Concrete ultrasonic propagation characteristic modeling method and system

Abstract

The invention discloses a concrete ultrasonic propagation characteristic modeling method and system, and relates to the technical field of ultrasonic non-destructive testing, and the method comprises the steps: obtaining the rheological behavior data of unsolidified cement slurry, building a concrete slurry fractional order viscoelastic constitutive model by adopting a Caputo type fractional order derivative, and obtaining a complex modulus; constructing a frequency domain wave equation by using the complex modulus, and calculating ultrasonic attenuation coefficients under different frequencies; dividing the concrete medium into thin layers along the propagation direction, and setting the thickness and characteristic impedance of each layer; a Waterman-Truell model is used to calculate a corrected complex wave number, and a structure factor is combined to correct scattering space correlation; calculating the total attenuation value of the attenuation coefficient of each thin layer, and establishing a propagation path total attenuation model. According to the method, the frequency response consistency is enhanced, the modeling precision of the heterogeneity and the multi-scale scattering characteristic of the concrete is improved, and the method has higher simulation accuracy and physical interpretation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ultrasonic nondestructive testing, in particular to a modeling method and system for ultrasonic wave propagation characteristics of concrete. BACKGROUND

[0002] As a key material in infrastructure engineering, the internal quality of concrete directly affects the mechanical properties and service life of the structure. In order to realize the detection of internal defects and the evaluation of compactness of concrete, ultrasonic nondestructive testing technology is widely used due to its strong penetration, high sensitivity, and strong non-destructive nature. In recent years, with the development of frequency domain analysis theory and viscoelastic model, researchers have gradually constructed ultrasonic propagation models suitable for heterogeneous materials, such as complex modulus modeling, wave equation solving and scattering correction methods, to simulate and explain the speed variation and attenuation behavior of sound wave propagation in concrete. It plays an important role in engineering quality monitoring and material performance evaluation.

[0003] However, the existing concrete ultrasonic modeling technology still faces many challenges in describing the real propagation characteristics. First, the mainstream model is mostly based on integer-order viscoelastic theory to construct the complex modulus expression, which is difficult to reflect the non-locality and time fractional derivative characteristics commonly existing in concrete paste, resulting in distortion of frequency correlation description and low prediction accuracy. Second, for the scattering loss problem caused by aggregate, the existing model mostly ignores the structural correlation and does not consider the modulation effect of scattering body spatial arrangement on wave propagation path, which cannot accurately quantify the cumulative attenuation of different scales of scattering. SUMMARY

[0004] In view of the above existing problems, the present application is proposed.

[0005] Therefore, the present application provides a modeling method for ultrasonic wave propagation characteristics of concrete to solve the problems of distortion of frequency correlation description and not considering the modulation effect of scattering body spatial arrangement on wave propagation path.

[0006] To solve the above technical problems, the present application provides the following technical solutions:

[0007] In a first aspect, the present application provides a concrete ultrasonic wave propagation characteristic modeling method, which comprises: obtaining rheological behavior data of unhardened cement paste; establishing a fractional order viscoelastic constitutive model of the concrete paste by using Caputo type fractional order derivative to obtain complex modulus; constructing a frequency domain wave equation by using the complex modulus to calculate ultrasonic wave attenuation coefficients of the material at different frequencies; dividing the concrete medium into several thin layers according to the ultrasonic propagation direction, defining the thickness of each thin layer, and setting interlayer reflection control parameters according to the characteristic impedance of each thin layer; calculating the modified complex wave number by using the Waterman-Truell model, and adjusting the modified term caused by the scattering space correlation through the structure factor; calculating the total attenuation value on the propagation path according to the ultrasonic wave attenuation coefficient of each thin layer to establish a total attenuation model of the ultrasonic wave propagation path in the concrete.

[0008] As a preferred scheme of the concrete ultrasonic wave propagation characteristic modeling method, the rheological behavior data comprises stress-strain relationship data, shear viscosity data, dynamic modulus data, relaxation time data and thixotropic recovery data.

[0009] As a preferred scheme of the concrete ultrasonic wave propagation characteristic modeling method, the steps of establishing the fractional order viscoelastic constitutive model of the concrete paste by using Caputo type fractional order derivative to obtain the complex modulus are as follows:

[0010] A frequency-complex modulus response curve is constructed based on the rheological behavior data of the unhardened cement paste, the fractional order, the instantaneous elastic modulus, the equivalent viscous modulus and the relaxation time factor are defined by fitting the frequency-complex modulus response curve, the fractional order, the instantaneous elastic modulus, the equivalent viscous modulus and the relaxation factor are used as parameters in the Caputo type fractional order derivative expression, and a Caputo type fractional order viscoelastic constitutive equation describing the viscoelastic response behavior of the unhardened cement paste is constructed; the Caputo type fractional order viscoelastic constitutive equation is applied to the concrete paste medium to establish the fractional order viscoelastic constitutive model of the concrete paste; the Caputo type fractional order derivative in the fractional order viscoelastic constitutive model is subjected to Fourier transform to obtain a frequency domain response function of the concrete paste containing a complex frequency term, and the frequency domain response function of the concrete paste is subjected to complex frequency conversion to obtain the complex modulus.

