Fast and slow longitudinal wave speed prediction method and system device considering concrete heterogeneity

Abstract

The invention relates to the technical field of civil engineering nondestructive testing, in particular to a fast and slow longitudinal wave speed prediction method and system device considering concrete heterogeneity, and the method comprises the steps: S1, introducing alpha and epsilon parameters; the alpha parameter is a consolidation coefficient and is used for representing the overall rigidity of the mortar framework; the epsilon parameter is a contact coefficient and is used for representing the connection degree between the aggregate and the mortar framework; epsilon = 0 is non-contact, and Epsilon = 1 is complete bonding. S2, according to the alpha and epsilon parameters, theoretical modeling is carried out, and the speed of fast and slow waves is calculated; and S3, determining alpha and epsilon parameters through simulation or experiments. Compared with the prior art, the method has the advantages that structural modeling better conforms to the real form of concrete, the prediction precision is remarkably improved, fast waves and slow waves can be predicted at the same time, and the engineering applicability is high.

Description

Technical Field

[0002] This invention relates to the field of non-destructive testing technology in civil engineering, specifically to a method for predicting fast and slow longitudinal wave velocities considering the heterogeneity of concrete. Background Technology

[0003] Concrete, as one of the most commonly used engineering structural materials, is widely used in bridges, tunnels, hydraulic structures, marine engineering, and nuclear power engineering. During long-term service, concrete inevitably experiences problems such as pore evolution, microcrack propagation, and aggregate-mortar interface deterioration. These internal damages are often difficult to detect directly through visual inspection.

[0004] Ultrasonic testing technology is widely used to achieve non-destructive testing and performance evaluation of the internal state of concrete. When ultrasound propagates in concrete, its propagation speed, attenuation characteristics, and waveform features are closely related to the material's internal elastic parameters, pore state, and multiphase structure. Therefore, establishing a theoretical model that accurately describes the wave propagation mechanism within concrete is a key technological foundation for improving testing accuracy and interpretation reliability.

[0005] However, concrete is not a simple homogeneous elastic body, but a typical multiphase, multiscale, porous composite material, which usually includes at least: a continuously distributed mortar skeleton; discretely embedded aggregate particles; and pore water distributed in the mortar and the interface transition zone.

[0006] Traditional elastic wave theory or simple equivalent medium models cannot accurately reflect the above-mentioned complex structural characteristics, especially in saturated conditions, where the coupling effect between different phases will significantly affect the propagation behavior of pressure waves (P waves).

[0007] Explanation of terms in this invention:

[0008] Biot theory describes the coupled mechanical behavior of solid skeleton and pore fluid in porous media. It is based on the condition that porous media can be equivalent to continuous media and reveals that in porous media, solid and fluid are not "subordinate" but "coupled and coexisting dynamic system".

[0009] Saturated porous media: Multiphase media systems in which the pore structure is completely filled with a single fluid (usually water).

[0010] Fast P-wave: The solid and fluid move in the same phase; similar to longitudinal waves in ordinary elastic media; with low attenuation and fast propagation speed.

[0011] Slow P-wave: Solids and fluids move in opposite phases; unique to Biot theory; strong attenuation, slow speed; extremely important in ultrasonic testing and geophysics.

[0012] Shear wave (S-wave): The fluid is almost not involved; it is dominated by the solid skeleton.

[0013] Existing patent applications CN202511091864.3 and CN202511091861.X disclose that transverse waves and longitudinal waves are two basic types of elastic waves: transverse waves vibrate in a direction perpendicular to the direction of wave propagation, such as S-waves in light waves and seismic waves; their propagation depends on the shear stiffness of the medium and they cannot propagate in fluids. Longitudinal waves vibrate in the same direction as the direction of propagation, such as P-waves in sound waves and seismic waves; their propagation depends on the compressibility of the medium and they can propagate in solids, liquids, and gases. The core difference between the two lies in the difference between the vibration direction and wave speed; longitudinal waves generally propagate faster than transverse waves.

