Effect of different clay additions to concrete on its ultrasonic acoustic parameters and compressive strength

Abstract

Due to various factors, the concrete may contain mud, a condition that can lead to a decrease in strength and changes in the ultrasonic acoustic parameters of the concrete. In order to study the effect of concrete mud content ($\:{\gamma\:}_{Mc}$) on ultrasonic acoustic parameters and compressive strength, this paper firstly derived the relationship equations between concrete mud content and acoustic parameters and compressive strength. Subsequently, the acoustic parameters and compressive strength were tested for concrete specimens with different mud contents cast on site. Finally, the effects of concrete mud content on wave velocity, sound time, amplitude, frequency and strength were analyzed according to the measured acoustic parameters, and the relational equations of mud content on acoustic parameters were verified, which provided a reference for evaluating the defective degree of concrete mud content. The main conclusions are: According to sound field theory, the higher the mud content of concrete, the lower its strength, the higher the sound time value, the lower the sound velocity value, and the smaller the amplitude value. The measured data shows that as the age of concrete containing mud increases, its sound velocity value increases, the sound duration value decreases, the amplitude changes are dispersed, and the frequency value increases. Specifically, with the increase of concrete age and when $\:{\gamma\:}_{Mc}$ is between 0 and 10%, the changes in concrete sound velocity and sound time are minimal; With the increase of concrete age and when$\:{\:\gamma\:}_{Mc}$ exceeds 20%, the frequency value significantly increases; The changes in amplitude values are similar during the age of concrete from 7 to 28 days. The measured parameters indicate that an increase in the mud content of concrete will lead to a decrease in its compressive strength, a decrease in sound velocity, an increase in sound duration, a decrease in amplitude, and a decrease in frequency. This law is highly consistent with theoretical deductions. Specifically, as $\:{\gamma\:}_{Mc}$ increases, there is a non-linear relationship between compressive strength and $\:{\gamma\:}_{Mc}$ (R²=0.97); When $\:{\gamma\:}_{Mc}$ is greater than 10%, the sound velocity and sound time values change significantly, and both show linear and nonlinear relationships with the mud content; As $\:{\gamma\:}_{Mc}$ increases, the amplitude also exhibits a nonlinear relationship with $\:{\gamma\:}_{Mc}$ (R²=0.91);When $\:{\gamma\:}_{Mc}$ is greater than 20%, the frequency value changes significantly and shows a linear relationship with $\:{\gamma\:}_{Mc}$ (R²=0.95).In addition, concrete with higher mud content has a longer first wave period, larger waveform spacing, and faster signal attenuation.

Introduction

Concrete materials are widely used in various structures such as bridges, tunnels, and house buildings due to their excellent properties¹. However, during the actual use of concrete, the concrete may contain mud or mud entrapment to different degrees due to a variety of factors. For example, the concrete aggregate and sand itself may contain mud (Fig. 1), in addition, the collapse of the pile foundation hole wall may also lead to the phenomenon of mud entrapment (Fig. 2)^2,3.Concrete containing mud will hinder the bonding of aggregate and cementitious materials, thus weakening its strength and affecting the safety and durability of the structure, which in turn affects the overall work performance, and there are certain safety hazards^4,5. Therefore, it is necessary to detect the mud content of new and old concrete structures. As a non-destructive testing technology, concrete ultrasonic testing has been widely used in the detection of defects in concrete structures by virtue of extremely high penetration, wide frequency range and good directionality^6,7,8. By analyzing the reflection and scattering laws of ultrasonic waves in concrete structures, and analyzing the echo information such as acoustic time value, frequency, amplitude, and wave speed and other parameters, information such as the location of the defects in the concrete structure and the strength of the concrete can be determined^9,10,11,12.

Fig. 1

Concrete aggregate with mud phenomenon.

Fig. 2

Mud content phenomenon of pile foundation.

