Evaluation of Tunnel Contour Quality Index on the Basis of Terrestrial Laser Scanning Data

The formula for the TCI_T evaluation, i.e., calculated for the entire tunnel or more than five blasting rounds, proposed by Kim and Bruland [1], is as follows: (1) TCIT=CrW1C1Od¯+W2C2RCL¯+W3C3Vo TC{I_T} = {{{C_r}} \over {{W_1}{C_1}\overline {{O_d}} + {W_2}{C_2}\overline {RCL} + {W_3}{C_3}{V_o}}} where the values of Od¯ \overline {{O_d}} and RCL¯ \overline {RCL} are the arithmetic means of the parameters O_d and RCL, respectively, calculated for all measured contour profiles of the tunnel or more than five blasting rounds. Two contour profiles were measured within a single blasting round, at one third and two thirds of its length (L_R). C_r is a dimensionless constant for the range adjustment and its value is equal to 300. W₁, W₂, and W₃ are the weights of the parameters O_d, RCL, and V_o, respectively. Their values correspond to importance of several parameters for the contour quality, and according to [1], they are equal to 4.5, 4.5, and 1.0, respectively. C₁, C₂, and C₃ are correction factors derived from the distribution of O_d, RCL, and V_o for all blasting rounds surveyed in [1], and they are suggested to be 0.008, 0.8, and 0.02, respectively. For a single measured contour profile, the value of the overbreak depth (O_d) is calculated according to the formula: (2) Od=1N∑i=1N|di| {O_d} = {1 \over N}\sum\limits_{i = 1}^N {\left| {{d_i}} \right|} where d_i is the distance of the i-th measurement point from the planned contour line (Fig. 7). In [1], the distance between successive measurement points on the planned contour profile (i.e., measurement interval) corresponds to approximately half of the normal drilling spacing for contour holes. Thus, overbreak depth (O_d) is defined as an average distance of the measurement points from the planned contour.

Figure 7

The contour roughness value (RCL) for a single section is given by the formula: (3) RCL=LaLp RCL = {{{L_a}} \over {{L_p}}} where L_a and L_p denote the lengths of the modeled and planned contour lines, respectively (Fig. 8). The L_a value should be calculated using the formula: (4) La=∑i=1N(Xi−Xi−1)2+(Yi−Yi−1)2 {L_a} = \sum\limits_{i = 1}^N {\sqrt {{{\left( {{X_i} - {X_{i - 1}}} \right)}^2} + {{\left( {{Y_i} - {Y_{i - 1}}} \right)}^2}} }

Figure 8

The value of the longitudinal overbreak variation (V_o) is calculated using the formula: (5) Vo=1N∑i=1N|Odi−1−Odi| {V_o} = {1 \over N}\sum\limits_{i = 1}^N {\left| {{O_d}_{_{i - 1}} - {O_{{d_i}}}} \right|} where O_di means the overbreak depth O_d calculated for the i-th measured contour profile. Thus, it is an arithmetic mean of all differences in the overbreak depth O_d calculated for the successive measured contour profiles.

In turn, the formula for the TCI_R value, i.e., calculated for a single blasting round, has the following form: (6) TCIR=CrW1C1Od¯+W2C2RCL¯ TC{I_R} = {{{C_r}} \over {{W_1}{C_1}\overline {{O_d}} + {W_2}{C_2}\overline {RCL} }} where Od¯ \overline {{O_d}} and RCL¯ \overline {RCL} denote the values of the overbreak depth (O_d) and the contour roughness (RCL), respectively, averaged for the two measured contour profiles. The maximum value of the TCI (TCI_T or TCI_R) is 83.(3) and corresponds to the highest quality of the contour. It is achieved when the parameters Od¯ \overline {{O_d}} , RCL¯ \overline {RCL} , and V_o equal 0 cm, 1, and 0 cm, respectively, and therefore, the actual contour profile is the same as a planned contour profile.

