Construction and application of rock strength and toughness property collaborative prediction model

Abstract

This invention relates to the construction and application of a collaborative prediction model for rock strength and toughness properties. Addressing the problems of size effect, single-parameter prediction limitations, and difficulties in cross-scale mapping in existing rock strength and toughness parameter testing technologies, the following key technical solutions are proposed: constructing a model that includes geometric parameters (L / W / S / B) and crack characteristics (…). a 0 / Δ a fic ), particle size parameters ( g av A dataset with 9-dimensional multi-source heterogeneous features, including Whale Optimization (WOA), is used to adaptively optimize the learning rate and hidden layer nodes of a Radial Basis Function Neural Network (RBFNN) to establish... f t - K IC A two-parameter synchronous prediction model. This model reveals the virtual crack propagation (Δ) through SHAP interpretability analysis. a fic ) and average particle size ( g av ) is the key controlling variable, for f t and K IC The predictive determination coefficient ( R ²) Reaching 0.997 and 0.996 respectively, it breaks through the limitation of small sample size effect and realizes cross-scale mapping from laboratory parameters to engineering scale, providing efficient and accurate technical support for the stability assessment of deep rock mass engineering.

Description

Technical Field

[0001] This invention relates to the field of civil engineering technology, and in particular to the construction and application of a collaborative prediction model for rock strength and toughness properties. Background Technology

[0002] Rocks, as naturally formed heterogeneous multiphase complex geological bodies, contain numerous randomly distributed defects within them. Tensile strength (f) t ) and fracture toughness (K IC Strength and toughness parameters are core material parameters for evaluating the mechanical properties of rocks and predicting the stability of engineering structures. However, accurately determining the strength and toughness parameters of rocks through experimental methods faces many challenges:

[0003] 1. Significant size and shape effects: The strength or toughness parameters measured by small-sized specimens commonly used in the laboratory are strongly affected by the physical size (height W, etc.) and shape of the specimens. The results are difficult to reflect the essential properties of rock materials, making the test results unsuitable for direct application to actual engineering scales.

[0004] 2. Inconsistent testing standards and separate parameters: Existing rock strength and toughness parameter testing standards (involving specimen type, loading fixtures, loading methods, and testing systems, etc.) Figure 1 , Figure 2 (As shown) there are differences, and f is usually not possible to obtain simultaneously in the same experiment. t With K IC Two key parameters. This leads to a cumbersome, inefficient, and costly testing process.

[0005] 3. Complex influencing factors and poor comparability of results: The test results are affected by a combination of factors such as sample size, shape, loading conditions, initial crack geometry (such as initial crack length a0), rock heterogeneity, and discontinuous fracture characteristics, making it difficult to effectively compare test data between different studies or laboratories.

[0006] 4. Limitations of existing theoretical models:

[0007] ① Size effect model (SEM): Early studies (such as...) Studies on concrete-like materials mainly focus on the influence of the physical dimensions (height W) of the specimen on the fracture behavior. The empirical formula (such as Equation (1)) is only applicable to geometrically similar specimens, and does not consider the initial crack length a0, the fracture process zone (FPZ), and the crack tip effect. Furthermore, the intrinsic parameter K of the material cannot be directly determined. IC and f t (See Table 1).

[0008] ② Boundary Effect Model (BEM): This theoretical model (its core formula is shown in equation (3)) assumes that the size effect originates from the interaction between the fracture process zone and the sample boundary, and explicitly considers the initial crack a0, the sample boundary, and the heterogeneity of the rock (by using the virtual crack propagation amount Δa). fic With average particle size g av And the correlation of discrete parameter β). The advancement of BEM lies in its provision of an analytical framework, which theoretically allows K to be directly determined through fitting fracture test data. IC and f t However, this method still heavily relies on a large amount of high-quality experimental data, has stringent requirements for experimental conditions, and its practicality is limited (see Table 1).

[0009] Table 1 Comparison between the size effect model and the boundary effect model

[0010]

[0011] 5. Limitations of single-parameter intelligent prediction methods: In recent years, intelligent algorithms such as machine learning (e.g., Artificial Neural Networks (ANN), Decision Trees, Random Forests, Fuzzy Inference Systems (FIS), Adaptive Neuro-Fuzzy Inference Systems (ANFIS), etc.) have been applied to rock fracture mechanics research, successfully predicting single parameters (e.g., fracture toughness K in Mode I). IC (Mixed-mode fracture toughness or Brazilian tensile strength BTS). Although these methods show certain accuracy advantages in single-parameter prediction, they still fail to break through the framework of single-parameter prediction and cannot achieve f t With K IC The synergistic prediction of these two key toughness parameters, and the modeling of them often does not delve into or effectively eliminate the effects of size.

