A New Evaluation Method for the Uniaxial Compressive Strength ahead of the Tunnel Face Based on the Driving Data and Specification Parameters of TBM

Uniaxial compressive strength (UCS) is a very important fundamental mechanical parameter for TBM construction. In this work, a predictive model of UCS was proposed according to the TBM parameters including torque, penetration, cutter number, and cutter diameter..e parameter of the new proposedmodel was established by fourteen existed TBM tunnels’ construction data. To describe the relationships of UCS with PLSI of the Murree tertiary hard rocks, regression analyses have been conducted and a fitting equation with high-prediction performance was developed. Validation from the data of Neelum–Jhelum (NJ) TBM diversion tunnel were carried out. .e absolute errors between predictive UCS and experimental UCS were presented. .rough comparison, it can be concluded that the proposed calculation equation of UCS has a high accuracy for a certain rock type with UCS from 50MPa to 200MPa. For special hard rock or soft rock, a new calculation equation between UCS and TBM parameters should be studied furthermore.


Introduction
At present, nearly 200 long and deep-buried tunnels with length approaching or exceeding 10 km have been built in the fields of transportation, water conservancy, hydropower, and urban sewage disposal all over the world. Encouraged by the opening of Japan's Sei-kan tunnel (50.5 km in length) and the British-French submarine tunnel (53.9 km in length), a large number of larger scheme extralong tunnels have been planned in China and abroad, for example, the Japanese-Korean submarine tunnel between Fukuoka and Busan (250.0 km), Gotthard railway tunnel in Switzerland (56.9 km), and the Basis Brenner railway tunnel between Austria and Italy (55.0 km). Compared with traditional techniques such as drilling and blasting, the fullface rock tunnel boring machine (TBM) has gradually become the first choice for long and deep tunnel construction in recent years since it has many advantages, such as high quality, high efficiency, environmental protection, and small disturbance of surrounding rock [1,2]. As one of the most fundamental mechanical parameters, UCS has widely been applied in the process of TBM construction including assessment of rockmass rating (RMR) and Q TBM rockmass system, hazard assessment of rockburst classification or TBM jamming and assessment of the reasonable supporting design [3][4][5][6]. erefore, it is very important to quickly and accurately obtain the in situ UCS characteristics of the surrounding rock [7,8].
However, one of the drawbacks for TBM construction is that the design prevents the direct observation near the tunnel face since TBMs excavate the entire face [22]. Due to the comprehensive cover and narrow space, it is impossible to carry out the standard laboratorial uniaxial compressive test in practical application. e previous testing methods on in situ rock strength were difficult to be applied timely and effectively. erefore, some beneficial attempts have been carried out by different researchers based on the relation between the rock strength and TBM performance. Nelson et al. [23] founded the rock strength is proportional to the field penetration index (FPI). Sanio [24] found strong correlations between UCS and the specific energy (SE) defined as the amount of energy needed to excavate a unit volume of rock. Fukui and Okubo [22] suggested a method for calculating rock strength at the face from the cutting force exerted by the TBM, based on the results of laboratory experiments. A good consistency was found between the rock strength estimated from the cutting force, the Schmidt hammer rebound hardness, and other rock properties. Hamidi et al. [25] founded the UCS is proportional to the field penetration index (FPI), in which the highest R 2 value is 0.70. Based on data obtained from main tunneling projects in Iran, Hassanpour et al. [26][27][28] evaluated the relationship between UCS and actual TBM performance and results demonstrated that FPI and UCS were positive in correlation logarithmically. e above studies have greatly promoted the development of the relationship among the UCS, PLSI, driving data, and specification parameters of TBM, but there are still obvious shortcomings in this area: first, most of the previous studies are based on qualitative or semiquantitative description of laboratory tests and did not give a general quantitative formula for engineering; second, the factors considered are relatively single, only through a specific TBM project, which means the operability and universality in engineering practice need to be improved.
Based on these findings, this work was organized as follows: a predictive model of UCS was proposed according to the TBM parameters such as torque, penetration, cutter number, and cutter diameter in Section 2. And then, the parameter of the new proposed model was established by fourteen existed TBM tunnels' construction data in Section 3. After that, the validation was carried out in Section 4. Finally, some conclusions were presented in Section 5.

A Predictive Model for the Uniaxial Compressive Strength
A large number of laboratory and in situ tests show that the relationship between normal thrust pressure and penetration of TBM can be described as a power function form, which can be expressed as follows [24]: where F N is the normal thrust force of TBM, kN; σ c is the UCS of the surrounding rock, MPa; P is the penetration, which is a ratio of injection depth and rotation rate of TBM, mm/rev; and α is an empirical coefficient. Bilgin et al. [29] suggested that the total torque of TBM can be calculated from the following formula: where T R is the total torque of the TBM cutter head, kN·m; F R is the mean rolling force of one cutter, kN; D TBM is the cutter head diameter of the TBM, m; f L is the coefficient for the frictional losses, 1.2 is used in this work; and N c is the number of the cutters. Furthermore, Sanio [24] suggested that the ratio of rolling force to normal thrust force is proportional to P 0.5 based on theoretical analysis and laboratory experiments, which can be written as (3) Substituting equations (1) and (3) into equation (2), the relationship among the UCS of the surrounding rock σ c , penetration, cutter number, and cutter diameter of the TBM can be obtained, that is, (4) (4) can be rewritten as where λ is an empirical parameter.