The methodology of determining the Tunnel Contour Quality Index (TCI) based on data from the terrestrial laser scanning (TLS) is generally based on formulas (1) and (6), but includes some modifications. It takes into account the redefined parameters of the overbreak depth (Od¯→Osd¯) \left( {\overline {{O_d}} \to \overline {{O^s}_d} } \right) , the contour roughness (RCL→RCLs)¯ \overline {\left( {RCL \to RC{L^s}} \right)} , and the longitudinal overbreak variation (Vo→Vos) \left( {{V_o} \to {V_o}^s} \right) , to adapt them to the effective use of TLS data. The values of the constant (C_r), the weights (W₁, W₂, and W₃), and the correction factors (C₁, C₂, and C₃) remain unchanged and are consequently applied throughout this paper. TCI_T and TCI_R calculated according to the TLS technique are proposed to be marked as TCI_s^T and TCI^s_R, respectively. According to the TLS technique:

Osd¯ \overline {{O^s}_d} is the overbreak depth defined as an arithmetic mean value for a distance between all measurement points of the resultant point cloud (Fig. 9) and the planned contour surface (7). When TCI^s_T is calculated, this cloud contains points measured over the entire length of the tunnel, or more than five blasting rounds; while for calculating TCI^s_R, the point cloud includes points measured within a single blasting round. (7) Ods¯=1N∑i=1N|dis| \overline {O_d^s} = {1 \over N}\sum\limits_{i = 1}^N {\left| {d_i^s} \right|}

Figure 9

Figure 10

All data used in the analyses were collected with a terrestrial laser scanner. Thus, for each analyzed cross-section, contour profiles for the laser profiling technique were obtained on the basis of the created TIN surface. For this purpose, the AutoCAD Civil 3D 2015 was used. As a result, six polylines were obtained, constituting cross-sections 1 and 2 of each of the three blasting rounds (Fig. 11).

Figure 11

For the studied niche, the normal drilling spacing for contour holes was approximately 70–80 cm (Fig. 3). Therefore, in accordance with [1], 35 cm was adopted as a measurement interval. This gives 35 measuring points evenly distributed on the planned contour profile. Taking into account the formulas (2–4, 6) and on the basis of the six previously prepared sections, the parameters of the overbreak depth (O_d) and the contour roughness (RCL) were calculated for the side 1, side 2, the roof, and, finally, the entire blasting round. The obtained results are summarized in Table 2.

The obtained results can be considered representative only for that short length of the niche that is in close proximity to the measured contour profiles. In addition, the small number of 35 measuring points evenly distributed along the planned contour profile does not allow for an accurate modeling of the actual profile line. Thus, these results only provide some approximation of the actual contour quality. The authors of this paper propose the TLS technique as an alternative to the laser profiling technique for the TCI evaluation proposed in [1], because it enables an efficient use of large amounts of TLS data. The starting point for determining the TLS technique is the statement that the possibility of accurate modeling of the tunnel contour surface increases with the number of measured points (provided, however, that all points are distributed on the surface as evenly as possible).

Table 3 presents the values of Osd¯ \overline {{O^s}_d} and RCLs¯ \overline {RC{L^s}} calculated in accordance with the TLS technique for individual elements (i.e., side 1, side 2, and roof) of each of the three blasting rounds for the studied niche. The areas of the modeled contour surfaces (A_a) of side 1, side 2, and roof were read from AutoCAD Civil 3D. The area of the planned contour surface (A_p) is 6.9 m² for each of the sides, and 23.56 m² for the roof.

Out of the three studied blasting rounds, round 3 has the highest quality of the contour, regardless of the technique used. This is due to the fact that the calculated values of the overbreak depth and the contour roughness are the lowest out of all three blasting rounds. For the laser profiling technique, they are Od¯=11.787 {\overline {{O_d}}} = 11.787 and RCL¯=1.037 {\overline {RCL}} = 1.037 , respectively. For the TLS technique, these values are Osd¯=11.350 {\overline {{O^s}_d}} = 11.350 and RCLs¯ =1.102 {\overline {RC{L^s}}} = 1.102 , respectively. Round 2 shows the poorest quality of the contour determined on the basis of the measured contour profiles (TCI_R = 71.343). It is also characterized by the greatest overbreak depth of all blasting rounds (O_d = 12.905 cm). On the other hand, round 1 has the lowest value of TCI^R_s = 64.232. It is characterized by the highest value of the contour roughness among all blasting rounds, of RCLs¯ =1.171 {\overline {RC{L^s}}} = 1.171 . The difference between the highest and the lowest TCI_R value calculated with the laser profiling technique amounts approximately to ΔTCI_R = 0.847. In the case of TLS technique, a similar difference is ΔTCI_s^R = 4.346. The quotient of each of these values and the appropriate lowest value of the TCI_R (ΔTCI_s^R) is 0.047/71.343 = 0.012 and 4.346/64.232 = 0.068, respectively. This means that the contour quality of individual blasting rounds is more diversified when we take into account the results obtained with the TLS technique for TCI calculation.