[0011] As a preferred scheme of the concrete ultrasonic wave propagation characteristic modeling method, the steps of constructing the frequency domain wave equation by using the complex modulus to calculate the ultrasonic wave attenuation coefficients of the material at different frequencies are as follows:

[0012] The complex modulus is substituted into the frequency domain constitutive relation of a one-dimensional linear viscoelastic medium to establish a relationship expression between stress spectrum and strain spectrum; the concrete medium is set as an unbounded homogeneous linear viscoelastic medium, and ultrasonic waves propagate along the x direction, so that the particle displacement spectrum of the ultrasonic waves is denoted as wherein, represents an angular frequency; the strain spectrum is expressed as a first-order derivative of the particle displacement spectrum with respect to space by combining the mass conservation equation and the momentum conservation equation, and the stress spectrum is expressed as a second-order partial derivative expression of the particle displacement spectrum; the particle displacement spectrum is substituted into a one-dimensional frequency domain wave equation containing the complex modulus based on the relationship between the stress spectrum and the particle displacement spectrum to construct the one-dimensional frequency domain wave equation; the complex wave number under different frequency domains is calculated; and the ultrasonic wave attenuation coefficient under different frequencies is obtained according to the complex value function of the imaginary part of the complex wave number.

[0013] As a preferred scheme of the concrete ultrasonic wave propagation characteristic modeling method, the concrete medium is divided into a plurality of thin layers according to the ultrasonic wave propagation direction, the thickness of each thin layer is defined, and the interlayer reflection control parameter is set according to the characteristic impedance of each thin layer, and the specific steps are as follows:

[0014] According to the entire ultrasonic wave propagation path along the main propagation direction, the spatial coordinate axis of the concrete medium is established, and the layering thickness control condition is set; the concrete is divided into a plurality of thin layers with fixed thickness along the main propagation direction according to the spatial coordinate axis and the layering thickness control condition; the characteristic impedance of each thin layer is calculated based on the local density and the local effective wave speed of each thin layer, and the characteristic impedances corresponding to adjacent two thin layers are sequentially extracted according to the spatial coordinate axis; the interface reflection coefficient is calculated and the interlayer reflection control coefficient is set according to the difference between the characteristic impedances of the adjacent two thin layers.

[0015] As a preferred scheme of the concrete ultrasonic wave propagation characteristic modeling method, the complex wave number is calculated by using the Waterman-Truell model, and the correction term caused by the scattering space correlation is adjusted by the structure factor, and the specific steps are as follows:

[0016] The complex modulus is substituted into the frequency domain wave equation, and the complex wave number and the spatial distribution density of the aggregate of each thin layer are obtained by solving the frequency domain wave equation; based on the condition that the size of the aggregate in the concrete medium satisfies the sparse distribution condition of the scatterer, the scattering amplitude function of the aggregate particles in each thin layer is obtained, the spatial distribution density of the aggregate and the scattering amplitude function are substituted into the Waterman-Truell model, and the complex wave number of each thin layer is corrected according to the integral expression in the Waterman-Truell model; the spatial arrangement information of the aggregate particles in the concrete medium is collected, and the structure factor is calculated by using Fourier spectrum analysis; the structure factor is introduced into the integral expression of the Waterman-Truell model as a scattering correction parameter, the contribution proportion of the scattering amplitude function to the perturbation term of the complex wave number is modified, and the corrected complex wave number is recalculated.

[0017] As a preferred scheme of the concrete ultrasonic wave propagation characteristic modeling method, wherein: the total attenuation value on the propagation path is calculated according to the ultrasonic wave attenuation coefficient of each thin layer, and a total attenuation model of the ultrasonic wave propagation path in the concrete is established, and the specific steps are as follows:

[0018] Based on the complex value function of the imaginary part of the corrected complex wave number, the ultrasonic wave attenuation coefficient corresponding to each thin layer with a fixed thickness is obtained; based on the thickness of each thin layer, the ultrasonic wave attenuation coefficient of each thin layer is multiplied by the thickness layer by layer to obtain the local attenuation of each thin layer; the local attenuation of all thin layers is linearly superimposed according to the spatial coordinate axis direction to obtain the total attenuation value on the ultrasonic wave propagation path; and based on the obtained local attenuation and total attenuation value, a total attenuation model of the ultrasonic wave propagation path in the concrete is established.

