# Experimental Research and Numerical Simulation on Grouting Quality of Shield Tunnel Based on Impact Echo Method

Authors: Fei Yao; Guangyu Chen; Jianhong Su
Journal: Shock and Vibration
 (2016)

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## Abstract

To identify shield grouting quality based on impact echo method, an impact echo test of segment-grouting (SG) test piece was carried out to explore effect of acoustic impedance of grouting layers and grouting defects on impact echo law. A finite element numerical simulation on the impact echo process was implemented. Test results and simulation results were compared. Results demonstrated that, under some working conditions, finite element simulation results and test results both agree with theoretical values. The acoustic impedance ratio of SG material influenced the echo characteristics significantly. But thickness frequency could not be detected under some working conditions because the reflected energy is weak. Frequency feature under grouting defects was more complicated than that under no grouting defects.


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## Body

## 1. Introduction

Shield method has advantages such as characteristic security, speediness, wide application range, and small disturbance to surrounding strata. It is widely applied in subway construction engineering in cities. Since the outer diameter of shield is larger than the circumferential outer diameter of segment, a circumferential overexcavation gap will be formed between the segment and surrounding rocks. Together with construction disturbance and blasting excavation, the supporting structure separates from surrounding rocks, thus resulting in relaxation of surrounding rocks. Consequently, the supporting structure will suffer excessive bending stress and its carrying capacity will be reduced, which threatens safe use of the tunnel. In the engineering, the backfill grouting is filled, which can fill the above-mentioned overexcavation gap in Figure1 but also can prevent relaxation of surrounding rocks and segment leakage as well as reducing surface subsidence significantly.Figure 1
Overexcavation gap caused in shield construction.However, when there is problem in grouting density and even development of holes, cross section of the tunnel will change and will affect traffic safety directly when such change becomes serious. Surface subsidence or stress changes of surrounding soil mass will be produced upon great surrounding rock strain, thus causing distortion of local soil mass and increasing segment load in the tunnel indirectly. This makes engineering practices disagree with design and investigation, which increases risks significantly. At present, shield grouting quality is mainly detected by radar method [1, 2]. However, radar method is expensive and easy to be disturbed by metallic shield. Therefore, exploring a new detection approach of grouting quality of shield segment becomes an urgent and hot new field.Impact echo method [3–6] is a structural nondestructive testing technology based on transient stress wave. It impacts the concrete surface by a steel ball or hammer as an exciter to produce longitudinal wave (P wave) and transverse wave (S wave) in the concrete structure as well as Rayleigh wave (R wave) on the concrete surface [7, 8]. Stress waves will form echoes through propagation and reflections in concrete [9, 10]. Surface displacement caused by reflection of these waves will be recorded by a sensor close to the impact position. After receiving these waves, the sensor will transform signals in time domain into the frequency domain through Fast Fourier Transform (FFT) and recognize the relationship between the received signal and concrete mass, thus realizing the goal of nondestructive test.Impact echo method has been used successfully in many engineering fields, such as girder test of bridges, pipeline inwall integrity test, bridge surface damage test, and highway pavement quality test [4, 11, 12]. However, there are few researches on shield grouting quality test. In shield tunnel, grouting defects belong to concealed defects and a layered structure will be formed by segment and grouting layer. With respect to the testing structure composed of layered materials, acoustic impedances of different layers of materials will affect the impact echo test results significantly. On this basis, this paper performed impact echo tests to SG samples with different acoustic impedances to discuss effect of acoustic impedance ratio and grouting defect on impact echo law. A finite element numerical simulation on the impact echo process was accomplished by using the finite element software MSC.MARC [13]. Test results and simulation results were compared.


