# Investigation of acoustic waves behavior of an underground tunnel in a multilayer soil – Scientific Reports

To quantify acoustic wave behavior in an underground structure in a multilayer soil by changing various tunnel-related parameters, the reflected and transmitted acoustic pressure is determined in the air layer at the ground surface and the air inside the tunnel, respectively. The considered parameters include mechanical properties of soil in each layer, the buried depth, and the lining concrete type. In addition, the behavior of the acoustic wave is examined once an extra tunnel is added to the model in various locations with respect to the main tunnel.

### Effects of soil properties on acoustic wave behavior

This section presents the effects of soil mechanical properties on acoustic wave behavior. Mechanical properties associated with each soil layer are represented in Table 2. Soil properties in each layer are altered (based on their reference, stiffer and softer soil properties in Table 2) in all three buried depths to consider the tunnel-soil interaction properly. Several numerical analyses are applied for any specific buried depth; the first one is associated with the soil reference properties, and the subsequent ones are due to the soil characteristics alteration of one layer, while the others remain unchanged, and the model results are compared with that of the reference model (based on the reference soil properties in Table 2).

The reference soil’s reflected and transmitted pressure values are 286.52 kPa, and 266.2 Pa for the 10-m buried depth, 306.94 kPa, and 178.39 Pa for the 20-m buried depth, and 306.99 kPa and 80.31 Pa for the 30-m buried depth. It should be noted that the reflected acoustic pressure values in this study consist of the reflected pressure values from the ground surface and the underground structure interior medium.

Concrete I (Table 3) is applied as the lining concrete in all models described in this section. Figure 4 shows the maximum reflected acoustic wave pressure with the reference soil characteristics alongside (a) the stiffened and (b) the softened ones for all the buried depths. Figure 5 presents the same for the transmitted acoustic wave. In both Figs. 4 and 5, cases 2, 3, and 4 are associated with altering the mechanical properties of soil in the first, second, and third layers, respectively.

Figure 4 shows that whether the soil stiffness increases (Fig. 4a) or reduces (Fig. 4b), regardless of the buried depth, the reflected acoustic waves are only affected by the properties of the first layer. The main reason behind this trend is the reflection coefficient effect between the soil and the air, which increases by stiffening the soil and reduces by softening it. An increase in the reflected acoustic wave value shows a more significant reflection coefficient. It is also observed that altering the properties of any layers except the first one hardly affects the reflected acoustic wave pressure. This shows the significant impact of the interaction of the first soil layer with air compared with the other factors (e.g., location of the underground structures, the interaction between the soil layers, and the interaction between the tunnel lining and the soil layers) on the reflected acoustic wave behavior. The same result was reported by Auersch42, in which, at higher frequencies (as in the case of an explosion), the top level of a layered soil significantly affects the foundation stiffness, and the acoustic wave reflected and transmitted by that foundation. In contrast, at lower frequencies, the deeper soil materials seem to have more influence on the foundation.

Figure 5 shows how the acoustic wave is transmitted when the properties of the soil layers are altered. The variation of the transmitted acoustic wave pressure depends on the relative position of the soil layers and the tunnel. Any changes in the properties of the soil layer containing the tunnel and the layers above them significantly affects the transmitted acoustic wave pressure. However, the stiffening or softening of the layers below the tunnel slightly affects the pressure value. Accordingly, in the case of a 10-m buried depth, stiffening the third layer (Fig. 5a) and softening it (Fig. 5b) cause the transmitted acoustic pressure to vary by 0.9% and 1.12%. The same scenario for a buried depth of 20 m leads to minimal variations of 0.66% and 1.69% of the transmitted acoustic wave pressure for the stiffer and softer third layer soil.