In recent years, many scholars have investigated the effects of concrete strength, integrity, and mud content on strength through ultrasonic technology, and many research results have been achieved. Wu Yonggen¹³ studied the effect of mud content on the strength and durability of dry-hard cementitious sand, and the results showed that when the mud content reaches 3%, the effect of mud on the slump of concrete has been more obvious, when the mud content increases to 5%, the concrete begins to become dry-hard, and when the mud powder content reaches 10%, the initial slump of the concrete mix is almost 0. Goldbeck¹⁴ discussed the effect of adding clay or silt to concrete, on the strength of concrete. The results of the study showed that when a certain amount of silt is present in concrete, increasing the unit water consumption can keep the slump of concrete unchanged, but the increase in the total water-cement ratio will make the strength of concrete decrease, so it is believed that there is a correlation between the amount of concrete silt and the compressive strength. Li Jinhui et al.¹⁵ added clay in concrete showed that with the increase of clay content, the compressive strength, flexural tensile strength and flexural tensile elastic modulus of concrete will show a significant downward trend, especially the clay content of more than 5%, the mechanical properties of the reduction of the more obvious, but the compressive elastic modulus of concrete does not change greatly. Elahi, A¹⁶ investigated the effect of different clay additions on concrete mixes ease, compressive strength, permeability and acid erosion. The results showed that as the clay content in concrete increases, the concrete availability decreases; a 12% decrease in compressive strength of concrete was observed with the addition of clay as compared to the control sample and it adversely affected the permeability and acid erosion resistance of concrete. Hailong Zhang¹⁷ et al., investigated T2 spectra to characterize the changes in internal porosity of concrete specimens using ultrasound and NMR techniques. The results showed that there were three wave peaks in the T2 spectrum of concrete during freeze-thaw cycle degradation, in which the area of the main peak, which indicated the microscopic small cracks inside the specimen, accounted for about 80% of the total area. Chen Jin⁶ and others, in order to more accurately identify the dehollowing defects and internal defects of steel pipe concrete, combined infrared thermography and ultrasonic detection technology, and proposed a non-destructive testing method for steel pipe concrete structural components. The results show that the combination of infrared thermography and ultrasonic method can more accurately identify the dehollowing defects and internal defects of steel pipe concrete columns. Ling Ganzhan et al.¹⁸, in order to study the effect of concrete compressive strength, detection age, steel pipe diameter and other parameters on ultrasonic acoustic parameters, carried out on-site testing of five steel pipe concrete arch bridges and seven steel pipe concrete specimens. Their results show that: when there is a tube steel structure such as stiffening plate in the measurement area, the ultrasonic wave velocity increase can be up to 3%~5%, and the wave amplitude and frequency reduction can be up to 12%~18% and 15%~20%, respectively; the correlation between acoustic parameters and the compressive strength of concrete, the detection age and the diameter of the steel pipe is large. HANG, H., Z. et al.¹⁹ carried out ultrasonic testing of concrete specimens, and utilized the spectral analysis method to derive the spectral characteristics of ultrasound. By comparing the spectral difference between intact concrete and defective concrete acoustic wave test, the internal defective condition of concrete was comprehensively judged, and the acoustic wave test of pile concrete of an actual project was used as an example to get the conclusion that the feasibility of using spectral analysis method to judge the concrete defects of the pile body is better.

The above studies have shown that the addition of clay or silt to concrete significantly affects a number of concrete properties, including parameters such as collapse, compatibility, permeability and acid attack. The compressive and tensile strengths of concrete decrease to different degrees with the increase of clay content in concrete, and there is a certain degree of correlation between clay content and concrete strength. In addition, the method of ultrasonic acoustic parameter analysis for judging the internal defects of concrete has high feasibility, and compared with other inspection methods, ultrasonic inspection has the advantages of high applicability, simple operation and convenience. However, there are no reports on the effects of different mud contents on ultrasonic acoustic parameters (e.g., wave speed, sound time, amplitude and frequency) in concrete structures.

In view of this, this paper firstly derives the relational equation for the effect of mud volume on the acoustic parameters of concrete based on the relevant theories of sound field and sound pressure. Subsequently, 8 concrete specimens, 1 pure mud specimen, 24 concrete cube specimens, 24 concrete prism specimens, and 6 pure mud specimens were designed and cast. The effects of mud content in concrete on ultrasonic acoustic parameters (e.g., wave speed, sound time, amplitude, and frequency) and mechanical properties were analyzed by testing the ultrasonic acoustic parameters and compressive strengths at different levels of mud content, aiming at clarifying the interrelationships between the degree of mud mixing and the ultrasonic acoustic parameters and mechanical properties of concrete. This will help to accurately identify potential hazards in concrete and assess its strength, thus ensuring the safety and reliability of concrete structures.

Effect of concrete strength on ultrasonic acoustic parameters

Effect of concrete mud content on sound velocity and sound time values

Ultrasonic waves in the same medium longitudinal wave propagation speed are the fastest, so in the concrete inspection receiving probe is the first to get is the longitudinal wave²⁰, the ultrasonic waves in the concrete medium is simplified to the ideal state along the straight line propagation^21,22, as shown in Fig. 3. Based on the differential equation of motion of solid medium and Hooke’s law, the fluctuation equation of acoustic wave in an infinite solid elastic medium can be derived, and the expression is shown in Eq. (1)^23,24,25.

$$\:\begin{array}{c}\left\{\begin{array}{c}\rho\:\frac{{\partial\:}^{2}u}{\partial\:{t}^{2}}=(\lambda\:+G)\frac{\partial\:e}{\partial\:x}+\mu\:{\nabla\:}^{2}u\\\:\rho\:\frac{{\partial\:}^{2}v}{\partial\:{t}^{2}}=(\lambda\:+G)\frac{\partial\:e}{\partial\:y}+\mu\:{\nabla\:}^{2}v\\\:\rho\:\frac{{\partial\:}^{2}w}{\partial\:{t}^{2}}=(\lambda\:+G)\frac{\partial\:e}{\partial\:z}+\mu\:{\nabla\:}^{2}w\end{array}\right.\end{array}$$

(1)

Where: u, v, and w are the displacements of the microelement in the three orthogonal directions of X, Y, and Z, respectively; ρ is the density of the solid medium; G is the shear modulus of the solid medium; λ is a constant; and ∇2 is the Laplace operator.

From Eq. (1), G and λ can be expressed by the elastic modulus E and Poisson’s ratio $\:\mu\:$ of the medium, and if the influence of the elastic dynamics’ boundary is ignored, the expressions of propagation velocity $\:{V}_{l}$ and propagation time $\:{T}_{l}$ are obtained as Eqs. (2) and (3) for the propagation of ultrasonic longitudinal wave in the infinite isotropic homogeneous elastic body.

