Abstract
To solve the problem of a potential void near a shallow rectangular masonry-concrete power tunnel, the ground-penetrating radar (GPR) detection technology is used and multiple GPR detection lines are placed to detect concealed void. The GPR images of circular and square voids are obtained, which can help increase accuracy of void identification. The models that cover 9 circular voids and 9 square voids are created to investigate how various forms and positions of void will affect the internal forces of the power tunnel structure and surrounding roads. In terms of morphological characteristics, according to the research results, the impact of a circular void on tunnel and surrounding roads is slightly stronger than that of a square void. If the circular void and square void are at 135° and 115°, respectively, the maximum shear force of the tunnel structure occurs at the floor. If both circular and square voids are at 115°, the maximum axial force of tunnel structure occurs at the right side wall. If both circular and square voids are at 135°, the maximum bending moment of tunnel structure occurs at the floor. If both circular and square voids are at 155°, the ground settlement and pavement stress of surrounding roads are maximized. Generally, if a void occurs at the middle or lower part of the side wall or near the side of the floor in a shallow rectangular masonry-concrete power tunnel, its adverse impact is at its worst. Therefore, GPR detection of the voids at the lower and middle parts and the side of the floor in the power tunnel should be intensified, in order to eliminate the risk of a void near power tunnel.
1. Introduction
In the early power tunnel construction projects in China, the cut and cover method was often used, and the tunnels were mostly of relatively simple rectangular masonry-concrete structure. This type of tunnel is clearly characterized by a small cross-sectional area, a shallow buried structure, and susceptibility to impact by the external environment, so it is a typical type of small-section shallow tunnel. In recent years, the urbanization of China has made fast progress. As a consequence of intensified human activities, the disturbance caused by external activities in power tunnels, particularly the shallow rectangular masonry-concrete tunnels, has been aggravated. This often induces the risk of voids in the soil layers near the tunnels and such a risk has been deteriorating so badly that the normal service of power tunnels is already impacted.
At present, most academic research into the void behind tunnel lining is focused on the engineering fields such as road tunnel, railway tunnel, and subway tunnel. For example, Luo et al. [1] treated subway voids by using the GPR and sleeve valve pipe grouting technologies and effectively eliminated the hazard of the subway voids in the deep, thick, and soft soil strata in coastal region; Hou et al. [2] used the voids in the Longmen Tunnel of the Provincial Highway 206 in Fujian to analyze the convergence and expansion pattern of lining deformation near void; Zhang et al. [3] conducted systematic research into the cracking evolution process of tunnel structure and variation pattern of internal forces under the condition of double voids behind crown and spandrel; Min et al. [4] conducted numerical simulation and model test to analyze how the voids behind the crown of twin-arch tunnel affect the cracking pattern of lining structure; Wang et al. [5] examined the results of model tests on the voids at spandrel, side wall, arch foot and arch bottom and revealed how the voids at various positions affect the mode of failure and sequence of failure in tunnel; and Zhao [6] used the Qingdao Metro Project as an example and conducted model test and numerical simulation to analyze how excavation affects stratum stability under the condition of void occurring right above the tunnel. Yasuda et al. [7] used the substructure matching method to theoretically prove the close correlation between the void behind tunnel lining and the seismic damage of tunnel. Choo et al. [8] used the GPR detection method to analyze the thickness of NATM tunnel lining and the conditions behind the lining, and discovered that void is very likely to occur between the secondary lining and initial support near the tunnel crown. Voznesenskii and Nabatov [9] used the impact sound response to develop a new method to identify the type of filling body in the void behind tunnel lining. Ren et al. [10] used the finite element modeling technique to analyze how the size and position of void and the multi-void combination effect affect the tunnel lining structure. Ko and Lee [11] obtained the spectrum signature of GPR signal and thus managed to detect and evaluate the thickness, void and waterproof layer of tunnel lining. Meguid and Dang [12] noted that presence of void behind the tunnel lining will result in redistribution of the earth pressure acting on the lining and consequently change the internal forces of lining, induce excessive deformation or even cracking and directly impact safe operation of symmetric or asymmetric twin-arch tunnel. The aforesaid research regarding the voids around tunnel is mostly focused on horse-shoe shaped or circular cast-in-situ tunnel, but rarely touches upon shallow rectangular masonry-concrete power tunnel. Shallow rectangular masonry-concrete power tunnel is structurally very different from the aforesaid tunnel types, and the voids around it mostly result from the disturbance by external factors after its completion and thus entail great uncertainty. Therefore, such voids pose safety risks to power tunnel and there is an absolute need to conduct technical research and investigation of the voids behind this type of tunnel.