In the studied niche, the average value of the TCI_s^R for three blasting rounds, calculated using the TLS technique, is 66.918. Therefore, it is approximately 6.7% lower than the value calculated using the laser profiling technique. The discrepancies in the results are caused by differences in the values of the overbreak depth and the contour roughness parameters calculated for the two techniques. The average value of the overbreak depth (Od¯) \left( {\overline {{O_d}} } \right) for three blasting rounds, calculated in accordance with [1], is 12.429 cm. However, when determined with the TLS technique, it is approximately 4.2% lower (Osd¯ =11.909 cm) \left( {\overline {{O^s}_d} \, = 11.909\,{\rm{cm}}} \right) . For the average value of the contour roughness, the relationship is opposite. In this case, using the TLS technique, RCLs¯=1.127 {\overline {RC{L^s}}} = 1.127 and is approximately 8.6% higher than the value calculated using the laser profiling technique (RCL¯=1.038) \left( {\overline {RCL} = 1.038} \right) . The differences in the mentioned results are caused by the fact that the results obtained for the laser profiling technique were based on measurements of only two contour profiles within the single blasting round, while for the TLS technique, the obtained results were based on measurements of the contour surface of the entire blasting round. The density of measurement points located along the length of the contour profile or on the contour surface is also important. According to the laser profiling technique, a measurement interval of 35 cm was adopted for the studied niche (i.e., 1 measurement point per 35 cm length of planned contour profile). The laser scanning (TLS) measurements of the studied niche were characterized by an average density of measurement points of approximately 1 point per 1 cm². Higher density of measurement points enables a more accurate modeling of the measured profile/surface. In case of TLS measurements, an influence of the uneven distribution of the measurement points over different parts of the measured surface should also be mentioned. Parts of the surface with higher density of measurement points will have a stronger impact on the TCI_s^R value (especially on the Osd¯ \overline {{O^s}_d} parameter). Therefore, when using TLS, as even as possible distribution of the measuring points over the entire measured surface should be ensured. This can be achieved by selecting appropriate measurement parameters, a correct position of the scanner in relation to the measured surface and, if necessary, by conducting measurements with several different stations.

The average TCI_R value for three blasting rounds of the studied niche, calculated using the laser profiling technique, is 71.730. This means that the quality of the niche contour should be assessed as high. Only about 7% of all blasting rounds of Korean tunnels (i.e., Sujeongsan, Iyang, Namseon, and Kyeryong) studied in [1] were similar or higher. However, none of the blasting rounds of Norwegian tunnels (i.e., LS02, Marienborg) studied in [1] achieved this level. Several factors can influence this result. One of them is the similarity of the Polish and the Korean approach to the design of tunnels, according to which any overbreak is filled with shotcrete. This implies that tunnel engineers strive to achieve the highest possible contour quality. Another factor is a relatively small cross-sectional area of the studied niche, i.e., approximately 21.30 m², which, according to [1], is conducive to precise drilling of blast holes. For comparison, the smallest cross-sectional area in all tunnels studied in [1] is approximately 45.50 m² (Sujeongsan Tunnel). Unfortunately, it is not possible to compare the obtained results to those reported in [2] (i.e., for a road tunnel in the northern province of Norway). Costamagna et al. [2] used different C₁ and C₂ factors to calculate the TCI_R. Thus, it is recommended to publish not only the TCI values but also the values of the O_d, RCL, and V_o parameters, which will enable the comparison of the obtained results from different studies.

