of each individual is proportional to its fitness value. The greater the fitness, the higher the probability of selection.

[0106] This embodiment proposes a method for obtaining the elastic mechanical parameters of hard rock under eccentric loading conditions and develops an improved simulated annealing particle swarm optimization algorithm to overcome the limitation of traditional particle swarm optimization algorithms that are prone to convergence to local extrema. This method combines finite element method (FEM) software and simulated annealing particle swarm optimization to determine the elastic mechanical parameters of rock samples. Unlike previous methods, this method also combines numerical inversion methods with digital image correlation (DIR) technology to improve accuracy. Based on DIR technology, the experimental displacement field of the rock at a specific loading moment is obtained. Using the automatic correction method in FEM software, a numerical calculation model of the experimental loading is established, a multi-objective error function between the experimental and simulated displacement fields is established, and the elastic mechanical parameters of each element are initialized. With the help of the simulated annealing particle swarm optimization algorithm, the elastic mechanical parameters are iteratively optimized until the objective function converges, and the elastic mechanical parameters of each element are output. Addressing the common eccentric loading phenomenon in indoor uniaxial compression experiments, an eccentric loading coefficient is introduced and treated as a parameter to be inverted. Even in indoor experiments with limited measurement points and challenging conditions, the elastic mechanical parameters of the rock can be obtained while reducing experimental costs. The method in this embodiment is flexible and can freely set boundary loading conditions according to whether there is an eccentric loading phenomenon. The inversion calculation is timely and can obtain the elastic mechanical parameters of the rock sample in real time.

[0107] To describe in detail a method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions, an example is given below:

[0108] The implementation process of this example is mainly divided into three parts, such as Figure 2 As shown, the process consists of three parts: First, a speckle field is prefabricated on the surface of the rock sample to be tested. During the uniaxial loading experiment, digital image correlation technology is used to process the loading images in real time, thereby obtaining the experimental displacement field (i.e., the first displacement) of the rock sample at different loading times. Second, by observing the experimental displacement cloud map, an eccentric loading phenomenon is found in the indoor uniaxial compression experiment. An eccentric loading coefficient is introduced, and a numerical calculation model with the same dimensions as the experiment is established in the finite element software. The elastic mechanical parameters of each element are initialized, the numerical model is loaded, and the finite element simulated displacement field (i.e., the second displacement) is calculated. Third, a multi-objective error function (i.e., the displacement field error) is established between the experimental displacement and the simulated displacement. By introducing the Metropolis criterion and the roulette wheel selection method from the simulated annealing algorithm, and probabilistically accepting the difference, a simulated annealing particle swarm optimization algorithm is created. This overcomes the disadvantage of traditional particle swarm algorithms being prone to getting trapped in local extrema. The simulated annealing particle swarm optimization algorithm iteratively optimizes the elastic mechanical parameters to minimize the difference in the multi-objective error function. When the convergence condition is met, the elastic mechanical parameters of the rock sample are output. The entire process is completed by calling MATLAB and the finite element software program through Visual Studio 2012.

[0109] The material used in the experimental study was red sandstone, a common material in indoor rock mechanics tests. The hardware and software environment for the computational tests consisted of a 64-bit Windows 10 operating system, an Intel Core i9 9900K CPU, 128GB of RAM, and a 1TB hard drive. The digital image acquisition system comprised a CCD industrial camera and its accompanying industrial lens, LED supplementary lighting, and a computer. During the rock sample loading process, surface speckle images were acquired. Visual Studio 2012 was used to call open-source programs in MATLAB to process the speckle images, thereby obtaining the experimental displacement field. The following description uses a uniaxial compression experiment on a red sandstone tunnel sample as an example.

[0110] The basic process of this example consists of the following 9 steps:

[0111] (1) Red sandstone tunnel samples were obtained by cutting, polishing, and high-pressure water jet cutting of the complete red sandstone block. The dimensions of the red sandstone tunnel samples were 150mm×150mm×30mm. A 100mm×100mm section was selected as the observation area. A speckle field was pre-fabricated on the observation area using black and white matte paint. The dimensions of the rock samples to be tested are as follows: Figure 3 As shown.

[0112] (2) The experimental loading device was an MTS press, the loading method was displacement loading, and the loading rate was 0.002 mm / s. The digital image correlation technology image acquisition rate was 8 frames / second, and the resolution of the acquired TIF image was 3376 pixels × 2704 pixels.

[0113] (3) Before loading the experiment, sand the upper and lower contact surfaces of the red sandstone tunnel sample with sandpaper, then apply lubricating oil, adjust the press head to align it with the horizontal line, and at the same time, evenly apply lubricating oil to the upper part of the press head. Place the red sandstone tunnel sample under the press head and adjust its position to be horizontal. Adjust the MTS press to make the press head contact the upper contact surface of the sample, adjust the position of the LED fill light, and adjust the brightness, distance, and focal length of the CCD camera to ensure that the outline of each pixel in the magnified speckle image is clearly visible.

