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Geomechanical Model Tests and Infrared Detection of Rock Responses for Tunnels Excavated in Sedimentary Rocks
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 191 (2017) 20 – 30
Symposium of the International Society for Rock Mechanics
Geomechanical Model Tests and Infrared Detection of Rock Responses for Tunnels Excavated in Sedimentary Rocks Weili Gonga,b*, Manchao Hea,b, Hong Yanb, Lifeng Lia,b,c, Xiaodong Xua,b a State Key Laboratory for Geomechanics & Deep Underground Engineering, Beijing 100083, China School of Mechanics & Civil Engineering, China University of Mining & Technology Beijing, Beijing 100083, China c School of Architecture & Civil Engineering, Guizhou University of Engineering Science, Guizhou, Bijie 551700, China b
Abstract Rock mass behavior is controlled mainly by weak planes in sedimentary rocks. Geomechanical model tests were conducted for simulating tunnel excavations in horizontal, the 45q and vertical inclined rock strata. Infrared thermography was employed for detecting rock responses during the excavations. Infrared temperature (IRT) curve obtained by averaging the matrices of the infrared sequence can be viewed as temporal observation of the overall energy release from the rock under excavation. The IRT curve characterizes the horizontal and vertical strata as linear behavior and the 45q inclined strata as piecewise linear behavior over the full-face excavation and the three strata as plastic-like behavior over the staged excavation, respectively. The constitutive heterogeneity can be represented by the Weibull modus obtained by curve-fitting to the Weibull model using the probability distribution of the IRT temporal observations. The vertical strata has the smallest Weibull modulus values corresponding to the higher heterogeneity compared with the else two strata models. The structural response of the rock under excavation was characterized by the IRT distribution of the infrared image. IRT distribution of the horizontal strata evolved from scattering distribution to localized high-temperature zone around the face. In contrast, IRT distribution for the 45q and vertical strata distributed as belt-like IRT parallel to the weak surface; indicating the frictional sliding damage mechanism. Most intense friction was observed in the excavation in the 45q inclined rock strata. © Published by Elsevier Ltd. This Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license © 2017 2017The TheAuthors. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EUROCK 2017. Peer-review under responsibility of the organizing committee of EUROCK 2017 Keywords: Geomechanical model test; Sedimentary rocks; Tunnel excavation; Infrared detection; Excavation damaged zone
* Corresponding author. Tel.: +8610-15910785289; fax: +8610-010-62339820. E-mail address: [email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EUROCK 2017
doi:10.1016/j.proeng.2017.05.149
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1. Introduction Sedimentary rocks cover the majority of earth’s surface and are frequently encountered in underground mining. In the sedimentary rocks, two main sources of discontinuities are beddings and joints. The beddings can be assumed continuous over areas greater than that of any designed excavation and joints, however, are typically constrained between beddings [1]. Both beddings and joints are surfaces of relatively low shear and negligible tensile strength. Under the condition of stratified rock masses stretching across the roadway section, the engineering geological behaviour during tunnel development and operation is mainly controlled by the characteristics of the stratification planes [2]. Thus, existence of the discontinuities may exert a significant impact on the stability of the surrounding rock masses. Excavation damaged zone (EDZ) is closely related geological disasters such as rock bursts, bumps and water inrush, etc. Better understanding of rock behaviour during the excavation, therefore, has been an important issue for design of the underground opening and mitigation of the potential geological disasters. Excavation induced damage has been investigated extensively with different methods including the field experiments [3], numerical study [4], and laboratory experiments [5–7]. Geomechanical model tests with judicious choice of the model materials may yield some important information on the mechanisms of the EDZ which are not available from numerical models or field experiments [8]. One of the critical issues in geomechanical model tests is the use of the monitoring techniques which were developed purposefully for acquiring the “real” information of the rock behaviour in varied regimes. Strain gauge is widely used because it can measure the stressed rocks consistent with the theory of rock mechanics but is limited to the elastic phase. Alternatively, the use of remote sensing techniques is getting more popular. Digital imaging has been applied for determining the displacement and strain [8, 9]. The photogrammetry requires supplementary lighting while three-dimensional laser scanning (Lidar) acts as its own source of “illumination”, and can be used in in active tunnelling environment under dusty, damp, and dark conditions and collected very accurate, high resolution 3-dimensional images of its surroundings [10]. The advantages of non-contact optical vision lie in their ability to represent the structural change by realistic and practical surface models or geometrical features such as cracks and fractures. However, it is hard to get a definite relationship with respect to the stress redistribution in large-deformation problems [1]. Infrared thermography is another remote sensing technique which produces thermal image by detecting electromagnetic waves within infrared band [11]. Infrared image represents rock response based on the thermal-mechanical coupling effect and does not require supplementary lighting as well. When processed with proper algorithms, thermal image will not only be able to detect geometrical features such as crack propagation, but also the static and dynamic friction [12] which could hardly be observed by the conventional optical visualization techniques. The outstanding feature of the thermography is that the image matrix represents the infrared temperature field on the surface in view induced by energy release of the straining rocks. IR thermography has been widely used in detecting damage in the deformed materials such as composite [13], carbon fiber reinforced polymers [14], metals [11, 15], concrete [16], and rocks [17–20]. In recent decades, infrared thermography has been employed to detect the EDZ in the large-scale geomechanical model tests for simulation of tunnel excavations at China University of Mining and Technology Beijing (CUMTB). Compared to detection of small-scale laboratory specimens with infrared thermography, major difficulty for detecting the large-scale geomechanical models is the small signal to noise ratio (SNR) of the raw image due to the environmental and instrumental noises and lower spatial resolution defined by imaging area per pixel. Hence enhanced imaging processing algorithms were developed to analyse the thermal images [12]. To date, the reported experimental investigations at CUMTB involved the excavation in the 0q [21], 45q [22], 60q [23] and 90q [24] inclined stratified rocks [21–24]. However, these experimental investigations were just reported separately and a comprehensive analysis is lacking. At same time, heterogeneity existed in the constitutive behaviour of the differently inclined stratified rocks under excavation has not been discussed. The objective of this research is to deepen our understanding on the mechanisms for EDZ from excavation in differently inclined sedimentary rocks. It was achieved by carrying out an comparative study on the thermal-infrared precursors including the energy release rate represented by the averaged infrared temperature (IRT), structural features
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manifested in the infrared image and Weibull modulus obtained by fitting the thermal temperature time series from the experimental results [21–22, 24]. 2. Experimental 2.1. Geomechanical model The field case simulated by these geomechanical model tests are the main haulageway excavated in Qishan underground coal mine in Xuzhou coal mining district, located in Jiangshu province, eastern China. The roadeay was at a depth of 1000 m below the ground surface. Main exposure rock types are sandy mud rock, mudstone and sandy rock. The coal seam is inclined at different inclination angles from 0q–90q with respect to the horizontal. Thus the 0q, 45q and 90q inclined strata model can be used as a miniature of the geological formations of the simulated field case. Fig. 1 shows schematically the three geomechanical models including 0q inclined strata model (Fig. 1a), the 45q inclined strata model (Fig. 1b) and 90q inclined strata model (Fig. 1c), respectively. Each of the models was constructed with nine strata consisting of one sandstone stratum, four mudstone strata and four coal seam strata, indicated by digits 1-9 respectively. Their thickness from No. 1–9 strata are: 440 mm. 140, 120, 250, 150, 60, 140, 60 and 240 mm, respectively.
Fig. 1. Schematic of large-scale geomechanical models; (a) 0q inclined stratified rocks; (b) the 45q inclined stratified rocks, and (c) 90q inclined stratified rocks.