[0014] Fast and slow waves in porous media are special concepts describing the propagation of elastic waves in fluid-saturated porous materials: fast waves refer to waves (including fast longitudinal and transverse waves) in solid-liquid coupled porous media where the solid skeleton and pore fluid move in essentially the same phase and propagate at relatively high speeds; slow waves refer to slow longitudinal waves where the solid skeleton and pore fluid move in opposite phases, with significantly lower wave speeds and strong attenuation. The main difference between the two lies in the relative motion modes and wave speeds of the solid and liquid phases: fast waves are dominated by the skeleton, similar to traditional elastic waves; slow waves, on the other hand, exhibit relative flow dissipation of the fluid and are a unique wave phenomenon characteristic of porous media.

[0015] The main drawbacks of existing technologies:

[0016] 1) The structural assumptions do not conform to the actual composition of concrete: the existing Biot class model only considers a single solid skeleton, which cannot reflect the strong connection between the mortar skeleton and the aggregate.

[0017] 2) The impact of aggregate-mortar coupling on wave velocity cannot be quantitatively described: the homogenization method can only provide macroscopic equivalent parameters and lacks the ability to physically interpret the contributions of different phases.

[0018] 3) Insufficient ability to predict slow compression waves (P2 waves): Most existing models cannot predict the propagation speed of fast and slow waves at the same time, which limits the utilization of information.

[0019] 4) Limited accuracy of experimental interpretation: There is a large deviation between theoretical prediction results and actual ultrasonic testing data, which affects the reliability of engineering applications. Summary of the Invention

[0020] The purpose of this invention is:

[0021] 1) Provide a theoretical modeling method for pressure wave propagation applicable to saturated concrete materials;

[0022] 2) The theoretical model simultaneously considers the three-phase structure of mortar skeleton, aggregate, and pore water;

[0023] 3) By introducing the consolidation coefficient and contact coefficient, the connection state between mortar and aggregate is quantitatively characterized;

[0024] 4) Achieve unified prediction of the propagation speeds of fast and slow compression waves;

[0025] 5) Improve the accuracy of interpreting the internal structural state of concrete in ultrasonic testing.

[0026] Detailed description of the technical solution of this invention:

[0027] In summary, this invention provides a method for predicting the velocities of fast and slow longitudinal waves considering the heterogeneity of concrete. The core idea is to treat saturated concrete as a three-phase coupled system composed of mortar skeleton, pore water, and aggregate. By modifying the traditional expression of potential energy in porous media and introducing key parameters reflecting concrete characteristics, a pressure wave propagation model suitable for concrete is established. This method can accurately predict the velocities of fast and slow longitudinal waves within concrete, providing fundamental information for non-destructive testing of concrete interiors.

[0028] The present invention provides a method for predicting fast and slow longitudinal wave velocities considering the heterogeneity of concrete, specifically comprising a method for predicting fast and slow longitudinal wave velocities considering the heterogeneity of concrete, the method comprising:

[0029] Step S1: Introduce the parameters α and ε; the α parameter is the consolidation coefficient, used to characterize the overall stiffness of the mortar skeleton; the ε parameter is the contact coefficient: used to characterize the degree of connection between the aggregate and the mortar skeleton; ε=0 means no contact, ε=1 means complete bonding;

[0030] Step S2: Based on the parameters α and ε, perform theoretical modeling and calculate the velocities of fast and slow waves;

[0031] Step S3: Determine the α and ε parameters through simulation or experiment.

[0032] As a specific embodiment of the present invention, the theoretical modeling in step S2 equates concrete to a three-phase coupled medium composed of a continuous mortar skeleton phase, a discrete aggregate solid phase, and a pore water fluid phase. The theoretical modeling is as follows: Figure 1 As shown.