Fig. 3

Simplified model of concrete ultrasonic propagation.

$$\:\begin{array}{c}{V}_{l}=\sqrt{\frac{E\left(1-\mu\:\right)}{\rho\:\left(1+\mu\:\right)\left(1-2\mu\:\right)}}\end{array}$$

(2)

$$\:\begin{array}{c}{T}_{l}=\frac{{L}_{l}}{\sqrt{\frac{E\left(1-\mu\:\right)}{\rho\:\left(1+\mu\:\right)\left(1-2\mu\:\right)}}}\end{array}$$

(3)

Where: E is the static modulus of elasticity of concrete; $\:{L}_{l}$ is the ultrasonic propagation distance; $\:\mu\:$ is the Poisson’s ratio of concrete; $\:\rho\:$ is the density of concrete medium.

From Eqs. (2) and (3), it can be concluded that the ultrasonic sound speed and sound time values are related to the density, Poisson’s ratio, and elastic modulus of the concrete medium. Where the relationship between the concrete ultrasonic wave velocity value, sound time value and concrete elastic modulus can be expressed as shown in Eq. (4):

$$\:\begin{array}{c}E={{V}_{l}}^{2}\cdot\:\rho\:\cdot\:\frac{\left(1+\mu\:\right)\left(1-2\mu\:\right)}{1-\mu\:}={{L}_{l}}^{2}\cdot\:\rho\:\cdot\:\frac{1}{{{T}_{l}}^{2}}\cdot\:\frac{\left(1+\mu\:\right)\left(1-2\mu\:\right)}{1-\mu\:}\end{array}$$

(4)

There is a proportional relationship between the static modulus of elasticity and compressive strength of concrete, i.e., when the compressive strength increases, the static modulus of elasticity also tends to increase²⁶. Based on the statistical analysis of different strength classes of concrete and static modulus of elasticity test values, Eq. (5) gives an empirical equation for the static modulus of elasticity of concrete and concrete strength values^27,28:

$$\:\begin{array}{c}E=\frac{{10}^{5}}{2.2+\left(\frac{34.74}{{f}_{cu}}\right)}\end{array}$$

(5)

Where: $\:{f}_{cu}$ is the axial compressive strength of concrete cube, MPa.

Bringing Eq. (5) into Eq. (4) yields the relationship between the compressive strength of concrete cube and sound time, sound velocity, Poisson’s ratio and density as shown in Eq. (6). It is worth noting that since the dynamic modulus of elasticity of concrete is not equal to the static modulus of elasticity, the modulus of elasticity used at this point is only the static modulus of elasticity:

$$\:\begin{array}{c}{f}_{cu}=\frac{34.74}{{10}^{5}}\cdot\:\frac{{{V}_{l}}^{2}\cdot\:\rho\:\cdot\:\left(1+\mu\:\right)\left(1-2\mu\:\right)}{1-\mu\:}=\frac{34.74}{{10}^{5}}\cdot\:\frac{{{L}_{l}}^{2}\cdot\:\rho\:\cdot\:\left(1+\mu\:\right)\left(1-2\mu\:\right)}{{{T}_{l}}^{2}\cdot\:\left(1-\mu\:\right)}\end{array}$$

(6)

Expressing $\:\left(1+\mu\:\right)\left(1-2\mu\:\right)/1-\mu\:$ in terms of a coefficient to be determined A, Eq. (6) can be expressed as Eq. (7):

$$\:\begin{array}{c}{f}_{cu}=\frac{34.74}{{10}^{5}}{{V}_{l}}^{2}\cdot\:\rho\:\cdot\:A=\frac{34.74}{{10}^{5}}\cdot\:\frac{{{L}_{l}}^{2}\cdot\:\rho\:\cdot\:}{{{T}_{l}}^{2}}\cdot\:A\end{array}$$

(7)

The ultrasonic sound time and speed of sound of concrete are related to the density of the medium, the coefficient of determination A and the compressive strength of the cube. The density of concrete is only related to mass and volume, and the effect of mud content on density can be neglected. Therefore, the ultrasonic sound time and sound velocity values are mainly influenced by the coefficient to be determined A, i.e. Poisson’s ratio. However, the Poisson’s ratio of concrete is not constant; it is affected by factors such as the type of cement, the type of aggregate and the density of the concrete. Literature shows that the Poisson’s ratio of concrete generally ranges from 0.14 to 0.36^29,30,31. In this paper, it is suggested that measured tests of Poisson’s ratio should be carried out for different types of concrete. However, in the absence of measurement data, a value of 0.2 can also be taken in accordance with the relevant recommendations of the European norm (EN 1992), the ISO international standard (ISO 1920-10, 2015) and the Chinese norm (GB/T 50010 − 2010).

In summary, under the above conditions, the ultrasonic sound time and sound velocity values are mainly related to the compressive strength of concrete. The mud content of concrete will lead to a decrease in the compressive strength of concrete^14,15,16, which will lead to an increase in the sound time value and a decrease in the sound velocity value.