[0019] In the second aspect, the present application provides a concrete ultrasonic wave propagation characteristic modeling system, which comprises: a rheological modeling module for obtaining the rheological behavior data of the un-solidified cement paste, establishing a fractional order viscoelastic constitutive model of the concrete paste by using Caputo type fractional order derivative to obtain a complex modulus; a wave analysis module for constructing a frequency domain wave equation by using the complex modulus to calculate the ultrasonic wave attenuation coefficient of the material at different frequencies; a layered impedance module for dividing the concrete medium into a plurality of thin layers according to the ultrasonic propagation direction, defining the thickness of each thin layer, and setting the interlayer reflection control parameter according to the characteristic impedance of each thin layer; a scattering correction module for calculating the corrected complex wave number by using the Waterman-Truell model and adjusting the correction term caused by the scattering spatial correlation by using the structure factor; and a path attenuation module for calculating the total attenuation value on the propagation path according to the ultrasonic wave attenuation coefficient of each thin layer to establish a total attenuation model of the ultrasonic wave propagation path in the concrete.

[0020] In a third aspect, the present application provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and wherein the computer program, when executed by the processor, implements any step of the method for modeling the ultrasonic wave propagation characteristics of concrete according to the first aspect of the present application.

[0021] In a fourth aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements any step of the method for modeling the ultrasonic wave propagation characteristics of concrete according to the first aspect of the present application.

[0022] The present application has the following beneficial effects: the viscoelastic behavior of concrete paste is more accurately characterized by constructing a viscoelastic constitutive model using Caputo-type fractional derivative, the fitting capability of complex modulus in the frequency domain is improved, and thus the frequency response consistency and simulation accuracy are improved; the non-ideal distribution characteristics of aggregates in space are effectively considered by introducing the Waterman-Truell scattering model and combining with the modification of the structure factor, and the ability to characterize multi-scale scattering characteristics and frequency-dependent attenuation is improved; the layer-by-layer attenuation modeling of ultrasonic wave propagation paths in heterogeneous concrete is realized by the layering model based on wave impedance difference and the wave amplitude transfer formula, combined with the interlayer reflection threshold judgment and weak reflection approximation, the model structure is simplified and the interpretability is improved. BRIEF DESCRIPTION OF DRAWINGS

[0023] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiment description. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0024] Fig. 1 Flowchart for the method for modeling the ultrasonic wave propagation characteristics of concrete.

[0025] Fig. 2 Flowchart for establishing the fractional viscoelastic constitutive model.

[0026] Fig. 3 Flowchart for establishing the total attenuation model of the ultrasonic wave propagation path. DETAILED DESCRIPTION

[0027] In order to make the above-mentioned purposes, features and advantages of the present application more apparent and easy to understand, the specific embodiments of the present application will be described in detail below with reference to the drawings of the specification.

[0028] In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application. However, it will be apparent to one skilled in the art that the present application can be practiced without the specific details set forth in this description. In other instances, well-known methods have not been described in detail in order not to unnecessarily obscure aspects of the present application.

[0029] It should also be noted that, as used herein, "one embodiment" or "an embodiment" means implementation of at least one of the described features, structures, or characteristics, but does not mean that all of the features, structures, or characteristics include in these implementations are present by necessity. Further, many embodiments are described in terms of sequences of actions to be performed by, for example, elements of a computing device. It will be recognized that various actions described herein can be performed by specific circuits, by program instructions being executed by one or more processors, or by a combination of both. Additionally, these sequences of actions described herein can be considered to be embodied entirely within any form of computer or information processing system. In other words, the actions described herein can be performed by a processor or circuit of a general purpose computer, a special purpose computer, or other programmable data processing apparatus.

[0030] Reference will now be made to Figs. 1-3 For one embodiment of the present application, the embodiment provides a method for modeling the ultrasonic propagation characteristics of concrete, comprising the following steps:

[0031] S1: Obtain the rheological behavior data of the unset cement paste, establish a fractional viscoelastic constitutive model of the concrete paste using Caputo type fractional derivative, and obtain the complex modulus.

[0032] The rheological behavior data of the unset cement paste includes stress-strain relationship data, shear viscosity data, dynamic modulus data, relaxation time data, and thixotropic recovery data.

[0033] Further, the rheological behavior data of the unset cement paste is obtained through rheological experiment analysis, and the rheological experiment usually includes steady shear experiment, dynamic oscillation experiment, stress relaxation experiment, creep and recovery experiment, thixotropic loop experiment, and three-section shear experiment.

[0034] It should be noted that the stress-strain response characteristics of the unset cement paste under various loading conditions are obtained through different types of rheological experiments, which provides data support for establishing the fractional viscoelastic constitutive model, thereby realizing high-precision fitting and parameter identification of the complex modulus in the frequency domain, and improving the modeling capability of the model for viscoelastic behavior, structural relaxation, and thixotropic effect.

