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Mechanical performance of TBM cutterhead in mixed rock ground conditions
Tunnelling and Underground Space Technology xxx (2016) xxx–xxx
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Mechanical performance of TBM cutterhead in mixed rock ground conditions Qi Geng a,⇑, Zhengying Wei a, Hao Meng a, Francisco Javier Macias b a b
School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, China Department of Civil and Transport Engineering, NTNU, Trondheim, Norway
a r t i c l e
i n f o
Article history: Received 12 September 2015 Received in revised form 22 February 2016 Accepted 22 February 2016 Available online xxxx Keywords: TBM tunnelling Mixed rock ground Ray intersection algorithm Experimental cutterhead
a b s t r a c t The mechanical performance of TBM cutterhead including thrust, torque, eccentric force and overturning moment was calculated and analysed in different mixed rock ground conditions. The calculation model was built by identifying the rock type under each cutter using a ray intersection algorithm and calculating the cutting forces of each cutter using the CSM model. The mixed rock ground conditions were simplified as rock type distribution and rock strength classification. In the present paper, the rock distributions of the Layer-Banded Rock (LBR) and Random-Distributed Rock (RDR) types were considered. The influences of rock strength (Uniaxial Compressive Strength: UCS, Brazilian Tensile Strength: BTS), rock locations and number of rock layers were studied. For verification, a boring experiment was designed and conducted using an experimental cutterhead with 14 disc cutters. The rock box was poured with concrete C20, C40 and C60 layer by layer to prepare the LBR condition. The average torque and thrust of the calculation model and experiment were in good agreement. Some conclusions were drawn from the study on the rock strength, rock locations, area percentages of different rock layers and number of rock layers. And hence, some suggestions were proposed to enhance the tunnelling efficiency and reduce damage to the cutterhead. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Mixed ground is one of the most difficult conditions for TBM tunnelling. Since tunnel alignment is often determined by practical engineering requirements rather than the ground conditions, TBMs often have to be driven in mixed ground conditions (Tóth et al., 2013). Even though many engineering problems have been encountered in these conditions (e.g. impact or eccentric loads), limited research has been conducted to study the influence mechanism of the mixed ground conditions on cutterhead mechanical performance. As a result, the study of cutterhead mechanical performance in mixed ground conditions is necessary to provide some precautions or suggestions for cutterhead design and TBM tunnelling. The mixed ground condition can be defined by the ratio of UCS between the weakest and the strongest rock layer of a maximum of 1:10 (Steingrimsson et al., 2002). Ground conditions can be classified into three types based on the geological formations of the tunnel face: the Rock–Soil Interface (RSI) mixed ground, the
⇑ Corresponding author.
Boulder–Soil Matrix (BSM) mixed ground and the Layer-Banded Rock (LBR) mixed ground (Tóth et al., 2013). The research topics on TBM tunnelling in mixed ground conditions can be divided into three types: TBM performance prediction, special construction techniques study and cutterhead mechanical performance study. Steingrimsson et al. (2002) assumed that the hard rock part controls the penetration rate in LBR conditions and introduced a correction factor kAB to access the net penetration rate (m/h) in mixed ground conditions using the NTNU prediction model (Bruland, 2000). Tóth et al. (2013) found the correction factor introduced by Steingrimsson et al. (2002) not suitable for RSI conditions in a specific case. Tóth et al. (2013) also analysed two cases of RSI conditions and proposed a correction factor based on variance and sensitivity analysis of mean penetration rate (mm/rev) for the soil and rock. Delisio et al. (2013) analysed the rock mass conditions and the TBM performance data of the Lotschberg Base Tunnel, and proposed a prediction model for blocky rock conditions introducing a relationship between the Field Penetration Index (FPI) and two rock mass parameters including the volumetric joint count and the UCS. Zhang et al. (2015) proposed a numerical model verified by some plane model tests, which can be used to study and predict the influence of multi-layered ground conditions
E-mail address: [email protected] (Q. Geng). http://dx.doi.org/10.1016/j.tust.2016.02.012 0886-7798/Ó 2016 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Geng, Q., et al. Mechanical performance of TBM cutterhead in mixed rock ground conditions. Tunnel. Underg. Space Technol. (2016), http://dx.doi.org/10.1016/j.tust.2016.02.012
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on lining behaviour. Special construction techniques and TBM modifications are needed to deal with problems encountered in mixed ground conditions. Modification of the cutterhead stiffness, combined use of disc cutters and drag bits in composite shield cutterhead and improvement of the soil flowability have been applied (Zhao et al., 2007; Zhongsheng et al., 2006). Regarding to ground stability problems at the tunnel face in heterogeneous ground conditions, Darrag (1999) proposed a solution to provide stability in tunnels excavated in mixed-ground conditions by using chemical grouting. In order to study the influencing mechanism of the mixed ground condition on cutterhead mechanical performance, several calculation models were built to predict cutterhead torque and thrust (Xiaoxing et al., 2010; Zhang et al., 2010). The existing calculation models mainly focused on LBR conditions without considering more complex tunnel face conditions. In the present paper, a calculation method has been proposed which can be used to calculate cutterhead mechanical performance including the torque, thrust, eccentric force and overturning moment in stable mixed ground conditions. The keys of the model are to identify the rock type under each individual cutter during the boring process and calculate its cutting forces. A ray intersection algorithm (Huang and Shih, 1997) was applied to determine the rock types and the Colorado School of Mines (CSM) model (Rostami, 2008) was used to calculate the cutter cutting forces in the cutterhead during boring. In order to verify the calculation model, a boring experiment was designed and conducted using an experimental cutterhead with 14 disc cutters (cutter diameter 17 in./432 mm) in the LBR condition. The model was applied for multi-layer LBR and RDR conditions.