## 2. Experimental Study

### 2.1. Experiment Design

To study the effect of acoustic impedance of the grouting layer, three segment-grouting (SG) samples with different proportions of grouting layers were designed: SG-A, SG-B, and SG-C. Specific materials parameters are listed in Table1. The three-shield capping segments made by Nanjing Ligao Segment Co., Ltd., were used. The compressive strength was 50 Mpa and the size was 1200 mm × 1200 mm × 350 mm (Figure 2). Thickness of the grouting layer was 100 mm (Figure 3).Table 1
Material parameters of SG samples.
Group Grouting elasticity modulus/EG (MPa) Grouting density/ρG (kg/m3) Segment elasticity modulus/ES (MPa) Segment density/ρS (kg/m3) SG-A 2350 1539 34500 2500 SG-B 6900 1913 34500 2500 SG-C 11330 1947 34500 2500Figure 2
Concrete segments.
(a)
Segment-A (b)
Segment-B (c)
Segment-CFigure 3
Structure of SG samples.Poisson’s ratios of the grouting layer and segment layer were approximately determined, 0.25 and 0.3, respectively [14]. Wave velocity, CP, acoustic impedance, Z, and reflectance of different layers of materials, R, were calculated by the following formula and represented in Table 2.(1)CP=E1-μρ1+μ1-2μ,where E is the elasticity modulus; G is the shear modulus; ρ is the density of medium; μ is the Poisson’s ratio.(2)Z=ρ×CP,where Z is the acoustic impedance of medium.(3)R=AReflectedAIncident=Z2-Z1Z2+Z1,where Z1 and Z2 are the acoustics impedance of medium 1 and medium 2; AIncident is amplitude of the incident wave; AReflected is amplitude of the reflected wave.Table 2
Acoustic parameters of SG samples.
Group Segment wave velocity (Cp1)(m/s) Segment acoustic impedance (Z1)(kg/m2s) Grouting wave velocity (Cp2)(m/s) Grouting acoustic impedance (Z2)(kg/m2s) Reflectance (R) SG-A 4390 10.98 × 106 1354 2.08 × 106 - 0.68 SG-B 4390 10.98 × 106 2081 3.98 × 106 - 0.47 SG-C 4390 10.98 × 106 2643 5.22 × 106 - 0.36To study effect of defects, a piece of foam board was embedded into the left half of three SG samples, which were compared with the SG sample without defect (the right half). To ensure that the embedded foam board could be detected [7], width of the foam board was set to be 150 mm. Thickness of the foam board was 20 mm and it was embedded at 30 mm away from the segment-grouting interface (Figure 3). The segment was simply supported at four corners. Therefore, SG-A samples were further divided into SG-A-DE (with defect) and SG-A-ND (without defect). Similarly, SG-B samples were divided into SG-B-DE and SG-B-ND, and SG-C samples were further divided into SG-C-DE and SG-C-ND.


### 2.2. Experimented Setup

The IES (Impact Echo Scanning) instrument which is manufactured by Olson Instrument Company was used in this test (Figure4). The instrument includes the host computer, cable, and a scrolling sensor which contain signal receiving sensor and can adjust the exciter to different excitation intensity.Figure 4
IES (Impact Echo Scanning) instrument.The sampling frequency is set as 2048 Hz, which indicates that data points collected every 10 microseconds, and order is set as 4th order.


### 2.3. Theoretical Calculation

The test principle of impact echo method is based on the relationship between the test frequency and stress wave velocity as well as sample thickness [15–17]:(4)fT=βCP2T,where fT is the peak frequency gained after FFT of time-history curve that is collected by the sensor; β is the shape factor and is determined as 1 in this paper [18]; CP is stress wave velocity in this medium; and T is thickness of the sample.When a component is composed of two different materials [19], the thickness frequency from the bottom surface to the top surface is(5)fh=12h1/βCp1+2h2/βCp2,where h1 and h2 are thicknesses of material 1 and material 2; Cp1 and Cp2 are stress wave velocities in material 1 and material 2.According to above theories, thickness frequencyf1 of the segment-grouting interface could be calculated from(6)f1=βCp12T1.Thickness frequencyf2 of the grouting-air interface is(7)f2=12T1/βCp1+2T2/βCp2,where T1 and T2 are thicknesses of concrete segment and grouting; Cp1 and Cp2 are stress wave velocities in concrete segment and grouting.Similarly, thickness frequencyf2′ at the defect could be calculated from(8)f2′=12T1′/βCp1+2T2′/βCp2,where T1′ and T2′ are thickness of the concrete segment and thickness from segment-grouting interface to defect surface; Cp1′ and Cp2′ are stress wave velocities in concrete segment and grouting, respectively.Theoretical peak frequencies at different interfaces of all samples are listed in Table3.Table 3
Theoretical peak frequencies.
Specimen number f 1 (Hz) f 2 ′ (Hz) f 2 (Hz) SG-A-DE 6271 4908 3256 SG-A-ND 6271 — 3256 SG-B-DE 6271 5311 3413 SG-B-ND 6271 — 3413 SG-C-DE 6271 5489 4253 SG-C-ND 6271 — 4253