[0035] Based on the rheological behavior data of the unset cement paste, a frequency-complex modulus response curve is constructed, and the fractional order, instantaneous elastic modulus, equivalent viscous modulus, and relaxation time factor are defined by fitting the frequency-complex modulus response curve.

[0036] Further, the stress-strain relationship data is used to reflect the deformation law of the material in the loading process; the shear viscosity data is used to characterize the flow resistance characteristics; the dynamic modulus data is used to reflect the rigidity response under different frequencies; and the relaxation time data and the thixotropic recovery data are used to describe the time-dependent viscoelastic evolution characteristics.

[0037] After acquiring rheological behavior data, the dynamic modulus data is resampled in the frequency domain to construct a frequency-complex modulus response curve. The frequency-complex modulus response curve is plotted with angular frequency on the x-axis and complex modulus on the y-axis. Using the frequency-complex modulus response curve, the objective function in the fractional-order viscoelastic constitutive model is called for least-squares fitting. The fitting parameter values ​​are iteratively adjusted until the error meets the accuracy requirements. After the fitting is completed, a set of fitting parameters is obtained, including the fractional order, instantaneous elastic modulus, equivalent viscous modulus, and relaxation time factor.

[0038] Among them, the fractional order is used to describe the non-integer order relationship between stress and strain; the instantaneous elastic modulus reflects the short-time elastic response; the equivalent viscous modulus describes the effective damping level; and the relaxation time factor is used to characterize the rate attenuation of stress over time.

[0039] By using the fractional order, instantaneous elastic modulus, equivalent viscous modulus, and relaxation factor as parameters in the Caputo-type fractional derivative expression, a Caputo-type fractional viscoelastic constitutive equation describing the viscoelastic response behavior of uncured cement paste is constructed.

[0040] The Caputo-type fractional viscoelastic constitutive equation is applied to concrete slurry medium to establish a fractional viscoelastic constitutive model of concrete slurry.

[0041] Furthermore, the fractional-order viscoelastic constitutive model is expressed as:

[0042] ;

[0043] in, Represents the instantaneous elastic modulus. Indicates the long-term modulus. Indicates the relaxation time for fractional-order corrections. Denotes the fractional derivative of the Caputo type. Indicates the fractional order. , Representing the time domain The stress under, Representing the time domain The strain under the circumstances.

[0044] Among them, instantaneous elastic modulus Used to reflect the instantaneous elastic response of slurry under ultrasonic action; long-term modulus Used to characterize the elastic modulus of slurry under steady-state load, reflecting the load-bearing capacity of the material after complete relaxation.

[0045] Caputo type fractional derivative The distribution width used to characterize the internal damping mechanism of a material When time goes to infinity, it degenerates into the classical Zener model, When time goes to infinity, it degenerates into the classical Zener model,

[0046] The frequency domain response function of the concrete paste is obtained by Fourier transform of the Caputo fractional derivative in the fractional viscoelastic constitutive model.

[0047] Further, the Caputo fractional derivative in the fractional viscoelastic constitutive model is expressed as:

[0048] ;

[0049] Wherein, ω represents the angular frequency, j represents the imaginary unit, σ represents the stress spectrum, ε represents the strain spectrum.

[0050] The complex modulus is obtained by substituting the frequency domain response function of the concrete paste into the complex frequency.

[0051] Further, the complex modulus is expressed as:

[0052] ;

[0053] S2: Construct the frequency domain wave equation using the complex modulus, and calculate the ultrasonic wave attenuation coefficient of the material at different frequencies.

[0054] Based on the obtained complex modulus, the complex modulus is substituted into the frequency domain constitutive relationship of one-dimensional linear viscoelastic medium to establish the relationship expression between the stress spectrum and the strain spectrum.

[0055] Further, the relationship expression between the stress spectrum and the strain spectrum is expressed as:

[0056] ;

[0057] Suppose the concrete medium is an unbounded homogeneous linear viscoelastic medium, and the ultrasonic wave propagates along the x direction, then the particle displacement spectrum of the ultrasonic wave is denoted as wherein, ω represents the angular frequency.

[0058] Combining the mass conservation equation and the momentum conservation equation, the strain spectrum is expressed as the first-order derivative of the particle displacement spectrum with respect to space; and the stress spectrum is expressed as the second-order partial derivative expression of the particle displacement spectrum.

[0059] Further, the strain spectrum is expressed as the first-order derivative of the particle displacement spectrum with respect to space, and is expressed as:

[0060] ;

[0061] wherein, represents the complex wave number.

[0062] The stress spectrum is expressed as a second-order partial derivative expression of the particle displacement spectrum, and is expressed as:

[0063] ;

[0064] Based on the relationship between the stress spectrum and the particle displacement spectrum, the particle displacement spectrum is substituted into the one-dimensional acoustic wave control equation to construct a one-dimensional frequency domain wave equation containing a complex modulus.