[0012] In summary, existing rock strength and toughness parameter testing and prediction technologies generally suffer from core shortcomings such as significant size effect interference, low testing efficiency, fragmented parameter acquisition, and model dependence requiring high-level experiments or only capable of single-parameter prediction. Therefore, there is an urgent need to develop a method that can efficiently, accurately, and simultaneously predict the tensile strength f of rocks. t With fracture toughness K IC This method can effectively overcome or verify the effects of size effects, thus serving as an innovative approach for predicting engineering scale.

[0013] The information disclosed in this background section is intended only to enhance the understanding of the background technology of this disclosure and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0014] This invention addresses the technical problems in existing rock strength and toughness parameter testing, such as size effect, limitations of single-parameter prediction, and difficulties in cross-scale mapping. It employs a key technique of constructing a 9-dimensional multi-source heterogeneous feature dataset including geometric parameters, crack features, and grain size parameters, combined with the Whale Optimization Algorithm (WOA) to optimize the parameters of the Radial Basis Function Neural Network (RBFNN), thereby achieving tensile strength (f... t ) and fracture toughness (K IC The system provides high-precision collaborative prediction and reveals through SHAP analysis that virtual crack propagation and average particle size are the key controlling variables, thus solving the size effect problem of small sample parameters. At the same time, it establishes a full curve prediction model for structural failure and peak load at the engineering scale, which significantly improves the efficiency and accuracy of rock mass engineering stability assessment.

[0015] According to one aspect of this disclosure, a method for constructing a synergistic prediction model for rock strength and toughness is provided, comprising the following steps:

[0016] S1. Construct a multidimensional feature dataset: Collect geometric parameters, crack feature parameters, grain size parameters, loading mode parameters, and equivalent structural parameters of rock samples to form a heterogeneous feature dataset containing at least 5 dimensions;

[0017] S2. Establish an optimized neural network model: Use a radial basis function neural network (RBFNN) tuned by an intelligent optimization algorithm as the core prediction architecture;

[0018] S3. Adaptive Parameter Optimization: At least one hyperparameter of the RBFNN is iteratively optimized using the Whale Optimization Algorithm (WOA). The optimization process includes:

[0019] ① Generate a set of candidate parameters based on the current optimal solution;

[0020] ② Update positional parameters using a prey-encircling strategy;

[0021] ③ Update position parameters using a spiral bubble network attack strategy;

[0022] ④ Evaluate candidate parameters using network prediction error as the fitness function;

[0023] S4. Model Validation: The interpretability analysis framework is used to validate the importance of features, and the robustness of the model is tested after removing the size parameter.

[0024] In some embodiments of this disclosure, in step S1, the multidimensional feature dataset includes: sample length L, width W, thickness S, height B, initial crack length a0, and virtual crack propagation Δa. fic Average particle size (g) av Loading mode LM and equivalent crack length a e .

[0025] In some embodiments of this disclosure, the network hyperparameters optimized in step S3 include at least one of the following: radial basis function width parameter, learning rate, and number of hidden layer nodes.

[0026] In some embodiments of this disclosure, the optimization process of the whale optimization algorithm includes:

[0027] a. Initialize the whale population parameters, setting the population size to 20, the maximum number of iterations to 20, and the parameter boundaries to [0.00001, 3];

[0028] b. Calculate the individual fitness value based on the fitness function, which is the reciprocal of the model prediction error;

[0029] c. Update the whale's position using a prey encirclement strategy and a spiral bubble net attack strategy. When the random number P < 0.5, update the position using the following formula:

[0030] X(t+1) = X*(t) - A×D;

[0031] When P ≥ 0.5, the position is updated using the following formula:

[0032] X(t+1)=D'.ebl(cos(2πl)+sin(2πl))+X*(t);

[0033] Where X(t+1) represents the updated position vector of the individual whale; X * (t) The distance vector between the current whale individual and the whale in the best position, A is the coefficient vector used to control the individual's exploration and development behavior; D is the distance between the individual and the optimal solution; the constant coefficient b determines the spiral shape when the whale individual spirals forward. When b is 1, it is a normal logarithmic spiral, and l is a random number between [-1, 1].

