Quantitative characterization method for rock mass joint contact behavior based on ultrasonic excitation

Abstract

The invention discloses a rock mass joint contact behavior quantitative characterization method based on ultrasonic excitation. The method comprises the following steps: establishing a response equation of joint points in elastic waves and line segments; simulating the propagation process of elastic waves in the line segment based on the response equation, obtaining elastic wave joint point response data, and forming a waveform data set; enhancing the waveform data set, and dividing the enhanced data set into a training set and a test set according to a ratio of 7: 3; constructing a joint point detection convolutional neural network model in the line segment and training the joint point detection convolutional neural network model; the method comprises the following steps: manufacturing a rock sample with a joint surface, exciting the sample, and collecting response waveform data; preprocessing the response waveform data; interpolating the preprocessed response waveform data, and detecting the interpolated response waveform data by using a joint point detection convolutional neural network model in the trained line segment to obtain the position of a joint point so as to reconstruct the geometric shape of the joint; and calculating the spatial distribution of the joint stiffness along the geometrical shape of the joint to realize quantitative characterization of the joint contact behavior.

Description

Technical Field

[0001] The invention relates to the technical field of rock mass engineering, and in particular to a method for quantitatively characterizing contact behavior of rock mass joints based on ultrasonic excitation. Background Art

[0002] To reduce the risk of rock slope instability disasters, minimize the economic losses and casualties caused by disasters, meet the requirements of safe and efficient engineering construction, and better serve national strategic development, in-depth research on the mechanical behavior of rock masses is necessary. Extensive engineering experience shows that rock slope stability is primarily controlled by the deformation and strength characteristics of joint surfaces. Rock slope instability failure typically occurs by sliding along existing joint surfaces, followed by joint expansion and penetration to form fracture surfaces of varying scales. Therefore, the contact behavior of joint surfaces is a key research topic in rock slope stability analysis and evaluation.

[0003] The nonlinear characteristics of the mechanical response of joint surfaces arise from the interaction of multiple factors: first, the uneven undulations and local contact differences at the contact interface; second, the elastic deformation and progressive damage of undulating elements during loading. This nonlinearity is evident in both normal and tangential mechanical behavior. Given the combined influence of factors such as joint scale parameters, surface morphology, friction characteristics, rock mechanical properties, stress state, and slip rate, constructing an accurate contact mechanics model has become a key scientific issue in the study of rock mechanical properties. To address this challenge, Goodman innovatively proposed a dual-parameter system of tangential and normal stiffness, which quantitatively characterizes the deformation response of joint surfaces under external loads and provides a theoretical basis for the mechanical modeling of complex joint topological behavior. Furthermore, the heterogeneity and anisotropy of joint surface morphology not only lead to differences in contact state and deformation behavior at different locations on the joint surface, but can also cause local failure at the joint surface before overall shear slip, generating precursor signals. Therefore, detecting the dynamic evolution of joint stiffness distribution and using it as a precursor signal can predict shear failure of rock joints at a macroscale. However, traditional joint stiffness measurements cannot characterize the local variability of joint surfaces and do not provide information on the micromechanics of joint deformation and local shear failure. Summary of the Invention

[0004] In order to solve the above technical problems, the purpose of the present invention is to provide a method for quantitative characterization of rock joint contact behavior based on ultrasonic excitation, which can achieve quantitative characterization of the spatial distribution of joint contact behavior.

[0005] The present invention provides a method for quantitatively characterizing the contact behavior of rock joints based on ultrasonic excitation, comprising the following steps:

[0006] Step 1: Establish the response equations of elastic waves and joint points in the line segment;

[0007] Step 2: Based on the response equation, simulate the propagation process of elastic waves in the line segment, obtain the elastic wave joint point response data, and form a waveform data set;

[0008] Step 3: Use random cropping to crop the data in the waveform dataset to enhance the dataset, and divide the enhanced dataset into a training set and a test set with a ratio of 7:3;

[0009] Step 4: Construct a convolutional neural network model for detecting joints in line segments;