Given this problem, we use a shallow rectangular masonry-concrete power tunnel as an example and use the ground-penetrating radar detection technology to investigate the risk of void lurking behind the power tunnel, create various models that reveal the conditions of the void distribution behind the power tunnel, probe into how various void distribution patterns affect the structural stress of the shallow rectangular masonry-concrete power tunnel and the surrounding roads, and thus afford certain technical references for the detection and control efforts in future similar projects.
2. Void Detection Technology Based on the Ground Penetrating Radar Method
2.1. Principles of Ground Penetrating Radar
Ground-penetrating radar (GPR) is a type of electromagnetic technology used to identify the distribution of various media underground. It is usually used to detect the risk of void behind the tunnel structure. If there is any void behind a tunnel, the electrical property difference between the void area and the original rock and soil media will create the electrical property difference interface. A high-frequency electromagnetic wave will be reflected by the electrical property difference interface to create the reflected wave that will be received by the receiving antenna [13, 14]. Therefore, by identifying the parameters such as two-way travel time, amplitude, and waveform of the GPR electromagnetic wave in the media, we can deduce the position, form, and range of the void behind the tunnel (see Figure 1).
Based on the two way travel time characteristics of electromagnetic wave [16, 17], the travel time can be calculated by the following formula:
If , the stratum depth of the rock and soil mass anomaly area can be simply calculated by the following formula:where h is the buried depth of anomaly area; x is the distance between transmitting antenna and receiving antenna; is the propagation velocity of electromagnetic wave in rock and soil mass; ε is the relative dielectric constant of medium [18] (see Table 1); and c is the velocity of electromagnetic wave in vacuum.
2.2. Detection Line Placement
In GPR detection, the GPR radar antenna must be placed tightly on the surface of the tunnel structure layer. Usually 5 detection lines are placed, with 1 placed at the center line and each side of tunnel roof and at each of the left and right side walls (see Figure 2). Besides, necessary adjustment must be done based on the actual conditions in the tunnel.
2.3. Analysis of Void Radar Image Characteristics
In order to more accurately explain void radar image characteristics, this paper uses rectangular masonry-concrete power tunnel as an example. Through GPR scanning of the center line and both sides of tunnel roof and the left and right side walls in the power tunnel, the detection images of 5 detection lines are obtained, as shown in Figure 3. If there is potential presence of void, the outer contour of GPR reflected wave is relatively clear, there is noticeable strong reflection inside, the diffracted wave and multiple wave are quite obvious, the overall amplitude is quite intense, the phase axis is relatively continuous, and the radar frequency changes from low frequency to high frequency. If the void is similar to a square, the reflected wave is in forward continuous tabulate form (see Figures 3(a) and 3(b)); if the void is similar to a circle, the reflected wave is in inverted hyperbolic curve form (see Figure 3(c)); and if there is no void, the transmitted wave group has no noticeable strong reflection (see Figures 3(d) and 3(e)).
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3. Void Analysis Model
3.1. Stratigraphic Characteristics
Rectangular masonry-concrete power tunnel is mostly built along urban roads. Its stratum mostly encompasses surface course and base course of road and also clay layer. Now we use the most common 2 m deep rectangular masonry-concrete power tunnel as example, to create the power tunnel analysis model that encompasses surface course, base course and clay layer. The model size is (W × H) 40 m × 20 m (see Figure 4). The surface course is 0.1 m thickness, base course 0.3 m thick, clay layer 19.6 m thick, tunnel size (W × H) 2 m × 2 m, roof and floor 0.2 m thick, and left and right side walls 0.37 m thick.