[0033] As a specific embodiment of the present invention, the theoretical modeling in step S2 derives the modified potential energy density into a new characteristic equation:

[0034] "Define material modulus" (mortar skeleton modulus, aggregate skeleton modulus, average modulus)

[0035] Mortar skeleton volume modulus and shear modulus:

[0036] Aggregate skeleton bulk modulus and shear modulus:

[0037] Average modulus:

[0038] (in )

[0039] "Establish constitutive relations" (based on the small deformation assumption, define the displacement of the mortar skeleton) pore water displacement Aggregate displacement (The stress-strain relationship is derived using the potential energy density function W).

[0040] Strain of mortar skeleton and aggregate:

[0041] Volumetric strain of mortar skeleton, pore water, and aggregate:

[0042] Deviatoric strain of mortar skeleton and aggregate:

[0043] Establish expressions for the potential energy, kinetic energy, and dissipated energy of the three-phase system, and derive the corresponding equations of motion.

[0044] Derivation of potential energy density

[0045] Bulk modulus:

[0046] Shear modulus:

[0047] Coupling bulk modulus between different phases:

[0048] Potential energy density:

[0049] (in )

[0050] Changes in potential energy:

[0051] The tensor expression for the corresponding stress:

[0052] Constitutive relation:

[0053] "Kinetic energy density": (used to account for the coupling between the mortar skeleton and the aggregate)

[0054] (The effective densities of the mortar skeleton, pore water, and aggregate are denoted as ρ11, ρ22, and ρ33, respectively. The coupling densities between any two phases are denoted as ρ12, ρ23, and ρ13, respectively.)

[0055] The relative movement between the mortar skeleton, pore water, and aggregates leads to energy dissipation, known as "dissipated energy density".

[0056] (where b is the dissipation matrix)

[0057] Considering dissipation, the momentum conservation equation is derived using the Lagrange equation.

[0058]

[0059] (Where the subscript i indicates the direction x or z, and the point above the scalar indicates the derivative with respect to time.)

[0060] "Solving the characteristic equation" (Obtain the characteristic equation of the pressure wave and solve for the propagation velocities of fast and slow compression waves.)

[0061] Using Helmholtz decomposition, the displacement vectors of the mortar skeleton, pore water, and aggregate are decomposed:

[0062] (Where, ϕ and A represent the scalar potential function and the vector potential function, respectively.)

[0063] Substituting the above equation into the equation of motion, we obtain an equation concerning the scalar potential function:

[0064]

[0065] Assuming the wave is a plane harmonic wave, its solution has the following form:

[0066]

[0067] (Where i represents the imaginary unit, ω represents the angular frequency, r represents the position vector, and k represents the wave vector.)

[0068] Since the wave vector is a complex number, its real part represents the direction of wave propagation, while its imaginary part represents the direction of wave attenuation. For a P-wave, its propagation direction and attenuation direction are the same. ,in, This represents the complex wave number.

[0069] Combining the above three equations:

[0070] in

[0071] The equation has non-zero solutions, so:

[0072] Based on the above characteristic equation, two solutions can be generated, corresponding to the phase velocities of the fast (P1) and slow (P2) P waves, respectively.

[0073] in .

[0074] As one embodiment of the present invention, step S3 includes:

[0075] Step S31: Prepare the sample for the experiment, measure the P-wave velocity using ultrasonic testing, and fit the consolidation coefficient and the bonding coefficient.

[0076] Step S32: Numerical simulation, establishing a finite element model of the interface transition zone and simulating P-wave propagation;

[0077] Step S33: Determine the coefficients. Based on theoretical derivation, calibrate the consolidation coefficient α and contact coefficient ε by fitting experimental or simulated data. When α and ε take specific values, the model and experimental data achieve optimal consistency.

[0078] As one embodiment of the present invention, the α consolidation coefficient and ε contact coefficient in step S1 can be described by other equivalent parameters, as long as they can reflect the aggregate-mortar coupling effect.