[0114] (4) At the start of the experiment, the MTS press and image acquisition system are started simultaneously until the specimen reaches its peak strength and macroscopic fracture occurs. Image acquisition is then stopped, and the acquired data is saved and processed. The stress-strain curves under experimental loading are shown below. Figure 4 As shown.

[0115] (5) Select speckle images at specific loading moments in the elastic stage of the rock, and use the speckle image at the start of the experiment as a reference image. Use the ncorr_2D open-source program in MATLAB to process the speckle images at specific loading moments to obtain the experimental displacement fields at four specific moments in the elastic loading stage, and extract the displacement data (i.e., the first displacement) of specific marker points.

[0116] (6) By observing the experimental displacement cloud map, it was found that there was an eccentric loading phenomenon in the experiment. An eccentric loading coefficient was introduced, and a numerical calculation model with the same size as the experiment was established in the finite element software. The size was 150mm×150mm×30mm, with a total of 1408 elements. Since the red sandstone particles are relatively fine and the mineral content is relatively simple, the red sandstone was regarded as a homogeneous material. The elastic mechanical parameters of all elements were initialized, and displacement constraints were applied to the upper and lower ends of the red sandstone tunnel numerical model to start loading.

[0117] (7) After the calculation is completed, the displacement field data at a specific loading time calculated by the finite element software is automatically output using a self-written C++ program, and the displacement data at the same location marker (i.e., the second displacement) is extracted by interpolation calculation.

[0118] (8) Establish a multi-objective error function for experimental displacement and simulated displacement, and write the objective function into a C++ program. The multi-objective error function is as follows:

[0119] ;

[0120] Indicates the number of markers involved in the inversion. It is to select the displacement marker point. It is the displacement of specific marker points obtained through digital image correlation technology, and This refers to the displacement of the marker points obtained through finite element software.

[0121] (9) The traditional particle swarm optimization algorithm is updated by introducing the Metropolis criterion and roulette wheel selection method from the simulated annealing algorithm. The differential solution is accepted with probability, which overcomes the disadvantage that the traditional particle swarm optimization algorithm is prone to getting trapped in local extrema. The simulated annealing algorithm is written into the C++ program. The elastic mechanical parameters are optimized iteratively through the simulated annealing particle swarm optimization algorithm, thereby minimizing the multi-objective error function. Given the convergence condition, if the iteration meets the convergence condition, the elastic modulus, Poisson's ratio and eccentric loading coefficient of the finite element software model at this time are output; if the iteration does not meet the convergence condition, the elastic modulus, Poisson's ratio and eccentric loading coefficient of each element of the finite element software model are updated through the simulated annealing particle swarm optimization algorithm, replacing the elastic modulus, Poisson's ratio and eccentric loading coefficient of the previous iteration, and are substituted into the finite element software model for calculation.

[0122] by Figure 4As shown in the figure, displacement contour maps for these four specific loading moments were obtained using digital image correlation techniques. Figure 5 The specific locations of the P1~P5 markers were determined, experimental displacement data were extracted, and a multi-objective error function between experimental and simulated displacements was established. To verify the stability of the method, inversion calculations were performed using different numbers of experimental markers, and 16 sets of inversion results were finally obtained, as shown in Table 1.

[0123] As shown in Table 1, the eccentric loading coefficients obtained from the 16 inversion calculations fluctuated little, basically hovering around the level of 1.100. The results of the 16 inversion calculations show that the elastic modulus fluctuates between 10.4 GPa and 14.4 GPa, and the Poisson's ratio fluctuates between 0.25 and 0.29, which is close to the material's true elastic modulus of 11.8 GPa and Poisson's ratio of 0.27.

[0124] First, the method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions proposed in this example yields elastic mechanical parameters with small errors and fluctuations, closely resembling the actual elastic mechanical parameters of rock samples. Second, a high-precision method for obtaining elastic mechanical parameters of hard rock based on digital image correlation technology effectively reduces the cost of indoor experiments. When preparing pre-fractured or tunnel rock samples, it is not necessary to conduct experiments on intact rocks from the same sampling site to obtain their elastic mechanical parameters. Understanding the deformation parameters and evolution characteristics of hard rock is crucial for analyzing its stability and controlling related hazards. By studying the deformation parameters and evolution characteristics of rocks, we can not only predict and control rock deformation and failure, reducing the occurrence of related hazards, but also have significant implications for the design, construction, operation, and maintenance of various major national engineering projects.