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3.2. Void Distribution
Given the fact that the voids behind tunnel are mostly in random distribution, the circular void with 1 m diameter and the square void with 0.887 m side length are used as example. The relative positional relations between void and power tunnel are shown in Table 2. The two have the same stratum loss, where the lost soil mass volume in the direction of unit length is 0.785 m3. Besides, 9 positional relations between void and power tunnel are taken into account, as shown in Figures 2, 5 and 6. The analysis and calculation models are established that cover various relative positions of circular/square voids and tunnel.
3.3. Model Parameters and Constraints
Based on the design requirements for the asphalt surface course and base course of urban roads in China, the applicable design specifications for roads, and the relevant survey and design data of power tunnels, the calculation parameters of this tunnel model are as shown in Table 3.
Besides, the model boundary condition is that both side boundaries are subject to normal constraint and the bottom boundary is subject to normal constraint and tangent constraint. The tunnel side wall and roof and floor of tunnel are hinged. Besides, this model only takes account of dead weight induced load.
4. Impact of Void on Tunnel Structure
4.1. Impact of Void on Tunnel Structure Shear Force
As indicated in Figures 7–9, the shear force of tunnel roof and floor is obviously greater than that of tunnel side wall, and as void position varies, the variation of tunnel roof and floor shear is greater than that of side wall shear. The maximum shear of tunnel structure under circular void appears at the tunnel floor with 135° void and is 58.184 kN, which is 42.24% greater than the tunnel floor shear without void. The maximum shear of tunnel structure under square void appears at the tunnel floor with 115° void and is 56.708 kN, which is 38.36% greater than the tunnel floor shear without void. Besides, void does not significantly affect the shear of left side wall of tunnel. The area where the void significantly affects the shear of right side wall of tunnel is at 135°. The areas where the void significantly affects the shear of tunnel roof are at 65° and 90°. The areas where the void significantly affects the shear of tunnel floor are at 115° and 135°. On the whole, the structural shear of a tunnel under circular void is slightly greater than that of a tunnel under square void.
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4.2. Impact of Void on Axial Force of Tunnel Structure
As indicated in Figures 10–12, the axial force of the left and right side walls of tunnel is obviously greater than that of tunnel roof and floor, and as void position varies, the change rate of axial force of tunnel roof and floor is slightly greater, but the absolute value of their axial force is less. Under both circular and square voids, the maximum value of axial force of tunnel structure appears at the tunnel right side wall with 115° void, and its value is 90.013 kN and 90.361 kN respectively, which is respectively 33.39% and 33.91% greater than the axial force of tunnel right side wall without void. Besides, void does not significantly affect the axial force of tunnel left side wall. The areas where void significantly affects the axial force of tunnel right side wall are mostly at 90° and 115°. The area where void significantly affects the axial force of tunnel roof is mostly at 0°. The area where void significantly affects the axial force of tunnel floor is mostly at 180°. On the whole, there is no significant difference between the axial force of a tunnel structure under circular void and that of a tunnel structure under square void.
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4.3. Impact of Void on Bending Moment of Tunnel Structure
As indicated in Figures 13–15, the bending moment of tunnel roof & floor is obviously greater than that of tunnel side wall, and as void position varies, the variation of tunnel roof & floor bending moment is greater than that of side wall bending moment. Under both circular and square voids, the maximum value of bending moment of tunnel structure appears at the tunnel floor with 135° void, and its value is 27.398 kN·m and 26.033 kN·m, respectively, which is respectively 56.20% and 48.42% greater than the bending moment of tunnel floor without void. Besides, the areas where void significantly affects bending moment of tunnel floor are mostly at 115°, 135°, and 155°. The areas where void significantly affects bending moment of the tunnel roof are mostly at 45° and 65°. Void does not significantly affect the bending moment of the tunnel left side wall. The areas where void significantly affects the bending moment of the tunnel right side wall are mostly at 115° and 135°. On the whole, the bending moment of a tunnel structure under circular void is slightly greater than that of a tunnel structure under square void.
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5. Impact of Void on Surrounding Roads
5.1. Impact of Void on Ground Settlement of Surrounding Roads
As indicated in Figures 16–18, the ground settlement of surrounding roads changes as void position changes. In the range of 0°∼90°, the ground settlement under circular and square voids does not change significantly overall. In the range of 90°∼155°, the ground settlement under both circular and square voids increases sharply and reaches the maximum values of −1.628 mm and −1.305 mm respectively at 155°. In the range of 155°∼180°, the ground settlement under both circular and square voids decreases markedly. Therefore if the void is at 90°∼155° of power tunnel, it significantly affects the ground settlement of surrounding roads.