[0010] Step 5: Input the training set into the convolutional neural network model for line segment joint detection to obtain a trained convolutional neural network model for line segment joint detection;

[0011] Step 6: Prepare a rock sample with joints, implement vibration excitation using a piezoelectric ceramic transducer, and obtain response waveform data using a 3D scanning laser Doppler vibrometer;

[0012] Step 7: Preprocess the response waveform data to convert the velocity wave field response waveform data into the quadratically differentiable displacement wave field response waveform data;

[0013] Step 8: Interpolate the preprocessed response waveform data to generate multiple one-dimensional waveform response sequences for lateral and vertical transmission. Use the trained joint recognition convolutional network model to perform feature recognition on the multiple sets of one-dimensional waveform response sequences, determine the coordinates of the crack points in the multiple sets of one-dimensional waveforms, and reconstruct the joint geometry.

[0014] Step 9: Calculate the spatial distribution of joint stiffness along the joint geometry to achieve quantitative characterization of joint contact behavior.

[0015] The present invention provides a method for quantitatively characterizing rock joint contact behavior based on ultrasonic excitation, which has at least the following beneficial effects:

[0016] Focusing on major disaster issues in mountainous rock slopes and deep underground engineering projects, this study conducts research on the response of rock joints under ultrasonic excitation, focusing on the quantitative characterization and dynamic monitoring of the spatial distribution of rock joint contact behavior. First, through theoretical analysis and numerical simulation, a systematic elastic wave-joint response analysis is carried out, and a rock joint response model under elastic wave action is established to clarify the joint response mechanism. This leads to a non-contact measurement method for the spatial distribution of joint stiffness based on active ultrasonic excitation, achieving quantitative characterization of the spatial distribution of rock joint contact state and deformation behavior. This provides a theoretical basis and support for the early identification and prediction of instability and failure of high-steep rock slopes in my country, which is of great scientific significance and engineering value. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1This is a flow chart of a method for quantitatively characterizing contact behavior of rock joints based on ultrasonic excitation according to the present invention;

[0018] Figure 2 It is a visualization of the simulation results of waveform propagation on a one-dimensional line segment;

[0019] Figure 3 Schematic diagram of the convolutional neural network model for detecting joints in line segments. DETAILED DESCRIPTION

[0020] like Figure 1 As shown, a method for quantitatively characterizing rock joint contact behavior based on ultrasonic excitation of the present invention includes the following steps:

[0021] Step 1: Establish the response equations of elastic waves and joints in the line segment. Specifically, based on the one-dimensional elastic wave equation, the crack points in the line segment are regarded as the elastic boundary between two solids, and the response equations of elastic waves and crack points in the line segment are established:

[0022]

[0023] f(x)∣ x＝a =0(2)

[0024]

[0025] Where (1) is the differential equation of one-dimensional elastic wave, and equations (2) and (3) define the boundary conditions of the line segment, where the starting point of the one-dimensional line segment is a and the end point is b, the displacement at end a is 0, and the load at end b is τ; c(x) represents the propagation velocity of the wave in the one-dimensional line segment, and equation (4) sets the c(x) value at the middle position of the line segment to be much smaller than that at other positions of the line segment, thereby realizing the definition of the crack point in the line segment. If there are multiple crack points in the line segment, c(x) is defined as a piecewise function; f(x) represents the amplitude of the one-dimensional elastic wave, ρ represents the rock density, and w represents the frequency.

[0026] Step 2: Based on the response equation, simulate the propagation process of elastic waves in the line segment, obtain the elastic wave joint point response data, and form a waveform data set, specifically:

[0027] Based on the response equation established in step 1, XLiFE++ software is used to simulate the propagation process of elastic waves on line segments with randomly distributed cracks, obtain elastic wave crack point response data, and form a waveform data set; the key programming statements include: defining the number and location of crack points, line segment length, material parameters, mesh division, response equation and boundary conditions, and visualizing the simulation results, such as Figure 2 As shown in the figure, the position circled by the rectangular box is the position of the joint point.

