Theoretical and Experimental Study on Multiparameter Criteria of Ultrasonic Method for Foundation Piles

Abstract

As one of the important methods to survey the foundation pile integrity in most engineering industries in China, ultrasonic testing (UT) has such advantages as determining the position and scope of defects accurately and good operability. In this paper, on the basis of the in-depth study of China’s industrial standards, main parameters for evaluating pile integrity in each standard were extracted, features and deficiencies of each parameter were analyzed in detail, and a multiparameter identification method of ultrasonically testing foundation pile integrity, which takes wave velocity, amplitude and basic frequency as the analytical parameters and outputs quantitative results, was proposed as an effective supplement to the ultrasonic testing of foundation pile integrity. This method has been applied to the result analysis of more than 800 engineering piles, and has obtained high consistency by comparing those results with core drilling results. Among them, $K_{(i)}$, the evaluation index of pile integrity with the pile complete and the buried acoustic pipe flat, is basically closed to the range $1 \le K_{(i)} \le 1.35$; when $K_{(i)} > 1.35$, all others, except for several points, are $K_{(i)}$ dispersion caused by head wave interpretation errors; when $0.85 \le K_{(i)} < 1$, all acoustic lines within this range reflect slight or obvious abnormalities of sound velocity and amplitude and obvious distortion of waveforms, that is, this acoustic line has slight or obvious defects; when $K_{(i)} < 0.85$, all acoustic lines within this range reflect serious abnormalities of sound velocity and amplitude and obvious distortion of waveforms, that is, this acoustic line has serious defects. Conclusion: This method can effectively reduce the impact of changes in critical values of wave velocity and amplitude caused by the misinterpretation of the head wave position, thus providing a rapid and accurate evaluation for the ultrasonic testing of foundation pile integrity for later engineering practice reference.

1 Introduction

The acoustic transmission method (ultrasonic method) is that the ultrasonic tester is used to measure the acoustic parameters of the pile concrete section point by point along the longitudinal axis of the pile, and determine the position, scope and extent of concrete defects by processing, analyzing and judging the test data, thereby inferring the concrete quality within the test range [1]. Ultrasonic testing (UT) of foundation pile integrity is mainly that pile concrete defects are qualitatively identified based on corresponding changes of wave velocity, amplitude and basic frequency in the received signals. The widely used probabilistic method can largely distinguish between accidental errors and negligent errors in concrete construction, but the UT method relies heavily on the on-site experience of test personnel and lacks automation and intelligence. After development in recent years, acoustic parameters develop from single factors to multiple factors, and judgment develops from being qualitative or empirical to quantitative. Concrete is a viscoelastic-plastic material that fluctuates to some extent in compactness, strength and other aspects, while the numerical statistics of acoustic parameters are basically in normal distribution; if there are pile defects (such as intercalated gouge, honeycomb, segregation) caused by the severe external environment or human errors, the concrete quality at the defect and the acoustic parameters of sound wave through the defective concrete will deviate from the normal distribution. However, concrete is not an ideal isotropic material, and fluctuations of strength and compactness in space caused by construction cannot be generalized as defects and deviations of different classes will also lead to fluctuations in the test values of acoustic parameters.

According to previous research results, there are great differences in the sensitivity of acoustic parameters such as wave velocity and amplitude to the quality of different forms of concrete. Wave velocity and amplitude reflect the elastic and plastic properties of concrete materials, reflectively. In terms of the multiparameter criteria of foundation piles tested by acoustic transmission method, Liu [2] conducted multi-angle and multi-level analysis and study on the pile foundation defects, and analyzed the characteristics of acoustic parameters corresponding to the common pile integrity defects tested by ultrasonic method. Zhang [3] introduced the advantages of the ultrasonic method in testing foundation piles and the theoretical basis of evaluating the quality of foundation piles using multiple synthetic criteria in fuzzy mathematics, and analyzed them based on engineering examples, proving that multivariate synthetic criteria can evaluate the quality of the foundation piles more accurately than univariate criteria. Zou [4] introduced a pile foundation test method that combines wavelet analysis with neural network, and conducted wavelet packet decomposition for the collected ultrasonic signals by wavelet analysis according to the ultrasonic propagation characteristics in the pile foundation; the neutral work which is constructed after obtaining ultrasonic signal eigenvectors by wavelet analysis can effectively identify pile foundation defects and defect types.

