SKEWED PRESSURE CHARACTERISTICS INDUCED BY STEP-BY-STEP EXCAVATION OF A DOUBLE-ARCH TUNNEL BASED ON INFRARED THERMOGRAPHY

Original scientific paper In order to obtain the skewed pressure characteristics, the physical model tests, adopting two kinds of excavation sequences of the bench method and the expanding method, were conducted under the different confining pressures for observation thermal radiation characteristics of the skewed pressure induced by step-by-step excavation for a double-arch tunnel. Firstly, under uniaxial compression test, the cylindrical specimen presented the cooling effect, the correlations between the axial stress of the cylindrical specimen and its surface thermal radiation temperature displayed negative nonlinear correlation in the pre-peak curve and linear correlation in the post-peak curve, respectively. Secondly, for the physical model tests, the stress-temperature-time curves showed obvious two-phase trend as first moderate decline and then rapid decline stages, and the latter was slower than the former for an excavation step after all excavations being completed. The results showed that for two different excavation sequences, the failure positions on the vault of the double-arch tunnel due to being unloaded are diametrically opposed. Then the corresponding relationships between the skewed pressure induced by double-arch tunnel excavation and the temperature field of the infrared thermal radiation were revealed, which can provide a reference for the reasonable excavation and security support of the double-arch tunnel.


Introduction
The infrared radiation imaging technology, using the infrared radiation principle to convert the infrared radiation temperature distribution of the surface into an infrared image, characterizing non-contact, real-time and full-range of features, can obtain the completely temporal and spatial information of stress-field of the material surface.Therefore, it was of an important application value in the practical engineering [1÷3].
In recent years, the thermal radiation imaging (TIR) technology in several countries has been widely applied to various aspects.For example, Etoa et al. examined the infrared radiation properties and surface characteristics of carbon-carbon compopoints and graphites from the viewpoint of the nondestructive detection of defects in these materials, and they found that the larger the pore size and roughness of specimen, the larger the variation of data points [4].Ploteau et al. aimed at presenting the development, the construction, the calibration, and the test of flux meters designed to make in situ measurements of infrared radiation in industrial furnaces [5].In order to have the distinct spectral features, Balick et al. used an hyperspectral imaging spectrometer measuring in the longwave thermal infrared in the field to observe the variability of emissivity spectra of individual rock surfaces [6].Park applied the thermal infrared camera to detect the increase of temperature and the distribution of thermal abnormalities before and after failure under uniaxial loading, for the granite, diorite, basalt and tuff specimens obtained in Korea [7].Baron et al. presented a new approach for mapping open cracks and tension fractures within rock slope instabilities and rock cliffs, which resided in high-resolution ground-based and airborne infrared thermography [8].Usamentiaga et al. presented a general introduction to infrared thermography and the common procedures for temperature measurement and non-destructive testing [9].Manuel et al. conducted the possibilities of the use of IR thermography in rotating tool processes such as milling [10].
So far, China has also made quite a number of important achievements in research of thermal radiation technology.For example, based on TIR detection during uniaxial loading of rock samples, Wu et al. found the TIR-anomaly characteristics of the rock surface reflect the features of rock deformation or rock failure [11].Li et al. discussed the main characteristics of infrared radiation thermography on temperature measurement and the development of infrared thermographic equipments.They also reviewed the applications of infrared thermographic techniques, thermal diagnosis of equipments, testing of structures and buildings, and prevention and cure of disasters [12].Zhang et al. conducted the research on TIR with rock deformation of tunnel without bolts and bolted tunnel in the process of confined compressions.They found that the TIR temperature of the bolted tunnel wall rock increased higher and changed more rapidly than that of tunnel wall rock without bolts, and that TIR is stronger in the location of stress concentration and bolted ranges than that in the location of stress relaxation and crushed ranges [13].Based on the thermodynamics theory and physical micro-properties of solid materials subjected to external loading at room temperature, Wang et al. deduced a formula of calculating temperature difference of infrared radiation (IR) in terms of the sum of three principal strains to quantitatively investigate the infrared radiation characteristics in test [14].He et al. simulated a roadway excavation in the geologically horizontal strata at great depth based on physical modeling test by using infrared thermography.The infrared thermography provided an enhanced understanding of the excavation response in terms of initiation, propagation and coalescence of rock damage in the spatial and frequency regimes respectively [15].Chen et al. employed the equivalent material simulating experiments and thermal infrared imager equipments to study the rules of deformation and failure of surrounding rock induced by rock burst [16].Gong et al. conducted experiments on roadway excavation in large-scale geological physical models and captured the structural behavior of the differently inclined rock strata based on infrared thermographic technique [17].Zhang et al. carried out an experiment to study the infrared radiation temperature characteristics of granites under different moisture conditions by using infrared thermal imager [18].
In a word, the infrared radiation imaging technology as a method of observation of the material surface temperature, was widely used in China and other countries and many research results had been achieved.However, the study of the infrared radiation characteristics of the skewed pressure during the doublearch tunnel excavation, together with considering the pressure conditions and excavation sequences of a double-arch tunnel, is rarely reported.Therefore, the similar material model tests were carried out for observation of thermal radiation characteristics of the skewed pressure induced by step-by-step excavation of a double-arch tunnel based on the infrared thermography.Furthermore, the corresponding relationships between the skewed pressure and the thermal radiation temperature field were revealed during the double-arch tunnel excavation.The results would provide the technical basis for reasonable excavation and security support of a double-arch tunnel.