[0079] As one embodiment of the present invention, the solution of the characteristic equation in step S2 can be achieved by finite element method, finite difference method or frequency domain algorithm.

[0080] The present invention also provides a system apparatus for predicting fast and slow longitudinal wave velocities considering the heterogeneity of concrete, comprising:

[0081] (1) Excitation module: used to generate ultrasonic excitation signals;

[0082] (2) Signal acquisition module: used to receive pressure wave signals propagating in concrete;

[0083] (3) Parameter input module: used to input material property parameters;

[0084] (4) Calculation and processing module: Built-in improved porous media model algorithm;

[0085] (5) Result output module: outputs fast wave speed, slow wave speed and related evaluation indicators.

[0086] As one embodiment of the present invention, the computing processing module in the system device structure can be implemented by a local processor or a cloud computing platform.

[0087] Advantages of this invention over existing technologies:

[0088] (1) The structural modeling is more in line with the real form of concrete. Through the three-phase model, the aggregate is not mistakenly equated to pores or its role is ignored.

[0089] (2) The prediction accuracy is significantly improved. After introducing the contact coefficient, the influence of different aggregate types and volume fractions on wave velocity can be effectively explained.

[0090] (3) It can predict fast waves and slow waves at the same time, improve the utilization rate of ultrasound detection information, and provide more criteria for internal state identification.

[0091] (4) It has strong engineering applicability, and the model parameters can be calibrated through experiments, making it easy to promote and apply. Attached Figure Description

[0092] Figure 1 To model the theory.

[0093] Figure 2 A transducer and experimental apparatus used for measuring P-wave velocity in ultrasonic experiments.

[0094] Figure 3 This is an equivalent model for concrete. Figure 4 For finite element models and networks.

[0095] Figure 5 The predicted velocity and the measured velocity show good consistency in the spectrum.

[0096] Figure 6 This is a typical received signal in the experiment.

[0097] Figure 7 The P1 wave velocity is based on theoretical, experimental, and simulated data.

[0098] Figure 8 This is due to the discrepancy between theoretical, experimental, and simulation data.

[0099] Figure 9 The P2 wave velocity is based on theoretical, experimental, and simulated data.

[0100] Figure 10 This is a graph showing the relationship between wave velocity and aggregate characteristics. Detailed Implementation

[0101] To make the technical problems, solutions, and advantages of this invention clearer, a detailed description will be provided below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0102] The theoretical modeling described in this invention equates concrete to a three-phase coupled medium consisting of a continuous mortar skeleton phase, a discrete aggregate solid phase, and a pore water fluid phase. The theoretical modeling is as follows: Figure 1 As shown.

[0103] Example 1: Determining the parameters α and ε through simulation or experiment.

[0104] (1) Experiment: Preparation of test samples (variable aggregate type and volume fraction)

[0105] The material properties of each constituent phase are shown in Table 1. The specimens were cubic units of 10 × 10 × 10 cm. Three aggregates were selected: soda-lime silicate glass, pebbles, and basalt, as their densities are compatible with the mortar skeleton, ensuring good mixability and preventing segregation. Since the excitation frequency was set to 500 kHz, with a wavelength of approximately 8 mm, the diameters of all aggregates were set to be close to the wavelength. This size selection enhances the representativeness of component interactions and ensures consistency with theoretical calculations and subsequent numerical simulations.

[0106] Table 1. Material properties of each component (unhomogenized)

[0107]

[0108] To ensure the consistency of the mechanical properties of the mortar skeleton, all specimens maintained a water-cement ratio of 0.4. The volume fractions of aggregate were set at 20%, 30%, 40%, and 50%, respectively. For each volume fraction, five identical specimens were prepared and subjected to standard curing for 28 days.