[0028] Step 3: Use random cropping operation to crop the data in the waveform dataset to enhance the dataset, and divide the enhanced dataset into training set and test set at a ratio of 7:3.

[0029] Step 4: Build a convolutional neural network model for detecting joints in line segments.

[0030] Based on a large number of waveform feature libraries generated by simulation, a convolutional network model for linear crack recognition is constructed based on the densely connected network architecture (DenseNet). Figure 3 As shown in the figure, the network framework includes: input layer, first convolutional layer, first pooling layer, multiple alternating dense blocks and transition layers, global average pooling and output layer.

[0031] The dense block realizes cross-layer reuse of waveform features and significantly improves the accuracy of joint surface recognition by enhancing the efficiency of feature flow. For the i-level dense block with input feature x0, the output x of the i-th layer is i satisfy:

[0032] x i =H i ([x1,x2,…,x i-1 ])(5)

[0033] Among them, [x0,x2,…,x i-1 ] is the concatenation of feature maps generated in layers 0 to i-1, H i Represents interconnected batch normalization. Normalizing the output signal accelerates network model convergence, reduces the number of training iterations, and ensures the reliability and stability of the network training process.

[0034] Dense topological connections lead to an increase in network parameters, and the transition layer improves training efficiency by compressing feature dimensions. The transition layer is composed of a second convolutional layer and a second pooling layer module.

[0035] Convolution extracts features from the input signal. Each convolution kernel is associated with a specific weight matrix, which is then weighted to generate the kernel's local feature response. The network utilizes a multi-core parallel computing mechanism. The second convolutional layer uses a 1×1 kernel size and a ReLU activation function to mitigate overfitting risks.

[0036] To reduce the computational load of the waveform data, the second pooling layer compresses the convolutional features, filtering out redundant data and preserving the integrity of key features. The second pooling layer applies a maximum sampling strategy, with a 2×2 sampling window. Through iterative convolution and downsampling, the high-dimensional features of the waveform signal are analyzed and their dimensions and size are compressed. Global mean pooling is then used to perform a mean operation on the feature map, converting the multidimensional features into a one-dimensional representation vector. This is then fed into a Softmax classifier to determine crack characteristics and output the crack location.

[0037] Step 5: Input the training set into the convolutional neural network model for line segment joint detection to obtain the trained convolutional neural network model for line segment joint detection. Specifically:

[0038] During the training process of the convolutional neural network model, the stochastic gradient descent (SGD) algorithm is used to iteratively optimize the network parameters. Based on the input sample X and its corresponding label Y, the parameters of the network model are continuously updated through the interaction between the two. The update formula is:

[0039]

[0040] Where η is the learning rate, J(θ; X; Y) is the objective function; θ J(θ; X; Y) is the gradient of the parameter θ. In order to quantify the difference between the probability distribution predicted by the model and the true distribution, the cross entropy loss function is selected as the evaluation criterion. The cross entropy loss function is as follows:

[0041] L(p,y)=-ylog(p)-(1-y)log(1-p)(7)

[0042] Here, y∈{0,1} is the sample label, and p is the probability of the corresponding category. A gradient descent algorithm is used to minimize the cross-entropy loss function. During this process, the algorithm intelligently adjusts the parameter values ​​based on the gradient information of the loss function with respect to the network parameters, aiming to gradually reduce the loss and drive the model toward the global optimal solution, thereby achieving joint detection and location.

[0043] Finally, the accuracy, sensitivity and specificity are used to evaluate the learning effect of the convolutional network model.

[0044] Step 6: Prepare a rock sample with joints, implement vibration excitation using a piezoelectric ceramic transducer, and obtain dynamic response waveform data using a 3D scanning laser Doppler vibrometer;

[0045] Specifically:

[0046] Step 6.1: Select a rock slab sample with a size of 0.96×0.3×0.03m and a density of 2750kg / m 3 , Poisson coefficient 0.23, elastic modulus 62.6GPa;

[0047] Step 6.2: A 3-cm-long notch was created in the middle of the bottom edge of the specimen to controllably expand the joint. The flat specimen was then fractured using a three-point bending method. Joint expansion was controlled by a closed-loop servo-hydraulic system, with the joint opening displacement as the feedback signal. Piezoelectric ceramic transducers were used for excitation, and waveform data of the in-plane joint expansion response during joint expansion was collected using a 3D scanning laser Doppler vibrometer.