### 2.4. Test Results

There is an evident peak value in the effective coverage of thickness frequency (2000~8000 Hz) in time domain graph collected from the experiment. Peaks may occur in low-frequency regions beyond the effective coverage, which are caused by surface wave or other noise interference waves. Therefore, a high-pass filtering that took about 2 kHz as the cut-off frequency was implemented to eliminate these strong low-frequency signals [9]. The filtered time domain graph of SG-A-ND is shown in Figure 5.Figure 5
Filtered time domain of SG-A-ND.Frequency domain graphs which were collected after FFT of time-history curves are presented in Figure6. Filtering of frequencies below 2 kHz is evident in these figures.Figure 6
Frequency domain graphs.
(a)
SG-A-ND frequency domain (b)
SG-A-DE frequency domain (c)
SG-B-ND frequency domain (d)
SG-B-DE frequency domain (e)
SG-C-ND frequency domain (f)
SG-C-DE frequency domainPeak frequencies picked from Figure6 were compared to the theoretical values in Table 4.Table 4
Comparison between tested peak frequency and theoretical results under different working conditions.
Model number f 1 (Hz) f 2 ′ (Hz) f 2 (Hz) SG-A-DE 6738 (6271) 4590 (4908) Not obvious (3256) SG-A-ND 6348 (6271) — 3027 (3256) SG-B-DE 6543 (6271) 4883 (5311) Not obvious (3413) SG-B-ND 6640 (6271) — 3516 (3413) SG-C-DE 6641 (6271) 5566 (5489) Not obvious (4253) SG-C-ND 6641 (6271) — 4499 (4253) Note: values in ( ) are theoretical results.It can be seen from Figure6 and Table 4 that,(1)
in all samples,f1 is evident. In samples without defect, f2 can be detected, but the peak is smaller than that of f1. In samples with defects, f2 could not be detected, but f2′ could and its peak is also smaller than f1. All tested peak frequencies are close to theoretical values;(2)
with the increase of grouting acoustic impedance, the absolute value of reflectance of grouting-segment interface decreases gradually and the amplitude off1 decreases gradually as evident from Figure 6. This indicates that, with the reduction of absolute values of the reflectance, the reflected energy of stress wave by this interface declines gradually and the reflectivity weakens. Hence, more energy will be transmitted to the next layer of materials (grouting layer).


## 2.1. Experiment Design

To study the effect of acoustic impedance of the grouting layer, three segment-grouting (SG) samples with different proportions of grouting layers were designed: SG-A, SG-B, and SG-C. Specific materials parameters are listed in Table1. The three-shield capping segments made by Nanjing Ligao Segment Co., Ltd., were used. The compressive strength was 50 Mpa and the size was 1200 mm × 1200 mm × 350 mm (Figure 2). Thickness of the grouting layer was 100 mm (Figure 3).Table 1
Material parameters of SG samples.
Group Grouting elasticity modulus/EG (MPa) Grouting density/ρG (kg/m3) Segment elasticity modulus/ES (MPa) Segment density/ρS (kg/m3) SG-A 2350 1539 34500 2500 SG-B 6900 1913 34500 2500 SG-C 11330 1947 34500 2500Figure 2
Concrete segments.
(a)
Segment-A (b)
Segment-B (c)
Segment-CFigure 3
Structure of SG samples.Poisson’s ratios of the grouting layer and segment layer were approximately determined, 0.25 and 0.3, respectively [14]. Wave velocity, CP, acoustic impedance, Z, and reflectance of different layers of materials, R, were calculated by the following formula and represented in Table 2.(1)CP=E1-μρ1+μ1-2μ,where E is the elasticity modulus; G is the shear modulus; ρ is the density of medium; μ is the Poisson’s ratio.(2)Z=ρ×CP,where Z is the acoustic impedance of medium.(3)R=AReflectedAIncident=Z2-Z1Z2+Z1,where Z1 and Z2 are the acoustics impedance of medium 1 and medium 2; AIncident is amplitude of the incident wave; AReflected is amplitude of the reflected wave.Table 2
Acoustic parameters of SG samples.
Group Segment wave velocity (Cp1)(m/s) Segment acoustic impedance (Z1)(kg/m2s) Grouting wave velocity (Cp2)(m/s) Grouting acoustic impedance (Z2)(kg/m2s) Reflectance (R) SG-A 4390 10.98 × 106 1354 2.08 × 106 - 0.68 SG-B 4390 10.98 × 106 2081 3.98 × 106 - 0.47 SG-C 4390 10.98 × 106 2643 5.22 × 106 - 0.36To study effect of defects, a piece of foam board was embedded into the left half of three SG samples, which were compared with the SG sample without defect (the right half). To ensure that the embedded foam board could be detected [7], width of the foam board was set to be 150 mm. Thickness of the foam board was 20 mm and it was embedded at 30 mm away from the segment-grouting interface (Figure 3). The segment was simply supported at four corners. Therefore, SG-A samples were further divided into SG-A-DE (with defect) and SG-A-ND (without defect). Similarly, SG-B samples were divided into SG-B-DE and SG-B-ND, and SG-C samples were further divided into SG-C-DE and SG-C-ND.