[0065] Further, the one-dimensional frequency domain wave equation is expressed as:

[0066] ;

[0067] wherein, represents the density of the concrete medium.

[0068] The complex wave number is calculated under different frequency domains through the one-dimensional frequency domain wave equation; wherein, the complex wave number is a complex function including a real part and an imaginary part.

[0069] Further, the complex wave number is expressed as:

[0070] ;

[0071] According to the complex function of the imaginary part in the complex wave number, the ultrasonic attenuation coefficient under different frequencies is obtained.

[0072] Further, the imaginary part of the complex wave number is the attenuation coefficient of the ultrasonic wave under the frequency, which is used to represent the absorption and energy consumption of the concrete medium to the ultrasonic wave propagation.

[0073] S3: The concrete medium is divided into several thin layers according to the ultrasonic propagation direction, the thickness of each thin layer is defined, and the interlayer reflection control parameter is set according to the characteristic impedance of each thin layer.

[0074] According to the entire ultrasonic propagation path along the main propagation direction, the spatial coordinate axis of the concrete medium is established, and the layering thickness control condition is set.

[0075] Further, the layering thickness control condition includes wavelet resolution constraint, statistical sufficiency constraint and Nyquist lower limit constraint.

[0076] Wherein, the wavelet resolution constraint is expressed as:

[0077] ;

[0078] wherein, denotes the layer thickness of the thin layer, denotes the wavelength of the ultrasonic wave propagating in the concrete medium, and is expressed as:

[0079]

[0080] wherein, denotes the wave velocity of the ultrasonic wave propagating in the concrete medium, denotes the frequency of the ultrasonic excitation signal.

[0081] the statistical sufficiency constraint is expressed as:

[0082]

[0083] wherein, denotes the volume fraction of the aggregate, denotes the maximum particle size of the aggregate particles.

[0084] the Nyquist lower bound constraint is expressed as:

[0085]

[0086] According to the spatial coordinate axis and the layer thickness control condition, the concrete is divided into a plurality of thin layers with fixed thickness along the main propagation direction.

[0087] Based on the local density and the local effective wave velocity of each thin layer, the characteristic impedance of each thin layer is calculated, and the characteristic impedance corresponding to adjacent two thin layers is sequentially extracted according to the spatial coordinate axis;

[0088] wherein, the local density is calculated by the concrete material ratio and the aggregate volume distribution, and the local effective wave velocity is obtained by the complex modulus and the density.

[0089] Further, based on the layer thickness constraint condition, the thin layer thickness under different frequencies is obtained After determining , according to the material local density and the local effective wave velocity of each thin layer, the characteristic impedance of each thin layer is calculated, which is expressed as:

[0090]

[0091] wherein, denotes the characteristic impedance of the thin layer of the i-th layer, denotes the local density of the thin layer of the i-th layer, denotes the local effective wave velocity of the thin layer of the i-th layer.

[0092] ​​​​​​​Calculate the interface reflection coefficient and set the interlayer reflection control coefficient based on the characteristic impedance difference between two adjacent thin layers;

[0093] Furthermore, the interface reflection coefficient is calculated and expressed as:

[0094] ;

[0095] in, Indicates the first Layer and First Interfacial reflectance between layers Indicates the first Characteristic impedance of the layer.

[0096] Set the interlayer reflection coefficient. Specifically, set a weak reflection threshold. If the interface reflection coefficient is less than the weak reflection threshold, set the interlayer reflection coefficient parameter corresponding to the interface to allow transmission dominance and use linear superposition. If the interface reflection coefficient is greater than or equal to the weak reflection threshold, set the interlayer reflection coefficient corresponding to the interface to have reflection interference and cannot be directly superimposed linearly.

[0097] Furthermore, to ensure that ultrasound waves primarily pass through the thin layers via transmission rather than reflection during propagation, a weak reflection threshold is set, expressed as:

[0098]

[0099] The weak reflection threshold is used to control energy reflection caused by abrupt changes in interlayer impedance. When the value is less than the weak reflection threshold, the transmission coefficient is considered to be approximately 1, and multiple reflections between layers can be ignored.

[0100] S4: Calculate the corrected complex wave number using the Waterman-Truell model and adjust the correction term caused by the spatial correlation of scattering by adjusting the structure factor.

[0101] Substituting the complex modulus into the frequency domain wave equation, the complex wave number of each thin layer and the spatial distribution density of the aggregate are obtained by solving the frequency domain wave equation.

[0102] Based on the fact that the aggregate size in the concrete medium satisfies the sparse distribution condition of the scatterer, the scattering amplitude function of aggregate particles in each thin layer is obtained. The spatial distribution density of the aggregate and the scattering amplitude function are substituted into the Waterman-Truell model, and the complex wave number of each thin layer is corrected according to the integral expression in the Waterman-Truell model.