Establishment of the Parameter of the Proposed Model
To obtain the empirical parameter λ in equation (5), driving data and specification parameters from 14 TBM tunnels were regressed and analyzed. e related data are list in Table 2.

Project Description of the Neelum-Jhelum TBM Diversion
Tunnel. e Neelum-Jhelum hydroelectric project is located in the Muzaffarabad district of Azad Jammu and Kashmir (AJK), Pakistan. A 19.6 km stretch of the tunnel from the Nauseri site will be constructed as a twin tunnel system, each with a cross section of about 52 m 2 ; 11.2 km of the twin tunnel system will be excavated by using the Herrenknecht gripper TBM and the remainder by drilling and blasting. Figure 5 shows the picture of the TBM which excavated the NJ TBM diversion tunnels, and the main technical specifications of TBM are summarized in Table 3. e diversion tunnel is located in the Himalayas, geologically young mountains with spectacular heights developed as a result of collision between various continental and microcontinental plate fragments during the late Mesozoic to late Cenozoic periods. e main geological formation outcropped in the project area is the Murree Formation except at the intake, which is partly in igneous or metamorphic rocks belonging to the Panjal Formation. Geological mapping of each TBM and drill and blast tunnel is conducted continuously as the tunnel advances. e Murree Formation consists of alternating beds of grey medium to fine-grained sandstone and reddish colored fine to very fine grained siltstone with occasional thin mudstone layers. Contacts are often gradational with no bedding parting. Sandstone, siltstone, and occasional thin mudstone beds are recognized. ick sandstone beds are often very massive and competent.

Estimation of UCS from PLSI.
As mentioned before, one of the drawbacks for TBM construction is that the design prevents the direct observation near the tunnel face since TBMs excavate the entire face [22]. Due to the comprehensive cover and narrow space, it is impossible to carry out the standard laboratorial uniaxial compressive test in practical application. us, in this work, a batch of typical rock samples were collected at first and were cut into a Φ50 × 100 mm standard cylindrical specimen, which can be seen in Figure 6. en, the standard laboratorial uniaxial compressive tests and point load tests were carried out to establish the relationship between them. e UCS was determined using the RMT∼201 rock test machine according to the ASTM standards, which can be seen in Figure 7. Its maximum load is 1 MN, and its maximum confining pressure is 50 MPa. e loading rate was set at 0.05 mm/s, and more details about the test machine can be seen in [30,31]. e point load tests were carried out using the point load testing machine with a digital display, as shown in Figure 8. In order to make rock test results with different sizes more scientific, it is necessary to establish corrected the point load where I s is the uncorrected point load strength index, F is the correction factor, and D e is the equivalent circle diameter of the destroyed cross-sectional area. e proper correlation between the UCS and PLSI is one of the most critical concerns in applying the point load test. e raw dataset was subjected to least squares regression analysis. In this work, linear (UCS � KI s(50) + b), exponential (UCS � Ke b * I s(50) ), logarithmic (UCS � K ln(I s(50) ) + b), and power (UCS � KI m s(50) ) curve fitting approximations were executed, and the approximation equations with highest R 2 were determined for each regression. Figure 9 shows the plot of the UCS versus the PLSI for 100 rock samples (50 sandstones and 50 siltstones). e empirical conversion equations between UCS and PLSI are also presented in Figure 9 and Table 4. It can be seen that when the value of PLSI is between 1.5 and 5 MPa, the predictive results from the four regressions have a great agreement. When the PLSI value is lower than 1.5 MPa or larger than 5.0 MPa, the deviation of exponential and logarithmic regression types are relatively larger than that of the other types. Based on the best correlation coefficient (R 2 ) of 0.9114, the new   Shock and Vibration power equation (Table 4) applied in the tertiary sandstone and siltstone of the Murree Formation was chosen.
In addition, the predicted values were drawn versus the measured values by using a 1 :1 slope line, as shown in Figure 10. It can be seen that the predicted results are in good agreement with the measured ones, and all the dataset lies exactly on a straight line without scatter, which indicated that PLSIs are reliable values for estimating UCS, avoiding the cumbersome and time-consuming standard laboratorial test carried out in the preliminary studies.