[0034] d. After iterating to the maximum number of times, output the optimal number of hidden layer nodes and learning rate parameters.

[0035] In some embodiments of this disclosure, the interpretability analysis in step S4 employs the SHAP framework, which quantifies the contribution of each parameter to the prediction result through feature attribution.

[0036] According to another aspect of this disclosure, a method for synergistic prediction of rock strength and toughness properties is provided, comprising the following steps:

[0037] (1) Obtain heterogeneous characteristic data of the rock sample to be tested, the data including at least three types of parameters among geometric parameters, crack characteristic parameters, grain size parameters, loading mode parameters and equivalent structural parameters;

[0038] (2) Input the feature data into the collaborative prediction model constructed by the above method, and output the tensile strength f. t and fracture toughness K IC The predicted value;

[0039] (3) Based on the predicted values, construct the full curve of failure and peak load prediction model of large-size rock structures to realize cross-scale mapping of small sample parameters to engineering scale.

[0040] In some embodiments of this disclosure, the cross-scale mapping is implemented in the following ways:

[0041] ①f based on synchronous prediction t and K IC Parameters are used to establish the structural failure evolution equation;

[0042] ② Calculate the stress distribution of rock structures at the engineering scale using the finite element method or analytical formulas;

[0043] ③ Combine the failure evolution equation to predict the peak load and the curve of the complete failure process of the structure.

[0044] Through innovation in its technical solution, this invention achieves the following significant technical effects:

[0045] 1. Breakthrough in the synergistic prediction of strength and toughness parameters: Constructing a system that includes geometric parameters (L / W / S / B) and crack features (a0 / Δa) fic ), particle size parameter (g) av A dataset with 9-dimensional multi-source heterogeneous features, including Whale Optimization (WOA), was used to adaptively optimize the Radial Basis Function Neural Network (RBFNN), and for the first time, f was established. t -K IC A two-parameter synchronous prediction model. The model has been validated and is effective for f. t With K IC The predictive determination coefficient (R) 2 The parameters achieved are 0.997 and 0.996 respectively, breaking through the limitations of traditional single-parameter prediction and significantly improving the efficiency of parameter acquisition.

[0046] 2. Verification of the size-free effect theory: Based on the SHAP interpretability analysis framework, the virtual crack propagation amount (Δa) is revealed. fic ) and average particle size (g av The key controlling variables for the evolution of toughness parameters are the sample size parameters (L / W / S / B), while the cumulative influence of these parameters is negligible. The model maintains high-precision predictive performance even after removing these size parameters, providing quantitative verification for the theory of size-effect-free small-scale samples and solving the parameter distortion problem caused by size effects in traditional experiments.

[0047] 3. Support for Cross-Scale Engineering Applications: Based on the dual-parameter prediction results, a full-curve failure prediction model and peak load prediction model for large-scale rock structures are constructed, realizing cross-scale mapping of parameters from small laboratory samples to engineering scales. This model provides a theoretical breakthrough for stability assessment and disaster prevention in deep rock mass engineering. For example, in tunnel excavation and underground storage construction, it can quickly predict structural failure behavior and optimize design parameters, reducing testing costs and time.

[0048] 4. Algorithm Optimization and Enhanced Generalization Ability: The WOA algorithm is used to globally optimize the learning rate and hidden layer nodes of the RBFNN, avoiding the problem of traditional neural networks easily getting trapped in local optima, and significantly improving the model's convergence speed and generalization ability. Validated on multiple sets of rock samples, the model's adaptability to different loading modes (LM) and crack morphologies is superior to single machine learning methods, providing a reliable tool for parameter prediction under complex working conditions. Attached Figure Description

[0049] Figure 1 This is a schematic diagram illustrating the principles of some existing traditional fracture toughness testing methods.

[0050] Figure 2 This is a schematic diagram illustrating the principles of some existing traditional strength testing methods.

[0051] Figure 3 These are scanning electron microscope (SEM) images of granite with three different grain sizes used in the test specimens in this application.

[0052] Figure 4 The embodiments of this application include a three-point bending load and acoustic emission test of a granite beam specimen; wherein, (a) the test loading device and acoustic emission device; (b) the beam specimen loading method; and (c) the beam specimen failure.