[0103] Furthermore, after dividing the concrete medium into thickness directions, for each thin layer with a fixed thickness, an equivalent scattering particle model is determined based on the physical size parameters, density differences, and sound velocity differences of the aggregate particles in the thin layer.

[0104] Under the condition of known incident wave direction and frequency, the scattering amplitude function of equivalent scattering particles in the direction of zero scattering angle is calculated based on the classical acoustic scattering theory and using the Ratleigh scattering approximation.

[0105] wherein the scattering amplitude function describes the variation characteristics of scattering wave amplitude and phase in the form of complex number.

[0106] Further, the scattering body is sparsely distributed, specifically, the average distance between scattering bodies is much larger than the wavelength.

[0107] On the basis of meeting the condition of sparsely distributed scattering bodies, the complex wave number of the thin layer is modified using the original Waterman-Truell expression, which is expressed as:

[0108] ;

[0109] wherein, represents the complex wave number modified by the Waterman-Truell model, represents the unmodified complex wave number, represents the spatial distribution density of the aggregate particles, represents the value of the scattering amplitude function in the direction of zero scattering angle.

[0110] The spatial arrangement information of the aggregate particles in the concrete medium is collected, and the Fourier spectrum analysis is used to calculate the structure factor;

[0111] The structure factor is introduced into the integral expression of the Waterman-Truell model as a scattering correlation correction parameter, the contribution proportion of the scattering amplitude function to the perturbation term of the complex wave number is modified, and the modified complex wave number is recalculated.

[0112] Further, the modified complex wave number is recalculated, which is expressed as:

[0113] ;

[0114] wherein, represents the complex wave number recalculated by combining the scattering spatial correlation correction term, represents the structure factor.

[0115] S5: According to the ultrasonic wave attenuation coefficients of each thin layer, the total attenuation value on the propagation path is calculated, and the total attenuation model of the ultrasonic wave propagation path in the concrete is established.

[0116] Based on the complex value function of the imaginary part of the modified complex wave number, the ultrasonic wave attenuation coefficient corresponding to each thin layer with fixed thickness is obtained.

[0117] Based on the thickness of each thin layer, the ultrasonic attenuation coefficient of each thin layer is multiplied by the thickness layer by layer to obtain the local attenuation of each thin layer.

[0118] Further, the local attenuation of each thin layer is multiplied by the thickness layer by layer to obtain the local attenuation of each thin layer. Indicated as:

[0119] ;

[0120] Wherein, Indicates the local attenuation of the first thin layer.

[0121] The local attenuations of all thin layers are linearly superimposed according to the spatial coordinate axis direction to obtain the total attenuation value on the ultrasonic propagation path.

[0122] Based on the obtained local attenuation and total attenuation value, an ultrasonic propagation path total attenuation model in concrete is established.

[0123] Further, the ultrasonic propagation path total attenuation model is indicated as:

[0124] ;

[0125] Wherein, Indicates the total number of layered thin layers, Indicates the total attenuation value of the concrete medium at the frequency, which is used to evaluate the material density and loss characteristics.

[0126] The embodiment also provides a concrete ultrasonic propagation characteristic modeling system, comprising: a rheological modeling module, which is used to obtain rheological behavior data of un-solidified cement paste, establish a fractional order viscoelastic constitutive model of concrete paste by using Caputo type fractional order derivative, and obtain complex modulus; a wave analysis module, which is used to construct a frequency domain wave equation by using the complex modulus, and calculate ultrasonic attenuation coefficients of the material at different frequencies; a layered impedance module, which is used to divide the concrete medium into a plurality of thin layers according to the ultrasonic propagation direction, define the thickness of each thin layer, and set interlayer reflection control parameters according to the characteristic impedance of each thin layer; a scattering correction module, which is used to calculate a corrected complex wave number by using a Waterman-Truell model, and adjust a correction term caused by scattering spatial correlation through a structure factor; and a path attenuation module, which is used to calculate a total attenuation value on a propagation path according to the ultrasonic attenuation coefficient of each thin layer, and establish an ultrasonic propagation path total attenuation model in concrete.

[0127] The embodiment also provides a computer device suitable for the case of the concrete ultrasonic propagation characteristic modeling method, comprising: a memory and a processor; the memory is used to store computer executable instructions, and the processor is used to execute the computer executable instructions to realize the concrete ultrasonic propagation characteristic modeling method proposed in the above embodiment.