Validations.
e in situ point load strength was manually recorded every day, and then the UCS of surrounding rock in the Neelum-Jhelum TBM diversion tunnel can be obtained with Table 4. Figure 11 is the UCS from in situ point load tests at different identified geological area along the TBM tunnel alignment regarded as actual UCS. From Figure 11, it can be seen that the rock strength varied from 24.38 MPa to 228.32 MPa and the average UCS is 131.83 MPa. It can be concluded that the rock type varied along the tunnel alignment from the moderately to closely jointed siltstone (UCS < 120 MPa) to primarily massive and blocky sandstone (UCS > 150 MPa). e TBM performance database was collected during construction phases, where the geological conditions and machine performance information were valid. As shown in equation (7), four parameters were involved here: cutter number, TBM cutter diameter, penetration, and torque. Figure 12 is the recorded torque along the Neelum-Jhelum TBM diversion tunnel in the conduction process. From Figure 12, it found that the maximum torque is 2.8 MN·m at 07 + 700.99 section where the estimated UCS from is 148.46 MPa. e minimum torque is 0.6 MN·m at 07 + 555.42 section where the estimated UCS is 48.74 MPa, which means that more torque is needed for a hard rock than a soft rock with the same penetration. Figure 13 is the recorded penetration along the Neelum-Jhelum TBM diversion tunnel in the conduction process. It can be seen that the maximum penetration is 15 mm at three sections where the estimated UCS from laboratory tests is 105.4 MPa, 48.7 MPa, and 42.96 MPa. e minimum penetration is 4.5 mm at 07 + 645.03 section where the estimated UCS from laboratory tests is 198.39 MPa. From the above data, it can be concluded that the penetration is not determined by rock strength.
With the data from Figures 12 and 13, equation (7) was used to calculate the UCS from TBM parameters at different construction time.
en, the calculated UCS was compared with the estimated UCS from laboratory tests which is shown in Figure 14. From Figure 14, it is shown that the calculated UCS from T R in equation (7) agrees with that from laboratory tests, even though there is some difference. When the actual UCS is over 200 MPa, the difference between calculated UCS from T R and actual UCS is much more obvious. is means that equation (7) seems more suitable for tunnels with a lower UCS less than 200 MPa. is is because that equation (7) is conducted from 14 TBM tunnels list shown in Table 2 where all the UCS is lower than 200 MPa.
To further analyze the errors between calculated UCS and actual UCS, the following formula was adopted to calculate the absolute errors: where E(%) is the absolute error; σ actual is the actual UCS that was obtained by in situ tests; and σ prediction is the predictive UCS that was obtained by using equation (7).  Figure 15. From Figure 15, it shows that the maximum absolute error is 34.32% and the minimum absolute error is 0.07%. e average absolute error is 8.28%. ere are 5 sections (only 1% sections) with an absolute error higher than 20%. is means that the calculated UCS agrees with that from the indoor tests. At (7) has a low accuracy for situation with a high actual UCS or a low actual UCS. is is because that equation (7) is calculated from 14 TBM tunnels list in Table 2 where the UCS varied from 53.4 MPa to 156 MPa. If we can collect more data from different TBM tunnels, a regressed equation for different kinds of rock could be conducted with the proposed method here.      Figure 11: UCS values from laboratory tests along the Neelum-Jhelum TBM diversion tunnel.

Conclusions
e uniaxial compressive strength (UCS) is a very important fundamental mechanical parameter for TBM construction. Nowadays, a large number of studies were carried out about the relationship among the UCS, PLSI, driving data, and specification parameters of TBM. But there are still several obvious shortcomings. In this study, a new evaluation method for the uniaxial compressive strength ahead of the tunnel face based on the driving data and specification parameters of TBM was proposed, and some conclusions were obtained, which can be given as follows: (1) A predictive model of UCS was proposed according to the TBM parameters such as torque, penetration, cutter number, and cutter diameter. (2) Based on the data from fourteen TBM tunnels, relationships between UCS and N c , T R , D TBM , and P were studied. e results show that the correlation between UCS and T R is strong with a correlation coefficient of 84.08%. Basing on this, the parameter of the new proposed model was established. (3) To describe the relationships of UCS with PLSI of the Murree tertiary hard rocks, regression analyses have been conducted and a fitting equation with highprediction performance (R 2 � 0.9114) was developed. (4) Validation from the data of the Neelum-Jhelum (NJ) TBM diversion tunnel was carried out. e absolute errors between predictive UCS and experimental UCS were presented. rough comparison, it can be concluded that the proposed calculation equation of UCS has a high accuracy for a certain rock type with UCS from 50 MPa to 200 MPa. For special hard rock or soft rock, a new calculation equation between UCS and TBM parameters should be studied furthermore.
is study provides the technical strut for the later thorough research on the assessment of rockmass classification, rockburst, or TBM jamming. To apply the research of this study to engineering practices preferably, a software system of the in situ rock strength estimation considering the PLSI and TBM performance will be developed as well in the subsequent study. en, combining with the proposed rockburst or large extrusion deformation criteria, the security status of the tunnel face will be evaluated in real time.

Data Availability
No additional data are available.

Conflicts of Interest
e authors declare that they have no conflicts of interest.  Shock and Vibration