[0053] Figure 5 This is a graph showing the relationship between acoustic emission energy, stress, and time in the acoustic emission test of the specimen in the embodiments of this disclosure.

[0054] Figure 6 This is a graph showing the relationship between acoustic emission ring count, stress, and time in the acoustic emission test of the specimen in this embodiment of the present disclosure.

[0055] Figure 7 This is a data distribution range diagram of the dataset collected in the embodiments of this disclosure.

[0056] Figure 8 This is a Pearsons correlation matrix diagram in an embodiment of this disclosure.

[0057] Figure 9 This is a schematic diagram of the RBFNN structure involved in the embodiments of this disclosure.

[0058] Figure 10This is a schematic diagram of the structure of the collaborative prediction model for rock strength and toughness in an embodiment of this disclosure.

[0059] Figure 11 For each feature variable in the embodiments of this disclosure, the model predicts f. t A SHAP analysis chart of contribution and influence.

[0060] Figure 12 For each feature variable in the embodiments of this disclosure, the model predicts K. IC A SHAP analysis chart of contribution and influence.

[0061] Figure 13 The model prediction result f in the embodiments of this disclosure t (above) and K IC (Below) Comparison chart with actual training and test set data.

[0062] Figure 14 The figures shown are the fracture failure curves and peak load prediction curves predicted by the model based on literature data in this embodiment of the present disclosure.

[0063] Figure 15 The model in this embodiment predicts the fracture failure curve and peak value prediction curve for the experimental data in this example. Detailed Implementation

[0064] To better understand the technical solution of this application, the above technical solution will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0065] Example 1: Construction of a Synergistic Prediction Model for Rock Strength and Toughness Properties

[0066] (I) Experimental setup and parameter acquisition

[0067] 1. Study on Three-Point Bending Test of Granite Beam Components

[0068] The rocks used in the experiment were all granite. To reduce experimental error, rock samples of the same grain size were taken from the same granite specimen, based on SEM images (…). Figure 3 The average grain size of the three granite specimens used in the experiment was observed to be approximately 2.2 mm, 4.6 mm and 5.9 mm, which are defined in the example as fine-grained, medium-grained and coarse-grained.

[0069] During the preparation of precast notched three-point bending beam specimens, the procedures recommended by ASTM were strictly followed, and the geometric parameters of the prepared beam specimens were recorded (Table 2). Three-point bending fracture tests were conducted using an MTS E45.105 electronic universal testing machine. Figure 4The fracture toughness of granite with three different grain sizes was tested, and the strength parameters were obtained by linear fitting of the boundary effect (Table 2). Acoustic emission monitoring method was used to study the acoustic emission activity during the rock deformation process.

[0070] Table 2 Geometric parameters and strength / toughness parameters of beam specimens

[0071]

[0072] This example introduces the design method of J. Guan et al. to describe the virtual crack propagation Δa. fic With particle size g av The quantitative relationship. Virtual crack propagation Δa fic This refers to the nonlinear crack propagation region present at the initial crack tip of a specimen under laboratory conditions, where the crack only expands to a size of a few aggregate pieces under peak load. Its expression is:

[0073] Δa fic =β.g av (4).

[0074] Since the crack propagates along the height of the specimen towards the point of force application, the value of the aggregate propagation amount β is related to the ligament height W-a0 of the specimen, and its value is defined as:

[0075]

[0076] 2. Acoustic emission monitoring of rock crack characteristics and damage deformation

[0077] Acoustic emission technology enables visualization of rock cracks, reflecting the crack initiation and propagation process in real time, and monitoring damage and deformation. Figure 5 The acoustic emission energies of coarse-grained, medium-grained, and fine-grained granite beam specimens with a length of 340 mm were revealed: the initial energies were all low, and the energy increased sharply when the stress dropped (reaching the peak strength); the energy fluctuated during the linear load stage, indicating internal crack activity; the energy increased sharply during the peak load, which was sudden, the main fracture surface was formed, and the rock specimen underwent brittle fracture failure (crack initiation, propagation, and fracture process), with poor toughness; and the smaller the particles, the earlier the energy peak appeared, because there were more particles, more contact points, faster stress transmission, and obvious concentration, and smaller particles were more likely to reach the strength limit.