In conclusion, it remains a difficult task to obtain the effective indexes for evaluating foundation pile integrity by analyzing single acoustic parameters with complex mathematical methods. In identifying the concrete defects of piles, it is more scientific and reasonable to comprehensively analyze the scope and severity of defects using multiple acoustic parameters.

2 Study on Relationship Between Concrete Strength and Ultrasonic Wave Velocity

In actual projects, specimens with concrete segregation, honeycomb, trench and other damages caused by external factors are usually characterized by low compressive strength. Moreover, concrete quality covers compressive strength, water-cement ratio, workability, durability, chlorine content, gas content and other indexes, while acoustic parameters obtained by UT can hardly directly reflect all the indexes of concrete. Thus, in this paper, a relationship was established between strength and wave velocity as one of the indexes to measure the quality of different concrete.

Assuming that concrete is an isotropic material composed of its composite materials and internal tiny cracks, it can be defined as follows using acoustic wave velocity [5]:

$$ D_{0} = 1 - \left( {\frac{{V_{p0} }}{{V_{pf} }}} \right)^{2} $$

(1)

where, $D_{0}$—initial damage variable of concrete; $V_{p0}$—sound velocity of unloaded concrete; $V_{pf}$—sound velocity of concrete matrix (no damage).

The relationship between $\sigma_{c}$ and $D_{0}$ is expressed by the power function curve [5]:

$$ \sigma_{c} = AD_{0}^{ - B} $$

(2)

where, $A$ and $B$ are parameters related to concrete $E_{c}$, $\nu$ and $\phi$, , and they are constants in the same concrete. The curve of the relationship between wave velocity and strength can be established by substituting (1) into (2):

$$ \sigma_{c} = A(1 - CV_{p0}^{2} )^{ - B} $$

(3)

In order to study the relationship between sound velocity and concrete failure strength, and establish the curve of the relationship between wave velocity and concrete strength, 450 * 450 * 150 mm concrete specimens were used in this test, which were cured under the temperature of 20 ± 5 °C and the relative humidity of 90%. The concrete marks were C30, C35, C40, C50, C60 and C80, with three specimens in each group. The curve relationship was obtained by testing the compressive strength and wave velocity of the specimens (see Fig. 1).

Fig. 1

Diagram of relationship between sound velocity and failure strength

Since the curve relationship obtained by (3) is not convenient to directly express the curve relationship of $\sigma_{c}$ − $D_{0}$, the above formula is exponentially transformed and can be expressed as:

$$ \sigma_{c} = A_{1} e^{{B_{1} V_{p0} }} $$

(4)

where, $A_{1}$ and $B_{1}$ are parameters related to concrete $E_{c}$, $\nu$ and $\phi$, and are constants in the same concrete.

According to the above results, concrete failure strength is basically positively correlated with wave velocity. When the concrete strength level is greater than 40 MPa, the ultrasonic wave velocity in concrete significantly increases.

3 Theoretical Study on Multiparameter Synthetic Criteria and Pile Defect Identification

In Code for Testing of Building Foundation (DBJ/T 15-60-2019) [6], the depth profile integrity function of each pile is $I(j,i);$ in Technical Specifications for Foundation Piles Testing of Highway Engineering (JTG/T 3512-2020) [7], main discriminant features are from amplitude and wave velocity. In the two standards, whether the measured waveform is distorted or not is also taken as a supplementary basis for discriminant features. For the above problems, in the defect screening process in the first step, wave velocity, amplitude and basic frequency were selected to establish the main mathematical model of this algorithm.

Based on practical engineering experience, the sensitivity of single criteria to different types of defects is different, with different orders of magnitude. Common wave velocities are generally in 3800–4500 m/s; common amplitudes are generally in 90–120 dB; common basic frequencies are generally in 35–55 kHz.

Because acoustic parameters have different orders of magnitude, if weighting each parameter by analytic hierarchy process, a certain acoustic parameter may dominate the integrity evaluation index and changes of other parameters have little influence. Judged at the maximum value of wave velocity, amplitude and basic frequency by single parameters, the optimal concrete quality position can be determined. In this algorithm, each parameter was normalized, the acoustic line position was compared with the optimal concrete quality position in this profile to reflect the concrete quality level in this position, and the ratio of acoustic parameters of the acoustic line position to those of the optimal concrete quality position was limited to 0 to 1.