Materials and methods 2.1 Test specimens
The typical dimensions of the double-arch tunnel were shown in Fig. 1a.The square plate for double-arch tunnel model, whose dimensions were length × height × thickness = 150 mm × 150 mm × 30 mm, was shown in Figure 1b.The white cement was selected as the similar material with the water-cement ratio of 0,8:1.And the same material standard cylindrical sample of diameter 50 mm and length 100 mm was made, with two ends being polished and the tolerance of parallelism less than 0,01 mm.The physical and mechanical parameters of the specimens were shown in Tab. 1.

Laboratory equipment
The loading device whose maximum load for 3000 kN was equipped with RLW-3000 servo control compression testing machine, as shown in Fig. 2. The biaxial testing machine was controlled by setting the displacement velocity to 0,0025 mm/s.A modern TIR imaging system, FLIR ThermaCAM SC3000 with temperature precision of 0,02.°C was applied for the TIR radiation detection and image recording during the step-by-step excavation of doublearch tunnel.The infrared camera with 7,5 to 13 μm spectral response range was performed with the given calibration temperature within the range of −40 to +500 °C, and the IR image resolution was for 640 × 480 pixels.

Experimental procedures
The laboratory tests were conducted according to the following procedures: (1) Turned on the computer, then started the devices, checked and debugged the mechanical testing system.
(2) Connected the infrared acquisition equipment of FLIR ThermaCAM SC3000 and debugged the corresponding devices.
(3) Placed the specimen just below the indenter, first made the indenter close to the specimen with a coarse control, then approximated the test specimen and loaded in accordance with the designed loading rate.The laboratory test was conducted according to the following procedures.
(4) The cylindrical specimens were loaded in the vertical direction at a constant rate of 0,0025 mm/s until the failure occured.The force and deformation of the specimens were monitored during the loading process.
(5) The physical model was loaded up to 7,5 kN in the biaxial direction at a constant rate 0,0025 mm/s firstly, then to 9,0 kN after the stabilization of 1.0 minute.(6) As shown in Fig. 3, the bench method and the expanding method were adopted for the step-by-step excavation in the experiment respectively.When all the excavations were completed, the loading was continued until the specimen failed.AR01, AR02 and AR03 were the monitoring points of the infrared temperature.
a) The bench method b) The expanding method Figure 3 Step-by-step excavation sequences of the double arch tunnel.(7) When the experiments were completed, at first the loadings in the horizontal direction and then in the axial direction were unloaded, uplifting the indenter, deriving the experimental data, removing the test specimen, and finally closing the related experimental equipment.