[0078] Ringing count quantifies acoustic emission activity; the higher the value, the more frequent the events. Figure 6The results show that in the initial stage of loading, the ringing count of the fractured rock sample is low, due to fracture closure and the initiation of new fractures. As loading continues, micro-fractures are irregularly generated, and the ringing count intermittently increases. When the pre-peak stress suddenly drops, the count increases sharply before recovering. When the crack develops to the peak load, the count increases dramatically in a short period of time, and as the stress reaches its peak, the main crack extends, leading to failure. The smaller the granite grains, the lower the ringing count at peak stress, because it is easier to form a small number of main cracks, which extend rapidly and result in fewer failures. This phenomenon reveals the correlation between acoustic emission and grain size.

[0079] Both energy and ring count increase with increasing stress, and both increase sharply near the failure point, indicating that internal cracks in the rock are propagating at an accelerated rate. Figure 4 The main crack formed after the fracture in (c) indicates that the rock sample has undergone tensile failure.

[0080] (II) Data Collection, Analysis and Preprocessing

[0081] 1. Multivariate data collection

[0082] A total of 283 sets of data were collected from existing literature and 18 sets of data obtained from the above experiments. These data sets are diverse and representative (see Table 3). Figure 7 In addition to the eight geometric parameters in the aforementioned experimental data, the loading method LM was added, comprehensively considering nine parameters that affect strength and toughness.

[0083] Table 3 Descriptive statistics of the dataset

[0084]

[0085] 2. Reliability assessment of multivariate datasets

[0086] To assess the reliability, accuracy, and validity of the multivariate dataset, reliability and validity analyses were performed. Alpha > 0.7 indicates good consistency of the data, and KMO > 0.6 indicates good correlation of the data (see Table 4).

[0087] Table 4 Reliability and Validity Analysis

[0088]

[0089] To gain a deeper understanding of the interactions between all input and output features in the dataset, we performed feature correlation analysis. The Pearson correlation coefficient is calculated using the following formula:

[0090]

[0091] from Figure 8 It can be observed that the virtual crack propagation amount Δa fic With average particle size gav The correlation coefficient between them is 0.417, showing a significant positive correlation. This is consistent with the inclusion of average particle size in the fracture model in the boundary effect, which links average particle size with virtual crack propagation. It also corroborates the Δa described in [the original text]. fic With g av The scientific validity and practicality of quantitative relationship methods.

[0092] 3. Technical Challenges and Countermeasures

[0093] (1) Technical difficulties

[0094] The dataset used in this example exhibits imbalance, with a large proportion of data on rock fractures under three-point bending loading and a relatively small proportion under four-point bending loading. This imbalance in data distribution presents the following challenges when using machine learning methods to study rock fracture behavior:

[0095] ①Class imbalance: During training, machine learning models may tend to predict the class with a larger proportion of classes, while learning too little about the minority classes;

[0096] ② Overfitting problem: The dataset contains a large number of sample parameters of the same size. The model may overfit these large proportions of data, resulting in a decrease in generalization ability when faced with unseen data.

[0097] ③ Prediction bias: The model may bias the sample that accounts for a large proportion of the dataset, thus failing to represent the true situation of the entire data distribution;

[0098] ④ Uneven resource allocation: The model may spend more time and computing resources processing the larger proportion of data, rather than learning all categories evenly.

[0099] (2) Coping strategies

[0100] ① Data cleaning: Remove similar fracture parameters;

[0101] ② Linear normalization: The data is linearly normalized to the [0,1] interval to ensure that the influence of all features on model training is on the same order of magnitude, thus accelerating the convergence of the algorithm.

[0102] ③Class weight adjustment: By using the loss function, higher weights are assigned to the minority class to improve the model's prediction of the minority class.

[0103] (III) Establishment of a Synergistic Prediction Model for Rock Strength and Toughness Properties

[0104] 1. WOA-RBFNN

[0105] Using traditional radial basis neural networks (RBFNN) (such asFigure 9 When performing data prediction, an inappropriate width parameter of the radial basis function can lead to overfitting, thereby reducing the model's generalization ability. To overcome this problem, this example uses the Whale Optimization Algorithm (WOA) to optimize the width parameter. WOA is an efficient metaheuristic algorithm that simulates the social behavior and hunting strategies of whales. According to the rules of the WOA algorithm, whales update their position based on the leader's position (the current optimal width parameter). This includes two main predation strategies: surrounding prey (when p < 0.5) and spiral bubble web attack (when p ≥ 0.5).