Effect of concrete mud content on amplitude

Due to the concrete mud will lead to the existence of internal defects in concrete, and concrete and its internal defects at the modulus of elasticity, Poisson’s ratio and density and other parameters of the difference is large, resulting in ultrasonic reflections and scattering in the defects, which leads to a reduction in the received acoustic wave energy^32,33. To analyze the internal cavity of concrete as an example, because the analysis method of cylinder scattering is also similar to that of circular sphere scattering, and the results are relatively similar, according to the acoustic foundation and theoretical acoustics, this paper directly gives the results of scattering acoustic field analysis under the condition of free-boundary circular sphere, as shown in Fig. (4).

Fig. 4

Coordinate model for scattering of plane wave on a spherical surface.

Equation (8) shows the sound pressure of an incident plane wave using spherical coordinates³⁴:

$$\:\begin{array}{c}{p}_{i}\left(x,t\right)={p}_{0}{e}^{j\left(\omega\:t-kx\right)}={p}_{0}{e}^{j\omega\:t}{e}^{-{jkrcos}\theta\:}\end{array}$$

(8)

Where: $\:k$ is the number of ultrasonic waves; $\:\omega\:$ represents the angular frequency; $\:r$ represents the radius; $\:\theta\:$ is the angle.

Taking the plane wave sound pressure of Eq. (8) and performing a spherical wave decomposition yields Eq. (9).

$$\:{p}_{i}(r,\theta\:,t)={p}_{0}{e}^{j\omega\:x}\sum\:_{m=0}^{{\infty\:}}\:(-j{)}^{m}\left(2m+1\right){P}_{m}\left({cos}\theta\:\right){j}_{m}\left(kr\right)$$

(9)

where: p_m represents the ball function; p represents the order, and j_m is the ball Bessel function.

Since the incident plane wave propagates along the x-axis, the sound field is symmetric along the x-axis, then the scattered wave sound pressure can be formally transformed:

$$\:\begin{array}{c}{p}_{s}\left(r,\theta\:,t\right)={e}^{j\omega\:t}\sum\:_{m=0}^{{\infty\:}}\:{a}_{m}{P}_{m}\left(\text{cos}\theta\:\right){h}_{m}^{\left(2\right)}\left(kr\right)\end{array}$$

(10)

Where: a_m is a constant, determined by the boundary conditions.

The boundary conditions for a free circular spherical surface are shown in Eq. (11):

$$\:\begin{array}{c}{\left.\left({p}_{i}+{p}_{s}\right)\right|}_{r=0}=0\end{array}$$

(11)

The scattered wave and incident wave equations can be substituted into the boundary condition Eq. (10) to find the coefficient a_m as shown in Eq. (12):

$$\:\begin{array}{c}{a}_{m}=\left[-(-j{)}^{m}(2m+1)\right]\frac{{j}_{m}\left(ka\right)}{{h}_{m}^{\left(2\right)}\left(ka\right)}{P}_{0}\end{array}$$

(12)

Therefore, the scattered sound field sound pressure of a free surface sphere can be expressed as Eq. (13):

$$\:\begin{array}{c}{p}_{s}\left(r,\theta\:,t\right)={p}_{0}{e}^{j\omega\:t}\sum\:_{m=0}^{{\infty\:}}\:\left[-(-j{)}^{m}(2m+1)\frac{ka}{{h}_{m}^{\left(2\right)}\left(ka\right)}\right]{h}_{m}^{\left(2\right)}\left(kr\right){P}_{m}\left(\text{cos}\theta\:\right)\end{array}$$

(13)

Further, the scattered acoustic field direction function may be as follows:

$$\:\begin{array}{c}R\left(\theta\:\right)=\frac{1}{ka}\sum\:_{m=0}^{{\infty\:}}\:{b}_{m}{e}^{j\frac{m+1}{2}\pi\:}{P}_{m}\left(\text{cos}\theta\:\right)\end{array}$$

(14)

In Eq. (14):

$$\:{b}_{m}=(-j{)}^{m}\left(2m+1\right)\frac{{j}_{m}\left(ka\right)}{{h}_{m}^{\left(2\right)}\left(ka\right)}$$

(15)

In Eq. (15), a represents the sphere radius dimension, ka represents the comparative dimension of both the acoustic wavelength and the object linearity, f represents the frequency, λ represents the wavelength, and k represents the object wave number. And $\:k=\frac{2\varPi\:}{}$and$\:=\frac{c}{f}$, can be obtained:

$$\:\begin{array}{c}ka=\frac{2\pi\:}{\lambda\:}\cdot\:a=\frac{2\pi\:f}{c}\cdot\:a\end{array}$$

(16)

Through the above analysis, it can be concluded that when the wave number k is certain, that is, when the wavelength is certain, along with the increase of the radius a of the free sphere, ka increases correspondingly, which leads to the enhancement of the sound intensity of the scattered wave, which indicates that the sound pressure changes in the sound field due to the natural sphere is bound to exist. When ka = 1, the defects in the concrete caused by the presence of mud make the radius of the natural sphere smaller than the wavelength of the sound wave, which results in weak scattering, i.e., acoustic wave bypassing. Therefore, the mud content of concrete leads to a weakening of the emitted ultrasonic signal.

Ultrasonic signals can be expressed in terms of acoustic field sound pressure, which in turn can be expressed as amplitude. Therefore, the presence of mud in concrete results in a decrease in the amplitude of the received ultrasonic signal, and the attenuation of the amplitude increases as the mud content increases.