2. Calculation models 2.1. Description of the calculation model Three mixed rock ground conditions are shown in Fig. 1. A typical LBR condition is illustrated in Fig. 1a, while Fig. 1b (rock inserted) and Fig. 1c (rock cave) can be classified as the RDR condition. In order to study cutterhead mechanical performance in these conditions, a calculation model using a ray intersection algorithm was proposed and illustrated in Fig. 2. The crucial issue of the model is to identify the rock type under each individual cutter during the boring process, which can be simplified as a mathematical problem of the ‘‘point-in-polygon” by regarding the disc cutters and rock zones as points and polygons, respectively. As is shown in Fig. 2b, when a point (p1) is inside the polygon, there will be odd number of intersection points between the polygon and the ray (l1) originating from the point (p1). However, when the point (p2) is outside the polygon, the number of the intersection points will be even. For the LBR condition, rock layers are simplified as enveloping rectangles (Fig. 2c); while for the RDR condition, inserted rocks or caves are simplified as enveloping circles (Figs. 1b, c and 2d). In order to improve the computing speed, a rotating speed with equal value but opposite to the cutterhead direction is used to the cutterhead and the tunnel face. This transforms the revolution of each disc cutter to the revolution of the rectangles or circles. The rock cutting forces including the normal (FN) and rolling forces (FR) of each cutter were calculated using the CSM force estimation formulas shown in Eq. (1). The centrifugal force (FE) was calculated based on classical mechanics. The side forces were ignored since they are relatively low compared with other forces according to Rostami (2008). Cutterhead mechanical performance indexes, including the thrust (f1), torque (f2), eccentric force (f3) and overturning moment (f4) were calculated using Eqs. (2)–(4). For the calculation of forces FX, FY, MX and MY, Eq. (3) was applied
for normal and centre cutters, and Eq. (4) was applied for the gage cutters. The performance indexes were calculated a total of 36 times during a revolution, with an interval of 10 angular degrees. Finally, the average values of these 36 groups were defined as the final mechanical performance indexes.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u 2 3 rc rt S pffiffiffiffiffiffiffi cos F N ¼ 2:12Trc u ; F R ¼ F N tan ; 2 2 u rc T rc P F E ¼ mc x2 r; u ¼ cos1 rc
ð1Þ
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 !2ffi u N N N N u X X X X FN ; f2 ¼ F Ri ri ; f 3 ¼ t F Xi þ F Yi ; f1 ¼ cos ci i¼1 i¼1 i¼1 i¼1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 !2 u N N u X X t ð2Þ f4 ¼ M Xi þ M Yi i¼1
i¼1
F X ¼ F R sin h þ F E cos h; F Y ¼ F R cos h þ F E sin h; MX ¼ F N r sin h; M Y ¼ F N r cos h
ð3Þ
F X ¼ F R sin h þ ðF E þ F N sin cÞ cos h;
F Y ¼ F R cos h þ ðF E þ F N sin cÞ sin h;
MX ¼ F N r sin h= cos c; MY ¼ F N r cos h= cos c
ð4Þ
where T denotes the cutter tip width (mm); u denotes the contact angle between the rock and disc cutter (rad); rc denotes the radius of the disc cutter (mm); mc denotes the weight of a disc cutter (kg); rc and rt denote the rock UCS and BTS respectively (MPa); S denotes the cutter spacing (mm); P denotes the penetration rate (mm/rev); x denotes the rotating speed of the cutterhead (rad/s); N denotes the number of the disc cutters; r, h and c denote the polar radius (m), polar angle (degree) and tilt angle (degree) of a disc cutter respectively. 2.2. Experimental verification of the calculation model In order to verify the model, a trial was designed using an experimental cutterhead system in the State Key Laboratory of Shield Machine and Boring Technology, Zhengzhou, China (Xingjian et al., 2013). The experimental system is mainly composed of a cutterhead, a rock box, a conveyor belt system and a control panel, as illustrated in Fig. 3. The cutterhead is mounted with 14 normal disc cutters (cutter diameter 17 in./432 mm). The cutter layout is illustrated in Fig. 4a and Table 1. The specimen box has an inner diameter of 2.5 m with a depth of 0.4 m. In order to prepare an LBR condition, three types of concretes, i.e. C20, C40 and C60 were poured into the specimen box layer by layer. The curing process of the concrete was assured, total of three weeks, to reach the highest strength for every concrete specification. The dimensions of different concrete samples were measured and illustrated in Fig. 4a. In order to test the concrete strength, the same grout was also used to obtain cubic concrete samples (Fig. 5a). The samples were then drilled into cylinders (Fig. 5b) for the UCS and BTS tests. These tests were conducted according to the Standard for Test Methods of Engineering Rock Mass in China (Chen et al., 2014). The tested UCS values are 18.9 MPa, 37.6 MPa and 58.4 MPa for the concretes C20, C40 and C60 respectively, and the BTS values are 1.7 MPa, 3.8 MPa and 5.6 MPa respectively. The boring experiments were conducted using one concrete sample for four times with penetrations of 3 mm/rev, 6 mm/rev, 9 mm/rev and 12 mm/rev respectively. Different penetrations can be achieved by controlling the advancing rate and the rotational speed of the propel cylinders and the driving motors, respectively. Each boring process with different penetrations was carried out for
Please cite this article in press as: Geng, Q., et al. Mechanical performance of TBM cutterhead in mixed rock ground conditions. Tunnel. Underg. Space Technol. (2016), http://dx.doi.org/10.1016/j.tust.2016.02.012
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Fig. 1. Rocks on possible tunnel face (a) Layer-Banded Rock mass; (b) different rock inserted; and (c) hollow in rock mass.
Fig. 2. The calculation model (a) schematic representation; (b) the ray intersection algorithm of the relationship between points and a polygon; (c) algorithm application in LBR condition; and (d) algorithm application in RDR condition: r1, r2 and b denote the polar radius, radius and polar angle of the enveloping circle respectively.
Fig. 3. The applied experimental cutterhead system (1-the specimen box; 2-the cutterhead; 3-the supporting frame; 4-the main thrust cylinder; 5-the belt convey system; and 6-the control panel).
a total boring depth of 60 mm. This can provide enough experimental data and assure the safety since the concrete after four tests is thicker than 100 mm. In each boring test, the cutterhead was
firstly adjusted to assure that the distance between the cutter tip and the concrete sample surface was about 20 mm before the test started and let the cylinders and motors operated to a smooth state before the cutter tips contact the sample surface. The friction torque of the cutterhead was recorded from the control panel. When the cutters contact the sample surface, the cutting process begins and the cutterhead total torque is recorded. The cutterhead rock cutting torque can be obtained by subtracting the friction torque from the total torque. The total thrust was also recorded. Using the calculation model described in Section 2.1, the total rock cutting torque and thrust applied on the cutterhead in the four tests were respectively calculated. During the calculation, when the cutterhead rotated a complete revolution, 36 groups of data are obtained. The comparison of the experimental and calculated results is shown in Figs. 6 and 7. It can be seen in Fig. 6 that the experimental torque has larger variation than the calculated one. This is because that the rock was represented by concrete whose strength is not as uniform as intact rock. The comparison of the average experimental and calculated torque have values in better agreement. The errors are 10.7%, 1.6%, 9.3%, and 2.9% for penetrations of 3 mm/rev, 6 mm/rev, 9 mm/rev and 12 mm/rev
Please cite this article in press as: Geng, Q., et al. Mechanical performance of TBM cutterhead in mixed rock ground conditions. Tunnel. Underg. Space Technol. (2016), http://dx.doi.org/10.1016/j.tust.2016.02.012
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Fig. 4. (a) Layout of the disc cutters on the cutterhead and concrete in the rock box; and (b) rock face after boring.