[0106] During the prey-surrounding phase, whales update their position using formula (7):

[0107] X(t +1) = X * (t) — A × D (7);

[0108] During a spiral bubble attack, whales form a spiral shape around the leader and update their position using formula (8):

[0109] X (t + 1) = D'. ebl (cos (2πl) + sin (2πl)) + X *(t) (8).

[0110] For each whale's position, which is a specific width parameter value, the fitness value is calculated using the objective tuning function. If the current whale's fitness value is better than the current leader's fitness value, i.e., a lower network prediction error, then the optimal position and optimal fitness value are updated.

[0111] By optimizing the width parameter of the radial basis function neural network using WOA, the following improvements were achieved:

[0112] ① The optimized width parameter significantly reduces the prediction error of RBFNN on both the training and test sets, improving the model's prediction accuracy; ② By finding the optimal width parameter, WOA helps the network better adapt to data features and reduces the risk of overfitting; ③ The optimized network performs more robustly on new data, demonstrating better generalization ability.

[0113] Radial basis function neural networks (RBFNNs) possess powerful nonlinear approximation capabilities, simple structure, and ease of training. However, their performance is highly dependent on the selection of network parameters, resulting in poor interpretability. Therefore, this invention introduces the Whale Algorithm (WOA) to optimize the learning rate and hidden layer nodes of the RBFNN, seeking the optimal parameters to improve the network's prediction accuracy and generalization ability.

[0114] (iv) Interpretability analysis of the collaborative prediction model

[0115] Machine learning algorithms, when efficiently simulating complex nonlinear relationships among multiple variables, inevitably face the following problems: ① Can variables be simplified to save computation time? ② Potential correlations between variables lead to redundancy. ③ Some variables contribute little or no to the results.

[0116] This example uses feature engineering to optimize variables and combines boundary effect theory to capture important properties related to rock fracture behavior.

[0117] 1. Prior multiple linear regression analysis

[0118] This example first uses multiple linear regression analysis to study the causal relationship between variables, clearly obtaining the influence of each input parameter on the toughness performance (Tables 5 and 6), and then uses the standardized regression coefficient β to describe the relationship between each parameter and f. t or K IC The strength of the association.

[0119] Table 5 Impact of f t Factor analysis

[0120]

[0121] Table 6 Influence of K IC Factor analysis

[0122]

[0123] Linear regression analysis shows that it can simultaneously affect f t and K IC The characteristic parameters are L and g av , Δa fic and LM, where g av For f t and K IC The effects are positive (β = 0.979 and β = 0.545), Δa fic For f t and K IC The effects are negative (β = -0.979 and β = -0.18). In the boundary effect model (BEM), considering the heterogeneity of the sample, the aggregate particle size g av It is considered an important parameter. In addition, the virtual crack propagation amount Δa fic Related to aggregate size and parameter β, it reflects the peak load P max The discontinuous crack propagation behavior under [condition]. Therefore, these two parameters affect f. t and K IC It has a significant impact.

[0124] 2. Post-event SHAP explanation

[0125] To further determine how the WOA-RBFNN model makes accurate predictions, we employ the ex post-interpretive Shapley regression method to assess the importance of features in a linear model, particularly in cases of feature multicollinearity. It assigns importance values ​​to each feature by comparing the differences in predictions between models including and excluding a particular feature. This is achieved by comparing predictions across all feature subsets and taking a weighted average. In short, it quantifies the contribution of each feature x = (x1, x2, ..., xn) to the model prediction f(x). The Shapley value is expressed as:

[0126]

[0127] based on Figure 11 , Figure 12 The SHAP analysis results can identify features that significantly influence the model's prediction results. For the model prediction f... t Key features include Δa fic g av a e B and its contribution values ​​are 4.51, 1, 0.7, and 0.21, respectively. As for the model's prediction of K... IC The important feature is Δa fic B, LM and g av Their contributions were 3.12, 1.15, 0.48, and 0.26, respectively. Whether explained by ex-ante multiple linear regression analysis or ex-post Shap value interpretation, Δa... fic and g av It showed a significant impact in both predictions.