[0128] The computer device can be a terminal, which includes a processor, a memory, a communication interface, a display screen and an input device connected by a system bus. The processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for running the operating system and the computer program in the non-volatile storage medium. The communication interface of the computer device is configured to perform wired or wireless communication with an external terminal. The wireless communication can be achieved by WIFI, an operator network, NFC (Near Field Communication) or other technologies. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen. The input device of the computer device can be a touch layer overlaid on the display screen, or a key, a trackball or a touchpad arranged on the shell of the computer device, or an external keyboard, a touchpad or a mouse, etc.

[0129] The embodiment also provides a storage medium having a computer program stored thereon, the program being executed by a processor to implement the modeling method for concrete ultrasonic wave propagation characteristics. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as a static random access memory (SRAM), an electrically erasable programmable read-only memory (EEPROM), an erasable programmable read-only memory (EPROM), a programmable read-only memory (PROM), a read-only memory (ROM), a magnetic memory, a flash memory, a magnetic disk or an optical disk.

[0130] In summary, the viscoelastic behavior of the concrete paste is more accurately characterized by constructing a viscoelastic constitutive model by using Caputo fractional derivative, the fitting ability of the complex modulus in the frequency domain is improved, and thus the frequency response consistency and simulation accuracy are improved; by introducing the Waterman-Truell scattering model and combining the structure factor for modification, the non-ideal distribution characteristics of the aggregate in space can be effectively considered, and the ability to characterize the multi-scale scattering characteristics and frequency-dependent attenuation is improved; by the layered model based on the wave impedance difference and the wave amplitude transfer formula, combined with the interlayer reflection threshold judgment and the weak reflection approximation, the layer-by-layer attenuation modeling of the ultrasonic propagation path in the heterogeneous concrete is realized, and the model structure is simplified and the interpretability is improved.

[0131] It should be noted that the above examples are only used to illustrate the technical solutions of the present application and are not limiting, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present application, which should be covered in the scope of the claims of the present application.

Claims

1. A method for modeling the ultrasonic wave propagation characteristics in concrete, characterized in that: include, The rheological behavior data of uncured cement paste were obtained, and a fractional viscoelastic constitutive model of concrete paste was established using Caputo-type fractional derivatives to obtain the complex modulus. A frequency domain wave equation was constructed using the complex modulus to calculate the ultrasonic attenuation coefficient of the material at different frequencies. The concrete medium is divided into several thin layers according to the direction of ultrasonic propagation, the thickness of each thin layer is defined, and the interlayer reflection control parameters are set according to the characteristic impedance of each thin layer. The corrected complex wave number was calculated using the Waterman-Truell model, and the correction term caused by the spatial correlation of scattering was adjusted by the structure factor. Based on the ultrasonic attenuation coefficient of each thin layer, the total attenuation value along the propagation path is calculated, and a total attenuation model of ultrasonic propagation path in concrete is established.

2. The method for modeling the ultrasonic wave propagation characteristics of concrete as described in claim 1, characterized in that: The rheological behavior data includes stress-strain relationship data, shear viscosity data, dynamic modulus data, relaxation time data, and thixotropic recovery data.

3. The method for modeling the ultrasonic wave propagation characteristics of concrete as described in claim 2, characterized in that: The steps for establishing a fractional viscoelastic constitutive model of concrete paste using Caputo-type fractional derivatives and obtaining the complex modulus are as follows: Frequency-complex modulus response curves were constructed based on the rheological behavior data of uncured cement paste. By fitting the frequency-complex modulus response curves, fractional order, instantaneous elastic modulus, equivalent viscous modulus, and relaxation time factor were defined. By using the fractional order, instantaneous elastic modulus, equivalent viscous modulus, and relaxation factor as parameters in the Caputo-type fractional derivative expression, a Caputo-type fractional viscoelastic constitutive equation describing the viscoelastic response behavior of uncured cement paste is constructed. The Caputo-type fractional viscoelastic constitutive equation is applied to concrete slurry medium to establish a fractional viscoelastic constitutive model of concrete slurry. By performing a Fourier transform on the expression of the Caputo-type fractional derivative in the fractional viscoelastic constitutive model, the frequency domain response function of the concrete slurry containing complex frequency terms is obtained. The complex modulus is obtained by performing a complex frequency transformation on the frequency domain response function of the concrete slurry.

4. The method for modeling the ultrasonic wave propagation characteristics of concrete as described in claim 3, characterized in that: The specific steps for constructing a frequency domain wave equation using complex modulus and calculating the ultrasonic attenuation coefficient of the material at different frequencies are as follows: Substituting the complex modulus into the frequency domain constitutive relation of a one-dimensional linear viscoelastic medium, an expression for the relationship between the stress spectrum and the strain spectrum is established. Assuming the concrete medium is an unbounded, homogeneous, linear viscoelastic medium, and the ultrasonic wave propagates principally along the x-direction, then the particle displacement spectrum of the ultrasonic wave is denoted as... ,in, Expressed as angular frequency; Combining the mass conservation equation and the momentum conservation equation, the strain spectrum is expressed as the first derivative of the particle displacement spectrum with respect to space, and the stress spectrum is expressed as the second partial derivative of the particle displacement spectrum. Based on the relationship between stress spectrum and particle displacement spectrum, the particle displacement spectrum is substituted into the one-dimensional acoustic wave control equation to construct a one-dimensional frequency domain wave equation containing complex modulus. Calculate the complex wavenumber in different frequency domains; The ultrasonic attenuation coefficient at different frequencies is obtained by using the complex-valued function of the imaginary part of the complex wavenumber.