Table 1 Layout of the disc cutters on the experimental cutterhead. Cutter number
Cutter coordinate (x, mm)
Cutter coordinate (y, mm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0 0 0 0 0 0 570 0 730 0 629.3 685.9 742.5 799
40 130 220 310 400 490 0 650 0 810 629.3 685.9 742.5 799
respectively. Fig. 7 illustrates the comparison of the experimental and calculated cutting thrust. It shows that the experimental thrust gives slightly higher values than the calculation results for the selected penetrations. This difference might be explained due to the fact that the thrust needed to push the cutterhead itself is
about 30 KN. The errors between the experimental and calculated average thrust are 3.8%, 3.4%, 3.1% and 3.6% for penetrations of 3 mm/rev, 6 mm/rev, 9 mm/rev and 12 mm/rev respectively. The discussed comparison validated the proposed calculation model.
3. Results and analysis 3.1. Influence of rock strength and area percentages of different layers (in two-layer LBR condition) The TBM cutterhead in West Qinling tunnel project was used to conduct the mechanical performance analysis. The influences of rock strength and area percentages of different rock layers were studied in two-layer LBR condition and the results are shown in Fig. 8. The ratio of the UCS value between soft rock and hard rock is defined as parameter a. For both, soft and hard rocks, their BTS values are defined as 1/10 of the UCS values. Parameter b stands for the area percentage of the soft rock on the tunnel face and is set to be 0.1, 0.3, 0.5, 0.7 and 0.9 in the calculations. Table 2 lists the parameters related to the cutterhead structure and disc cutters.
Fig. 5. Concrete samples (a) the sample box and the cubic samples of 100 ⁄ 100 ⁄ 100 mm; and (b) the standard cylinder samples with the diameter of 50 mm and length of 100 mm.
Fig. 6. Results comparison (a) cutterhead’s rock cutting torque with a penetration of 6 mm/rev; and (b) cutterhead’s average rock cutting torque with different penetrations.
Please cite this article in press as: Geng, Q., et al. Mechanical performance of TBM cutterhead in mixed rock ground conditions. Tunnel. Underg. Space Technol. (2016), http://dx.doi.org/10.1016/j.tust.2016.02.012
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Fig. 7. Comparison of the results (a) cutterhead rock cutting thrust with penetrations of 3 mm/rev and 9 mm/rev; and (b) cutterhead average rock cutting thrust with different penetrations.
Fig. 8. Cutterhead mechanical performance indexes in two-layer LBR condition (a) thrust f1; (b) torque f2; (c) eccentric moment f3; and (d) overturning moment f4.
Indexes f1 and f2 increase with parameter a and decrease with parameter b as shown in Fig. 8. This is because the rock cutting forces of each cutter increase when the strength of soft rock increases with parameter a, and the percentage of soft rock on the tunnel face increases with the parameter b. Indexes f3 and f4 decrease with parameter a since the strength difference between the hard and soft rocks decreases with a. For each parameter a, f3 and f4 reach their highest values when parameter b equals 0.5, and fall to their lowest when b is 0.1 or 0.9. This illustrates that the eccentric force and overturning moment are relatively high when the area percentages of soft and hard rocks are close to each other, which might produce damages in the cutterhead and even the main bearing. This situation should be avoided in tunnel projects by advance detection and analysis of the tunnel alignment design in advance.
Table 2 Parameters set for mixed ground considering the cutterhead and disc cutter. Parameters
Value
Cutterhead diameter (m) Cutterhead rotational speed (x, rev/min) Penetration (P, mm) Hard rock UCS (MPa) Hard rock BTS (MPa) Cutter radius (rc, mm) Cutter weight (mc, kg) Cutter tip width (T, mm) centre cutter amount Normal cutter amount Gage cutter amount centre cutter spacing (mm) Normal cutter spacing (mm)
10.23 6.6 6 150 15 241.3 200 20 8 49 11 100 76
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Fig. 9. Three-layer LBR condition analysis (a) the equal layer thickness; and (b) the equal area percentage.
3.2. Influence of different rock locations (in three-layer LBR condition) In order to study the influence of different rock locations, two calculation models of the three-layer LBR condition with equal layer thickness (ELT, Fig. 9a) and equal area percentage (EAP, Fig. 9b) were built, respectively. The layer thickness of Fig. 9a is 3410 mm, and the area of each layer in Fig. 9b is 27.38 m2. For each model, the calculations were conducted six times with the rock strength of each layer set as listed in Table 3. The indexes are shown in Fig. 10. As shown in Fig. 10a, the highest rock cutting thrust (f1) is in groups 3 and 4 in which the strongest rock is in the central layer (green layer) for both the ELT and the EAP models. Compared with this, it can be seen from Fig. 10a that the lowest f1 occurs in groups 2 and 5 in which the weakest rock was in the centre. Besides, the highest and lowest f1s for the ELT model are higher and lower than those of the EAP model, respectively. These results can be explained considering that most disc cutters are in the central layer (about 41 and 31 for the two models respectively as shown in Fig. 9a and b). The varying tendency of cutterhead cutting torque (f2) with the group number is generally the same to that of f1 for the ELT model. But for the EAP model, it is different that the highest f2 is in groups 2 and 5 while the lowest is in groups 3 and 4, though the difference between the highest and lowest f2s was not significant (only about 5.6% of the highest f2). This is because that f2 is determined by cutter rolling forces and polar radii together, as shown in Eq. (2). Even though there are more cutters in the green layer, their polar radii are generally smaller than those in the red or blue layers. As illustrated in Fig. 10c and d, the varying curves of f3 and f4 with the group number are like ditches. The highest f3 and f4 are in groups 1 and 6 in which the strongest and weakest rocks are in the side layers coloured red1 and blue, respectively. The lowest f3 and f4 occur in groups 3 and 4 where the strongest rock is in the central green layer. The values of f3 and f4 are a little higher for the EAP model than the ELT model since they are also related to the cutters’ polar radii as illustrated in Eqs. (1) and (2). It was also found that each index has generally the same value in groups 1 and 6, groups 2 and 5, groups 3 and 4 respectively. This is because that the rock types in the central layer are the same, and the influence of the side layers on the indexes is generally the same considering the tunnel face structure and cutter layout. The results illustrated that for TBM boring, the strongest rock layer should be planned in the middle of the tunnel face for