2.2. Dimensional analysis and model materials The constructed models have a 1.6 m u 1.6 m plane dimension and 0.4 m thickness. The excavation zones were located in the No. 4 stratum (coal seam) centered on the model with a 250 u 200 mm sectional dimension. The model is able to simulate a real excavation problem with rock mass dimension of 19.2 u 19.2 m and tunnel face dimension of 3 u 2.4 m, by employing the geometrical scaling factor ߙ ൌ ͳʹ. The force scaling factor was determined as ߙఙ ൌ ͺ and body force scaling factor ߙఊ ൌ ߙఙ Τߙ ൌ ͺΤͳʹ ൌ ͲǤ. The following stress boundary condition was adopted, i.e., vertical stress ߪଵ was at 1 MPa while lateral stress ߪଶ at 0.3 MPa, corresponding to a lateral pressure coefficient ߣ ൌ ߪଵ Τߪଶ ൌ ͲǤ͵. The loading was applied by the testing machine YDM-C developed by Manchao He. Mechanical parameters of the model rock materials was also presented in Table 1. Three real rock properties were simulated by using gypsum with three water-gypsum ratios, among them 0.8:1 for sandstone, 1:1 for mudstone and 1.2:1 for coal respectively. Detailed introduction could be found in [21–22, 24]. Table 1. Real and artificial rock properties. Rock type
Sandstone Mudstone Coal seam
Unit weight (kN/m3)
Tensile strength (MPa)
UCS (MPa)
Young’s modulus (GPa)
Internal friction angle δqε Real rock
Artificial rock
Real rock
Artificial rock
34 36 40
32 33 33
0.15 0.13 0.36
0.13 0.12 0.32
Real rock
Artificial rock
Real rock
Artificial rock
Real rock
Artificial rock
Real rock
27 26 14
15 11 8
64 44 26
8 5 3
5.83 5.59 0.90
0.72 0.69 0.11
26 21 5
Artificial rock 3.22 2.62 0.61
Poisson’s ratio
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2.3. Rock strata fabrication Fig. 2 shows the principle for producing rock strata. The rock strata are constructed with a large number of small prismatic plates, the so-called “elementary slab”. The elementary slab is made by model materials reported previously and casted in a mold. All the elemental slabs were fabricated with a same surface dimension 400 u 400 m and three thicknesses of 1, 2 and 3 cm, respectively [21]. A large number of the elementary slabs with the same model-rock property were used to ensemble a rock layer of the same property and a certain number of the rock layers with the same rock property were used to construct a rock stratum. As seen in the figure, the mudstone stratum and coal seam stratum are assembled by placing the elementary slabs in layers with perfectly mating interfaces. A weak surface is formed between the two different model rock strata. This weak surface is homogeneous along its striking at macroscopic scale. At the same time, the strata also have many asperities constituted by many small gaps (secondary joints) between the parallel-placed elemental slabs in the rock layer. Three classes of the model-rock strata were constructed, i.e. sandstone, mudstone and coal seam which were t used for construction of the geomechanical models.
Fig. 2. Model rock strata construction.
2.4. Infrared detection Fig. 3 shows schematically the scenario where the operator performs the excavation with the hammer and chisel, starting from the back side of the model and went through to the front face. At the same time, the infrared camera detects the temperature rise at the front face. Infrared images were acquired by an infrared thermography TVS8100MKII which was cooled and operated in a passive mode (no extra heat sources used). It works at wave length of 3.64.6 Pm with measuring temperature range of -40 to 300 qC; minimum detection temperature difference of 0.025 qC; a field of view of 13.6q u 18.2q/25 mm; spatial resolution of 2 mrad; on-line display resolution 240 u 320 pixels. The raw thermogram were stored in the computer as digital image of 120 u 160 pixels for off-line processing. The IR camera was fixed to a photographic tripod and placed in the front side of the geological model at a distance of 1333 mm so as to have an imaging area of 400 u 367 mm indicated by a 400 u 300 mm red-colored frame of plastic tape glued to the model front face as shown in Fig. 3. Before the imaging, the emissivity was set to 0.92 for the simulated model rocks. The image acquisition frequency was set as one frame every four seconds. All the instruments were placed in the same room with the geomechanical models 24 hours prior to the tests, so that the detected infrared temperatures show the temperature variation due to the excavation impact.
Fig. 3. Infrared detection of the tunnel excavation; (a) schematic illustration of the excavation without support using drill and blast method simulated by an operator using a hammer and a chisel and (b) photo of the testing site of the 90q inclined strata models.
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2.5. Excavation plan The tunneling work is to excavate a tunnel-like cubical space by 250 u 200 u 400 mm in the stratum #4 (coalseam). The excavation volume was divided into seven sub-spaces, termed rock block (RB), along the strike of the #4 stratum. The RBs were numbered #1#7 corresponding to the roadway excavation sequence (see Fig. 3a). Roadway development in the three geological models is schematically shown in Fig. 5. The excavation was designed as two phases, i.e. phase 1 (full-face excavation): tunneling on the #1 RB and the adjacent rocks until a small passage is cut through, and phase 2 (staged excavation): removing one RB at each tunneling stage. Four panels in Fig. 4 show the excavation plan. Fig. 4a shows the full-face excavation at a sectional view for three models (also see Fig. 3). Figs. 4b, c and d show the staged excavation for the 0q, 45q, and 90q strata models respectively.
Fig. 4. Excavation plan; (a) full-face excavation for the three models (sectional view); (b) staged excavation for 0q inclined strata (at front view); (c) staged excavation for 60q inclined strata (front view) and (d) staged excavation for 90q inclined strata (front view).
For the full-face excavation, the excavated volume was referred to as “footage” and for the staged excavation, the term “excavation stage” denotes the removing each of the RBs, and total of seven excavation stages were performed. The capical letters E0E6 stand for the excavation steps in the full-face excavation and P0P7 stand for the excavation stages in the staged excavation. E0 denotes the onset of the excavation, E1E5 denote the face advancement from step1 to step 5, and E6 denotes the time instant when a small passage was about to cut through (destruction of the #1 RB for the first time). P0 denotes the time instant at which a small passage on the #1 RB was cut through. P0P7 correspond to the removal of the RBs during each of the excavation stage. 3. Data reduction 3.1. Excavation plan When using the thermography in the passive mode, although no requirement for the physical calibration of the temperature increment, however, finding a reference point mathematically is needed for characterization of the detected temperature variation. The mathematical calibration can be realized by the image subtraction algorithm. While the object under detection is subjected to the external loading, the interested features of the infrared sequence are the temperature increment relative to the initial state. Taking the first frame of infrared sequence as a benchmark, acquired when the object was at the initial state, subtraction of the first frame from the following images obtains the temperature increment relative to the initial state of the object. It can be expressed mathematically that,
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݂መ ሺݔǡ ݕሻ ൌ ݂ ሺݔǡ ݕሻ െ ݂ ሺݔǡ ݕሻ
(1)
where,݂ ሺǡ ݕሻ represents the image matrix of kth frame in the sequence; ݂መ (x,y) the incremental temperature field (also image matrix) at the ݇௧ instant, and ݂ ሺǡ ݕሻ the first frame of the thermal sequence taken at the initial state of the loading; the subscript k is an integer served as frame index; ݔൌ ͳǡ ʹǡ ǥ ǡ ܯand ݕൌ ͳǡ ʹǡ ǥ ǡ ܰ are the pixel coordinates, and ܯൌ ͳͲ and ܰ ൌ ͳʹͲ are the maximum pixel number respectively for the image matrix. 3.2. Image processing Structural changes of the straining rocks could be observed from the infrared sequence when they are processed with robust and efficient image processing algorithms. The tasks for processing thermal image acquired in the largescale geomechanical model tests generally involve the removal of different types of noises and the enhancement of the low-contrast image in order to extract the interested features such as edges, borders, and high and low temperature regions. The image processing algorithms used in this research are summarized in the following. x For removal of the environmental radiation noise, the image subtraction expressed in Eq. (1) should be employed. The image subtraction can also be used as the temperature calibration procedure as introduced above; x For eliminating the salt-and-pepper noise induced by the electronic current in the measurement instruments, median filter should be used; x For reduction the additive-periodical noise which may come from the rotating parts in the cooling system embedded in the infrared camera, Gaussian high-pass filters (GHPF) in the frequency domain could be utilized; x When detecting a large-scale object with infrared camera working in the passive mode, the raw thermal image will have a small dynamic scope. As a result, the images should be enhanced in order to represent the rock response clearly. In our research, the morphological enhancement filter, ܨܫܯ, proved to be very effective which was developed by Gong et al. (2015) [12]. Detailed discussion on the image process algorithms for the treatment of the low-contrast and noisy thermal images can be found in the references [1, 12]. 3.3. Energy release rate Apart from the image analysis, the infrared sequence can be transferred into observations of energy release at a specific instnat of time. In fact, matrix for an thermal image is the infrared temperature (IRT) filed created by the thermal-mechanical coupling effect, representing the energy release from the stressed rocks. Mean value of the matrix is accordingly the averaged IRT field, representing the overall energy release at the time instant. Computing the statistical mean on the infrared sequence yields a time series which is observations of the energy release. Statistical mean value of the matrix of a thermal image, ൏ ܴܶܫ, can be written as, ଵ ଵ
ே ൏ ܴܶܫൌ ெ ே σெ ௫ୀଵ σ௬ୀଵ ݂ሺݔǡ ݕሻ
(2)
Compute statistical mean over the processed infrared sequence using Eq. (2), time series, ൏ ܴܶܫ , ݇ ൌ Ͳǡͳǡʹǡ ǥ, can be generated, where k corresponds to the sampling period of time, i.e. 4 second. As introduced in section 3.1, the first frame, ݇ ൌ Ͳ, of the sequence was taken when the physical model was at initial state and performing the image subtraction using Eq. (1) makes the time series ൏ ܴܶܫ being the IRT variations relative to the initial loading state. In the following, to make the decription simple, we use IRT stands for ൏ ܴܶܫ in the related context.