## 2.2. Experimented Setup

The IES (Impact Echo Scanning) instrument which is manufactured by Olson Instrument Company was used in this test (Figure4). The instrument includes the host computer, cable, and a scrolling sensor which contain signal receiving sensor and can adjust the exciter to different excitation intensity.Figure 4
IES (Impact Echo Scanning) instrument.The sampling frequency is set as 2048 Hz, which indicates that data points collected every 10 microseconds, and order is set as 4th order.


## 2.3. Theoretical Calculation

The test principle of impact echo method is based on the relationship between the test frequency and stress wave velocity as well as sample thickness [15–17]:(4)fT=βCP2T,where fT is the peak frequency gained after FFT of time-history curve that is collected by the sensor; β is the shape factor and is determined as 1 in this paper [18]; CP is stress wave velocity in this medium; and T is thickness of the sample.When a component is composed of two different materials [19], the thickness frequency from the bottom surface to the top surface is(5)fh=12h1/βCp1+2h2/βCp2,where h1 and h2 are thicknesses of material 1 and material 2; Cp1 and Cp2 are stress wave velocities in material 1 and material 2.According to above theories, thickness frequencyf1 of the segment-grouting interface could be calculated from(6)f1=βCp12T1.Thickness frequencyf2 of the grouting-air interface is(7)f2=12T1/βCp1+2T2/βCp2,where T1 and T2 are thicknesses of concrete segment and grouting; Cp1 and Cp2 are stress wave velocities in concrete segment and grouting.Similarly, thickness frequencyf2′ at the defect could be calculated from(8)f2′=12T1′/βCp1+2T2′/βCp2,where T1′ and T2′ are thickness of the concrete segment and thickness from segment-grouting interface to defect surface; Cp1′ and Cp2′ are stress wave velocities in concrete segment and grouting, respectively.Theoretical peak frequencies at different interfaces of all samples are listed in Table3.Table 3
Theoretical peak frequencies.
Specimen number f 1 (Hz) f 2 ′ (Hz) f 2 (Hz) SG-A-DE 6271 4908 3256 SG-A-ND 6271 — 3256 SG-B-DE 6271 5311 3413 SG-B-ND 6271 — 3413 SG-C-DE 6271 5489 4253 SG-C-ND 6271 — 4253