[0125] Table 1. Inversion calculation results;

[0126] ;

[0127] Example 2:

[0128] This embodiment also provides a device for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions, such as... Figure 6 As shown, it includes: a sample acquisition module, a first displacement acquisition module, a second displacement acquisition module, an error function calculation module, and a mechanical parameter output module. The sample acquisition module is connected to the first displacement acquisition module, the first displacement acquisition module is connected to the second displacement acquisition module, the second displacement acquisition module is connected to the error function calculation module, the error function calculation module is connected to the mechanical parameter output module, and the mechanical parameter output module is connected to the second displacement acquisition module.

[0129] The sample acquisition module is used to acquire rock samples to be tested;

[0130] The first displacement acquisition module is used to perform uniaxial loading experiments on the rock sample to be tested and obtain the first displacement of the specified displacement marker point through digital image methods.

[0131] The second displacement acquisition module is used to introduce the eccentric loading coefficient, define the simulation loading conditions, initialize the elastic modulus and Poisson's ratio, establish the same numerical calculation model as the uniaxial loading experiment in the finite element software, and calculate the second displacement of the specified displacement marker point.

[0132] The error function calculation module is used to establish a multi-objective error function based on the first displacement and the second displacement.

[0133] The mechanical parameter output module outputs the final elastic modulus, Poisson's ratio, and eccentric loading coefficient when the multi-objective error function reaches convergence. If the multi-objective error function does not reach convergence, the mechanical parameters are treated as individuals within the particle swarm, and an improved simulated annealing algorithm is used to optimize the mechanical parameters. The module then returns to the second displacement acquisition module, where the optimized mechanical parameters are recalculated in the finite element software. The mechanical parameters include the elastic modulus, Poisson's ratio, and eccentric loading coefficient. The improved simulated annealing algorithm includes a dynamic temperature adjustment strategy based on particle swarm diversity, enabling adaptive matching between the temperature decay rate and the particle swarm state.

[0134] Example 4:

[0135] This embodiment proposes an electronic device, including: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions.

[0136] The electronic device can be a mobile phone, computer, or tablet computer, etc., and includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements a method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions as described in the embodiments. It is understood that the electronic device may also include an input / output (I / O) interface and communication components.

[0137] The processor is used to execute all or part of the steps in the method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions as described in the above embodiments. The memory is used to store various types of data, which may include, for example, instructions for any application or method in an electronic device, as well as application-related data.

[0138] The processor can be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic components, and is used to execute the method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions described in the above embodiments.

[0139] Example 5:

[0140] This embodiment proposes a computer-readable storage medium that stores executable instructions. When these instructions are executed, if they are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0141] The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method for obtaining hard rock elastic mechanical parameters under eccentric loading conditions as described in various embodiments of this application.

[0142] The aforementioned storage media include: flash memory, hard disks, multimedia cards, card-type memory (e.g., SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR) memory), random access memory (RAM), static random-access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, disks, optical discs, servers, APP (Application) application stores, and other media capable of storing program verification codes. These media store computer programs, which, when executed by a processor, can implement the various steps of the method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions described above.

[0143] Example 6:

[0144] This embodiment proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions.

[0145] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a computer program product.

[0146] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0147] The scope of protection of this application is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of equivalent technology of this disclosure, then the intent of this disclosure also includes such modifications and variations.

Claims

1. A method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions, characterized in that, include: Step S1: Obtain the rock sample to be tested; Step S2: Perform a uniaxial loading experiment on the rock sample to be tested, and obtain the first displacement of the specified displacement marker point through digital image method; Step S3: Introduce the eccentric loading coefficient, define the simulation loading conditions, initialize the elastic modulus and Poisson's ratio, establish the same numerical calculation model as the uniaxial loading experiment in the finite element software, and calculate the second displacement of the specified displacement marker point. Step S4: Establish a multi-objective error function based on the first displacement and the second displacement; Step S5: If the multi-objective error function reaches the convergence condition, output the final elastic modulus, Poisson's ratio, and eccentric loading coefficient. Step S6: If the multi-objective error function does not reach the convergence condition, the mechanical parameters are used as individuals in the particle swarm. The improved simulated annealing algorithm is used to optimize the mechanical parameters. Then, return to step S3 and recalculate in the finite element software using the optimized mechanical parameters. The mechanical parameters include: elastic modulus, Poisson's ratio, and eccentric loading coefficient. The improved simulated annealing algorithm includes: a dynamic temperature adjustment strategy based on particle swarm diversity, which enables the temperature decay rate in the simulated annealing algorithm to adaptively match the particle swarm state. The dynamic temperature adjustment strategy based on particle swarm diversity enables adaptive matching between the temperature decay rate and the particle swarm state in the simulated annealing algorithm, including: The average distance between all particles in the particle swarm is calculated using the following formula: ； in, This represents the average distance between the particles. For the i-th particle, Let N be the j-th particle, and N be the total number of particles; Set threshold The temperature in the simulated annealing algorithm is adjusted in stages, and the calculation formula is as follows: ； in, , As the first parameter, For the second parameter, To set a threshold, Let be the temperature in the simulated annealing algorithm of generation t. The temperature is the simulated annealing temperature in the (t+1)th generation.