[0048] Step 6.3: After the joints are fabricated, the specimen is unloaded and mounted on a fixture. Different axial forces are applied to the specimen. The joints under different axial stress states are excited using a piezoelectric ceramic transducer. At the same time, static joint response waveform data are collected using a 3D scanning laser Doppler vibrometer.

[0049] Step 7: Preprocess the response waveform data to convert the velocity wavefield response waveform data into the displacement wavefield response waveform data that is twice differentiable. Specifically:

[0050] Step 7.1: Input the response waveform data into a bandpass filter. This filter selects only the signal components that pass through the set frequency band, attenuating the interference components and noise in the out-of-band frequency band, and achieving spectrum matching with the 30kHz center frequency excitation waveform.

[0051] In specific implementation, the response waveform data may be the extended joint response waveform data obtained in step 6.2, or the static joint response waveform data obtained in step 6.3.

[0052] Step 7.2: Numerically integrate the response waveform data after bandpass filtering to obtain the corresponding displacement wavefield response waveform data. The displacement wavefield after integration is affected by the integration constant, so a high-pass filter with a cutoff frequency of 500 Hz is used to eliminate the influence of the integration constant.

[0053] Step 7.3: When using the displacement field to calculate the traction force on the joint surface, the displacement field on both sides of the joint surface needs to satisfy quadratic differentiability. The displacement field obtained by numerical integration is smooth and differentiable in time, but not in space. Therefore, the displacement field after numerical integration is smoothed.

[0054] In the specific implementation, the median filter and the mean filter are used to eliminate the pulse noise (low signal-to-noise ratio data points) in the response waveform data of the displacement wavefield. Then, the response waveform data of the filtered displacement wavefield are independently fitted by a one-dimensional Fourier expansion along the orthogonal coordinate axes to construct the response waveform data of the quadratically differentiable displacement wavefield.

[0055] Step 8: Interpolate and reconstruct the processed response waveform data to generate multiple sets of single-dimensional waveform response sequences for horizontal and vertical transmission. Use the trained crack recognition convolutional network model to perform scanning analysis on the multiple sets of single-dimensional waveform response sequences to determine the coordinates of the joint points and reconstruct the rock joint geometry. Specifically:

[0056] Step 8.1: Perform interpolation reconstruction on the response waveform data of the quadratically differentiable displacement wave field to generate multiple sets of single-dimensional waveform response sequences in the lateral and normal directions;

[0057] Step 8.2: Use the trained one-dimensional crack point identification convolutional network model to perform scanning analysis on the one-dimensional waveform response sequence of each row / column to determine the existence and spatial location of the crack point coordinates in each signal sequence;

[0058] Step 8.3: Summarize the detection results of each row and column of waveforms, and finally connect the joint points detected on adjacent waveforms to reconstruct the joint geometry.

[0059] Step 9: Calculate the spatial distribution of joint stiffness along the joint geometry to quantitatively characterize the joint contact behavior, specifically:

[0060] Step 9.1: Based on the response waveform data of the twice-differentiable displacement wave field, calculate the jump displacement on both sides of the joint, specifically:

[0061] Step 9.1.1: Measure the displacements (u) on both sides of the joint along the x and y directions. + x ,u + y ) and (u - x ,u - y ).

[0062] Step 9.1.2: Determine the normal and tangential orientations of each joint node based on the joint geometry. Analyze the displacement components along the normal and tangential directions on both sides of the joint using the following equations:

[0063]

[0064] Among them, u + s 、u - s Corresponding to the tangential displacement components on both sides of the joint, u + n 、u - n are the normal displacement components on both sides of the joint surface, and θ is the angle between the horizontal direction and the normal direction of the joint surface.