## 2.4. Test Results

There is an evident peak value in the effective coverage of thickness frequency (2000~8000 Hz) in time domain graph collected from the experiment. Peaks may occur in low-frequency regions beyond the effective coverage, which are caused by surface wave or other noise interference waves. Therefore, a high-pass filtering that took about 2 kHz as the cut-off frequency was implemented to eliminate these strong low-frequency signals [9]. The filtered time domain graph of SG-A-ND is shown in Figure 5.Figure 5
Filtered time domain of SG-A-ND.Frequency domain graphs which were collected after FFT of time-history curves are presented in Figure6. Filtering of frequencies below 2 kHz is evident in these figures.Figure 6
Frequency domain graphs.
(a)
SG-A-ND frequency domain (b)
SG-A-DE frequency domain (c)
SG-B-ND frequency domain (d)
SG-B-DE frequency domain (e)
SG-C-ND frequency domain (f)
SG-C-DE frequency domainPeak frequencies picked from Figure6 were compared to the theoretical values in Table 4.Table 4
Comparison between tested peak frequency and theoretical results under different working conditions.
Model number f 1 (Hz) f 2 ′ (Hz) f 2 (Hz) SG-A-DE 6738 (6271) 4590 (4908) Not obvious (3256) SG-A-ND 6348 (6271) — 3027 (3256) SG-B-DE 6543 (6271) 4883 (5311) Not obvious (3413) SG-B-ND 6640 (6271) — 3516 (3413) SG-C-DE 6641 (6271) 5566 (5489) Not obvious (4253) SG-C-ND 6641 (6271) — 4499 (4253) Note: values in ( ) are theoretical results.It can be seen from Figure6 and Table 4 that,(1)
in all samples,f1 is evident. In samples without defect, f2 can be detected, but the peak is smaller than that of f1. In samples with defects, f2 could not be detected, but f2′ could and its peak is also smaller than f1. All tested peak frequencies are close to theoretical values;(2)
with the increase of grouting acoustic impedance, the absolute value of reflectance of grouting-segment interface decreases gradually and the amplitude off1 decreases gradually as evident from Figure 6. This indicates that, with the reduction of absolute values of the reflectance, the reflected energy of stress wave by this interface declines gradually and the reflectivity weakens. Hence, more energy will be transmitted to the next layer of materials (grouting layer).


## 3. Numerical Studies

### 3.1. Establishment of SG Finite Element Model

The finite element mode used plane analysis method and number 11 two-dimensional plane integrated cells [20]. The impact point was taken as the origin and the excitation directional line was taken as the symmetry axis. A symmetry model was established which was composed of segment and grouting from top to down. The thickness and semiwidth of segment were 350 mm and 600 mm, while thickness of the grouting was 100 mm as shown in Figures 2(a) and 2(b). Samples were divided into SG-A-ND (no defect) and SG-A-DE (defect). The defect in SG-A-DE model was a hole whose semilength was 75 mm and thickness was 20 mm. The upper edge of the hole was 30 mm below the segment-grouting interface. Parameters of the model materials were same with samples (Figure 7).Figure 7
SG finite element models.
(a)
Without defect SG-A-ND (b)
With defect SG-A-DEThe maximum exciting force and excitation time were set as 8 N and 40μs [21], respectively. Excitation simulation was achieved by applying a concentrated load at the axis of symmetry by using the TABLE function in MSC.MARC as depicted in Figure 8.Figure 8
Simulation parameters of exciting force.
(a)
Time-history curve (b)
Frequency