Tests

Test conditions and concrete ratio

The concrete used in this test is Yiliang Red Lion P. O 42.5 ordinary silicate cement of Yunnan Province, according to the information provided by the manufacturer, the technical performance indexes are shown in Table 1; the fineness modulus of the sand is 2.94, continuous grading, 2 area sand, gravel particle size range of 5 ~ 20 mm, continuous grading; the water is city water; the red clay used in the test is taken from Kunming City, Yunnan Province, and the depth of soil is about 1 m. The color is dark red, the physical properties are shown in Table 2. In order to accurately assess the effect of mud content on the acoustic parameters of concrete, the aggregate was washed during the test, and the mud-containing concrete test conditions shown in Table 3 were designed and cast. Among them, Case 1 is ordinary concrete; Case 2 to Case 8 are concrete with different mud contents; Case 9 is pure mud specimen. The mud content of concrete was calculated as shown in Eq. (17).

$$\:\begin{array}{c}{\gamma\:}_{Mc}=\frac{{\gamma\:}_{C}+{\gamma\:}_{W}+{\gamma\:}_{St}+{\gamma\:}_{Sa}}{{\gamma\:}_{M}}\times\:100\%\end{array}$$

(17)

Table 1 Performance indexes of P. O 42.5 grade ordinary silicate cement.

Table 2 Physical properties of clay.

Table 3 Concrete mix ratio for each condition.

Where: $\:{\gamma\:}_{Mc}$ is the mud content of concrete; $\:{\gamma\:}_{C}$ is the amount of concrete cement, kg-m^− 3; $\:{\gamma\:}_{W}$ concrete water consumption, kg-m^− 3; $\:{\gamma\:}_{St}$ is the amount of concrete primary aggregates, kg-m^− 3; $\:{\gamma\:}_{Sa}$ is the amount of concrete mechanical sand, kg-m^− 3; $\:{\gamma\:}_{M}$ is the amount of concrete participating in the soil, kg-m^− 3.

Specimen profile and testing methods

The test equipment used in this test is ZBL-U5200 nonmetallic ultrasonic detector (as shown in Fig. 5) produced by Beijing ZhiBoLian Science and Technology Co. and YAW-2000D microcomputer-controlled electro-hydraulic servo pressure tester produced by Jinan Times Trying Gold Testing Machine Co. The specimen process refers to the provisions of the Standard for Test Methods of Physical and Mechanical Properties of Concrete (GB/T50081-2019)³⁵. For the concrete ultrasonic test components, the design strength grade is C30, corresponding to the working condition 1 ~ working condition 9, and the dimensions are 450 mm×450 mm×450 mm, as shown in Fig. 6. Concrete axial compressive specimens, 6 specimens (3 cubes and 3 prisms) were cast for each condition, totaling 54 concrete specimens. The specimens were placed on the pressure testing machine to apply compressive stress until the specimens were damaged and their ultimate load capacity was recorded, as shown in Fig. 7. The arrangement of the measurement points of the concrete members is shown in Fig. 8, and all of them were measured in pairs.

Fig. 5

ZBL-U5200 Non-metallic Ultrasonic Detector.

Fig. 6

Concrete specimens containing mud.

Fig. 7

Loading diagram of concrete specimen.

Fig. 8

Schematic diagram of ultrasonic inspection of concrete components.

Data-processing methods

Due to the inherent non-homogeneous properties of concrete materials, even in the absence of obvious defects, the sound velocity, amplitude and main frequency parameters of normal concrete structures fluctuate within a certain range. Therefore, for the judgment of ultrasonic acoustic parameters of concrete, there usually does not exist a specific critical value, but a probabilistic statistical method is used for defect determination^36,37. Similarly, the compressive strength of concrete should be assessed in the same way. In order to reasonably judge the ultrasonic acoustic parameters and compressive strength values of concrete at a certain stage, the arithmetic mean value of ultrasonic acoustic parameters and concrete mechanical property parameters measured several times should usually be calculated according to the actual situation in the field, as shown in Eq. (18). Therefore, the ultrasonic acoustic parameters and concrete compressive strength mentioned subsequently in this paper are arithmetic mean values.

$$\:\begin{array}{c}{m}_{x}=\frac{1}{n}\sum\:_{i=1}^{n}\:{x}_{i}\end{array}$$

(18)

Where: $\:{x}_{i}$ represents the acoustic parameter value or concrete compressive strength value of the ith measurement point, and n is the number of measurement points included in the statistics.

Test results and analysis

Effect of mud content on compressive strength of concrete

In order to investigate the effect of mud content on the compressive strength of concrete, Case 1 to Case 9 were taken and analyzed and the axial compressive strength values of cubes and prisms measured after 28 days of curing of concrete specimens from Case 1 to Case 9 according to the standards are plotted in Figs. 9 and 10³⁵. Figures 9 and 10 show the relationship between axial compressive strength values of concrete and mud content. The mud content versus concrete strength curves for each condition were fitted using Origin (Origin 2024b, OriginLab,https://www.originlab.com) software. Combined with Table 4; Figs. 9 and 10, the analysis shows that the axial compressive strength of concrete shows a decreasing trend as the clay content of concrete increases and this decreasing trend is more pronounced as the clay content increases, this is due to the fact that when the clay content is too high, it may lead to the formation of additional defects in the concrete which will weaken the concrete strength³⁸. There is a nonlinear relationship between axial compressive strength of concrete and clay content of concrete with high correlation coefficients, both of which are 0.97. The results of the tests in this paper, the relationship between clay content of concrete and its compressive strength are also in general agreement with the results of the tests in the literature^{2,3,4] and [13}.