1 For interpretation of colour in Fig. 10, the reader is referred to the web version of this article.
Table 3 Rock strength set of each layer. Groups
1 2 3 4 5 6
Red layer
Green layer
Blue layer
UCS (MPa)
BTS (MPa)
UCS (MPa)
BTS (MPa)
UCS (MPa)
BTS (MPa)
200 200 100 50 100 50
20 20 10 5 10 5
100 50 200 200 50 100
10 5 20 20 5 10
50 100 50 100 200 200
5 10 5 10 20 20
better boring conditions of lower eccentric force and overturning moment. 3.3. Influence of the number of rock layers (in multi-layer LBR condition) The influence of the number of rock layers on cutterhead mechanical performance was studied in multi-layer LBR condition. As is illustrated in Fig. 11, the tunnel face is defined into 2–9 layers using the ELT model and each layer is numbered. Based on the conclusions drawn from Section 3.2, the influences of rock locations can be summarized into two types when the strongest rock is in the central or side layers. According to this, the rock strength of the multi-layer tunnel face was defined as two situations as shown in Fig. 12. The rock strength was defined mainly considering the UCS value, while the rock BTS value was calculated by dividing UCS by 10 according to experience. Fig. 12a illustrates that the UCS decreases evenly from the upper side layer of the tunnel face to the down side layer (UTD situation), and Fig. 12b illustrates that the UCS decreases from the central layer (CTS situation). The highest rock UCS is 200 MPa and the lowest is 20 MPa. The results of the performance indexes are shown in Fig. 13. It can be seen that f1 and f2 are higher while f3 and f4 are lower for the CTS situation than the UTD situation, respectively. This is because that for multi-layer conditions, more disc cutters were located in the layers closer to the cutterhead centre, as shown in Fig. 13, and the stronger rock in the centre can bring in lower eccentric force and overturning moment, as described in Section 3.2. f3 and f4 decrease dramatically from 2-layer condition to 3-layer (or 4-layer) condition and then generally keep stable. This illustrates that the adverse effects of eccentric loads will not increase with the number of rock layers. However, for tunnel projects, more layers may result in the instability of the tunnel face. As
Please cite this article in press as: Geng, Q., et al. Mechanical performance of TBM cutterhead in mixed rock ground conditions. Tunnel. Underg. Space Technol. (2016), http://dx.doi.org/10.1016/j.tust.2016.02.012
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Fig. 10. Cutterhead mechanical performance indexes in three-layer LBR condition (a) thrust f1; (b) torque f2; (c) eccentric moment f3; and (d) overturning moment f4.
Fig. 11. Schematic representation of the multi-layer LBR condition (a) 2 layers; (b) 3 layers; (c) 4 layers; (d) 5 layers; (e) 6 layers; (f) 7 layers; (g) 8 layers; and (h) 9 layers.
Fig. 12. Rock UCS definition of each layer for different layer conditions (a) rock UCS decrease from the side layer; and (b) rock UCS decrease from the central layer.
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Fig. 13. Cutterhead mechanical performance indicators in multi-layer LBR condition (a) thrust f1; (b) torque f2; (c) eccentric moment f3; and (d) overturning moment f4.
Fig. 14. Cutterhead mechanical performance indicators in RDR condition (a) thrust f1; (b) torque f2; (c) eccentric moment f3; and (d) overturning moment f4.
Please cite this article in press as: Geng, Q., et al. Mechanical performance of TBM cutterhead in mixed rock ground conditions. Tunnel. Underg. Space Technol. (2016), http://dx.doi.org/10.1016/j.tust.2016.02.012
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a result, the 3-layer or 4-layer situations are optimal considering the cutterhead mechanical performance and engineering practices. 3.4. Mechanical performance analysis in RDR condition As is illustrated in Section 2.1, the final mechanical performance indexes are the average values of each index during a revolution. As a result, influence of the enveloping circle’s (representing the inserted rock or cave on the tunnel face) polar angle (Fig. 2d) is not necessary to study. Setting the UCS of the rocks inside and outside the enveloping circle to be 200 MPa and 20 MPa respectively, the calculations were conducted by setting parameters r1 and r2 to be 1, 2, 3, 4 and 5 m respectively. Fig. 14a and b shows that f1 and f2 generally decrease with r1 and the changing speed increases with r2. This is because that the number of cutters in the enveloping circle decreases with the circle polar radius since the distribution density of the cutters on the cutterhead decreases with the polar radius. It is also shown that f1 and f2 increase with r2 since the rock inside the enveloping circle is defined to be hard rock. As illustrated in Fig. 14c and d, the highest f3 and f4 values generally occur when r1 is equal to r2. The values of f3 and f4 are relatively low when r2 is low. Fig. 14 shows the calculated results for the hard rock inserted RDR condition. For the hollow (or soft rock) inserted RDR condition, the only difference is that f1 and f2 generally increase with r1 and the results will not be discussed in detail. The analysis on the cutterhead mechanical performance suggests that in TBM tunnel projects, the inserted rocks or hollows should be planned closer to cutterhead centre by micro-adjusting the boring direction if the rocks or hollows are detected in advance. 4. Conclusions In the present paper, a calculation model has been built to study the mechanical performance of TBM cutterhead in mixed rock ground conditions using the ray intersection algorithm. The model has been verified to be feasible using a designed experiment in the three-layer LBR condition. The calculations were conducted in the (two-layer, three-layer and multi-layer) LBR and RDR conditions considering the rock strength, rock locations, area percentages of different rock layers and number of rock layers. The following conclusions were drawn. (1) For the two-layer LBR condition, the eccentric force and overturning moment are high when the percentages of soft and hard rocks are close to each other, which can produce damages in the cutterhead and main bearing. (2) For the three-layer and multi-layer LBR condition, lower eccentric force and overturning moment will be obtained if the strongest rock layer is in the middle of the tunnel face, though the cutterhead thrust and torque will be higher.