The multifactor probabilistic method adopts the three acoustic parameters of wave velocity $V$, amplitude $A$ and frequency $F$. The amplitude and wave velocity are sensitive to defects, which is mainly reflected in the sharp decline of the two parameters, the basic frequency reflects waveform distortion, and obtaining one synthetic criterion critical value is considered to have defects.

Using the probability statistics in this algorithm and by the normal distribution principle, the measured values of acoustic parameters of defective concrete were mainly distributed in the outlier range and were less than the statistical critical value, then the ratio of normal concrete to statistical critical value of concrete was greater than or equal to 1, and those less than 1 were judged as outliers. The specific algorithm is established as follows:

$$ K_{(i)} = \frac{{V_{i} \cdot F_{i} \cdot A_{i} }}{{\frac{1}{n}\sum\nolimits_{i = 1}^{n} {(V_{i} \cdot F_{i} \cdot A_{i} )} - m\sigma_{i} }} $$

(5)

where, $V_{i}$—the ratio of the actual wave velocity of the $i$-th acoustic line on the test profile to the maximum wave velocity on this profile; $F_{i}$—the ratio of the actual basic frequency of the $i$-th acoustic line on the test profile to the maximum basic frequency on this profile; $A_{i}$—the ratio of the actual amplitude of the $i$-th acoustic line on the test profile to the maximum amplitude on this profile; $m$—probability assurance coefficient; $\sigma_{i}$—standard deviation of $V_{i} \cdot F_{i} \cdot A_{i}$ for all calculated values of a single test profile; $K_{(i)}$—integrity evaluation index of this acoustic line.

The wave velocity, amplitude and basic frequency of the acoustic line were tested, and the integrity evaluation index of this acoustic line ($K_{(i)}$) was calculated. $K_{(i)} \ge 1$ indicates this acoustic line is complete; $K_{(i)} < 1$ indicates this acoustic line is defective. The lower the $K_{(i)}$, the higher the degree it deviates from the abnormal probability statistic, and the greater the degree of the defect.

The acoustic line integrity function $I\left( {j,i} \right)$ was compared with the integrity evaluation index $K_{(i)}$ in this method. If $I\left( {j,i} \right)$ = 1 and $K_{(i)}$ > 1, it is denoted as a conformance sample. In this test, 836 acoustic lines containing complete concrete and defects were selected; the number of non-conformance samples in the integrity results of the two acoustic lines was reduced by adjusting the value of the probability assurance coefficient $m$, so as to determine the probability assurance coefficient $m$ suitable for this method (see Fig. 2).

Fig. 2

Probability assurance coefficient ($m$) and number of non-conformance samples in acoustic line integrity results ($n$)

Based on the above calculation analysis, when $m = 2.2$, there were only nine non-conformance samples in the results of the two lines, with the accuracy rate reaching 98.9%.

In addition, the data tested and collected on the site are often affected by other sound sources or factors such as transducer vibration and aging, thereby resulting in the superposition of various sound source signals in ultrasonic data and the failure of the instrument to accurately and automatically identify the head wave position, and then an abnormal curve of acoustic parameters. There are many “spray waves” in the unprocessed waveform data graph. Interpretation based on the sound velocity-depth curve and amplitude-depth curve leads to a large number of outliers below the critical value, which makes it impossible to make interpretation accurately. After artificial interpretation of head wave, we can find that both sound velocity and amplitude are greater than the critical value, and the amplitude and wave velocity of the acoustic line on this profile are greater than the critical value (see Fig. 3).

Fig. 3

Comparison between the waveform of head wave automatically interpreted by instrument and the waveform after manual adjustment

As shown below, both waveforms belong to complete concrete without obvious distortion. It is hard to reflect the actual category of foundation pile integrity if the unadjusted waveform is automatically interpreted by the traditional method. However, the concrete quality can be calculated by the integrity evaluation index $K_{(i)}$ in this paper (see Fig. 4).

Fig. 4

Diagram of correct and abnormal interpretation of head wave of single wave

Different from traditional acoustic data, the impact of noise wave generated by other sound sources or factors such as transducer vibration and aging on the single wave curve is required. However, the above factors will not reduce the wave velocity, amplitude and basic frequency at the same time, namely $K_{(i)} < 1$. Therefore, the multi-parameter method is effective in identifying foundation pile integrity under the impact of the noise wave.