Table 4 Reduced strength values of concrete with mud compared to normal concrete.

Fig. 9

Relationship between different mud content and compressive strength of cubes.

Fig. 10

Relationship between different mud content and compressive strength of prisms.

Effect of mud content on sound velocity and sound time values of concrete

To study the effect of mud content on the sound velocity value and sound time value of concrete. The ultrasonic velocity values measured for concrete specimens under conditions 1 to 9 after curing for 7 days, 14 days, and 28 days according to standard³⁵ are plotted in Table 5. The relationship between age and concrete ultrasonic velocity values is shown in Fig. 11, the relationship between concrete ultrasonic velocity values and clay content is shown in Fig. 12, the relationship between age and concrete first wave sound value is shown in Fig. 13, and the relationship between concrete first wave sound value and clay content is shown in Fig. 14. Fit the mud content, ultrasonic velocity, and ultrasonic time curves of the above working conditions using Origin (Origin 2024b, OriginLab, https://www.originlab.com) software.

Table 5 Reduction of ultrasonic wave velocity values at different ages of concrete compared to normal concrete.

Combined with Figs. 11 and 13; Table 5, it can be analyzed. Except for 100% mud content, the ultrasonic sound velocity value increases with the increase of concrete age, and the ultrasonic sound time value decreases with the increase of concrete age, and the changes are small, especially in the mud content of 0–10%, the maximum is only 0.06%. This indicates that the effect of clay content of concrete on the ultrasonic sound velocity values and sound time values at different ages is small. As the age of concrete increases, the hydration of cementitious materials in clay-containing concrete develops further³⁹ and the strength of concrete increases, which leads to an increase in the value of sound velocity and a decrease in the value of sound time.

Combined with the analysis of Figs. 12 and 14; Table 5, it can be seen. The increase in the mud content of concrete leads to a decrease in the ultrasonic sound velocity value, and when the mud content is in the range of 0–10%, the change in the wave velocity value is small compared to normal concrete, with a maximum of 18.41%. However, when the mud content exceeded 10%, especially on day 28, the magnitude of change in ultrasonic wave velocity increased significantly with a growth rate of 261.36%. The first wave acoustic time value increases gradually with the increase of mud content of concrete. When the mud content is in the range of 0–10%, the variation of the first wave sound time value is small compared to that of normal concrete, with a maximum variation of 17.90 us. When the mud content is more than 10%, the variation of the first wave sound time value increases significantly, with a maximum variation of 246.57 us. This indicates that when the mud content of concrete is small, the mud containing the This indicates that when the mud content of concrete is small, the extra defects formed by the mud content are less, and the ultrasonic wave bypassing phenomenon is more limited, and thus the effect on the sound velocity value and sound time value is smaller. When the mud content is high, the sound pressure of the sound field changes significantly during the ultrasonic propagation process, which leads to the bypassing phenomenon of ultrasonic propagation paths in the mud-containing concrete, i.e., the propagation paths L_l increase, resulting in a decrease in the speed of sound and an increase in the time of sound values. This phenomenon verifies the previous conclusion: the higher the mud content of concrete, the smaller the ultrasonic sound velocity value and the larger the ultrasonic sound time value.

According to the fitting equation, the ultrasonic sound velocity value and concrete mud content are linear and nonlinear, with correlation coefficients of 0.88 and 0.98, respectively, as shown in Eqs. (19) and (20). The sound time value and concrete mud content were linear and nonlinear relationships, respectively, with high correlation coefficients of 0.97 and 0.96, as shown in the following Eqs. (21) and (22). In summary, the mud content has a small effect on the ultrasonic sound velocity value and sound time value of concrete of different ages, and the increase of mud content of concrete brings about a decrease in the ultrasonic sound velocity value and an increase in the sound time value, especially when the mud content is greater than 10%, which has the greatest effect.

$$\:\begin{array}{c}{V}_{l}\left({\gamma\:}_{Mc}\right)={3.89}^{e-\frac{{\gamma\:}_{Mc}}{47.51}}+0.81\end{array}$$

(19)

$$\:\begin{array}{c}{V}_{l}\left({\gamma\:}_{Mc}\right)=4.28{\gamma\:}_{Mc}-0.03\end{array}$$

(20)

$$\:\begin{array}{c}{T}_{l}\left({\gamma\:}_{Mc}\right)={67.30}^{e+\frac{{\gamma\:}_{Mc}}{43.10}}+28.14\end{array}$$

(21)

$$\:\begin{array}{c}{T}_{l}\left({\gamma\:}_{Mc}\right)=2.40{\gamma\:}_{Mc}+90.42\end{array}$$

(22)

Where: $\:{V}_{l}$ is the value of ultrasonic sound velocity of concrete; $\:{\gamma\:}_{Mc}$ is the mud content: $\:{T}_{l}$ is the value of sound time of the first wave of concrete.