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4. Comparison 4.1. Energy release precursors Fig. 5 shows the energy release rate against time with respect to the face development for the three models. The capical letters E0E6 and P0P7 correspond to the excavation plans in the full face excavation and staged excavation respectively (see Fig. 4). It is seen from Fig. 5a (horizontal strata model) that IRT increased linearly with the face development over the full face excavation; it attained the global maximum energy release by a temperature increment of 31.25 qC at E6. Cutting through a small passage on #1 RB (state P0) caused an abrupt drop of the energy release by 31.25 30.86 = 0.39 qC. After that the IRT evolves in the plastic manner fluctuating with multiple small peaks corresponding to removing the RBs. The energy release level much lower than that in the fullface excavation. It demonstrates that less energy was consumed in removing the RBs and expanding the tunnel space.
Fig. 5. Energy release rate < IRT> against time with respect to the face development; (a) horizontal strata model; (b) the 45q inclined strata model and, (c) vertical strata model.
IRT of the 45q inclined strata model (Fig. 5b) has a piecewise linear increase against face development during the full face excavation. The global maximum energy release was found at E2 by 25.83 qC, much smaller than that of the horizontal strata. At steps E2, E4 and E6, sharp drops of the IRT were found and the maximum value corresponding to E2 equals to 25.83 25.13 = 0.7 qC, much larger than the IRT drop in the horizontal strata. These sharp drops were caused by the relative sliding along the weak surfaces. It revealed the fact that the steep-inclined rock strata are prone to slide and hard to store the elastic energy under loading. At the cutting through step E6, IRT dropped by 25.49 25.21 = 0.28 qC, much smaller than that of the horizontal strata showing a drop of 0.39 qC, indicating less energy being consumed over the full-face excavation in the 45q inclined strata than that in horizontal strata as a result of the energy dissipation in the frictional sliding. Over the staged excavation, IRT oscillates with high amplitudes. The local peaks for the stages P1–P6 increased as the excavation stage advances. The intense energy release was due primarily to the excavation-induced static friction of the strata caused by removing the RBs. The time-marching scheme of the IRT fully revealed the unstable nature for the steep-angled strata under excavation. IRT of the vertical strata model (Fig. 5c) increased monotonically against the face development, similar to the IRT curve for the horizontal strata. The global maximum IRT was attained at E6 with 31.24 qC, higher than those for the 0q and the 45q strata models. The IRT had a sharp drop at P0 by 31.42 30.99 = 0.43 qC, larger than that of the horizontal strata with 0.39 qC. These differences of the IRT evolution pattern was attributed to the stronger static friction between the vertically inclined layers under the excavation impact. During the staged excavation, IRT increased sharply with multiple peaks with higher amplitude than those for the horizontal and the 45q inclined strata models, demonstrating the fact that vertical strata is the most unstable geological structure during the staged excavation.
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4.2. Constitutive heterogeneity Time series, ൏ ܴܶܫ , ݇ ൌ Ͳǡͳǡʹǡ ǥ, can be viewed as a stochastic process sampled in the IRT ensemble space. Rock behavior can also be characterized by means of p.d.d. (probability density distribution) or c.d.f. (cumulative distribution function) of the ൏ ܴܶܫ data sets. Among the probability distributions, Weibull model has been widely used in rock mechanics for developing the stochastic constitutive equations used in numerical simulation of the rock mechanics studies [25]. The p.d.d. for the Weibull model is given by, ݂ሺݔሻ ൌ ሺ݉Τߟ ሻሺ ݔΤߟሻିଵ ݁ݔሾെሺݔȀߟሻ ሿ
(3)
where, K is the scale factor; m is the homogeneity index (also known as Weibull modulus). The parameter m characterizes degree of the homogeneity for rock masses. An infinitely high m value corresponds to a homogeneous structure with a uniform strength, whereas a heterogeneous structure with a broad distribution of local strength is associated with a relatively small m value [26]. Integration of Eq. (3) yields c. d. f. of the Weibull distribution, ܨሺݔሻ ൌ ͳ െ ݁ݔሾെሺݔȀߟሻ ሿ
(4)
For evaluating the constitutive heterogeneity exhibited by the three geomechanical models under excavation, IRT curve fitting was performed for obtaining the Weibull modulus from the thermal time series, by using the c.d.f. Weibull model given by Eq. (4). It was done based on the assumption that the IRT time series data follow a Weibull distribution. Fig. 6 shows the curve fitting results for the three strata models; the rectangular solid blue square stands for the data sets ൏ ܴܶܫ and the red line for the fitted curves. It is seen that all the IRT data follow the c. d. f. Weibull model very well.
Fig. 6. Weibull model-based IRT curve fitting results for the three geomechanical models: (a) horizontal strata; (b) 45q inclined strata, and (c) vertical strata; it was done based on the assumption that the IRT time series data follow a Weibull distribution.
The upper panel for Fig. 6a is the curve-fitting result for the full-face excavation, and the lower panel for Fig. 6a is the fitting result for the staged excavation. Likewise, Fig. 6b and 6c are the curve-fitting relusts for tow phase excavations in the 45q inclined strata and vertical strata models respectively. By observing the Weibull modulus presented in Fig. 6, the constitutive heterogeneous precursors can be understood as: x horizontal strata: having the largest Weibull modulus values, i.e., 2.9868 for full-face excavation and 2.4933 for staged excavation, exhibited a relatively weak heterogeneity behavior;
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x the 45q inclined strata: having a moderate Weibull modulus values, i.e. 1.5606 for the full-face excavaiton and 2.1073 for the staged excavation, exhibited a moderate heterogeneity; x vertical strata: having the smallest Weibull modulus values, i.e. 1.3767 for full-face excavation and 1.5061 for staged excavation, corresponding to the most heterogeneity as compared with the horizontal and the 45q strata models. 4.3. Image precursors for full-face excavation Comprehension and interpretation of an infrared image is based on such image features as colors, borders and edges that segment different zones in the image, as well as the temperature distribution scale [12]. Pseudo-colors represent the temperature levels; hot (positive) colors stand for high-level temperatures and cool (negative) colors for the low-level temperatures. High-level temperature indicates high stress level due to friction, shear or stress concentration, and low-level temperature indicates low stress level due to tensile cracking, stress release or unloading. Borders or edges that separate hot and cool colored zones reflect different modes of the rock behavior and scale of the high temperature zones corresponds to the scale of the EDZ. Image precursors for characterizing the EDZ will be extracted by analyzing the infrared sequence processed using the algorithms presented in section 3.2. Fig. 7 shows the infrared sequences corresponding to E0 – E6 for the full-face excavation. Fig. 7a is for horizontal strata, Fig. 7b for the 45q inclined strata and Fig. 7c for vertical strata geomechanical models respectively. By analyzing these infrared sequences, the following image features could be regarded as the image puecursors, i.e. (a) at onset of the excavation corresponding to E0, images for the three strata exhibit a random-scattering IRT distribution indicating the intact state of the model rocks; (b) heterogeneous IRT distribution was observed in the subsequent excavation steps E2–E6, but the configurations of the EDZ are different: x for horizontal strata model, IRT evolved from the scattered distribution to the localized high-temperature zone (i.e. EDZ) distributed around the face, behaving like isotropic materials; x for the 45q inclined and vertical strata models, belt-like IRT parallel to the weak surface was observed; indicating the frictional sliding damage mechamisms; x for the 45q strata, most intense static friction took place at the excavation step E5 and E6; for the vertical strata, intense frictions were observed over the entire excavation steps E1–E6.