### 3.2. Analysis of Numerical Simulation Results

Velocity-time curve and accelerated-time curve at the node which is 40 mm away from the impact point were chosen. Figure9 shows the normalized acceleration-time curve of SG-A with surface waves, while Figure 10 is normalized accelerated-time curves of SG-A with surface waves eliminated.Figure 9
Acceleration-time curves of SG-A with surface waves.Figure 10
Acceleration-time curves of SG-A without surface waves.Through FFT of acceleration-time curves of SG-A without Rayleigh wave, frequency domain graphs under different working conditions were obtained and are shown in Figure11.Figure 11
Frequency domain graphs after FFT of accelerated velocity-time curves.
(a)
SG-A (b)
SG-B (c)
SG-CThe finite element simulation results and theoretical results were compared in Table5. The following can be seen from Figure 11 and Table 5:(1)
f1 of all samples is evident. Peaks of f2 and f2′ are smaller than that of f1. The tested peak frequency is close to the theoretical value.(2)
With the increase of grouting acoustic impedance, the absolute value of reflectance of the grouting-segment interface declines gradually and amplitude off1 decreases gradually, while the amplitude of f2 increases. This reflects that the energy reflected by grouting-segment interface is negatively correlated with acoustic impedance ratio. With the increase of acoustic impedance ratio, more and more energies will be transmitted to grouting and reflected on the grouting-air interface.(3)
Same group of SG model showed different frequency features after being given the same stress excitation under conditions with and without defects. SG model with defect presented more complicated frequency features than SG model without defect. Except for SG-A-DE which has not obviousf2, SG-B-DE and SG-C-DE achieved smaller f2 and produced “low-frequency drifts.”Table 5
Comparison of peak frequency between finite element simulation and theoretical calculation.
Model number f 1 (Hz) f 2 ′ (Hz) f 2 (Hz) SG-A-DE 6104 (6271)−2.7% 5127 (4908)4.5% Not obvious (3256) SG-A-ND 6104 (6271)−2.7% — 2930 (3256)−10.0% SG-B-DE 6104 (6271)−2.7% 4639 (5311)−12.7% 3418 (3413)0.1% SG-B-ND 6348 (6271)2.1% — 3662 (3413)7.3% SG-C-DE 6348 (6271)2.1% 4883 (5489)−11.0% 3662 (4253)−13.9% SG-C-ND 6104 (6271)−2.7% — 4639 (4253)−13.9% Note: content in ( ) is theoretical results; content in bold is percentage difference between finite element simulated results and theoretical results.Comparison between test results and finite element simulation results is shown in Table6.Table 6
Comparison of peak frequency between test results and finite element simulation under different working conditions.
Model number f 1 (Hz) f 2 ′ (Hz) f 2 (Hz) SG-A-DE 6738[6104]10.4% 4590[5127]−10.5% Not obvious[not obvious] SG-A-ND 6348[6104]4.0% — 3042[2930]3.8% SG-B-DE 6543[6104]7.2% 4883[4639]5.3% Not obvious[3418] SG-B-ND 6640[6348]4.6% — 3571[3662]−2.5% SG-C-DE 6641[6348]4.6% 5566[4883]13.9% Not obvious[3662] SG-C-ND 6641[6104]8.8% — 4199[4639]−9.5% Note: content in [ ] is finite element simulation results; content in bold is percentage difference between tested results and finite element simulated results.Additionally, viewed from amplitude and variation law off2, the experiment detected fewer wave energies entering into the grouting layer than the finite element simulation and fewer energies reflecting at the defect and the grouting-air interface. This may be because the grouting and segment have not been bonded completely during grouting construction, thus resulting in the difference between stress wave transmission and the ideal state.Theoretical values, test values, and finite element simulation values of thickness frequency of segment-grouting interface (f1), thickness frequency at defect (f2′), and thickness frequency of the grouting-air interface (f2) of different samples are expressed in broken line graphs in Figures 12 and 13.Figure 12
Comparison of theoretical values, test values, and finite element simulation values of peak frequency of samples (without defect).Figure 13
Comparison of theoretical values, test values, and finite element simulation values of peak frequency of samples (with defect).It can be seen thatf2 (tested) are not obvious in defective specimens. So if the second peak frequency and the theoretical value of f2 vary widely, there may be defects.


## 3.1. Establishment of SG Finite Element Model

The finite element mode used plane analysis method and number 11 two-dimensional plane integrated cells [20]. The impact point was taken as the origin and the excitation directional line was taken as the symmetry axis. A symmetry model was established which was composed of segment and grouting from top to down. The thickness and semiwidth of segment were 350 mm and 600 mm, while thickness of the grouting was 100 mm as shown in Figures 2(a) and 2(b). Samples were divided into SG-A-ND (no defect) and SG-A-DE (defect). The defect in SG-A-DE model was a hole whose semilength was 75 mm and thickness was 20 mm. The upper edge of the hole was 30 mm below the segment-grouting interface. Parameters of the model materials were same with samples (Figure 7).Figure 7
SG finite element models.
(a)
Without defect SG-A-ND (b)
With defect SG-A-DEThe maximum exciting force and excitation time were set as 8 N and 40μs [21], respectively. Excitation simulation was achieved by applying a concentrated load at the axis of symmetry by using the TABLE function in MSC.MARC as depicted in Figure 8.Figure 8
Simulation parameters of exciting force.
(a)
Time-history curve (b)
Frequency