Results and discussions 3.1 Characteristics of stress-temperature-time curves of cylindrical sample
The average infrared radiation temperature (T AIR ) of the specimen surface, reflecting the infrared radiation energy of the entire specimen, is an important indicator to characterize the infrared radiation variation of the specimen in the loading process.The T AIR of the specimen front surface (at a front view) was captured by IR camera in the test and the T AIR -time curve was plotted.The uniaxial compressive stress-time curve is important to reflect the mechanical properties of the rock sample.
In the process of uniaxial loading tests, the cylindrical specimen stress-time curve experienced two-phase changes composed of a nonlinear rise until the peak value and then nearly a linear decline, and the stress-time curve showed larger fluctuations (Fig. 4a).The T AIR -time curve of the cylindrical specimen showed a monotonically decreasing trend with time increasing, and the T AIR dropped from 11.50 °C to 10,95 °C, the variation magnitude of the temperature was 0,55 °C.In order to reflect the infrared radiation characteristics of the sample under the uniaxial compression test, the relationship curves between the T AIR and the axial stress of the sample were plotted.As seen from Fig. 4b, the relationships between the axial stress σ (MPa) and the average infrared radiation temperature t (°C) of the sample demonstrated a striking change with the load increasing, i.e. the negative nonlinear correlation in the front-peak phase and the linear correlation in the postpeak phase.The fitted equations were as follows: (2)

Characteristics of temperature and stress fields of the bench method 3.2.1 Characteristics of stress-temperature-time curves of the bench method
As shown in Fig. 5, the stress-temperature-time curves showed a downward trend as a whole with time.The second step excavation of the bench method was a critical step, before which the stress-temperature-time curves showed a moderate decline, after that the stresstemperature-time curves showed a rapid decline.When the first step excavation (840 s) of the doublearch tunnel was conducted, the temperatures of three monitoring points were t AR01 = 13,70 °C, t AR02 = 13,62 °C and t AR03 = 13,54 °C, namely t AR01 ˃ t AR02 ˃ t AR03 .
When the third, the fourth or the fifth step excavations were carried out, the temperature curves of three monitoring points showed the rapid downward trend, indicating that the surrounding rock of the tunnel was in a stress relaxation or a plastic deformation stage.Due to the temperatures of three monitoring points were t AR03 ˂ t AR02 ˂ t AR01 , according to Eq. ( 2), the stresses of the surrounding rock of the double arch tunnel were σ AR01 ˂ σ AR02 ˂ σ AR03 .

Characteristics of IR image of the bench method
The timing sequence of the double-arch tunnel excavation and the surface infrared image changes of the bench method were shown in Figs. 6 and 7, respectively.
The second step excavation was a critical step, before which the surrounding rock of the double-arch tunnel was in an elastic deformation stage, after that the failure appeared in the vault of the left tunnel (Fig. 6c), indicating that the surrounding rock of the tunnel was in a stress relaxation or a plastic deformation stage.It could be seen from Fig. 7 that corresponding to the excavation sequence, the infrared image colors of the specimen surface underwent the changes from warm to cool, which were consistent with the results from the infrared radiation temperature-time curves of the monitoring sites.