Fig. 7. Infrared sequences corresponding to E0 – E6 in the full-face excavations; (a) horizontal strata model; (b) the 45q inclined strata and (c) vertical strata.
4.4. Image precursors for staged excavation Fig. 12 shows the infrared sequences corresponding to P1–P7 for the staged excavation. Fig. 7a is for horizontal strata, Fig. 7b for the 45q inclined strata and Fig. 7c for vertical strata geomechanical models respectively.
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Following image features could be regarded as the image precursors, i.e. (a) for horizontal strata, EDZ was localized around the face, closely associated with removing RBs, appearing on overlying rock and floor (P2, P3, P4), the side walls (P4, P5, P6, P7); (b) for the 45q strata, EDZ was hybrid, including localized damage around the face plus frictional sliding represented by the IRT belts over the entire excavation stages, and (c) for vertical strata, during P2–P4, the frictions along the weak surfaces were appreciable by the distinct IRT belts; while over P5–P7, EDZ was localized around face without frictional sliding being observed. Difference of the EDZ among the three strata may be attributed to the extent of the excavation influence area. Apparently, the excavation in the 45q strata has the largest influenced zone.
Fig. 8. Infrared sequences corresponding to P1–P7 for the staged excavation: (a) horizontal strata model; (b) the 45q inclined strata model, and (c) vertical strata model.
5. Conclusions IRT time series, obtained by averaging matrices of the infrared sequence, can be viewed as time observations of the energy release characterizing overall rock response to the excavation. During the full-face excavation, IRT of the horizontal and vertical strata increased linearly with the global maximum energy release rate higher than that of the 45q strata. IRT of the 45q strata has a piecewise increase with several major energy release induced by the frictional sliding along the weak surface. At the transfer point from the full-face excavation to staged excavation, the vertical strata has larger IRT drop than those of the horizontal and 45q strata, indicating the fact that the frictional sliding occurred in the vertical strata was more intense than that in the other two strata models. Over the staged excavation, the time-marching scheme of the IRT for the three strata models had a plastic manner with multiple local peaks. Among them, the vertical strata had higher energy release level. Constitutive heterogeneity precursor could be represented by the Weibull modulus which can be obtained by curve fitting of probability distribution of the time observation ൏ ܴܶܫ to Weibull model. By comparing the resultant Weibull moduli, constitutive heterogeneous precursors could be understood as horizontal strata model has the largest Weibull modulus values, i.e., 2.9868 for full-face excavation and 2.4933 for staged excavation, exhibited a weak heterogeneity behavior; the 45q inclined strata model has a moderate Weibull modulus values, i.e. 1.5606 for the full-face excavaiton and 2.1073 for the staged excavation, exhibited a moderate heterogeneity; and vertical strata has the largest Weibull modulus values, i.e. 1.3767 for full-face excavation and 1.5061 for staged excavation, exhibited the most heterogeneity behavior. Image precursors for characterizing the EDZ were extracted from IRT distribution pattern in the processed infrared sequence. Over the full-face excavation, IRT distribution for horizontal strata evolved from scattered distribution to localized high-temperature zone (i.e. EDZ) distributed around the face, behaving like isotropic materials; IRT distribution for the 45q and vertical strata models distributed as belt-like IRT parallel to the weak surface; indicating the frictional sliding damage mechamism. The most intense friction was observed in the 45q
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strata. During the staged excavation, for horizontal strata, EDZ was localized around the face, closely associated with removing each of the rock blocks; for the 45q and vertical strata, EDZ was hybrid, including localized damage around the face plus frictional sliding represented by the IRT belts. Likewise, in the 45q strata, the most intense frictional EDZ was also observed. Acknowledgement Financial support from the Special Funds for the National Natural Science Foundation of China under Grant No.51574248 are gratefully acknowledged. Heartfelt thanks should also be given to the anonymous reviewer for the valuable comments and modification suggestions on the improvement of this article. References [1] W.L. Gong et al., Thermal image and spectral characterization of roadway failure process in geologically 45q inclined rocks, Tunnel. Underg. Space Technol. 49 (2015) 156–173. [2] P. Fortsakis, K. Nikas, V. Marinos, P. Marinos, Anisotropic behavior of stratified rock masses in tunneling. Eng. Geol., 141-142 (2012) 74–83. [3] R.S. Read, 20 years of excavation response studies at AECL’s Underground Research Laboratory, Int. J. Rock Mech. Min. Sci. 41(8) (2004) 1251–1275. [4] T.G. Sitharam, L.G. Madhavi, Simulation of excavations in jointed rock masses using a practical equivalent continuum approach, Int. J. Rock Mech. Min. Sci. 39 (2002) 517–525. [5] M.A. Meguid, O. Saada, M.A. Nunes, J. Mattar, Physical modeling of tunnels in soft ground: A review. Tunnel. Underg. Space Technol. 23 (2008) 185–198. [6] S. Fekete, M. Diederichs, M. Lato, Geotechnical and operational applications for 3-dimentional laser scanning in drill and blast tunnels, Tunnel. Underg. Space Technol. 25 (2010) 614–628. [7] S.C. Li, H.L. Liu, L.P. Li, Q.Q. Zhang, K. Wang, Large scale three-dimensional seepage analysis model test and numerical simulation research on undersea tunnel, App. Ocean Res. 5 (2016) 129–142. [8] W.S. Zhu, Y. Li, S.C. Li, S.G. Wang, Q.B. Zhang, Quasi-three-dimensional physical model tests on a cavern complex under high in-situ stresses, Int. J. Rock Mech. Min. Sci. 48 (2011)199–209. [9] Y.J. Lee, R.H. Bassett, Application of a photogrammetric technique to a model tunnel, Tunnel. Underg. Space Technol. 21(1) (2006) 79–65. [10] S. Fekete, M. Diederichs, M. Lato, Geotechnical and operational applications for 3-dimensional laser scanning in drill and blast tunnels. Tunnel. Underg. Space Technol. 25 (2010) 614–628. [11] M.P. Long, Infrared thermographic scanning of fatigue in metals, Nuclear Eng. Design 158 (1995) 363–376. [12] W.L. Gong, Y.Y. Peng, X.M. Sun, M.C. He, S.Y. Zhao, H.Q. Chen, T. Xie, Enhancement of low-contrast thermograms for detecting the stressed tunnel in horizontally stratified rocks, Int. J. Rock Mech. Min. Sci. 74 (2015) 69–80. [13] M. Connolly, D. Copley, Thermographic inspection of composite material, Materials Evaluation 48(12) (1990) 1461–1463. [14] R. Steinberger, T.I.V. Leitão, E. Ladstätter, G Pinter, Infrared thermographic techniques for non-destructive damage characterization of carbon fiber reinforced polymers during tensile fatigue testing, Int. J. Fatig. 28 (2006) 1340–1347. [15] M.L. Pastor, X. Balandraud, M. Grédiac, J.L. Robert, Applying infrared thermography to study the heating of 2024-T3 aluminum specimens under fatigue loading, Infrared Physics & Technology, 51 (2008) 505–515. [16] M.P. Luong, Infrared thermovision of damage processes in concrete and rock, Engineering Fracture Mechanics 35 (1990) 127–135. [17] B.T. Brady, G.A. Rowell, Laboratory investigation for the electrodynamics of rock fracture, Nature. 321 (1986) 488–492. [18] M.P. Luong, Introducing infrared thermography in soil dynamics, Infrared Phys. Technol. 49 (2007) 306–311. [19] E. Grinzato, S. Marinetti, P.G. Bison, M. Concas, S. Fais, Comparison of ultrasonic velocity and IR thermography for the characterization of stones, Infrared Phys. Technol. 46 (2004) 63–68. [20] L.X. Wu, S.J. Liu, Y.H. Wu, C.Y. Wang, Precursors for rock fracturing and failure-Part I, IRR image abnormalities, Int J Rock Mech Min Sci. 43 (2006) 473–482. [21] M.C. He, W.L. Gong, H.M. Zhai, H.P. Zhang, Physical modeling of deep ground excavation in geologically horizontally strata based on infrared thermography. Tunnel.Underg. Space Technol. 25 (2010) 366–376. [22] M.C. He, X.N. Jia, W.L. Gong, L. Faramarzi, Physical modeling of an underground roadway excavation vertically stratified rock using infrared thermography, Int. J. Rock Mech. Min. Sci. 47 (2010) 1212–1221. [23] M.C. He, Physical modeling of an underground roadway excavation in geologically 45 inclined rock using infrared thermography, Eng. Geol. 121(3-4) (2011) 165–176. [24] W.L. Gong, J. Wang, Y.X. Gong, P.Y. Guo, Thermography analysis of a roadway excavation experiment in 60th inclined stratified rocks, Int. J. Rock Mech. Sci. 60 (2013) 134–147. [25] S.C. Yuan, J.P. Harrison, A review of the state of the art in modeling progressive mechanical breakdown and associated fluid flow in intact heterogeneous rocks, Int. J. Rock Mech. Min. Sci. 43 (2006) 1001-1022. [26] C.A. Tang, P.K. Kaiser, 1998. Numerical simulation of cumulative damage and seismic energy release during brittle rock failure-Partĉ: Fundamentals. Int. J. Rock Mech. Min. Sci. 35(2) (1998) 113–121.