## 3.2. Analysis of Numerical Simulation Results

Velocity-time curve and accelerated-time curve at the node which is 40 mm away from the impact point were chosen. Figure9 shows the normalized acceleration-time curve of SG-A with surface waves, while Figure 10 is normalized accelerated-time curves of SG-A with surface waves eliminated.Figure 9
Acceleration-time curves of SG-A with surface waves.Figure 10
Acceleration-time curves of SG-A without surface waves.Through FFT of acceleration-time curves of SG-A without Rayleigh wave, frequency domain graphs under different working conditions were obtained and are shown in Figure11.Figure 11
Frequency domain graphs after FFT of accelerated velocity-time curves.
(a)
SG-A (b)
SG-B (c)
SG-CThe finite element simulation results and theoretical results were compared in Table5. The following can be seen from Figure 11 and Table 5:(1)
f1 of all samples is evident. Peaks of f2 and f2′ are smaller than that of f1. The tested peak frequency is close to the theoretical value.(2)
With the increase of grouting acoustic impedance, the absolute value of reflectance of the grouting-segment interface declines gradually and amplitude off1 decreases gradually, while the amplitude of f2 increases. This reflects that the energy reflected by grouting-segment interface is negatively correlated with acoustic impedance ratio. With the increase of acoustic impedance ratio, more and more energies will be transmitted to grouting and reflected on the grouting-air interface.(3)
Same group of SG model showed different frequency features after being given the same stress excitation under conditions with and without defects. SG model with defect presented more complicated frequency features than SG model without defect. Except for SG-A-DE which has not obviousf2, SG-B-DE and SG-C-DE achieved smaller f2 and produced “low-frequency drifts.”Table 5
Comparison of peak frequency between finite element simulation and theoretical calculation.
Model number f 1 (Hz) f 2 ′ (Hz) f 2 (Hz) SG-A-DE 6104 (6271)−2.7% 5127 (4908)4.5% Not obvious (3256) SG-A-ND 6104 (6271)−2.7% — 2930 (3256)−10.0% SG-B-DE 6104 (6271)−2.7% 4639 (5311)−12.7% 3418 (3413)0.1% SG-B-ND 6348 (6271)2.1% — 3662 (3413)7.3% SG-C-DE 6348 (6271)2.1% 4883 (5489)−11.0% 3662 (4253)−13.9% SG-C-ND 6104 (6271)−2.7% — 4639 (4253)−13.9% Note: content in ( ) is theoretical results; content in bold is percentage difference between finite element simulated results and theoretical results.Comparison between test results and finite element simulation results is shown in Table6.Table 6
Comparison of peak frequency between test results and finite element simulation under different working conditions.
Model number f 1 (Hz) f 2 ′ (Hz) f 2 (Hz) SG-A-DE 6738[6104]10.4% 4590[5127]−10.5% Not obvious[not obvious] SG-A-ND 6348[6104]4.0% — 3042[2930]3.8% SG-B-DE 6543[6104]7.2% 4883[4639]5.3% Not obvious[3418] SG-B-ND 6640[6348]4.6% — 3571[3662]−2.5% SG-C-DE 6641[6348]4.6% 5566[4883]13.9% Not obvious[3662] SG-C-ND 6641[6104]8.8% — 4199[4639]−9.5% Note: content in [ ] is finite element simulation results; content in bold is percentage difference between tested results and finite element simulated results.Additionally, viewed from amplitude and variation law off2, the experiment detected fewer wave energies entering into the grouting layer than the finite element simulation and fewer energies reflecting at the defect and the grouting-air interface. This may be because the grouting and segment have not been bonded completely during grouting construction, thus resulting in the difference between stress wave transmission and the ideal state.Theoretical values, test values, and finite element simulation values of thickness frequency of segment-grouting interface (f1), thickness frequency at defect (f2′), and thickness frequency of the grouting-air interface (f2) of different samples are expressed in broken line graphs in Figures 12 and 13.Figure 12
Comparison of theoretical values, test values, and finite element simulation values of peak frequency of samples (without defect).Figure 13
Comparison of theoretical values, test values, and finite element simulation values of peak frequency of samples (with defect).It can be seen thatf2 (tested) are not obvious in defective specimens. So if the second peak frequency and the theoretical value of f2 vary widely, there may be defects.


## 4. Conclusions

(1)
With respect to peak frequenciesf1, f2, and f2′, theoretical values, finite element simulation values, and test values are in high accordance under different working conditions, which proves that the impact echo method is feasible to test grouting defect in shield tunnel. (2)
The acoustic impedance ratio between grouting and segment determines reflectance of grouting-segment interface and influences the echo characteristics significantly. In this paper, higher acoustic impedance ratio leads to smaller absolute value of reflectance and smaller echo energy on the segment-grouting interface. Consequently, peak frequency on the frequency graph after FFT is more unobvious, and thickness frequency could not be detected under some working conditions. (3)
Same group of SG model shows different frequency features after being given the same stress excitation under conditions with and without defects. SG model with defect has more complicated frequency features than that without defect due to the existence of three reflective interfaces. (4)
Because of the poor bonding strength between the segment and the grouting during sample preparation, test results disagree with finite element simulation results (ideal conditions). Wave energy transmission in the experiment was more complicated.



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