On the other hand, considering the case of a 10-m buried depth shows that if even a small section of the tunnel is located in a soil layer, that layer can significantly affect the transmitted acoustic wave behavior. In such a model, the transmitted acoustic pressure is reduced by 40.95% and 6.23% (compared with the reference case), respectively, with the first and the second stiffer layers (Fig. 5a). The transmitted wave pressure increases by 30.78% and 6.67% (compared with the reference case), respectively, with the first and the second softer layers (Fig. 5b). The same behavior pattern is observed in the cases of 20 and 30-m buried depths, where stiffening the second and third layers reduces the transmitted wave pressure by 22.23% and 14.6%, respectively. In contrast, decreasing the soil stiffness in such layers results in a 13.13% and 24.6% increase in acoustic pressure, respectively.

When increasing a soil layer stiffness, the soil particle and particularly the lining vibrations (accelerations) are reduced. This reduction in acceleration leads to the mitigation of the acoustic wave energy propagated through the soil and transmitted inside the tunnel. Therefore, amplifying the soil layer stiffness, which contains the tunnel (partial or complete), diminishes the transmitted acoustic wave energy and hence the acoustic wave pressure transmitted into the tunnel.

As for the layers above the tunnel level, alongside the soil stiffness effect, the reflection coefficient between the soil layers is another determinant factor affecting the transmitted acoustic wave behavior. Considering the case of 20-m buried depth, for both the stiffer (Fig. 5a) and the softer (Fig. 5b) first layer, reduction of 41.14% and 16.97% are respectively experienced by the transmitted acoustic wave pressure (compared with the reference cases). In both instances, the calculated reflection coefficients between the first and the second layers appear to be greater than the ones of the reference model. It explains the transmitted wave pressure drops in both cases. However, the decreased values depend on how the soil stiffness varies for each case. The soil particle vibration and the acoustic wave propagated through the layer are reduced for the case with stiffer first layers. Therefore, higher pressure drops are observed in comparison with the softer case.

On the other hand, in the case of 30-m buried depth, no such trend occurs when altering the first layer. In this case, despite the reflection coefficient rise between the first and the second layers, the transmitted acoustic wave behavior is highly influenced by the soil stiffness of the first layer. When this layer is stiffer, the pressure drops (Fig. 5a), and when it is softer, the pressure increases (Fig. 5b). Such independence of the results from the reflection coefficient in the aforementioned case is due to the attenuation of this factor caused by the considerable distance between the tunnel and the interface of the first and the second layers. By reducing the distance, the reflection coefficient effect on the transmitted acoustic wave behavior is amplified, as shown in cases of 20 and 30-m buried depths.

The reflection coefficient mentioned earlier is defined based on the acoustic impedance of the two adjacent mediums through which the acoustic wave is transmitted. This coefficient is the ratio of reflected wave intensity from the interface of two adjacent mediums to the transmitted wave intensity passed from that interface. In this study, the reflection coefficient is calculated as the squared ratio of the difference between two adjacent mediums’ acoustic impedance and the sum of the acoustic impedances. Aristizábal-Tique et al.34 used the same definition, except its second power. Comparing this definition with Guan et al.’s43 evaluation of the sound absorption of the porous media indicates the same concept imagined, except that the present study uses the characteristic acoustic impedance in calculating the reflection coefficient applied in nondispersive linear acoustics in one dimension. This coefficient shows “the amount of acoustical energy being reflected when propagating waves meet an obstacle or a different medium of propagation”43. It indicates how much radiated acoustic wave energy reflects from the two mediums’ interface on a scale of zero to one, where zero means that all the acoustic wave passes through the interface and one indicates the complete reflection of the radiated wave. The reflection coefficient between the air and the surface soil layer, between the various soil layers, and between the soil layers and the tunnel lining affects the transmitted and reflected acoustic wave pressure, but it is not the only factor. The other contributing factors are amplifying effect of soil particle vibration and the time when the acoustic wave impacts the interface.