[0109] Ultrasonic experimental measurement of P-wave velocity:

[0110] Transducers were placed on both sides of the sample. The P-wave velocity of the sample under saturation was measured. An excitation signal was generated by a pulse generator, amplified, and transmitted through the sample. The received signal was captured by a digital oscilloscope. Fifteen measurements were performed and averaged for each aggregate type and volume fraction to reduce environmental uncertainties. Figure 2 A transducer and experimental apparatus used for measuring P-wave velocity in ultrasonic experiments.

[0111] Fitted consolidation coefficient, contact coefficient

[0112] A 5-cycle sinusoidal signal with a center frequency of 500 kHz is modulated using a Hanning window to form the excitation signal. The Hanning window reduces high-frequency interference and spectral leakage in ultrasonic pulses. The expression for the Hanning window is:

[0113]

[0114] in, , is the center frequency, and n is a positive integer that controls the sharpness of the excitation signal.

[0115] (2) Numerical simulation

[0116] Establishing a finite element model of the interface transition zone and simulating P-wave propagation

[0117] The aggregate and mortar of concrete should be able to transfer stress, thus requiring the formation of an interfacial transition zone. Since pores are mainly distributed within this zone, the porosity typically decreases radially from the aggregate surface inwards. Due to the complex microstructure, the mechanical properties of the interfacial transition zone are not yet fully understood. In practical engineering, it is often considered as mortar with reduced strength, and its equivalent strength is generally taken as 70% to 80% of the mortar strength. Figure 3 A concrete equivalent model is used, where aggregate represents aggregate material and ITZ represents the interface transition zone. A two-dimensional finite element model (10 cm × 10 cm) is constructed. The model assumes that all materials are homogeneous, isotropic, and linearly elastic, neglecting viscoelastic decay and thermal conduction. To establish the relationship between phase volume and acoustic response, P-wave propagation is simulated under plane stress conditions, neglecting the influence of normal stress in the z-axis direction. Three aggregates are represented by circular inclusions with a diameter of 8 mm, each surrounded by a uniform annular interface transition zone with a thickness of 0.2 mm. This configuration avoids numerical errors caused by excessive mesh refinement while maintaining sufficient accuracy. The maximum mesh size is limited to less than 1 / 6 of the wavelength to ensure solution convergence. The finite element model and mesh are as follows. Figure 4 As shown.

[0118] The stress boundary is realized in the form of the Neumann condition. .in, Indicates load, This represents the unit normal vector pointing outwards. (Neumann condition: specifies the normal derivative of an unknown function on the boundary).

[0119] (3) Determining coefficients:

[0120] Based on theoretical derivation, the consolidation coefficient α and contact coefficient were determined by fitting experimental or simulation data. Calibration was performed. When α and When a specific value is selected, the model achieves optimal consistency with the experimental data. As follows: Figure 5 As shown, the proposed model exhibits good consistency between the predicted speed and the measured speed.

[0121] Example 2: The parameters α and ε were determined experimentally, and the effectiveness of this patent was evaluated through simulation:

[0122] 1. Results Comparison and Verification of Theoretical Predictions

[0123] The experimental and simulation setup is as described in the previous steps. Two pressure waves were observed in the experiment. The first wave is denoted as the fast longitudinal wave (P1 wave), and the second wave as the slow longitudinal wave (P2 wave). To prevent boundary reflections from interfering with the identification of P1 and P2 waves, the receiving and transmitting points were placed at the center of opposite surfaces, consistent with the experimental setup. In this way, the boundary reflections form a clear wave packet, thus separating the peak value of the P2 wave, as follows: Figure 6 As shown.

[0124] 2. Results Analysis

[0125] The predicted and measured P-wave velocities are presented below. The effects of aggregate volume fraction and porosity on P-wave velocities were investigated.

[0126] "Characteristic Analysis of P1 Waves": The P1 wave velocities predicted by the homogenization theory and the proposed theory are as follows: Figure 7 As shown, the experimental and simulated wave velocities of P1 are also listed. The predicted values ​​of the proposed theory are closer to the experimental and simulated data than those of the homogenized theory because the proposed theory more accurately characterizes the microstructure of concrete and quantitatively describes the influence of cement skeleton, pore water and aggregate on wave velocity.