Fig. 11

Relationship between age and ultrasonic sound velocity of concrete with different cement content.

Fig. 12

Effect of different mud content on ultrasonic sound velocity of concrete.

Fig. 13

Relationship between first wave sound time and age of concrete.

Fig. 14

Relationship between first-wave sound time and different mud contents.

Typical ultrasonic waveforms obtained from the tests are plotted in Figs. 15 and 16. The results show that for normal concrete, the first wave period is short, the waveform is smooth and the signal attenuation is slow (as shown in Fig. 15). For concrete with high mud content, the first wave period is longer, the waveforms show anomalies and are more widely spaced (anomalies in the second half of the waveforms), and the signals decay faster than for normal concrete (as shown in Fig. 16).

Fig. 15

Normal concrete.

Fig. 16

Concrete with 50% mud.

Effect of mud content on wave amplitude values of concrete

The ultrasonic amplitudes of the concrete specimens from Case 1 to Case 9, which were cured for 7, 14 and 28 days according to the standards, are plotted in Table 6, and the relationship between age and ultrasonic amplitude of concrete is shown in Fig. 17. The relationship between ultrasonic amplitude of concrete and mud content is shown in Fig. 18. The above conditions were fitted to the mud content versus ultrasonic amplitude curves using Origin (Origin 2024b, OriginLab,https://www.originlab.com) software.

Table 6 Reduction of amplitude at different ages of concrete compared to normal concrete.

Combined with Figs. 17 and 18; Table 6, it can be analyzed. At the age of 7 days, the change of ultrasonic amplitude is small when the mud content of concrete is 0 ~ 10%. This is mainly because at this time, the pore water content inside the concrete is high, and the hydration process of cement is still going on⁴⁰, the ultrasonic signal is reflected and scattered in the concrete, which leads to the reduction of sound pressure. Meanwhile, the presence of clay fills the pore structure of the concrete and absorbs some of the water, which improves the densification of the concrete and indirectly enhances its performance. This results in less variation in amplitude. During the age period from 7 to 14 days, the ultrasonic amplitude varied as follows: a small increase in amplitude was observed for concrete with 0–10% clay content, while a small decrease in amplitude was observed for concrete with more than 10% clay content. This phenomenon is due to the fact that with the extension of the age, the hydration process of the cement is further advanced and the densification of the concrete is improved. Lower mud content has less negative effect on the concrete structure and hence the magnitude increases. However, when the mud content is greater than 10%, the negative effect of clay begins to increase significantly, and this effect leads to a decrease in the overall structural properties of the concrete, which in turn leads to a decrease in the ultrasonic amplitude. This is due to the fact that high clay content makes the concrete less dense, leading to increased attenuation and scattering of the ultrasonic signal. At the age of 28 days, the amplitude decreases with the increase of concrete mud content, and the change rule tends to be stable. In addition to the age of concrete for 7 days and mud content rate of 0 ~ 10% when the ultrasonic amplitude is more stable, in the age of 14 days and 28 days, the amplitude change is more obvious. With the increase of mud content, the ultrasonic amplitude decreased significantly. This is because the high mud content leads to a decrease in the structural densification of the concrete, increasing the reflection and scattering of ultrasonic waves at the concrete defects, reducing the sound pressure and the amplitude signal at the receiving point. In normal concrete structures, ultrasonic interfacial reflections are less and energy transmission is greater, resulting in higher amplitudes. This verifies the conclusion that the higher the mud content of concrete, the lower the ultrasonic amplitude value.

According to the fitting equation, it can be seen that the ultrasonic amplitude value has a nonlinear relationship with concrete mud content, with a high correlation coefficient of 0.91, and the relationship is shown in Eq. (23).

$$\:\begin{array}{c}{f}_{a}\left({\gamma\:}_{Mc}\right)={133.63{\gamma\:}_{Mc}}^{-0.05}\end{array}（23）$$

(23)

Where: $\:{f}_{a}\left({\gamma\:}_{Mc}\right)$ is the value of ultrasonic amplitude of concrete; $\:{\gamma\:}_{Mc}$ is the mud content.

Fig. 17

Relationship between age and ultrasonic amplitude of concrete with different mud contents.

Fig. 18

Effect of different mud content on ultrasonic amplitude of concrete.

Effect of mud content on frequency values of concrete

In order to investigate the effect of mud content on the frequency peak of concrete, the ultrasonic time-domain signals measured on the concrete specimens from Case 1 to Case 9 were subjected to fast Fourier transform⁴¹. The peak frequency of condition 1 ~ 8 is plotted in Table 7, the relationship between peak frequency and age of concrete is shown in Fig. 19, and the relationship between peak frequency and mud content of concrete is shown in Fig. 20, and the above curves of mud content and peak frequency are fitted by Origin (Origin 2024b, OriginLab,https://www.originlab.com) software.

Table 7 Peak frequency ratios for different concrete ages compared to normal concrete ratio.