2. The method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions according to claim 1, characterized in that, The acquisition of the rock sample to be tested includes: The rock sample to be tested is cut and polished to ensure that the surface smoothness of the rock sample reaches the smoothness threshold and the perpendicularity of the adjacent surfaces of the rock sample to be tested reaches the perpendicularity threshold. High-pressure water jets were used to cut a tunnel chamber in the center of the rock sample after cutting and polishing, and black and white matte paint was used to pre-create a speckle field on the surface of the rock sample after cutting and polishing.

3. The method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions according to claim 1, characterized in that, The introduction of an eccentric loading coefficient and the definition of simulation loading conditions include: adding an eccentric load above the finite element model at a specified loading rate; defining the addition of a first eccentric load at the leftmost Z1 point above the finite element model with an eccentric load coefficient of 1.0; adding a second eccentric load at Z2 point adjacent to Z1 with an eccentric load coefficient of λ; the eccentric load coefficient increases linearly from point Z1 to point Z2 until the nth eccentric load is added at the rightmost point above the finite element model.

4. The method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions according to claim 3, characterized in that, The eccentric loading coefficient is calculated as follows: ； in, Let x be the eccentric load factor when the lateral coordinate of the finite element model is x. Let Z2 be the eccentric load factor at point Z2, and x be the transverse coordinate of the finite element model.

5. The method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions according to claim 3, characterized in that, The specified loading rate is calculated as follows: ； in, This is the specified loading rate for the finite element model when the horizontal coordinate is x. Let Z2 be the eccentric load factor at point Z2, and x be the transverse coordinate of the finite element model.

6. The method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions according to claim 1, characterized in that, The multi-objective error function is calculated as follows: ； in, The number of markers participating in the inversion. For the i-th displacement marker point, Let i be the first displacement of the i-th displacement marker point. It represents the second displacement of the i-th displacement marker point.

7. A device for obtaining elastic mechanical parameters of hard rock under eccentric loading, implemented using the method for obtaining elastic mechanical parameters of hard rock under eccentric loading as described in any one of claims 1 to 6, characterized in that, include: The sample acquisition module is used to acquire rock samples to be tested; The first displacement acquisition module is used to perform uniaxial loading experiments on the rock sample to be tested and obtain the first displacement of the specified displacement marker point through digital image methods. The second displacement acquisition module is used to introduce the eccentric loading coefficient, define the simulation loading conditions, initialize the elastic modulus and Poisson's ratio, establish the same numerical calculation model as the uniaxial loading experiment in the finite element software, and calculate the second displacement of the specified displacement marker point. The error function calculation module is used to establish a multi-objective error function based on the first displacement and the second displacement. The mechanical parameter output module is used to output the final elastic modulus, Poisson's ratio, and eccentric loading coefficient when the multi-objective error function reaches the convergence condition. If the multi-objective error function fails to converge, the mechanical parameters are treated as individuals in the particle swarm. An improved simulated annealing algorithm is used to optimize the mechanical parameters. The algorithm is then returned to the second displacement acquisition module, where the optimized mechanical parameters are recalculated in the finite element software. The mechanical parameters include: elastic modulus, Poisson's ratio, and eccentric loading coefficient. The improved simulated annealing algorithm includes: a dynamic temperature adjustment strategy based on particle swarm diversity, which enables the temperature decay rate in the simulated annealing algorithm to adaptively match the particle swarm state. The dynamic temperature adjustment strategy based on particle swarm diversity enables adaptive matching between the temperature decay rate and the particle swarm state in the simulated annealing algorithm, including: The average distance between all particles in the particle swarm is calculated using the following formula: ； in, This represents the average distance between the particles. For the i-th particle, Let N be the j-th particle, and N be the total number of particles; Set threshold The temperature in the simulated annealing algorithm is adjusted in stages, and the calculation formula is as follows: ； in, , As the first parameter, For the second parameter, To set a threshold, Let be the temperature in the simulated annealing algorithm of generation t. The temperature is the simulated annealing temperature in the (t+1)th generation.

8. An electronic device, characterized in that, include: One or more processors, and a memory for storing instructions that, when executed by the one or more processors, cause the one or more processors to perform the method for obtaining elastic mechanical parameters of hard rock under eccentric loading as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed, cause the processor to perform a method for obtaining elastic mechanical parameters of hard rock under eccentric loading conditions as described in any one of claims 1 to 6.

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