### Effect of tunnel buried depth on acoustic wave behavior

Buried depth is another investigated parameter to quantify its effect on the acoustic wave in a layered soil medium. The reference properties of soil layers are used in this section. The maximum pressure value increases with the buried depth increase for the reflected acoustic wave, as illustrated in Fig. 4. However, Fig. 4 does not include the time shift of the absolute maximum pressure alongside its value when changing the buried depth. The reflected acoustic wave pressure–time history is represented in Fig. 6 for the three buried depths to show both variations.

As observed in Fig. 6, the maximum reflected acoustic pressure increases with the buried depth growth; the peak time is shifted from t = 27 ms in the case of a 10-m buried depth to (approximately) t = 60 ms for the two other cases. Such value and time shifts of the reflected acoustic wave are due to how the acoustic wave energy and the soil particle vibration vary with time. Accordingly, the soil particle acceleration is the first parameter influenced by the acoustic wave energy level and the resultant particle vibration. Consequently, the total acceleration value at the soil surface level can represent the acoustic wave energy propagated through the soil and reflected. So, interpreting the soil total acceleration behavior when changing buried depth allows explaining such behavior seen in Fig. 6.

The total acceleration time history of the surface soil for various buried depths is shown in Fig. 7. Due to the soil structure interaction and particularly the first layer’s constant properties when changing the buried depth, the air–soil interaction and the reflection coefficient factors are not applicable when analyzing such behavior.

The surface soil acceleration represented in Fig. 7 is generated by the free air explosion accompanied by the acoustic wave reflected with a time lag. These two acoustic wave sources were identified and investigated exclusively by Albert et al.44. The way these two soil acceleration sources interact is the fundamental reason behind how the reflected acoustic wave behaves when changing the buried depth in the numerical model. Taking the case of 30-m depth (with the highest reflected acoustic pressure value) as an example, the surface acceleration peak is obtained before the reflected pressure absolute peak (Fig. 6). While the air explosion is still in progress (Fig. 7), it induces the primitive air explosion-induced acoustic wave amplification by the acoustic wave reflected from the tunnel and the soil layers interfaces. As a result of such acoustic wave strengthening, the reflected acoustic wave pressure absolute peak increases compared to the local one (at t = 27 ms), and its instant is modified to t = 60 ms. However, in the case of a 20-m buried depth, although a relatively higher surface soil acceleration than the 30-m buried depth case, a lower reflected acoustic wave pressure is observed due to the lower acoustic wave amplification at the surface level. This is justified because the surface soil acceleration peak instant occurs after the air explosion. The same reason added to the lowest surface soil acceleration magnitude among all cases stops the acoustic wave amplification at the surface level in the case of 10-m buried depth and induces the lowest reflected acoustic wave value with no peak instant shift. The fundamental reason for such behavior (10-m buried depth) is because, for this specific lining concrete, the energy radiated into the soil pile is sent out by the tunnel lining before reaching the soil layer interface. Thus the energy amplification does not occur. A similar conclusion was made by Aristizábal-Tique et al.34 about the peak time shift of the reflected acoustic wave associated with the three buried depths. It happened due to the phase change and the time lag between the reflected wave from the interior space of soil (the buried structure and the soil layers interface) and the explosion. The position of the acoustic wave pressure peaks is shifted due to the density difference between the soil and the buried structure and is sensitive to the depth of the underground structure and the wave propagation in the first layer of the soil.

The maximum pressure value of transmitted acoustic waves (Fig. 5) and their time history for all buried depths (Fig. 8) indicate that increasing the buried depth results in transmitted acoustic wave pressure drop in the same soil structure. This trend is expected due to the higher acoustic wave energy deterioration in reaching the tunnel with greater buried depths.

### Effect of lining concrete on acoustic wave behavior

This section discusses the lining concrete impact on the behavior of the acoustic wave for the buried depth of 20 m, the reference soil properties, and two concrete types. Time histories of the reflected acoustic wave pressure and the corresponding maximum value of such pressure associated with each concrete type are illustrated in Fig. 9.