5. The method for modeling the ultrasonic wave propagation characteristics of concrete as described in claim 4, characterized in that: The specific steps for dividing the concrete medium into several thin layers according to the direction of ultrasonic propagation, defining the thickness of each thin layer, and setting interlayer reflection control parameters according to the characteristic impedance of each thin layer are as follows: Based on the entire ultrasonic wave propagation path along the main propagation direction, a spatial coordinate axis for the concrete medium is established, and layer thickness control conditions are set. Based on the spatial coordinate axes and the layer thickness control conditions, the concrete is divided into several thin layers with fixed thickness along the main propagation direction. Based on the local density and local effective wave velocity of each thin layer, the characteristic impedance of each thin layer is calculated, and the characteristic impedances of two adjacent thin layers are extracted sequentially according to the spatial coordinate axis order. Based on the difference in characteristic impedance between two adjacent thin layers, the interface reflection coefficient is calculated and the interlayer reflection control coefficient is set.

6. The method for modeling the ultrasonic wave propagation characteristics of concrete as described in claim 5, characterized in that: The steps for calculating the corrected complex wavenumber using the Waterman-Truell model and adjusting the correction term caused by scattering spatial correlation using the structure factor are as follows: Substitute the complex modulus into the frequency domain wave equation, and obtain the complex wave number and spatial distribution density of the aggregate for each thin layer by solving the frequency domain wave equation. Based on the fact that the aggregate size in the concrete medium satisfies the sparse distribution condition of the scatterer, the scattering amplitude function of aggregate particles in each thin layer is obtained. The spatial distribution density of aggregate and the scattering amplitude function are substituted into the Waterman-Truell model, and the complex wave number of each thin layer is corrected according to the integral expression in the Waterman-Truell model. The spatial arrangement information of aggregate particles in concrete medium is collected, and the structural factor is calculated using Fourier spectral analysis. The structure factor is introduced as a scattering correlation correction parameter into the integral expression of the Waterman-Truell model to modify the contribution ratio of the scattering amplitude function to the complex wavenumber perturbation term, and the corrected complex wavenumber is recalculated.

7. The method for modeling the ultrasonic wave propagation characteristics of concrete as described in claim 6, characterized in that: The steps for calculating the total attenuation value along the propagation path based on the ultrasonic attenuation coefficient of each thin layer and establishing a total attenuation model for ultrasonic wave propagation path in concrete are as follows: Based on the complex-valued function of the imaginary part of the modified complex wavenumber, the ultrasonic attenuation coefficient corresponding to each thin layer with a fixed thickness is obtained. Based on the thickness of each thin layer, the ultrasonic attenuation coefficient of each thin layer is multiplied by the thickness layer by layer to obtain the local attenuation of each thin layer. The local attenuation values ​​of all thin layers are linearly superimposed according to the spatial coordinate axis to obtain the total attenuation value along the ultrasonic wave propagation path. Based on the obtained local attenuation and total attenuation values, a total attenuation model for the ultrasonic wave propagation path in concrete is established.

8. A concrete ultrasonic wave propagation characteristic modeling system, based on the concrete ultrasonic wave propagation characteristic modeling method according to any one of claims 1 to 7, characterized in that: include, The rheological modeling module is used to obtain rheological behavior data of uncured cement paste. It uses Caputo-type fractional derivatives to establish a fractional viscoelastic constitutive model of concrete paste and obtain the complex modulus. The wave analysis module is used to construct frequency domain wave equations using complex modulus and calculate the ultrasonic attenuation coefficient of materials at different frequencies. The layered impedance module is used to divide the concrete medium into several thin layers according to the direction of ultrasonic propagation, define the thickness of each thin layer, and set the interlayer reflection control parameters according to the characteristic impedance of each thin layer. The scattering correction module is used to calculate the corrected complex wave number using the Waterman-Truell model and adjust the correction term caused by the spatial correlation of scattering through the structure factor. The path attenuation module is used to calculate the total attenuation value along the propagation path based on the ultrasonic attenuation coefficient of each thin layer, and to establish a total attenuation model of ultrasonic wave propagation path in concrete.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the concrete ultrasonic wave propagation characteristic modeling method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the concrete ultrasonic wave propagation characteristic modeling method according to any one of claims 1 to 7.

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