[0065] Step 9.1.3: The joint jump displacement can be calculated based on the difference between the piecewise smooth displacement wave fields on both sides of the joint. The jump displacement of the joint along the tangent direction is u + s -u - s , the jump displacement along the normal direction is u + n -u - n .

[0066] Step 9.2: Based on the response waveform data of the twice-differentiable displacement wave field, calculate the traction forces on both sides of the joint, specifically:

[0067] Step 9.2.1: According to the grid points divided into the specimen when measuring vibration by 3D scanning laser Doppler vibrometer, obtain the coordinates of the grid points around the joints, the response displacement of each grid point (u x ,u y ) and the number of the grid points, build a finite element model based on ABAQUS, load the inp format file into the software to automatically calculate the stress field around the joints, and extract the stress component value of each grid node;

[0068] Step 9.2.2: Calculate the traction force at each joint point according to the following formula to obtain the distribution of traction force on both sides of the joint:

[0069]

[0070] τ n =τ·[cosθsinθ](13)

[0071] τ s =τ·[sinθcosθ](14)

[0072] Where τ represents the traction force of the joint, τ n represents the normal traction at the joint point, τ s represents the tangential traction at the joint point, Represents the stress value at the grid point.

[0073] Step 9.3: Based on the normal stress and displacement increments at each joint node, the normal stiffness is derived by solving the normal stress-displacement increment ratio. The evolution curve of the joint normal stiffness distribution is constructed by topologically connecting the stiffness parameters of adjacent nodes. The shear stiffness is obtained by calculating the ratio of the tangential traction and the tangential jump displacement of each joint point. The change curve of the joint shear stiffness distribution is obtained by connecting the stiffness values ​​of adjacent crack joints.

[0074] The above description is only a preferred embodiment of the present invention and is not intended to limit the concept of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A quantitative characterization method for rock joint contact behavior based on ultrasonic excitation, characterized in that: The steps include: Step 1: Establish the response equations of elastic waves and joint points in the line segment; Step 2: Based on the response equation, simulate the propagation process of elastic waves in the line segment, obtain the elastic wave joint point response data, and form a waveform data set; Step 3: Use random cropping to crop the data in the waveform dataset to enhance the dataset, and divide the enhanced dataset into a training set and a test set with a ratio of 7:3; Step 4: Construct a convolutional neural network model for detecting joints in line segments; Step 5: Input the training set into the convolutional neural network model for line segment joint detection to obtain a trained convolutional neural network model for line segment joint detection; Step 6: Prepare a rock sample with joints, implement vibration excitation using a piezoelectric ceramic transducer, and obtain response waveform data using a 3D scanning laser Doppler vibrometer; Step 7: Preprocess the response waveform data to convert the velocity wave field response waveform data into the quadratically differentiable displacement wave field response waveform data; Step 8: Interpolate the preprocessed response waveform data to generate multiple one-dimensional waveform response sequences for lateral and vertical transmission. Use the trained joint recognition convolutional network model to perform feature recognition on the multiple sets of one-dimensional waveform response sequences, determine the coordinates of the crack points in the multiple sets of one-dimensional waveforms, and reconstruct the joint geometry. Step 9: Calculate the spatial distribution of joint stiffness along the joint geometry to achieve quantitative characterization of joint contact behavior.

2. The method for quantitative characterization of rock joint contact behavior based on ultrasonic excitation according to claim 1, characterized in that: The step 1 is specifically as follows: based on the one-dimensional elastic wave equation, the crack point in the line segment is regarded as the elastic boundary between two solids, and the response equation of the elastic wave and the crack point in the line segment is established: f(x)∣ x＝a =0 (2) Where (1) is the differential equation of one-dimensional elastic wave, and equations (2) and (3) define the boundary conditions of the line segment, where the starting point of the one-dimensional line segment is a and the end point is b, the displacement at end a is 0, and the load at end b is τ; c(x) represents the propagation velocity of the wave in the one-dimensional line segment, and equation (4) sets the c(x) value at the middle position of the line segment to be much smaller than that at other positions of the line segment, thereby realizing the definition of the crack point in the line segment. If there are multiple crack points in the line segment, c(x) is defined as a piecewise function; f(x) represents the amplitude of the one-dimensional elastic wave, ρ represents the rock density, and w represents the frequency.