Combined with Table 7; Figs. 19 and 20, it can be analyzed. The peak frequency increases with the increase of the age of concrete, and the increase is small in the mud content of 0–20%, the maximum is only 11.41%, the mud content is greater than 20%, the increase is more obvious, with the increase of the age of concrete, the compressive strength increases, so that the attenuation of ultrasonic signals in the concrete is weakened. As a result, the peak ultrasonic frequency is enhanced²⁰. When the mud content of the concrete is 0–20%, the variation of the peak ultrasonic frequency is small, with a maximum of 4.11 kHz, and the frequency tends to stabilize. However, when the mud content is more than 20%, the variation of the peak frequency increases significantly up to 40.73 kHz, which indicates that the effect on the peak frequency of the concrete is small when the mud content is 0 ~ 20%, while the effect is significant when the mud content is 20 ~ 100%. The attenuation of the acoustic pressure signal is more pronounced at concrete defects, resulting in a reduction in the primary frequency of the received ultrasonic signal. Therefore, frequency is usually used as an auxiliary criterion rather than a primary acoustic detection parameter, as it is also affected by the frequency of the transducer itself^42,43.

According to the fitting equation, when the concrete mud content is from 20 to 50%, the peak frequency has a linear variation relationship with the concrete mud content, and the correlation coefficient is high at 0.95, as shown in Eq. (24). Figures 21 and 22 show the spectral curves of normal concrete and concrete with mud content of 50%, respectively. When the mud content of concrete increases, the peak frequency signal is abnormal and decreases more obviously.

$$\:\begin{array}{c}{f}_{f}\left({\gamma\:}_{Mc}\right)=1.2{\gamma\:}_{Mc}+70.64\end{array}$$

(24)

Where: $\:{f}_{f}\left({\gamma\:}_{Mc}\right)$ is the peak frequency of the ultrasonic spectral curve of concrete; $\:{\gamma\:}_{Mc}$ is the mud content.

Fig. 19

Relationship between age and frequency peaks of different mud contents.

Fig. 20

Relationship between different mud contents and frequency peaks.

Fig. 21

Normal concrete.

Fig. 22

50% mud content.

Conclusion

In this paper, the relationship between ultrasonic acoustic parameters and compressive strength of concrete with different mud content is investigated. Firstly, based on the existing theories, the relational equations of the effect of concrete mud content on ultrasonic sound time, sound velocity and amplitude were derived. Then, the ultrasonic acoustic parameters and their corresponding compressive strengths under different mud content conditions were tested by casting specimens on site. Finally, based on the measured ultrasonic acoustic parameters, the influence of concrete mud content on ultrasonic parameters such as wave velocity, sound time, amplitude and frequency were analyzed, and the empirical equations between concrete mud content and acoustic parameters and compressive strength were proposed to provide a reference basis for determining the degree of concrete mud defects. The main conclusions of this paper are as follows:

(1) Based on the theory of ultrasonic acoustic field sound pressure, the relationship of concrete mud content on ultrasonic acoustic parameters is deduced, that is, with the increase of concrete mud content, the ultrasonic acoustic time value shows a tendency to increase, while the value of the speed of sound shows a tendency to decrease, and the value of the ultrasonic amplitude and frequency shows a tendency to decrease.

(2) With the increase of concrete mud content, the axial compressive strength of concrete shows a decreasing trend, and this decreasing trend is more obvious with the increase of mud content, which is because when the clay content is too high, it may lead to the formation of additional defects in the concrete, and these defects weaken the concrete strength.

(3) Except for the mud content of 100%, the speed of sound value increases with the increase of the age of concrete and the time value of sound decreases with the increase of the age of concrete, and the magnitude of the change is small, especially when the mud content is in the range of 0 ~ 10%, the maximum is only 0.06%. The increase of concrete mud content will lead to the decrease of sound velocity value and the increase of sound time value, when the mud content is in the range of 0 ~ 10%, the change is small, when the mud content is more than 10%, the change is larger, both of which are linear and non-linear relationship with the mud content.

(4) When the mud content of concrete is small, the additional defects formed by mud are less and the ultrasonic wave bypassing phenomenon is more limited, while when the mud content is high, the ultrasonic wave bypassing phenomenon is more obvious. Concrete with higher mud content rate has longer first wave period, larger waveform spacing and faster signal attenuation.

(5) At the age of 7 days, the ultrasonic amplitude change is small when the mud content of concrete is from 0 to 10%. When the age is extended to 14 days, the amplitude of concrete with 0–10% mud content increases slightly, while the amplitude of concrete with more than 10% mud content decreases slightly. The increase in age and the advancement of the cement hydration process enhanced the densification of the concrete, which led to an increase in the magnitude. However, the negative effect of clay significantly intensified when the mud content exceeded 10%, leading to a decrease in the ultrasonic amplitude. By the age of 28 days, the amplitude decreased with the increase of clay content and the change leveled off. In addition to the age of 7 days and mud content of 0–10% of the concrete ultrasonic amplitude is more stable, in the age of 14 days and 28 days, the amplitude changes are more obvious. Ultrasonic amplitude value and concrete mud content is a nonlinear relationship, correlation coefficient is 0.91.

(6) The frequency value increases with the increase of the age of concrete, and the increase is small in the mud content of 0–20%, the maximum is only 11.41%, the mud content is greater than 20%, the increase is more obvious. The higher the mud content, the lower the peak frequency, when the mud content is greater than 20%, the peak frequency change is more obvious, the rate of change is 390.38%; when the mud content of concrete is greater than 20%, the peak frequency and the mud content of concrete is a linear relationship, the correlation coefficient is 0.95.