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5.2. Impact of Void on Pavement Stress of Surrounding Roads
As indicated in Figures 19–21, in the lengthwise direction, the areas where the pavement stress of surrounding roads is affected are mostly in −5 m∼7.5 m. In terms of void distribution, the pavement stress of surrounding roads changes as void position changes. In the range of 0°∼90°, the pavement stress under circular and square voids fluctuates slightly. In the range of 90°∼155°, pavement stress of road under both circular and square voids increases sharply and reaches the maximum values 110.724 kN/m2 and 87.554 kN/m2 at 155°. In the range of 155°∼180°, the pavement stress of road under both circular and square voids decreases markedly. Therefore, the void near 90°∼155° of power tunnel significantly affects pavement stress of surrounding roads.
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6. Suggestions on Detection and Grouting
6.1. Suggestions on Detection
According to the above model calculations and research results, if the void is in the middle or lower part of rectangular masonry-concrete tunnel structure, its hazardous effect is greater than its hazardous effect when in rectangular masonry-concrete tunnel. Therefore, in detection of void behind rectangular masonry-concrete tunnel, detection of the potential voids in the middle and lower parts of tunnel structure should be intensified, i.e., 3 detection lines are added at the left, middle, and right of tunnel floor. Besides, given that there are some limitations in this study, e.g., the impact of external loads of the upper ground is not considered, it is recommended that the full-space layout detection should be carried out for the power tunnel (see Figure 22).
6.2. Suggestions on Grouting
If there is risk of void near shallow rectangular masonry-concrete power tunnel, reinforcement by grouting in void should be conducted as soon as possible [19, 20], to eliminate the adverse impact of void on tunnel structure and surrounding roads and to prevent irreversible structural damage induced by further development of void. Besides, for treatment of the voids near power tunnel based on the structural characteristics of shallow rectangular masonry-concrete power tunnel, it is recommended to conduct grouting outside the tunnel, in order to prevent grouting work from damaging the tunnel structure and consequently compromising the impermeability of power tunnel. If grouting outside the tunnel is difficult, grouting inside the tunnel is also acceptable, provided that proper seepage-proofing of grouting hole is done in the tunnel (see Figure 23). In addition, the grouting parameters must be strictly controlled and proper grouting materials selected, to prevent the grouting pressure, unit weight of grouting material and expansion from creating excessive unsymmetrical pressure effect on the power tunnel, for such effect will induce great local internal force in the power tunnel structure, cause local failure of power tunnel and compromise long-term operational safety of power tunnel.
7. Conclusion
In this paper, the ground-penetrating radar (GPR) detection technique commonly used in engineering is employed to conduct layout detection research on the geological conditions behind the rectangular power tunnel. The detection results show that there are two typical forms of voids behind the power tunnel, i.e., round void and square void. In view of the differences in the form characteristics of voids and the randomness of spatial distribution, the finite element modeling method is used in this paper to build 18 finite element models, including 9 models for round voids and 9 for square voids. Specifically, starting from 0° right above the rectangular power tunnel roof to 180° directly below the rectangular power tunnel floor, two types of voids are arranged clockwise to study the impact of different voids under different location conditions behind the rectangular power tunnel on the power tunnel and its surrounding environment. The results show that ① the impact of round voids on the power tunnel and its surrounding environment is slightly greater than that of square voids under the same conditions of stratum loss, but on the whole, the differences between these two types of voids are not significant. ② From the perspective of the distribution of voids around the power tunnel, the impact of voids on the power tunnel and its surrounding environment is the most significant if round voids or square voids are located between 115° and 155°, so the disposal of voids at this location should be strengthened. ③ Given that there are some limitations in this study, e.g., the impact of external loads of the upper ground is not considered, it is recommended that the full-space layout detection should be carried out for the power tunnel to reduce the adverse impact of voids.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest.
Acknowledgments
This work was supported by the Key Research and Development Project of Science and Technology Department of Hebei Province, (Grant 21375408D).