Based on the pressure time histories in Fig. 9, when the lining concrete stiffness reduces, the absolute peak value of the reflected acoustic wave rises. A time shift in the occurrence of such absolute value is observed from t = 60 ms in the concrete I model (with an absolute pressure of 306.94 kPa) to t = 27 ms in the two other softer lining cases (with absolute pressures of 313.33 kPa and 319.29 kPa in Concrete II and III models, respectively). These behaviors are due to the lining concrete time-dependent effect on the reflected acoustic waves. Shortly after the explosion, overpressure peaks at t = 21.88 ms (Fig. 1), and the explosion’s acoustic pressure mainly dominates the measured acoustic wave at the surface. It is less affected by the acoustic waves reflected from the soil and tunnel interior space. In this situation, reducing the lining concrete stiffness and, consequently, the far end boundaries damping reduction leads to the lining energy attenuation reduction. This phenomenon results in a reflected acoustic pressure growth at the beginning of the analysis, which is reflected by an increased pressure value at t = 27 ms when lowering the lining concrete stiffness, Fig. 9.

As time passes, high-amplitude acoustic waves are reflected from the tunnel lining and the soil layers’ interfaces, especially at the explosion process end. Consequently, changing the concrete stiffness affects the acoustic waves’ energy variation reflected back to the surface and thus their pressure value. Accordingly, reducing the lining concrete stiffness reduces the reflection coefficient between the lining and the soil. It then reduces the reflected waves from the lining, but on the other hand, it causes a lining particle’s vibration growth, leading to the reflected acoustic wave amplification. These inhomogeneous outcomes result in a non-uniform reflected acoustic wave pressure variation at the explosion period end. This non-uniform variation is observed in the reflected pressure value at t = 60 ms. It drastically diminishes in the model with Concrete II and then increases back to the primary value in the third model.

Vanishing the acoustic wave energy before reaching the tunnel lining for different lining concrete types also impacts the transmitted acoustic wave pressure. Figure 10 presents the transmitted acoustic wave pressure–time history and the maximum values of such pressure for each lining concrete type. As observed in Fig. 10, the transmitted acoustic pressure decreases from 178.39 Pa in the concrete I model by 14.01% and 22.88% for the concrete II and concrete III models by reducing the lining concrete stiffness. This behavior is due to the acoustic wave energy decreasing from the soil surface to the lining and how the acoustic wave energy varies in the tunnel vicinity.

As discussed earlier, the total acceleration is a better parameter to represent the acoustic wave energy level of soil and lining concrete. Therefore, to illustrate the acoustic wave energy variation for different concrete models, the maximum total accelerations for soil in various elevations in the vicinity of the lining and the maximum acceleration for lining with the three concrete types are represented in Table 5. The elevations, which are considered based on the tunnel section center, are the highest lining section point (Elev. 14.85 m), the middle of the lining section (Elev. 10 m), and the lowest lining section point (Elev. 5.15 m).

Table 5 shows that the highest soil acceleration around the tunnel and the highest lining acceleration are in the Concrete I and Concrete II models. Consequently, the lining and soil acceleration variation pattern in the tunnel lining vicinity and how the transmitted acoustic wave pressure varies when lowering the concrete stiffness (Fig. 10) indicate the lining concrete effects on the acoustic energy and how the transmitted acoustic wave pressure varies.

### Extra underground structure

In a buried structure system, underground utility lines and their maintenance and reparations can interfere with the construction and operation of the main structure. Locating the exact positions of these lines by applying the acoustic wave necessitates an investigation of the reflected and transmitted acoustic wave behavior for wide structure positions for the main tunnel. An extra underground structure (E.U.S.) is set up in various relative positions to the main tunnel with the 20-m buried depth (reference case) to study the behavior of acoustic waves (Fig. 11). The inner diameter of the E.U.S. is 0.8 m, surrounded by a 0.1-m-thick lining made of Concrete I.