3. The method for quantitatively characterizing rock joint contact behavior based on ultrasonic excitation according to claim 1, wherein: The convolutional neural network model for detecting crack points in line segments in step 4 includes: an input layer, a first convolutional layer, a first pooling layer, a plurality of alternating dense blocks and transition layers, a global average pooling layer, and an output layer; The dense block strengthens the transmission of crack waveform features and enhances the flow of information between layers. For an i-layer dense block with input x0, the output x of the i-th layer is i for: x i =H i ([x1,x2,…,x i-1 ]) (5) Among them, [x0,x2,…,x i-1 ] is the concatenation of feature maps generated in layers 0 to i-1, H i represents interconnected batch normalization; The transition layer includes a second convolutional layer and a second pooling layer. The second convolutional layer uses a 1×1 convolution kernel and the activation function selects the ReLU function. The second pooling layer applies a maximum sampling operation strategy, and this layer is configured with a 2×2 sampling window. Through the iterative convolution and downsampling process, the high-dimensional features of the waveform signal are analyzed and the feature dimensions and size are compressed. Then, a global mean pooling layer is applied to perform a mean operation on each feature map, converting the multidimensional features into a one-dimensional representation vector, which is finally fed into the output layer Softmax classifier to perform crack feature classification and determine the coordinate position of the crack point.

4. The method for quantitatively characterizing rock joint contact behavior based on ultrasonic excitation according to claim 1, wherein: The step 5 is specifically as follows: During the training process of the convolutional neural network model, the stochastic gradient descent (SGD) algorithm is used to iteratively optimize the network parameters. Based on the input sample X and its corresponding label Y, the parameters of the network model are continuously updated through the interaction between the two. The update formula is: θ=θ-η·▽ θ J(θ;X;Y) (6) Where η is the learning rate, J(θ; X; Y) is the objective function; θ J(θ; X; Y) is the gradient of the parameter θ. In order to quantify the difference between the probability distribution predicted by the model and the true distribution, the cross entropy loss function is selected as the evaluation criterion. The cross entropy loss function is as follows: L(p,y)=-ylog(p)-(1-y)log(1-p) (7) Among them, y∈{0,1} is the true label of the sample, and p is the probability predicted by the model that the sample belongs to a certain category; the gradient descent algorithm is used to minimize the cross entropy loss function. During this process, the algorithm will intelligently adjust the parameter value according to the gradient information of the loss function on the network parameters, in order to gradually reduce the loss and promote the model to converge to the global optimal solution.

5. The method for quantitatively characterizing rock joint contact behavior based on ultrasonic excitation according to claim 1, wherein: The step 6 is specifically as follows: Step 6.1: Select a rock slab sample with a size of 0.96×0.3×0.03m and a density of 2750kg / m 3 , Poisson coefficient 0.23, elastic modulus 62.6GPa; Step 6.2: A 3-cm-long notch was created in the middle of the bottom edge of the specimen to controllably expand the joint. The flat specimen was then fractured using a three-point bending method. Joint expansion was controlled by a closed-loop servo-hydraulic system, with the joint opening displacement as the feedback signal. Piezoelectric ceramic transducers were used for excitation, and waveform data of the in-plane joint expansion response during joint expansion was collected using a 3D scanning laser Doppler vibrometer. Step 6.3: After the joints are fabricated, the specimen is unloaded and mounted on a fixture. Different axial forces are applied to the specimen. The joints under different axial stress states are excited using a piezoelectric ceramic transducer. At the same time, static joint response waveform data are collected using a 3D scanning laser Doppler vibrometer.