ScienceDirect Procedia Engineering 191 (2017) 20 – 30
Symposium of the International Society for Rock Mechanics
Geomechanical Model Tests and Infrared Detection of Rock Responses for Tunnels Excavated in Sedimentary Rocks Weili Gonga,b*, Manchao Hea,b, Hong Yanb, Lifeng Lia,b,c, Xiaodong Xua,b a State Key Laboratory for Geomechanics & Deep Underground Engineering, Beijing 100083, China School of Mechanics & Civil Engineering, China University of Mining & Technology Beijing, Beijing 100083, China c School of Architecture & Civil Engineering, Guizhou University of Engineering Science, Guizhou, Bijie 551700, China b
Abstract Rock mass behavior is controlled mainly by weak planes in sedimentary rocks. Geomechanical model tests were conducted for simulating tunnel excavations in horizontal, the 45q and vertical inclined rock strata. Infrared thermography was employed for detecting rock responses during the excavations. Infrared temperature (IRT) curve obtained by averaging the matrices of the infrared sequence can be viewed as temporal observation of the overall energy release from the rock under excavation. The IRT curve characterizes the horizontal and vertical strata as linear behavior and the 45q inclined strata as piecewise linear behavior over the full-face excavation and the three strata as plastic-like behavior over the staged excavation, respectively. The constitutive heterogeneity can be represented by the Weibull modus obtained by curve-fitting to the Weibull model using the probability distribution of the IRT temporal observations. The vertical strata has the smallest Weibull modulus values corresponding to the higher heterogeneity compared with the else two strata models. The structural response of the rock under excavation was characterized by the IRT distribution of the infrared image. IRT distribution of the horizontal strata evolved from scattering distribution to localized high-temperature zone around the face. In contrast, IRT distribution for the 45q and vertical strata distributed as belt-like IRT parallel to the weak surface; indicating the frictional sliding damage mechanism. Most intense friction was observed in the excavation in the 45q inclined rock strata. © Published by Elsevier Ltd. This Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license © 2017 2017The TheAuthors. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EUROCK 2017. Peer-review under responsibility of the organizing committee of EUROCK 2017 Keywords: Geomechanical model test; Sedimentary rocks; Tunnel excavation; Infrared detection; Excavation damaged zone
* Corresponding author. Tel.: +8610-15910785289; fax: +8610-010-62339820. E-mail address: [email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EUROCK 2017
doi:10.1016/j.proeng.2017.05.149
Weili Gong et al. / Procedia Engineering 191 (2017) 20 – 30
1. Introduction Sedimentary rocks cover the majority of earth’s surface and are frequently encountered in underground mining. In the sedimentary rocks, two main sources of discontinuities are beddings and joints. The beddings can be assumed continuous over areas greater than that of any designed excavation and joints, however, are typically constrained between beddings [1]. Both beddings and joints are surfaces of relatively low shear and negligible tensile strength. Under the condition of stratified rock masses stretching across the roadway section, the engineering geological behaviour during tunnel development and operation is mainly controlled by the characteristics of the stratification planes [2]. Thus, existence of the discontinuities may exert a significant impact on the stability of the surrounding rock masses. Excavation damaged zone (EDZ) is closely related geological disasters such as rock bursts, bumps and water inrush, etc. Better understanding of rock behaviour during the excavation, therefore, has been an important issue for design of the underground opening and mitigation of the potential geological disasters. Excavation induced damage has been investigated extensively with different methods including the field experiments [3], numerical study [4], and laboratory experiments [5–7]. Geomechanical model tests with judicious choice of the model materials may yield some important information on the mechanisms of the EDZ which are not available from numerical models or field experiments [8]. One of the critical issues in geomechanical model tests is the use of the monitoring techniques which were developed purposefully for acquiring the “real” information of the rock behaviour in varied regimes. Strain gauge is widely used because it can measure the stressed rocks consistent with the theory of rock mechanics but is limited to the elastic phase. Alternatively, the use of remote sensing techniques is getting more popular. Digital imaging has been applied for determining the displacement and strain [8, 9]. The photogrammetry requires supplementary lighting while three-dimensional laser scanning (Lidar) acts as its own source of “illumination”, and can be used in in active tunnelling environment under dusty, damp, and dark conditions and collected very accurate, high resolution 3-dimensional images of its surroundings [10]. The advantages of non-contact optical vision lie in their ability to represent the structural change by realistic and practical surface models or geometrical features such as cracks and fractures. However, it is hard to get a definite relationship with respect to the stress redistribution in large-deformation problems [1]. Infrared thermography is another remote sensing technique which produces thermal image by detecting electromagnetic waves within infrared band [11]. Infrared image represents rock response based on the thermal-mechanical coupling effect and does not require supplementary lighting as well. When processed with proper algorithms, thermal image will not only be able to detect geometrical features such as crack propagation, but also the static and dynamic friction [12] which could hardly be observed by the conventional optical visualization techniques. The outstanding feature of the thermography is that the image matrix represents the infrared temperature field on the surface in view induced by energy release of the straining rocks. IR thermography has been widely used in detecting damage in the deformed materials such as composite [13], carbon fiber reinforced polymers [14], metals [11, 15], concrete [16], and rocks [17–20]. In recent decades, infrared thermography has been employed to detect the EDZ in the large-scale geomechanical model tests for simulation of tunnel excavations at China University of Mining and Technology Beijing (CUMTB). Compared to detection of small-scale laboratory specimens with infrared thermography, major difficulty for detecting the large-scale geomechanical models is the small signal to noise ratio (SNR) of the raw image due to the environmental and instrumental noises and lower spatial resolution defined by imaging area per pixel. Hence enhanced imaging processing algorithms were developed to analyse the thermal images [12]. To date, the reported experimental investigations at CUMTB involved the excavation in the 0q [21], 45q [22], 60q [23] and 90q [24] inclined stratified rocks [21–24]. However, these experimental investigations were just reported separately and a comprehensive analysis is lacking. At same time, heterogeneity existed in the constitutive behaviour of the differently inclined stratified rocks under excavation has not been discussed. The objective of this research is to deepen our understanding on the mechanisms for EDZ from excavation in differently inclined sedimentary rocks. It was achieved by carrying out an comparative study on the thermal-infrared precursors including the energy release rate represented by the averaged infrared temperature (IRT), structural features
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manifested in the infrared image and Weibull modulus obtained by fitting the thermal temperature time series from the experimental results [21–22, 24]. 2. Experimental 2.1. Geomechanical model The field case simulated by these geomechanical model tests are the main haulageway excavated in Qishan underground coal mine in Xuzhou coal mining district, located in Jiangshu province, eastern China. The roadeay was at a depth of 1000 m below the ground surface. Main exposure rock types are sandy mud rock, mudstone and sandy rock. The coal seam is inclined at different inclination angles from 0q–90q with respect to the horizontal. Thus the 0q, 45q and 90q inclined strata model can be used as a miniature of the geological formations of the simulated field case. Fig. 1 shows schematically the three geomechanical models including 0q inclined strata model (Fig. 1a), the 45q inclined strata model (Fig. 1b) and 90q inclined strata model (Fig. 1c), respectively. Each of the models was constructed with nine strata consisting of one sandstone stratum, four mudstone strata and four coal seam strata, indicated by digits 1-9 respectively. Their thickness from No. 1–9 strata are: 440 mm. 140, 120, 250, 150, 60, 140, 60 and 240 mm, respectively.