For the studied niche, the average value of the overbreak depth for both sides calculated according to laser profiling technique is Od¯=10.171 cm {\overline {{O_d}}} = 10.171\,{\rm{cm}} (Fig. 12). For roofs, this value is 37.2% higher, i.e., Od¯=13.952 cm {\overline {{O_d}}} = 13.952\,{\rm{cm}} . According to the TLS technique, these values amount to Osd¯=9.767 cm {\overline {{O^s}_d}} = 9.767\,{\rm{cm}} for both sides and Osd¯=12.954 cm {\overline {{O^s}_d}} = 12.954\,{\rm{cm}} for roofs (32.6% higher than the values for sides), respectively (Fig. 14). Therefore, regardless of the technique used, it can be concluded that for the studied niche, the average value of the overbreak depth within the roof is more than 30% higher than that within the sides. Regardless of the technique used, the average value of the contour roughness for the roofs is approximately 5% higher than that for sides (Figs 13 and 15). The above results may be influenced by the dense network of rock fractures occurring in the Carpathian flysch [27] (a quality aspect of the rock mass), in particular, by the value of an angle between the dominant direction of the fractures and the planned contour surface. It should also be remembered that parts of the rock mass weakened (detached) by the explosion remain in their place, within the sides, while they fell off from the roof. The value of the overbreak depth for the roof located near the tunnel face is also influenced by the value of the angle between the direction of the fall of the rock layers and the direction of tunnel boring. The obtained results confirm the observations of Kim and Bruland [1] who reported that the TCI value is influenced by many factors, and in particular, the factors of quality of the rock mass and the shape of the tunnel.

Figure 12

Figure 13

Figure 14

Figure 15

On a basis of the RMR classification, the rock mass located around the studied niche was classified as class three rock mass, which is a high result for the Carpathian flysch. This corresponds to the so-called medium-strong rock mass. The total score for this class ranges from 41 to 60 points. The linear relationship proposed in [1]: TCI_R=0.045·RMR+62.830 was characterized by a very low value of R₂ = 0.088; therefore, it cannot be considered reliable. The relationship between TCI and RMR for the Carpathian flysch has not been specified in this article due to the small amount of data, but in the future, such a relationship will be the subject of more detailed studies, especially taking into account the analysis of individual parameters on the basis of which the RMR is determined.

Defining a more precise relationship between the quality of a rock mass (assessed according to, e.g., RMR) and the TCI value requires further studies in different geological conditions. It may be very difficult to establish such relationship; however, it will enable the tunnel engineers to conduct ongoing local monitoring of the quality of the rock mass using the TCI. It can also be assumed that there is a relationship between the TCI value and the parameters of contact between the tunnel lining and the surrounding rock. It appears that the aforementioned contact phenomenon is important for the safety of the structure [28]. Thus, apart from the economic aspect [29], the TCI can also potentially become a useful tool for evaluation of the geotechnical and safety aspects of the structure.

In addition to the rock mass quality, the tunnel shape, and the cross-sectional area, a number of other factors affect the TCI value. They include a location of blast holes, types and amounts of explosives used, and quality of blasting works [1]. Further comprehensive studies are needed to accurately assess the impact of above-mentioned factors. The effectiveness of those studies will largely depend on the effective and accurate measurement of the contour surface geometry. Such measurements can be performed with the TLS technology. For this reason, the TLS technique presented in this paper is especially useful.

Although the TLS technique is based on a large amount of data (such as the measured point cloud), it cannot be considered optimal for calculating the overbreak depth parameter Osd¯ \overline {{O^s}_d} (7). It does not take into account the spatial distribution of the measured points, but only their distance from the planned contour surface. For the sides, this can be remedied by defining the parameter Osd¯ \overline {{O^s}_d} as the ratio of a volume between the modeled contour surface (TIN) and the planned contour surface (V_a) to the area of the planned contour surface (A_p) (Fig. 16): (10) Ods¯=VaAp \overline {O_d^s} = {{{V_a}} \over {{A_p}}}

Figure 16

The calculation of the volume V_a, defined as above, is not problematic, as it can be done successfully in the AutoCAD Civil 3D software. Unfortunately, it is not possible for the roof. To determine the parameter Osd¯ \overline {{O^s}_d} for the roof, the so-called F-operator [30] for the modeled contour surface (TIN) and the planned contour surface must be used. This operation consists in “erasing” the original shape of the surface. However, in this case, both the planned contour surface and the modeled contour surface (TIN) should be developed with the same radius of curvature, i.e., the radius of curvature of the planned contour surface (for the studied niche, this radius is 2.5 m). Then, the value of the parameter Osd¯ \overline {{O^s}_d} for the roof is equal to the ratio of the volume between the modeled contour surface (TIN) and the planned contour area (following the operation described above) (V_a^F) to the area of the planned contour surface (A_p): (11) Ods¯=VaFAp \overline {O_d^s} = {{V_a^F} \over {{A_p}}}

According to the authors’ knowledge, currently no software is available that allows the above-described operation to be performed for the TIN surface created on the basis of a point cloud. Therefore, it is planned to start works on development of a computational algorithm that would enable such operation in the future.