6. The method for quantitatively characterizing rock joint contact behavior based on ultrasonic excitation according to claim 5, characterized in that: The step 7 is specifically as follows: Step 7.1: Inputting response waveform data into a bandpass filter; the response waveform data is extended joint response waveform data or static joint response waveform data; Step 7.2: numerically integrate the response waveform data after bandpass filter processing to obtain the corresponding displacement wavefield response waveform data; Step 7.3: Use a median filter and a mean filter to eliminate the pulse noise in the response waveform data of the displacement wavefield. Then, perform independent fitting of the filtered response waveform data of the displacement wavefield along the orthogonal coordinate axes using a one-dimensional Fourier expansion to construct the response waveform data of the displacement wavefield that is twice differentiable.

7. The method for quantitatively characterizing rock joint contact behavior based on ultrasonic excitation according to claim 1, wherein: The step 8 is specifically as follows: Step 8.1: Perform interpolation reconstruction on the response waveform data of the twice-differentiable displacement wave field to generate multiple one-dimensional waveform response sequences of lateral and vertical propagation; Step 8.2: Use the pre-trained convolutional network model for identifying joints in line segments to detect the single-dimensional waveform response sequence of each row / column to determine the existence and location of the joint coordinates in each signal sequence; Step 8.3: Summarize the detection results of each row and column of waveforms, and finally connect the joint points detected on adjacent waveforms to reconstruct the joint geometry.

8. The method for quantitatively characterizing rock joint contact behavior based on ultrasonic excitation according to claim 1, wherein: The step 9 is specifically as follows: Step 9.1: Calculate the jump displacements on both sides of the joint based on the response waveform data of the twice-differentiable displacement wave field; Step 9.2: Calculate the traction forces on both sides of the joint based on the response waveform data of the twice-differentiable displacement wave field; Step 9.3: Based on the normal stress and displacement difference of each node on the joint surface, the normal stiffness is derived by solving the ratio of the normal stress to the normal displacement difference of each node. The normal stiffness distribution evolution curve of the joint surface is constructed by topologically connecting the stiffness parameters of adjacent nodes. The shear stiffness is obtained by calculating the ratio of the tangential traction and the tangential jump displacement of each joint point. The change curve of the joint shear stiffness distribution is obtained by connecting the stiffness values ​​of adjacent joint points.

9. The method for quantitatively characterizing rock joint contact behavior based on ultrasonic excitation according to claim 8, wherein: The step 9.1 is specifically as follows: Step 9.1.1: Measure the displacements (u) on both sides of the joint along the x and y directions. + x ,u + y ) and (u - x ,u - y ); Step 9.1.2: Determine the normal and tangential orientations of each joint based on the joint geometry. Analyze the displacement components along the normal and tangential directions on both sides of the joint using the following equations: Among them, u + s 、u - s Corresponding to the tangential displacement components on both sides of the joint surface, u + n 、u - n are the normal displacement components on both sides of the joint surface, and θ is the angle between the horizontal direction and the normal direction of the joint surface; Step 9.1.3: The joint jump displacement is calculated based on the difference between the piecewise smooth displacement wave fields on both sides of the joint. The jump displacement of the joint along the tangential direction is u + s -u - s , the jump displacement along the normal direction is u + n -u - n .

10. The method for quantitatively characterizing rock joint contact behavior based on ultrasonic excitation according to claim 8, wherein: The step 9.2 is specifically as follows: Step 9.2.1: According to the grid points divided into the specimen when measuring vibration by 3D scanning laser Doppler vibrometer, obtain the coordinates of the grid points around the joints, the response displacement of each grid point (u x ,u y ) and the number of the grid points, build a finite element model based on ABAQUS, load the inp format file into the software to automatically calculate the stress field around the joints, and extract the stress component value of each grid node; Step 9.2.2: Calculate the traction force at each joint point according to the following formula to obtain the distribution of traction force on both sides of the joint: t n =τ·[cosθsinθ] (13) t s =τ·[sinθcosθ] (14) Where τ represents the traction force of the joint, τ n represents the normal traction at the joint point, τ s represents the tangential traction at the joint point, Represents the stress value at the grid point.

Images