Fig. 1. Schematic of large-scale geomechanical models; (a) 0q inclined stratified rocks; (b) the 45q inclined stratified rocks, and (c) 90q inclined stratified rocks.
2.2. Dimensional analysis and model materials The constructed models have a 1.6 m u 1.6 m plane dimension and 0.4 m thickness. The excavation zones were located in the No. 4 stratum (coal seam) centered on the model with a 250 u 200 mm sectional dimension. The model is able to simulate a real excavation problem with rock mass dimension of 19.2 u 19.2 m and tunnel face dimension of 3 u 2.4 m, by employing the geometrical scaling factor ߙ ൌ ͳʹ. The force scaling factor was determined as ߙఙ ൌ ͺ and body force scaling factor ߙఊ ൌ ߙఙ Τߙ ൌ ͺΤͳʹ ൌ ͲǤ. The following stress boundary condition was adopted, i.e., vertical stress ߪଵ was at 1 MPa while lateral stress ߪଶ at 0.3 MPa, corresponding to a lateral pressure coefficient ߣ ൌ ߪଵ Τߪଶ ൌ ͲǤ͵. The loading was applied by the testing machine YDM-C developed by Manchao He. Mechanical parameters of the model rock materials was also presented in Table 1. Three real rock properties were simulated by using gypsum with three water-gypsum ratios, among them 0.8:1 for sandstone, 1:1 for mudstone and 1.2:1 for coal respectively. Detailed introduction could be found in [21–22, 24]. Table 1. Real and artificial rock properties. Rock type
Sandstone Mudstone Coal seam
Unit weight (kN/m3)
Tensile strength (MPa)
UCS (MPa)
Young’s modulus (GPa)
Internal friction angle δqε Real rock
Artificial rock
Real rock
Artificial rock
34 36 40
32 33 33
0.15 0.13 0.36
0.13 0.12 0.32
Real rock
Artificial rock
Real rock
Artificial rock
Real rock
Artificial rock
Real rock
27 26 14
15 11 8
64 44 26
8 5 3
5.83 5.59 0.90
0.72 0.69 0.11
26 21 5
Artificial rock 3.22 2.62 0.61
Poisson’s ratio
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2.3. Rock strata fabrication Fig. 2 shows the principle for producing rock strata. The rock strata are constructed with a large number of small prismatic plates, the so-called “elementary slab”. The elementary slab is made by model materials reported previously and casted in a mold. All the elemental slabs were fabricated with a same surface dimension 400 u 400 m and three thicknesses of 1, 2 and 3 cm, respectively [21]. A large number of the elementary slabs with the same model-rock property were used to ensemble a rock layer of the same property and a certain number of the rock layers with the same rock property were used to construct a rock stratum. As seen in the figure, the mudstone stratum and coal seam stratum are assembled by placing the elementary slabs in layers with perfectly mating interfaces. A weak surface is formed between the two different model rock strata. This weak surface is homogeneous along its striking at macroscopic scale. At the same time, the strata also have many asperities constituted by many small gaps (secondary joints) between the parallel-placed elemental slabs in the rock layer. Three classes of the model-rock strata were constructed, i.e. sandstone, mudstone and coal seam which were t used for construction of the geomechanical models.
Fig. 2. Model rock strata construction.
2.4. Infrared detection Fig. 3 shows schematically the scenario where the operator performs the excavation with the hammer and chisel, starting from the back side of the model and went through to the front face. At the same time, the infrared camera detects the temperature rise at the front face. Infrared images were acquired by an infrared thermography TVS8100MKII which was cooled and operated in a passive mode (no extra heat sources used). It works at wave length of 3.64.6 Pm with measuring temperature range of -40 to 300 qC; minimum detection temperature difference of 0.025 qC; a field of view of 13.6q u 18.2q/25 mm; spatial resolution of 2 mrad; on-line display resolution 240 u 320 pixels. The raw thermogram were stored in the computer as digital image of 120 u 160 pixels for off-line processing. The IR camera was fixed to a photographic tripod and placed in the front side of the geological model at a distance of 1333 mm so as to have an imaging area of 400 u 367 mm indicated by a 400 u 300 mm red-colored frame of plastic tape glued to the model front face as shown in Fig. 3. Before the imaging, the emissivity was set to 0.92 for the simulated model rocks. The image acquisition frequency was set as one frame every four seconds. All the instruments were placed in the same room with the geomechanical models 24 hours prior to the tests, so that the detected infrared temperatures show the temperature variation due to the excavation impact.
Fig. 3. Infrared detection of the tunnel excavation; (a) schematic illustration of the excavation without support using drill and blast method simulated by an operator using a hammer and a chisel and (b) photo of the testing site of the 90q inclined strata models.
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2.5. Excavation plan The tunneling work is to excavate a tunnel-like cubical space by 250 u 200 u 400 mm in the stratum #4 (coalseam). The excavation volume was divided into seven sub-spaces, termed rock block (RB), along the strike of the #4 stratum. The RBs were numbered #1#7 corresponding to the roadway excavation sequence (see Fig. 3a). Roadway development in the three geological models is schematically shown in Fig. 5. The excavation was designed as two phases, i.e. phase 1 (full-face excavation): tunneling on the #1 RB and the adjacent rocks until a small passage is cut through, and phase 2 (staged excavation): removing one RB at each tunneling stage. Four panels in Fig. 4 show the excavation plan. Fig. 4a shows the full-face excavation at a sectional view for three models (also see Fig. 3). Figs. 4b, c and d show the staged excavation for the 0q, 45q, and 90q strata models respectively.
Fig. 4. Excavation plan; (a) full-face excavation for the three models (sectional view); (b) staged excavation for 0q inclined strata (at front view); (c) staged excavation for 60q inclined strata (front view) and (d) staged excavation for 90q inclined strata (front view).