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(3) Three or four is the optimal layer number for multi-layer LBR condition considering the cutterhead eccentric loads and stability of the tunnel face. (4) For the RDR condition, the inserted rock or hollow should be arranged closer to the cutterhead centre, while the situation that the distance from the hollow (or inserted rock) centre to cutterhead centre equalling to the hollow radius should be avoided. The conclusions drawn from the calculation results revealed some preferred and adverse situations in mixed rock ground conditions considering cutterhead mechanical performance indexes and tunnel face stability. According to these suggestions, the tunnel line can be planed adaptively or micro-adjusted by controlling the TBM boring direction. This relies much on the distance and accuracy of the advance detection to the ground. Acknowledgment This work is supported by the Major State Basic Research Development Program of China (the 973 program) (Granted No. 2013CB035402). References Bruland, A., 2000. Hard rock tunnel boring. Geology and Site Investigations, vol. 5. Doctoral thesis. Chen, L., Liu, J., Wang, C., Liu, J., Su, R., Wang, J., 2014. Characterization of damage evolution in granite under compressive stress condition and its effect on permeability. Int. J. Rock Mech. Min. Sci. 71, 340–349. Darrag, A., 1999. Ground stabilization for tunnel construction in mixed-face conditions. Tunn. Undergr. Space Technol. 14, 319–326. Delisio, A., Zhao, J., Einstein, H., 2013. Analysis and prediction of TBM performance in blocky rock conditions at the Lötschberg base tunnel. Tunn. Undergr. Space Technol. 33, 131–142. Huang, C.-W., Shih, T.-Y., 1997. On the complexity of point-in-polygon algorithms. Comput. Geosci. 23, 109–118. Rostami, J., 2008. Hard rock TBM cutterhead modeling for design and performance prediction. Geomech. Tunnelling 1, 18–28. Steingrimsson, J., GRV, E., Nilsen, B., 2002. The significance of mixed-face conditions for TBM performance. Mixed Face TBM Performance. World Tunnelling, Sydney, pp. 435–441. Tóth, Á., Gong, Q., Zhao, J., 2013. Case studies of TBM tunneling performance in rock–soil interface mixed ground. Tunn. Undergr. Space Technol. 38, 140–150. Xiaoxing, Z., Haidong, Y., Hao, W., Xinmin, L., Kaizhi, Z., 2010. Equivalent load model on the cutterheads of TBM excavating in heterogeneous geologic strata. Rock Soil Mech. 31, 1199–1203. Xingjian, Z., Puqing, L., Fei, H., 2013. Development of TBM boring test bench. Tunnel Construction 33, 615–618 (in Chinese). Zhang, D.-M., Huang, H.-W., Hu, Q.-F., Jiang, F., 2015. Influence of multi-layered soil formation on shield tunnel lining behavior. Tunn. Undergr. Space Technol. 47, 123–135. Zhang, K., Yu, H., Liu, Z., Lai, X., 2010. Dynamic characteristic analysis of TBM tunnelling in mixed-face conditions. Simul. Model. Pract. Theory 18, 1019–1031. Zhao, J., Gong, Q.M., Eisensten, Z., 2007. Tunnelling through a frequently changing and mixed ground: a case history in Singapore. Tunn. Undergr. Space Technol. 22, 388–400. Zhongsheng, T., Kairong, H., Jianglin, W., Mengshu, W., 2006. Study on composite shield and construction technique in complex uneven strata. Chin. J. Rock Mech. Eng. 2, 3945–3952.
Please cite this article in press as: Geng, Q., et al. Mechanical performance of TBM cutterhead in mixed rock ground conditions. Tunnel. Underg. Space Technol. (2016), http://dx.doi.org/10.1016/j.tust.2016.02.012
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Mechanical performance of TBM cutterhead in mixed rock ground conditions Qi Geng a,⇑, Zhengying Wei a, Hao Meng a, Francisco Javier Macias b a b
School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, China Department of Civil and Transport Engineering, NTNU, Trondheim, Norway
a r t i c l e
i n f o
Article history: Received 12 September 2015 Received in revised form 22 February 2016 Accepted 22 February 2016 Available online xxxx Keywords: TBM tunnelling Mixed rock ground Ray intersection algorithm Experimental cutterhead
a b s t r a c t The mechanical performance of TBM cutterhead including thrust, torque, eccentric force and overturning moment was calculated and analysed in different mixed rock ground conditions. The calculation model was built by identifying the rock type under each cutter using a ray intersection algorithm and calculating the cutting forces of each cutter using the CSM model. The mixed rock ground conditions were simplified as rock type distribution and rock strength classification. In the present paper, the rock distributions of the Layer-Banded Rock (LBR) and Random-Distributed Rock (RDR) types were considered. The influences of rock strength (Uniaxial Compressive Strength: UCS, Brazilian Tensile Strength: BTS), rock locations and number of rock layers were studied. For verification, a boring experiment was designed and conducted using an experimental cutterhead with 14 disc cutters. The rock box was poured with concrete C20, C40 and C60 layer by layer to prepare the LBR condition. The average torque and thrust of the calculation model and experiment were in good agreement. Some conclusions were drawn from the study on the rock strength, rock locations, area percentages of different rock layers and number of rock layers. And hence, some suggestions were proposed to enhance the tunnelling efficiency and reduce damage to the cutterhead. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Mixed ground is one of the most difficult conditions for TBM tunnelling. Since tunnel alignment is often determined by practical engineering requirements rather than the ground conditions, TBMs often have to be driven in mixed ground conditions (Tóth et al., 2013). Even though many engineering problems have been encountered in these conditions (e.g. impact or eccentric loads), limited research has been conducted to study the influence mechanism of the mixed ground conditions on cutterhead mechanical performance. As a result, the study of cutterhead mechanical performance in mixed ground conditions is necessary to provide some precautions or suggestions for cutterhead design and TBM tunnelling. The mixed ground condition can be defined by the ratio of UCS between the weakest and the strongest rock layer of a maximum of 1:10 (Steingrimsson et al., 2002). Ground conditions can be classified into three types based on the geological formations of the tunnel face: the Rock–Soil Interface (RSI) mixed ground, the
⇑ Corresponding author.