The E.U.S.s aligned with the vertical centerline of the cross-section of the main tunnel is named by the letter “c”. The E.U.S.s on the right and left sides of the main tunnel are denoted by “r” and “l”, respectively. The subscripts “1” and “2” indicate whether the E.U.S. is above or below the main tunnel, respectively. In addition, an extra variable $${y}_{d}$$ with two values of 2 m and 5 m is introduced as the vertical distance between the main tunnel and the E.U.S. to allow investigation of how the acoustic waves react when altering the soil layer containing the E.U.S.. Figure 12 shows the maximum reflected and transmitted (from the main tunnel) acoustic wave pressures for various E.U.S. positions with the two values of $${y}_{d}$$ are illustrated.

By comparing the results represented in Fig. 12 with the reflected and transmitted acoustic wave pressures of the same model without E.U.S. (306.94 kPa and 178.39 Pa, respectively), it is found that adding the E.U.S. to the model acts as an energy absorber mechanism. It makes the radiated acoustic wave energy lead out of the system and causes a reduction in the reflected and transmitted acoustic wave pressures. Besides the energy absorption effect, the E.U.S. reflects the radiated acoustic waves toward the main tunnel and the soil surface. As shown in Fig. 12b, for both $${y}_{d}$$ values the transmitted acoustic wave pressure drops for the E.U.S.s below the tunnel compared with those above it. The reflected acoustic waves radiated from the E.U.S. towards the soil surface, and the main tunnel decreases when the E.U.S. is located below the tunnel. The same behavior is observed for the reflected acoustic waves (Fig. 12a), especially in the case of $${y}_{d}$$=5 m. Increasing the $${y}_{d}$$ value reduces the acoustic pressure (reflected and transmitted) when the E.U.S. elevation decreases. Increasing the $${y}_{d}$$ value has a more significant impact on the E.U.S.s above the main tunnel than those below it.

The E.U.S.s above the main tunnel move from the second to the first layer by increasing the $${y}_{d}$$, but the E.U.S.s below the main tunnel remain in the same soil layer (the third layer) for both values of $${y}_{d}$$. Moving the E.U.S. from the second to the first layer causes a reflection coefficient increase between the E.U.S. and the soil. Therefore, the reflected acoustic wave radiated from the E.U.S. towards the main tunnel, and the ground surface increased. Consequently, the acoustic pressures reflected back to the surface and transmitted into the main tunnel increase, as shown in Fig. 12. If the E.U.S. is located above the soil layer interface, it prevents attenuation of the reflected acoustic wave (from the E.U.S.) through that interface. For the E.U.S.s below the main tunnel, such layer alteration does not occur, and the acoustic wave pressure changes in a more limited range by increasing $${y}_{d}$$.

The importance of investigating the acoustic wave behavior emitted in an underground medium was pointed out earlier in the introduction to acoustic wave-based methods. The propagated signals from a buried structure fracture are severely influenced by the structural components and the soil surrounding it. Using the acoustic emission (A.E.) method as an underground structure health monitoring technique, the lack of knowledge about the acoustic wave behavior when interacting with these parameters would result in misinterpretation of the recorded signals. For example, the presence of an extra underground structure (like the utility lines) in the vicinity of the main tunnel can interfere with the signals emitted from the tunnel lining to the surface and cause misinterpretation of the structural health of the main tunnel. Therefore, investigating the acoustic wave behavior in the presence of E.U.S. (in various positions with respect to the main tunnel) in comparison with the original scenario (main tunnel without E.U.S.) helps avoid misinterpreting the recorded signals.

The soil structure (single layer or multilayer), the relative position of the tunnel and the soil layers, and the resultant multi-peak reflected acoustic wave pressure (discussed in “Effect of tunnel buried depth on acoustic wave behavior” section) can also affect the interpretation of the reflected acoustic signals in the A.E. method. This may lead to incorrect judgment of a probable fracture on tunnel lining if not appropriately investigated. The same applies to the lining concrete stiffness and the soil mechanical properties, which drastically influence the acoustic wave behavior and the consequent interpretation of the signals.

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