For the full-face excavation, the excavated volume was referred to as “footage” and for the staged excavation, the term “excavation stage” denotes the removing each of the RBs, and total of seven excavation stages were performed. The capical letters E0E6 stand for the excavation steps in the full-face excavation and P0P7 stand for the excavation stages in the staged excavation. E0 denotes the onset of the excavation, E1E5 denote the face advancement from step1 to step 5, and E6 denotes the time instant when a small passage was about to cut through (destruction of the #1 RB for the first time). P0 denotes the time instant at which a small passage on the #1 RB was cut through. P0P7 correspond to the removal of the RBs during each of the excavation stage. 3. Data reduction 3.1. Excavation plan When using the thermography in the passive mode, although no requirement for the physical calibration of the temperature increment, however, finding a reference point mathematically is needed for characterization of the detected temperature variation. The mathematical calibration can be realized by the image subtraction algorithm. While the object under detection is subjected to the external loading, the interested features of the infrared sequence are the temperature increment relative to the initial state. Taking the first frame of infrared sequence as a benchmark, acquired when the object was at the initial state, subtraction of the first frame from the following images obtains the temperature increment relative to the initial state of the object. It can be expressed mathematically that,
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݂መ ሺݔǡ ݕሻ ൌ ݂ ሺݔǡ ݕሻ െ ݂ ሺݔǡ ݕሻ
(1)
where,݂ ሺǡ ݕሻ represents the image matrix of kth frame in the sequence; ݂መ (x,y) the incremental temperature field (also image matrix) at the ݇௧ instant, and ݂ ሺǡ ݕሻ the first frame of the thermal sequence taken at the initial state of the loading; the subscript k is an integer served as frame index; ݔൌ ͳǡ ʹǡ ǥ ǡ ܯand ݕൌ ͳǡ ʹǡ ǥ ǡ ܰ are the pixel coordinates, and ܯൌ ͳͲ and ܰ ൌ ͳʹͲ are the maximum pixel number respectively for the image matrix. 3.2. Image processing Structural changes of the straining rocks could be observed from the infrared sequence when they are processed with robust and efficient image processing algorithms. The tasks for processing thermal image acquired in the largescale geomechanical model tests generally involve the removal of different types of noises and the enhancement of the low-contrast image in order to extract the interested features such as edges, borders, and high and low temperature regions. The image processing algorithms used in this research are summarized in the following. x For removal of the environmental radiation noise, the image subtraction expressed in Eq. (1) should be employed. The image subtraction can also be used as the temperature calibration procedure as introduced above; x For eliminating the salt-and-pepper noise induced by the electronic current in the measurement instruments, median filter should be used; x For reduction the additive-periodical noise which may come from the rotating parts in the cooling system embedded in the infrared camera, Gaussian high-pass filters (GHPF) in the frequency domain could be utilized; x When detecting a large-scale object with infrared camera working in the passive mode, the raw thermal image will have a small dynamic scope. As a result, the images should be enhanced in order to represent the rock response clearly. In our research, the morphological enhancement filter, ܨܫܯ, proved to be very effective which was developed by Gong et al. (2015) [12]. Detailed discussion on the image process algorithms for the treatment of the low-contrast and noisy thermal images can be found in the references [1, 12]. 3.3. Energy release rate Apart from the image analysis, the infrared sequence can be transferred into observations of energy release at a specific instnat of time. In fact, matrix for an thermal image is the infrared temperature (IRT) filed created by the thermal-mechanical coupling effect, representing the energy release from the stressed rocks. Mean value of the matrix is accordingly the averaged IRT field, representing the overall energy release at the time instant. Computing the statistical mean on the infrared sequence yields a time series which is observations of the energy release. Statistical mean value of the matrix of a thermal image, ൏ ܴܶܫ, can be written as, ଵ ଵ
ே ൏ ܴܶܫൌ ெ ே σெ ௫ୀଵ σ௬ୀଵ ݂ሺݔǡ ݕሻ
(2)
Compute statistical mean over the processed infrared sequence using Eq. (2), time series, ൏ ܴܶܫ , ݇ ൌ Ͳǡͳǡʹǡ ǥ, can be generated, where k corresponds to the sampling period of time, i.e. 4 second. As introduced in section 3.1, the first frame, ݇ ൌ Ͳ, of the sequence was taken when the physical model was at initial state and performing the image subtraction using Eq. (1) makes the time series ൏ ܴܶܫ being the IRT variations relative to the initial loading state. In the following, to make the decription simple, we use IRT stands for ൏ ܴܶܫ in the related context.
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4. Comparison 4.1. Energy release precursors Fig. 5 shows the energy release rate against time with respect to the face development for the three models. The capical letters E0E6 and P0P7 correspond to the excavation plans in the full face excavation and staged excavation respectively (see Fig. 4). It is seen from Fig. 5a (horizontal strata model) that IRT increased linearly with the face development over the full face excavation; it attained the global maximum energy release by a temperature increment of 31.25 qC at E6. Cutting through a small passage on #1 RB (state P0) caused an abrupt drop of the energy release by 31.25 30.86 = 0.39 qC. After that the IRT evolves in the plastic manner fluctuating with multiple small peaks corresponding to removing the RBs. The energy release level much lower than that in the fullface excavation. It demonstrates that less energy was consumed in removing the RBs and expanding the tunnel space.
Fig. 5. Energy release rate < IRT> against time with respect to the face development; (a) horizontal strata model; (b) the 45q inclined strata model and, (c) vertical strata model.
IRT of the 45q inclined strata model (Fig. 5b) has a piecewise linear increase against face development during the full face excavation. The global maximum energy release was found at E2 by 25.83 qC, much smaller than that of the horizontal strata. At steps E2, E4 and E6, sharp drops of the IRT were found and the maximum value corresponding to E2 equals to 25.83 25.13 = 0.7 qC, much larger than the IRT drop in the horizontal strata. These sharp drops were caused by the relative sliding along the weak surfaces. It revealed the fact that the steep-inclined rock strata are prone to slide and hard to store the elastic energy under loading. At the cutting through step E6, IRT dropped by 25.49 25.21 = 0.28 qC, much smaller than that of the horizontal strata showing a drop of 0.39 qC, indicating less energy being consumed over the full-face excavation in the 45q inclined strata than that in horizontal strata as a result of the energy dissipation in the frictional sliding. Over the staged excavation, IRT oscillates with high amplitudes. The local peaks for the stages P1–P6 increased as the excavation stage advances. The intense energy release was due primarily to the excavation-induced static friction of the strata caused by removing the RBs. The time-marching scheme of the IRT fully revealed the unstable nature for the steep-angled strata under excavation. IRT of the vertical strata model (Fig. 5c) increased monotonically against the face development, similar to the IRT curve for the horizontal strata. The global maximum IRT was attained at E6 with 31.24 qC, higher than those for the 0q and the 45q strata models. The IRT had a sharp drop at P0 by 31.42 30.99 = 0.43 qC, larger than that of the horizontal strata with 0.39 qC. These differences of the IRT evolution pattern was attributed to the stronger static friction between the vertically inclined layers under the excavation impact. During the staged excavation, IRT increased sharply with multiple peaks with higher amplitude than those for the horizontal and the 45q inclined strata models, demonstrating the fact that vertical strata is the most unstable geological structure during the staged excavation.