[0128] The thickness B of the specimen directly affects the stress field and the size of the plastic zone near the crack tip, which in turn affects the stress state and distribution of the specimen under stress, thus affecting the fracture toughness and tensile strength of the rock.

[0129] Δa fic This reflects the accumulated plastic deformation capacity of the rock during loading. In boundary effects, the plastic deformation of the rock tends to concentrate in the boundary region, leading to stress redistribution and affecting the overall tensile behavior. Higher accumulated plastic strain causes the rock to consume more energy during crack propagation, thereby improving its fracture resistance. Larger grain size leads to more significant stress concentration in the boundary region, indirectly modulating the resistance to crack propagation, thus affecting crack initiation and propagation, and consequently affecting fracture toughness and tensile strength. Therefore, combined with boundary effect analysis, Δa fic and g av By influencing stress distribution, crack propagation, and energy dissipation mechanisms within the rock, it significantly affects tensile and fracture behavior.

[0130] 3. Analysis of Prediction Results

[0131] This example uses multiple statistical metrics to evaluate the performance of the WOA-RBFNN model, including the coefficient of determination (R²). 2 The four main indicators are: Mean Absolute Error (MAE), Mean Bias Error (MBE), Root Mean Square Error (RMSE), and Mean Square Error (MSE). The specific calculation methods for these indicators are as follows:

[0132]

[0133] As shown in Table 7, the model's accuracy remains almost unaffected when the characteristics of the specimen, such as length L, width W, thickness B, span S, and initial crack length a0, are completely disregarded. This result provides a theoretical basis for determining size-independent material parameters from small-sized specimens in boundary effects. Table 8 demonstrates that the WOA-RBFNN model constructed in this example can accurately and efficiently predict the strength and toughness properties of rocks.

[0134] Table 7 Model Prediction Results

[0135]

[0136] Table 8 Comparison of Model Predictions and Actual Values

[0137]

[0138] exist Figure 13 The image shows a comparison between the prediction results of the WOA-RBFNN model and the actual values, demonstrating the model's extremely high accuracy.

[0139] This invention successfully constructed a collaborative prediction model for rock strength and toughness parameters based on WOA-RBFNN, and verified the accuracy and reliability of the model through experimental data. Based on this, fracture full curves and peak load prediction curves for large-scale rock structures were established. The main conclusions are as follows:

[0140] (1) In physical experiments, the testing methods for tensile strength and fracture toughness of rocks are not uniform, making it difficult to compare experimental results and consuming a lot of time and effort. The model of this invention can predict strength and toughness parameters at the same time, saving a lot of manpower and resources.

[0141] (2) Only when the sample size is at least greater than 1500 mm can size-free material parameters be obtained. However, in traditional physical experiments, the size of rock samples is limited by laboratory conditions, making it impossible to avoid size effects. The WOA-RBFNN model method used in this invention verifies the size-free material parameters through feature selection. t and K IC These are real material parameters that are independent of size.

[0142] (3) Traditional empirical formulas can only consider a limited number of factors. This invention considers nine characteristic parameters and discovers the virtual crack propagation amount Δa. fic and average grain size of rock g av The size of the specimen has the greatest impact on the prediction results, while the size of the specimen has a smaller impact on the prediction results, providing a basis for determining the size-free material parameters from small-sized specimens in the boundary effect theory.

[0143] (4) The WOA-RBFNN model used in this invention has high prediction accuracy. The coefficient of determination, mean absolute error, mean deviation error, root mean square error and mean square error all perform very well, indicating that the model can effectively predict the strength and toughness parameters of rocks.

[0144] (5) Based on the fracture parameters predicted by the WOA-RBFNN model, a complete design curve describing structural failure can be established, and the actual structural failure can be predicted through the peak load prediction curve. t and K IC The peak load and other parameters verified the accuracy and practicality of the model, providing an efficient and accurate solution for predicting the fracture behavior of engineering structures.