The above scatter plot was obtained according to the results of the integrity evaluation indexes of the measured 836 acoustic lines. The peak value of the samples in this test was 1.08; the integrity evaluation index $K_{(i)}$ was selected in the samples, and it was close to 1.0–1.35. When the integrity evaluation index $K_{(i)} > 1.35$, all others, except for several points, were $K_{(i)}$ discretions caused by head wave interpretation errors. When $0.85 \le K_{(i)} < 1$, all acoustic lines within this range reflect slight or obvious abnormalities of sound velocity and amplitude and obvious distortion of waveforms, that is, this acoustic line has slight or obvious defects. When $K_{(i)} < 0.85$, all acoustic lines within this range reflect serious abnormalities of sound velocity and amplitude and obvious distortion of waveforms, that is, this acoustic line has serious defects (see Fig. 5).

Fig. 5

$K_{(i)}$ scatter plot of acoustic line of the sample

4 Application of Multiparameter Synthetic Criteria of Ultrasonic Method

In an engineering, there was a 1# pile with the diameter of 1 400 mm and the length of 27.8 m, and three acoustic pipes were arranged at average in the reinforcement cage. The test results showed that the profile 1–2 was complete, the parameters of acoustic lines at the depth of 9.4–10.0 m on the profile 1–3 and 9.5–9.9 m on the profile 2–3 were seriously abnormal and the waveforms were distorted seriously, and the wave velocity-depth curve and amplitude-depth curve within this depth range were less than the critical value. Taking the depth of 9.6 m on the profile 1–3 as an example, the integrity evaluation index of this acoustic line $K_{(i)}$ was calculated. Tables 1 and 2 give a calculation of profile 1–3 and profile 2–3.

Table 1 Integrity evaluation index of profile 1–3 within the depth range of 9.4–10.0 m

Table 2 Integrity evaluation index of profile 2–3 within the depth range of 9.5–9.9 m

At 9.6 m of profile 1–3, the wave velocity of this acoustic line was 3 086 km/s, the amplitude was 78.1 dB, and the basic frequency was 25.5 kHz. Substituting them into (Formula 7), we obtained:

$$ K_{(i)} = \frac{{V_{i} \cdot F_{i} \cdot A_{i} }}{{\frac{i}{n}\sum\nolimits_{i = 1}^{n} {(V_{i} \cdot F_{i} \cdot A_{i} )} - 2.2\sigma_{i} }} = 0.83 < 1 $$

Based on the above calculation procedures, this was determined to be a serious defect (see Fig. 6).

Fig. 6

Diagram of wave velocity and amplitude-depth curve of profiles 7 1–3 and 2–3

After validation and test by drilled core method, concrete core samples were taken from the position 10 cm away from the center of the 2# acoustic pipe, and the concrete core samples were broken at about 9.5 m at the 8th time, with a length of 16 cm (see Fig. 7).

Fig. 7

Diagram of core sample drilled 10 cm away from the 2# acoustic pipe

5 Conclusion

Based on the study of China’s industry standards, this paper extracted the main parameters for evaluating the pile integrity in each standard, analyzed the characteristics of each parameter, and completed the test on the basic theories and related parameters of UT of foundation pile integrity. On this basis, the method of comprehensively identifying the pile defect positions and severity according to sound velocity, amplitude and basic frequency was obtained by using the probability statistics method. A multiparameter synthetic identification method was proposed for the UT of foundation pile integrity, and the quantitative results calculated by this method could be used as an effective supplement to the UT of foundation pile integrity.

More than 800 acoustic lines were used for the statistics of integrity evaluation indexes, of which the integrity evaluation index $K_{(i)}$ with the pile complete and the buried acoustic pipe flat was basically close to $1 \le K_{(i)} \le 1.35$; when the integrity evaluation index $K_{(i)} > 1.35$, all others, except for several points, were $K_{(i)}$ dispersion caused by head wave interpretation errors; when $0.85 \le K_{(i)} < 1$, all acoustic lines within this range reflected slight or obvious abnormalities of sound velocity and amplitude and obvious distortion of waveforms, that is, this acoustic line had slight or obvious defects; when $K_{(i)} < 0.85$, all acoustic lines within this range reflected serious abnormalities of sound velocity and amplitude and obvious distortion of waveforms, that is, this acoustic line had serious defects.

This method can effectively reduce the impact on the critical value changes caused by the misinterpretation of the head wave position, providing a method for rapidly and accurately interpreting the ultrasonic testing of foundation piles for later engineering practice reference.