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4.2. Constitutive heterogeneity Time series, ൏ ܴܶܫ , ݇ ൌ Ͳǡͳǡʹǡ ǥ, can be viewed as a stochastic process sampled in the IRT ensemble space. Rock behavior can also be characterized by means of p.d.d. (probability density distribution) or c.d.f. (cumulative distribution function) of the ൏ ܴܶܫ data sets. Among the probability distributions, Weibull model has been widely used in rock mechanics for developing the stochastic constitutive equations used in numerical simulation of the rock mechanics studies [25]. The p.d.d. for the Weibull model is given by, ݂ሺݔሻ ൌ ሺ݉Τߟ ሻሺ ݔΤߟሻିଵ ݁ݔሾെሺݔȀߟሻ ሿ
(3)
where, K is the scale factor; m is the homogeneity index (also known as Weibull modulus). The parameter m characterizes degree of the homogeneity for rock masses. An infinitely high m value corresponds to a homogeneous structure with a uniform strength, whereas a heterogeneous structure with a broad distribution of local strength is associated with a relatively small m value [26]. Integration of Eq. (3) yields c. d. f. of the Weibull distribution, ܨሺݔሻ ൌ ͳ െ ݁ݔሾെሺݔȀߟሻ ሿ
(4)
For evaluating the constitutive heterogeneity exhibited by the three geomechanical models under excavation, IRT curve fitting was performed for obtaining the Weibull modulus from the thermal time series, by using the c.d.f. Weibull model given by Eq. (4). It was done based on the assumption that the IRT time series data follow a Weibull distribution. Fig. 6 shows the curve fitting results for the three strata models; the rectangular solid blue square stands for the data sets ൏ ܴܶܫ and the red line for the fitted curves. It is seen that all the IRT data follow the c. d. f. Weibull model very well.
Fig. 6. Weibull model-based IRT curve fitting results for the three geomechanical models: (a) horizontal strata; (b) 45q inclined strata, and (c) vertical strata; it was done based on the assumption that the IRT time series data follow a Weibull distribution.
The upper panel for Fig. 6a is the curve-fitting result for the full-face excavation, and the lower panel for Fig. 6a is the fitting result for the staged excavation. Likewise, Fig. 6b and 6c are the curve-fitting relusts for tow phase excavations in the 45q inclined strata and vertical strata models respectively. By observing the Weibull modulus presented in Fig. 6, the constitutive heterogeneous precursors can be understood as: x horizontal strata: having the largest Weibull modulus values, i.e., 2.9868 for full-face excavation and 2.4933 for staged excavation, exhibited a relatively weak heterogeneity behavior;
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x the 45q inclined strata: having a moderate Weibull modulus values, i.e. 1.5606 for the full-face excavaiton and 2.1073 for the staged excavation, exhibited a moderate heterogeneity; x vertical strata: having the smallest Weibull modulus values, i.e. 1.3767 for full-face excavation and 1.5061 for staged excavation, corresponding to the most heterogeneity as compared with the horizontal and the 45q strata models. 4.3. Image precursors for full-face excavation Comprehension and interpretation of an infrared image is based on such image features as colors, borders and edges that segment different zones in the image, as well as the temperature distribution scale [12]. Pseudo-colors represent the temperature levels; hot (positive) colors stand for high-level temperatures and cool (negative) colors for the low-level temperatures. High-level temperature indicates high stress level due to friction, shear or stress concentration, and low-level temperature indicates low stress level due to tensile cracking, stress release or unloading. Borders or edges that separate hot and cool colored zones reflect different modes of the rock behavior and scale of the high temperature zones corresponds to the scale of the EDZ. Image precursors for characterizing the EDZ will be extracted by analyzing the infrared sequence processed using the algorithms presented in section 3.2. Fig. 7 shows the infrared sequences corresponding to E0 – E6 for the full-face excavation. Fig. 7a is for horizontal strata, Fig. 7b for the 45q inclined strata and Fig. 7c for vertical strata geomechanical models respectively. By analyzing these infrared sequences, the following image features could be regarded as the image puecursors, i.e. (a) at onset of the excavation corresponding to E0, images for the three strata exhibit a random-scattering IRT distribution indicating the intact state of the model rocks; (b) heterogeneous IRT distribution was observed in the subsequent excavation steps E2–E6, but the configurations of the EDZ are different: x for horizontal strata model, IRT evolved from the scattered distribution to the localized high-temperature zone (i.e. EDZ) distributed around the face, behaving like isotropic materials; x for the 45q inclined and vertical strata models, belt-like IRT parallel to the weak surface was observed; indicating the frictional sliding damage mechamisms; x for the 45q strata, most intense static friction took place at the excavation step E5 and E6; for the vertical strata, intense frictions were observed over the entire excavation steps E1–E6.
Fig. 7. Infrared sequences corresponding to E0 – E6 in the full-face excavations; (a) horizontal strata model; (b) the 45q inclined strata and (c) vertical strata.
4.4. Image precursors for staged excavation Fig. 12 shows the infrared sequences corresponding to P1–P7 for the staged excavation. Fig. 7a is for horizontal strata, Fig. 7b for the 45q inclined strata and Fig. 7c for vertical strata geomechanical models respectively.
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Following image features could be regarded as the image precursors, i.e. (a) for horizontal strata, EDZ was localized around the face, closely associated with removing RBs, appearing on overlying rock and floor (P2, P3, P4), the side walls (P4, P5, P6, P7); (b) for the 45q strata, EDZ was hybrid, including localized damage around the face plus frictional sliding represented by the IRT belts over the entire excavation stages, and (c) for vertical strata, during P2–P4, the frictions along the weak surfaces were appreciable by the distinct IRT belts; while over P5–P7, EDZ was localized around face without frictional sliding being observed. Difference of the EDZ among the three strata may be attributed to the extent of the excavation influence area. Apparently, the excavation in the 45q strata has the largest influenced zone.
Fig. 8. Infrared sequences corresponding to P1–P7 for the staged excavation: (a) horizontal strata model; (b) the 45q inclined strata model, and (c) vertical strata model.
5. Conclusions IRT time series, obtained by averaging matrices of the infrared sequence, can be viewed as time observations of the energy release characterizing overall rock response to the excavation. During the full-face excavation, IRT of the horizontal and vertical strata increased linearly with the global maximum energy release rate higher than that of the 45q strata. IRT of the 45q strata has a piecewise increase with several major energy release induced by the frictional sliding along the weak surface. At the transfer point from the full-face excavation to staged excavation, the vertical strata has larger IRT drop than those of the horizontal and 45q strata, indicating the fact that the frictional sliding occurred in the vertical strata was more intense than that in the other two strata models. Over the staged excavation, the time-marching scheme of the IRT for the three strata models had a plastic manner with multiple local peaks. Among them, the vertical strata had higher energy release level. Constitutive heterogeneity precursor could be represented by the Weibull modulus which can be obtained by curve fitting of probability distribution of the time observation ൏ ܴܶܫ to Weibull model. By comparing the resultant Weibull moduli, constitutive heterogeneous precursors could be understood as horizontal strata model has the largest Weibull modulus values, i.e., 2.9868 for full-face excavation and 2.4933 for staged excavation, exhibited a weak heterogeneity behavior; the 45q inclined strata model has a moderate Weibull modulus values, i.e. 1.5606 for the full-face excavaiton and 2.1073 for the staged excavation, exhibited a moderate heterogeneity; and vertical strata has the largest Weibull modulus values, i.e. 1.3767 for full-face excavation and 1.5061 for staged excavation, exhibited the most heterogeneity behavior. Image precursors for characterizing the EDZ were extracted from IRT distribution pattern in the processed infrared sequence. Over the full-face excavation, IRT distribution for horizontal strata evolved from scattered distribution to localized high-temperature zone (i.e. EDZ) distributed around the face, behaving like isotropic materials; IRT distribution for the 45q and vertical strata models distributed as belt-like IRT parallel to the weak surface; indicating the frictional sliding damage mechamism. The most intense friction was observed in the 45q
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strata. During the staged excavation, for horizontal strata, EDZ was localized around the face, closely associated with removing each of the rock blocks; for the 45q and vertical strata, EDZ was hybrid, including localized damage around the face plus frictional sliding represented by the IRT belts. Likewise, in the 45q strata, the most intense frictional EDZ was also observed. Acknowledgement Financial support from the Special Funds for the National Natural Science Foundation of China under Grant No.51574248 are gratefully acknowledged. Heartfelt thanks should also be given to the anonymous reviewer for the valuable comments and modification suggestions on the improvement of this article. References [1] W.L. Gong et al., Thermal image and spectral characterization of roadway failure process in geologically 45q inclined rocks, Tunnel. Underg. Space Technol. 49 (2015) 156–173. [2] P. Fortsakis, K. Nikas, V. Marinos, P. 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