Boulder–Soil Matrix (BSM) mixed ground and the Layer-Banded Rock (LBR) mixed ground (Tóth et al., 2013). The research topics on TBM tunnelling in mixed ground conditions can be divided into three types: TBM performance prediction, special construction techniques study and cutterhead mechanical performance study. Steingrimsson et al. (2002) assumed that the hard rock part controls the penetration rate in LBR conditions and introduced a correction factor kAB to access the net penetration rate (m/h) in mixed ground conditions using the NTNU prediction model (Bruland, 2000). Tóth et al. (2013) found the correction factor introduced by Steingrimsson et al. (2002) not suitable for RSI conditions in a specific case. Tóth et al. (2013) also analysed two cases of RSI conditions and proposed a correction factor based on variance and sensitivity analysis of mean penetration rate (mm/rev) for the soil and rock. Delisio et al. (2013) analysed the rock mass conditions and the TBM performance data of the Lotschberg Base Tunnel, and proposed a prediction model for blocky rock conditions introducing a relationship between the Field Penetration Index (FPI) and two rock mass parameters including the volumetric joint count and the UCS. Zhang et al. (2015) proposed a numerical model verified by some plane model tests, which can be used to study and predict the influence of multi-layered ground conditions
E-mail address: [email protected] (Q. Geng). http://dx.doi.org/10.1016/j.tust.2016.02.012 0886-7798/Ó 2016 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Geng, Q., et al. Mechanical performance of TBM cutterhead in mixed rock ground conditions. Tunnel. Underg. Space Technol. (2016), http://dx.doi.org/10.1016/j.tust.2016.02.012
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on lining behaviour. Special construction techniques and TBM modifications are needed to deal with problems encountered in mixed ground conditions. Modification of the cutterhead stiffness, combined use of disc cutters and drag bits in composite shield cutterhead and improvement of the soil flowability have been applied (Zhao et al., 2007; Zhongsheng et al., 2006). Regarding to ground stability problems at the tunnel face in heterogeneous ground conditions, Darrag (1999) proposed a solution to provide stability in tunnels excavated in mixed-ground conditions by using chemical grouting. In order to study the influencing mechanism of the mixed ground condition on cutterhead mechanical performance, several calculation models were built to predict cutterhead torque and thrust (Xiaoxing et al., 2010; Zhang et al., 2010). The existing calculation models mainly focused on LBR conditions without considering more complex tunnel face conditions. In the present paper, a calculation method has been proposed which can be used to calculate cutterhead mechanical performance including the torque, thrust, eccentric force and overturning moment in stable mixed ground conditions. The keys of the model are to identify the rock type under each individual cutter during the boring process and calculate its cutting forces. A ray intersection algorithm (Huang and Shih, 1997) was applied to determine the rock types and the Colorado School of Mines (CSM) model (Rostami, 2008) was used to calculate the cutter cutting forces in the cutterhead during boring. In order to verify the calculation model, a boring experiment was designed and conducted using an experimental cutterhead with 14 disc cutters (cutter diameter 17 in./432 mm) in the LBR condition. The model was applied for multi-layer LBR and RDR conditions.
2. Calculation models 2.1. Description of the calculation model Three mixed rock ground conditions are shown in Fig. 1. A typical LBR condition is illustrated in Fig. 1a, while Fig. 1b (rock inserted) and Fig. 1c (rock cave) can be classified as the RDR condition. In order to study cutterhead mechanical performance in these conditions, a calculation model using a ray intersection algorithm was proposed and illustrated in Fig. 2. The crucial issue of the model is to identify the rock type under each individual cutter during the boring process, which can be simplified as a mathematical problem of the ‘‘point-in-polygon” by regarding the disc cutters and rock zones as points and polygons, respectively. As is shown in Fig. 2b, when a point (p1) is inside the polygon, there will be odd number of intersection points between the polygon and the ray (l1) originating from the point (p1). However, when the point (p2) is outside the polygon, the number of the intersection points will be even. For the LBR condition, rock layers are simplified as enveloping rectangles (Fig. 2c); while for the RDR condition, inserted rocks or caves are simplified as enveloping circles (Figs. 1b, c and 2d). In order to improve the computing speed, a rotating speed with equal value but opposite to the cutterhead direction is used to the cutterhead and the tunnel face. This transforms the revolution of each disc cutter to the revolution of the rectangles or circles. The rock cutting forces including the normal (FN) and rolling forces (FR) of each cutter were calculated using the CSM force estimation formulas shown in Eq. (1). The centrifugal force (FE) was calculated based on classical mechanics. The side forces were ignored since they are relatively low compared with other forces according to Rostami (2008). Cutterhead mechanical performance indexes, including the thrust (f1), torque (f2), eccentric force (f3) and overturning moment (f4) were calculated using Eqs. (2)–(4). For the calculation of forces FX, FY, MX and MY, Eq. (3) was applied
for normal and centre cutters, and Eq. (4) was applied for the gage cutters. The performance indexes were calculated a total of 36 times during a revolution, with an interval of 10 angular degrees. Finally, the average values of these 36 groups were defined as the final mechanical performance indexes.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u 2 3 rc rt S pffiffiffiffiffiffiffi cos F N ¼ 2:12Trc u ; F R ¼ F N tan ; 2 2 u rc T rc P F E ¼ mc x2 r; u ¼ cos1 rc
ð1Þ
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 !2ffi u N N N N u X X X X FN ; f2 ¼ F Ri ri ; f 3 ¼ t F Xi þ F Yi ; f1 ¼ cos ci i¼1 i¼1 i¼1 i¼1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 !2 u N N u X X t ð2Þ f4 ¼ M Xi þ M Yi i¼1
i¼1
F X ¼ F R sin h þ F E cos h; F Y ¼ F R cos h þ F E sin h; MX ¼ F N r sin h; M Y ¼ F N r cos h
ð3Þ
F X ¼ F R sin h þ ðF E þ F N sin cÞ cos h;
F Y ¼ F R cos h þ ðF E þ F N sin cÞ sin h;
MX ¼ F N r sin h= cos c; MY ¼ F N r cos h= cos c
ð4Þ