[0127] 3. Cause Analysis

[0128] Meanwhile, discrepancies exist between experimental and simulated data. These discrepancies are due to the introduction of the interfacial transition zone (ITZ). Since the ITZ treats the interface between mortar and aggregate as a homogeneous medium, it does not incorporate strain-energy-based constitutive relations and cannot clearly characterize the porous phase at the interface. Therefore, the simulated data falls between the data from the homogenization theory and the proposed theory, as follows: Figure 8 As shown, the absolute error between the proposed theory and experimental data is less than 200 m / s, and the relative error is less than 10%, indicating that the prediction of the P1 wave velocity is accurate.

[0129] "Characteristic Analysis of P2 Waves": The P2 wave velocity predicted by the proposed theory is as follows. Figure 9 As shown, the experimentally measured P2 wave velocity is also listed. Since homogenization theory cannot calculate the P2 wave velocity, and the interface transition region cannot simulate the propagation of the P2 wave, Figure 8 Only a comparison between the proposed theory and experimental data is shown. The absolute error between the proposed theory and experimental data is less than 250 m / s, and the relative error is less than 12.5%, indicating that the prediction of P2 wave velocity is accurate.

[0130] "Analysis of the Influence of Aggregate Characteristics": When the wave velocity in the aggregate is greater than that in the mortar, the P-wave velocity of the concrete increases with the increase of the aggregate volume fraction. First, the P-wave velocity is affected by the elastic modulus of the aggregate. Comparing the P-wave velocities of glass and gravel, aggregates with a higher elastic modulus have higher P-wave velocities. Simultaneously, the P-wave velocity is also affected by the aggregate density. Comparing the P-wave velocities of gravel and basalt, although their elastic moduli differ, their P-wave velocities are similar at the same volume fraction. Therefore, it can be seen that the P-wave velocity in concrete is influenced by both the elastic modulus and density of the aggregate. Figure 10 .

Claims

1. A method for predicting fast and slow longitudinal wave velocities considering the heterogeneity of concrete, characterized in that, The method includes: Step S1: Introduce the parameters α and ε; the α parameter is the consolidation coefficient, used to characterize the overall stiffness of the mortar skeleton; the ε parameter is the contact coefficient: used to characterize the degree of connection between the aggregate and the mortar skeleton; ε=0 means no contact, ε=1 means complete bonding; Step S2: Based on the parameters α and ε, perform theoretical modeling and calculate the velocities of fast and slow waves; Step S3: Determine the α and ε parameters through simulation or experiment.

2. The method for predicting fast and slow longitudinal wave velocities considering the heterogeneity of concrete according to claim 1, characterized in that, The theoretical modeling described in step S2 equates concrete to a three-phase coupled medium consisting of a continuous mortar skeleton phase, a discrete aggregate solid phase, and a pore water fluid phase.