Characteristics of temperature and stress fields of the expanding method 3.3.1 Characteristics of stress-temperature-time curves of the expanding method
As shown in Fig. 8, the stress-temperature-time curves showed a downward trend as a whole with time increasing.The third step excavation of the double-arch tunnel is a critical step, before which the stresstemperature-time curves showed a moderate decline, after that the stress-temperature-time curves showed a rapid decline.When the first step excavation (480 s) was conducted, the temperatures of three monitoring sites were t AR01 = 12,20 °C, t AR02 = 12,28 °C and t AR03 = 12,15 °C, respectively.When the second step excavation (545 s) was conducted, the temperatures of three monitoring sites were t AR01 = 12,19 °C, t AR02 = 12,26 °C and t AR03 = 12,14 °C, respectively.After the third step excavation, the temperatures of three monitoring points were t AR01 = 12,11 °C, t AR02 = 12,08 °C and t AR03 = 12,13 °C, respectively.According to Eq. ( 1), the stresses of the surrounding rock of the double arch tunnel were σ AR03 ˂ σ AR01 ˂ σ AR02 .
When the fourth and the fifth step excavations were carried out, the temperature curves of three monitoring sites showed a rapid downward trend, indicating that the surrounding rock of the tunnel was in the stress relaxation or plastic deformation stage.Due to the temperatures of three monitoring points being t AR02 ˂ t AR01 ˂ t AR03 , according to Eq. ( 2), the stresses of the surrounding rock of the double arch tunnel were σ AR02 ˂ σ AR01 ˂ σ AR03 .

Characteristics of IR image of the expanding method
The timing sequence of the double-arch tunnel excavation and the surface infrared image changes of the expanding method were shown in Figs. 9 and  The third excavation step was a critical step, before which the surrounding rock of the double-arch tunnel was in the elastic deformation stage, after that as a result of failure appeared in the vault of the right tunnel (Fig. 8d), indicating that the surrounding rock of the tunnel was in a stress relaxation or a plastic deformation stage.
It could be seen from Fig. 10 that corresponding to the excavation sequence, the infrared image colors of the specimen surface underwent the changes from warm to cool, which were consistent with the results derived from the infrared radiation temperature-time curves of the monitoring points.

Conclusions
The uniaxial stress-time curve experienced two-phase changes for a rise till peak value and then decline with time, and the stress-time curve showed larger fluctuations.The thermal radiation temperature-time curve showed a monotonically decreasing trend, and the cylindrical specimen displayed the cooling effect.The relationships between the axial stress and the average infrared radiation temperature of the sample demonstrated the negative nonlinear correlation in the pre-peak phase and the linear correlation in the post-peak phase.
By the bench method and the expanding method excavations of the double-arch tunnel, the stresstemperature-time curves showed two-stage trend composed of a moderate decline and a rapid decline stages with time, and the latter was slower than the former for an excavation step.Corresponding to the excavation sequence of two different excavation methods, the specimen surface colors of the infrared images underwent changes from warm to cool, which were consistent with the results derived from the infrared radiation temperature-time curves of the monitoring points.
Before the failure of the double-arch tunnel, the stresses of monitoring points at the top of the tunnel by the bench method excavation were the right tunnel, the middle rock pillar and the left tunnel in order of size.While the stresses of monitoring points at the top of the tunnel by the expanding method excavation were the middle rock pillar, the left tunnel and the right tunnel respectively.After the second step excavation by the bench method, the failure appeared in the vault of the left tunnel.While after the third step excavation by the expanding method, the failure appeared in the vault of the right tunnel.
The monitoring stresses were carried out from point information to field information during the step-by-step excavations of the double-arch tunnel by using the infrared thermography.The results in the paper changed so that we could not obtain the post-peak stress information due to material failure inducing the strain gauge peeling in the traditional way of point information monitoring stress.So the results in the paper are of important meaning to develop the infrared thermography to conduct the stress field monitoring.

Table 1
a) Typical dimensions of the tunnel b) Cylinder specimen c) Physical model Figure 1 Typical dimensions and physical model of the double-arch tunnel.Physical and mechanical parameters of the model.Density (Diameter × length = 50 × 100 mm 2 ; Square plate with holes: Length × height × thickness = 150 × 150 × 30 mm 3 .a) Testing equipment b) Scheme of testing system Figure 2 Testing equipment and testing system layout.

4
a) Stress-temperature-time curves b) Stress-temperature curves Figure Stress-temperature-time and stress-temperature curves of the cylindrical specimen.

Figure 5
Figure 5 Stress-temperature-time variation curves of bench method.

Figure 8 Figure 9
Figure 8 Stress-temperature-time variation curves of the expanding method.