where T denotes the cutter tip width (mm); u denotes the contact angle between the rock and disc cutter (rad); rc denotes the radius of the disc cutter (mm); mc denotes the weight of a disc cutter (kg); rc and rt denote the rock UCS and BTS respectively (MPa); S denotes the cutter spacing (mm); P denotes the penetration rate (mm/rev); x denotes the rotating speed of the cutterhead (rad/s); N denotes the number of the disc cutters; r, h and c denote the polar radius (m), polar angle (degree) and tilt angle (degree) of a disc cutter respectively. 2.2. Experimental verification of the calculation model In order to verify the model, a trial was designed using an experimental cutterhead system in the State Key Laboratory of Shield Machine and Boring Technology, Zhengzhou, China (Xingjian et al., 2013). The experimental system is mainly composed of a cutterhead, a rock box, a conveyor belt system and a control panel, as illustrated in Fig. 3. The cutterhead is mounted with 14 normal disc cutters (cutter diameter 17 in./432 mm). The cutter layout is illustrated in Fig. 4a and Table 1. The specimen box has an inner diameter of 2.5 m with a depth of 0.4 m. In order to prepare an LBR condition, three types of concretes, i.e. C20, C40 and C60 were poured into the specimen box layer by layer. The curing process of the concrete was assured, total of three weeks, to reach the highest strength for every concrete specification. The dimensions of different concrete samples were measured and illustrated in Fig. 4a. In order to test the concrete strength, the same grout was also used to obtain cubic concrete samples (Fig. 5a). The samples were then drilled into cylinders (Fig. 5b) for the UCS and BTS tests. These tests were conducted according to the Standard for Test Methods of Engineering Rock Mass in China (Chen et al., 2014). The tested UCS values are 18.9 MPa, 37.6 MPa and 58.4 MPa for the concretes C20, C40 and C60 respectively, and the BTS values are 1.7 MPa, 3.8 MPa and 5.6 MPa respectively. The boring experiments were conducted using one concrete sample for four times with penetrations of 3 mm/rev, 6 mm/rev, 9 mm/rev and 12 mm/rev respectively. Different penetrations can be achieved by controlling the advancing rate and the rotational speed of the propel cylinders and the driving motors, respectively. Each boring process with different penetrations was carried out for
Please cite this article in press as: Geng, Q., et al. Mechanical performance of TBM cutterhead in mixed rock ground conditions. Tunnel. Underg. Space Technol. (2016), http://dx.doi.org/10.1016/j.tust.2016.02.012
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Fig. 1. Rocks on possible tunnel face (a) Layer-Banded Rock mass; (b) different rock inserted; and (c) hollow in rock mass.
Fig. 2. The calculation model (a) schematic representation; (b) the ray intersection algorithm of the relationship between points and a polygon; (c) algorithm application in LBR condition; and (d) algorithm application in RDR condition: r1, r2 and b denote the polar radius, radius and polar angle of the enveloping circle respectively.
Fig. 3. The applied experimental cutterhead system (1-the specimen box; 2-the cutterhead; 3-the supporting frame; 4-the main thrust cylinder; 5-the belt convey system; and 6-the control panel).
a total boring depth of 60 mm. This can provide enough experimental data and assure the safety since the concrete after four tests is thicker than 100 mm. In each boring test, the cutterhead was
firstly adjusted to assure that the distance between the cutter tip and the concrete sample surface was about 20 mm before the test started and let the cylinders and motors operated to a smooth state before the cutter tips contact the sample surface. The friction torque of the cutterhead was recorded from the control panel. When the cutters contact the sample surface, the cutting process begins and the cutterhead total torque is recorded. The cutterhead rock cutting torque can be obtained by subtracting the friction torque from the total torque. The total thrust was also recorded. Using the calculation model described in Section 2.1, the total rock cutting torque and thrust applied on the cutterhead in the four tests were respectively calculated. During the calculation, when the cutterhead rotated a complete revolution, 36 groups of data are obtained. The comparison of the experimental and calculated results is shown in Figs. 6 and 7. It can be seen in Fig. 6 that the experimental torque has larger variation than the calculated one. This is because that the rock was represented by concrete whose strength is not as uniform as intact rock. The comparison of the average experimental and calculated torque have values in better agreement. The errors are 10.7%, 1.6%, 9.3%, and 2.9% for penetrations of 3 mm/rev, 6 mm/rev, 9 mm/rev and 12 mm/rev
Please cite this article in press as: Geng, Q., et al. Mechanical performance of TBM cutterhead in mixed rock ground conditions. Tunnel. Underg. Space Technol. (2016), http://dx.doi.org/10.1016/j.tust.2016.02.012
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Fig. 4. (a) Layout of the disc cutters on the cutterhead and concrete in the rock box; and (b) rock face after boring.
Table 1 Layout of the disc cutters on the experimental cutterhead. Cutter number
Cutter coordinate (x, mm)
Cutter coordinate (y, mm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0 0 0 0 0 0 570 0 730 0 629.3 685.9 742.5 799
40 130 220 310 400 490 0 650 0 810 629.3 685.9 742.5 799
respectively. Fig. 7 illustrates the comparison of the experimental and calculated cutting thrust. It shows that the experimental thrust gives slightly higher values than the calculation results for the selected penetrations. This difference might be explained due to the fact that the thrust needed to push the cutterhead itself is
about 30 KN. The errors between the experimental and calculated average thrust are 3.8%, 3.4%, 3.1% and 3.6% for penetrations of 3 mm/rev, 6 mm/rev, 9 mm/rev and 12 mm/rev respectively. The discussed comparison validated the proposed calculation model.
3. Results and analysis 3.1. Influence of rock strength and area percentages of different layers (in two-layer LBR condition) The TBM cutterhead in West Qinling tunnel project was used to conduct the mechanical performance analysis. The influences of rock strength and area percentages of different rock layers were studied in two-layer LBR condition and the results are shown in Fig. 8. The ratio of the UCS value between soft rock and hard rock is defined as parameter a. For both, soft and hard rocks, their BTS values are defined as 1/10 of the UCS values. Parameter b stands for the area percentage of the soft rock on the tunnel face and is set to be 0.1, 0.3, 0.5, 0.7 and 0.9 in the calculations. Table 2 lists the parameters related to the cutterhead structure and disc cutters.