3. The method for predicting fast and slow longitudinal wave velocities considering the heterogeneity of concrete according to claim 1, characterized in that, The theoretical modeling described in step S2 derives the modified potential energy density into a new characteristic equation: (1) Define material modulus: mortar skeleton modulus, aggregate skeleton modulus, average modulus; Mortar skeleton volume modulus and shear modulus: ； Aggregate skeleton bulk modulus and shear modulus: ； Average modulus: ; in ; (2) Establish constitutive relations: Based on the small deformation assumption, define the displacement of the mortar skeleton. pore water displacement Aggregate displacement The stress-strain relationship is derived using the potential energy density function W, along with strain. Strain of mortar skeleton and aggregate: ; Volumetric strain of mortar skeleton, pore water, and aggregate: ; Deviatoric strain of mortar skeleton and aggregate: ; Establish expressions for the potential energy, kinetic energy, and dissipated energy of a three-phase system, and derive the corresponding equations of motion; Derivation of potential energy density Bulk modulus: ; Shear modulus: ; Coupling bulk modulus between different phases: ; Potential energy density: ; in ; Changes in potential energy: ; The tensor expression for the corresponding stress: ; Constitutive relation: ; Kinetic energy density: used to account for the coupling between the mortar skeleton and the aggregate; ; The effective densities of the mortar skeleton, pore water, and aggregate are denoted as ρ11, ρ22, and ρ33, respectively; the coupling densities between each pair of phases are denoted as ρ12, ρ23, and ρ13, respectively. The relative motion between the mortar skeleton, pore water, and aggregates leads to energy dissipation, with the dissipated energy density being: ； Where b is the dissipation matrix; Considering dissipation, the momentum conservation equation is derived using the Lagrange equation: ； The subscript i indicates the direction x or z, and the point above the scalar indicates the derivative with respect to time; (3) Solving the characteristic equation: The characteristic equation of the pressure wave is obtained, and the propagation speeds of the fast compression wave and the slow compression wave are solved; Using Helmholtz decomposition, the displacement vectors of the mortar skeleton, pore water, and aggregate are decomposed: ； Where ϕ and A represent the scalar potential function and the vector potential function, respectively; Substituting the above equation into the equation of motion, we obtain an equation concerning the scalar potential function: ； Assuming the wave is a plane harmonic wave, its solution has the following form: ； Where i represents the imaginary unit, ω represents the angular frequency, r represents the position vector, and k represents the wave vector; Since the wave vector is a complex number, its real part represents the direction of wave propagation, while its imaginary part represents the direction of wave attenuation; for a P-wave, its propagation direction and attenuation direction are the same. ,in, Represents the complex wave number; Combining the above three equations: ; in ; The equation has non-zero solutions, so: ; Based on the above characteristic equation, two solutions can be generated, corresponding to the phase velocities of the P-waves, fast P1 and slow P2, respectively. ;in .

4. The method for predicting fast and slow longitudinal wave velocities considering the heterogeneity of concrete according to claim 1, characterized in that, Step S3 includes: Step S31: Prepare the sample for the experiment, measure the P-wave velocity using ultrasonic testing, and fit the consolidation coefficient and the bonding coefficient. Step S32: Numerical simulation, establishing a finite element model of the interface transition zone and simulating P-wave propagation; Step S33: Determine the coefficients. Based on theoretical derivation, calibrate the consolidation coefficient α and contact coefficient ε by fitting experimental or simulated data. When α and ε take specific values, the model and experimental data achieve optimal consistency.

5. The method for predicting fast and slow longitudinal wave velocities considering the heterogeneity of concrete according to claim 1, characterized in that, The α consolidation coefficient and ε contact coefficient mentioned in step S1 can be described by other equivalent parameters, as long as they can reflect the aggregate-mortar coupling effect.

6. The method for predicting fast and slow longitudinal wave velocities considering the heterogeneity of concrete according to claim 1, characterized in that, The solution to the characteristic equation in step S2 can be achieved through finite element method, finite difference method, or frequency domain algorithm.

7. A system apparatus for predicting fast and slow longitudinal wave velocities considering the heterogeneity of concrete, characterized in that... include: (1) Excitation module: used to generate ultrasonic excitation signals; (2) Signal acquisition module: used to receive pressure wave signals propagating in concrete; (3) Parameter input module: used to input material property parameters; (4) Calculation and processing module: Built-in improved porous media model algorithm; (5) Result output module: outputs fast wave speed, slow wave speed and related evaluation indicators.

8. The system device structure for providing a method for predicting fast and slow longitudinal wave velocities considering the heterogeneity of concrete, as described in claim 7, is characterized in that: The computing module in the system device can be implemented by a local processor or a cloud computing platform.

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