[0145] Although some preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0146] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of its inventive concept. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for constructing a synergistic prediction model for rock strength and toughness, characterized in that, Includes the following steps: S1. Construct a multidimensional feature dataset: Collect geometric parameters, fracture feature parameters, grain size parameters, loading mode parameters, and equivalent fracture lengths of rock samples. a e This forms a heterogeneous feature dataset containing at least five dimensions; S2. Establish an optimized neural network model: The radial basis function neural network (RBFNN) tuned by the whale optimization algorithm is used as the core prediction architecture; S3. Adaptive Parameter Optimization: The Whale Optimization (WOA) algorithm is used to iteratively optimize at least one hyperparameter of the RBFNN to output tensile strength. f t and fracture toughness K IC The predicted value and optimization process include: ① Initialize the whale population and the hyperparameters of the RBFNN as position vectors. During the iteration process, combine the position of the best individual in the current population with the global population information to iteratively update and generate and update the candidate hyperparameter set. ② Update the individual whale position parameters by using a prey-surrounding strategy; ③ Update the individual whale position parameters using a spiral bubble web attack strategy; ④ Using the RBFNN to measure tensile strength f t and fracture toughness K IC The reciprocal of the prediction error is used as the fitness function to evaluate candidate hyperparameters, and the optimal individual position is updated based on the evaluation results; S4. Model Validation: The SHAP interpretability analysis framework is used to validate the importance of each input feature. f t and K IC The contribution of the prediction results was evaluated, and the robustness of the model's prediction performance was tested after removing the sample size characteristic parameters, in order to verify that the model can eliminate the influence of size effect.

2. The construction method according to claim 1, characterized in that, In S1, the multidimensional feature dataset includes: sample length L ,width W ,thickness S ,high B Initial crack length a 0. Virtual crack propagation Δ a fic Average particle size g av Loading mode LM and equivalent crack length a e The loading mode LM is a discrete variable representing different loading methods, and it uses integer encoding to distinguish between three-point bending loading and four-point bending loading.

3. The construction method according to claim 1, characterized in that, The optimized network hyperparameters in S3 include at least one of the following: radial basis function width parameter, learning rate, and number of hidden layer nodes.

4. The construction method according to claim 1, characterized in that, The optimization process of the whale optimization algorithm includes: a. Initialize the whale population parameters, setting the population size to 20, the maximum number of iterations to 20, and the parameter boundaries to [0.00001, 3]; b. Calculate the individual fitness value based on the fitness function, which is the reciprocal of the model prediction error; c. Update the whale's position using both the prey encirclement strategy and the spiral bubble net attack strategy. When the random number P < 0.5, the prey encirclement strategy is adopted, following the... X ( t +1) = X * ( t ) - A × D Update position; when P≥0.5, adopt the spiral bubble net attack strategy, according to X ( t +1) = D' . e bl (cos (2π l )+ sin (2π l ))+ X *( t Update location; in, X(t+ 1 ) This represents the updated position vector of an individual whale. X * (t) The distance vector between the current individual whale and the whale in the optimal position. A This is a coefficient vector used to control an individual's exploration and development behavior; D The distance between the individual and the optimal solution; b The constant for defining the spiral shape is set to 1. l It is a random number between [-1, 1]; d. After iterating to the maximum number of times, output the optimal number of hidden layer nodes and learning rate parameters.

5. The construction method according to claim 1, characterized in that, The SHAP interpretability analysis in S4 employs the SHAP framework, quantifying the relationship between parameters by calculating the Shapley value for each feature. f t and K IC The contribution of the prediction results.

6. A method for synergistic prediction of rock strength and toughness properties, characterized in that, Includes the following steps: (1) Obtain heterogeneous characteristic data of the rock sample to be tested, the data including at least three types of parameters among geometric parameters, crack characteristic parameters, grain size parameters, loading mode parameters and equivalent crack length parameters; (2) Input the feature data into the collaborative prediction model constructed according to any one of claims 1-5, and output the tensile strength. f t and fracture toughness K IC The predicted value; (3) Based on the predicted values, construct the full curve of failure and peak load prediction model of large-size rock structure to realize cross-scale mapping of small sample parameters to engineering scale.

7. The method for synergistic prediction of rock strength and toughness properties according to claim 6, characterized in that, The cross-scale mapping in step (3) is achieved in the following way: ① Based on synchronous prediction f t and K IC Based on parameters and fracture mechanics theory, a structural failure evolution equation is established to describe the propagation and failure evolution of structural cracks. ②Use the finite element method or analytical formulas to... f t and K IC The parameters are used as material constitutive inputs to calculate the stress distribution of rock structures at the engineering scale under loading conditions; ③ Combining the stress distribution and structural failure evolution equations, the load-displacement relationship of the structure from loading to complete failure is calculated through numerical simulation, thereby predicting the peak load and the curve of the complete failure process.

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