Fig. 5. Concrete samples (a) the sample box and the cubic samples of 100 ⁄ 100 ⁄ 100 mm; and (b) the standard cylinder samples with the diameter of 50 mm and length of 100 mm.
Fig. 6. Results comparison (a) cutterhead’s rock cutting torque with a penetration of 6 mm/rev; and (b) cutterhead’s average rock cutting torque with different penetrations.
Please cite this article in press as: Geng, Q., et al. Mechanical performance of TBM cutterhead in mixed rock ground conditions. Tunnel. Underg. Space Technol. (2016), http://dx.doi.org/10.1016/j.tust.2016.02.012
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Fig. 7. Comparison of the results (a) cutterhead rock cutting thrust with penetrations of 3 mm/rev and 9 mm/rev; and (b) cutterhead average rock cutting thrust with different penetrations.
Fig. 8. Cutterhead mechanical performance indexes in two-layer LBR condition (a) thrust f1; (b) torque f2; (c) eccentric moment f3; and (d) overturning moment f4.
Indexes f1 and f2 increase with parameter a and decrease with parameter b as shown in Fig. 8. This is because the rock cutting forces of each cutter increase when the strength of soft rock increases with parameter a, and the percentage of soft rock on the tunnel face increases with the parameter b. Indexes f3 and f4 decrease with parameter a since the strength difference between the hard and soft rocks decreases with a. For each parameter a, f3 and f4 reach their highest values when parameter b equals 0.5, and fall to their lowest when b is 0.1 or 0.9. This illustrates that the eccentric force and overturning moment are relatively high when the area percentages of soft and hard rocks are close to each other, which might produce damages in the cutterhead and even the main bearing. This situation should be avoided in tunnel projects by advance detection and analysis of the tunnel alignment design in advance.
Table 2 Parameters set for mixed ground considering the cutterhead and disc cutter. Parameters
Value
Cutterhead diameter (m) Cutterhead rotational speed (x, rev/min) Penetration (P, mm) Hard rock UCS (MPa) Hard rock BTS (MPa) Cutter radius (rc, mm) Cutter weight (mc, kg) Cutter tip width (T, mm) centre cutter amount Normal cutter amount Gage cutter amount centre cutter spacing (mm) Normal cutter spacing (mm)
10.23 6.6 6 150 15 241.3 200 20 8 49 11 100 76
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Fig. 9. Three-layer LBR condition analysis (a) the equal layer thickness; and (b) the equal area percentage.
3.2. Influence of different rock locations (in three-layer LBR condition) In order to study the influence of different rock locations, two calculation models of the three-layer LBR condition with equal layer thickness (ELT, Fig. 9a) and equal area percentage (EAP, Fig. 9b) were built, respectively. The layer thickness of Fig. 9a is 3410 mm, and the area of each layer in Fig. 9b is 27.38 m2. For each model, the calculations were conducted six times with the rock strength of each layer set as listed in Table 3. The indexes are shown in Fig. 10. As shown in Fig. 10a, the highest rock cutting thrust (f1) is in groups 3 and 4 in which the strongest rock is in the central layer (green layer) for both the ELT and the EAP models. Compared with this, it can be seen from Fig. 10a that the lowest f1 occurs in groups 2 and 5 in which the weakest rock was in the centre. Besides, the highest and lowest f1s for the ELT model are higher and lower than those of the EAP model, respectively. These results can be explained considering that most disc cutters are in the central layer (about 41 and 31 for the two models respectively as shown in Fig. 9a and b). The varying tendency of cutterhead cutting torque (f2) with the group number is generally the same to that of f1 for the ELT model. But for the EAP model, it is different that the highest f2 is in groups 2 and 5 while the lowest is in groups 3 and 4, though the difference between the highest and lowest f2s was not significant (only about 5.6% of the highest f2). This is because that f2 is determined by cutter rolling forces and polar radii together, as shown in Eq. (2). Even though there are more cutters in the green layer, their polar radii are generally smaller than those in the red or blue layers. As illustrated in Fig. 10c and d, the varying curves of f3 and f4 with the group number are like ditches. The highest f3 and f4 are in groups 1 and 6 in which the strongest and weakest rocks are in the side layers coloured red1 and blue, respectively. The lowest f3 and f4 occur in groups 3 and 4 where the strongest rock is in the central green layer. The values of f3 and f4 are a little higher for the EAP model than the ELT model since they are also related to the cutters’ polar radii as illustrated in Eqs. (1) and (2). It was also found that each index has generally the same value in groups 1 and 6, groups 2 and 5, groups 3 and 4 respectively. This is because that the rock types in the central layer are the same, and the influence of the side layers on the indexes is generally the same considering the tunnel face structure and cutter layout. The results illustrated that for TBM boring, the strongest rock layer should be planned in the middle of the tunnel face for
1 For interpretation of colour in Fig. 10, the reader is referred to the web version of this article.
Table 3 Rock strength set of each layer. Groups
1 2 3 4 5 6
Red layer
Green layer
Blue layer
UCS (MPa)
BTS (MPa)
UCS (MPa)
BTS (MPa)
UCS (MPa)
BTS (MPa)
200 200 100 50 100 50
20 20 10 5 10 5
100 50 200 200 50 100
10 5 20 20 5 10
50 100 50 100 200 200
5 10 5 10 20 20
better boring conditions of lower eccentric force and overturning moment. 3.3. Influence of the number of rock layers (in multi-layer LBR condition) The influence of the number of rock layers on cutterhead mechanical performance was studied in multi-layer LBR condition. As is illustrated in Fig. 11, the tunnel face is defined into 2–9 layers using the ELT model and each layer is numbered. Based on the conclusions drawn from Section 3.2, the influences of rock locations can be summarized into two types when the strongest rock is in the central or side layers. According to this, the rock strength of the multi-layer tunnel face was defined as two situations as shown in Fig. 12. The rock strength was defined mainly considering the UCS value, while the rock BTS value was calculated by dividing UCS by 10 according to experience. Fig. 12a illustrates that the UCS decreases evenly from the upper side layer of the tunnel face to the down side layer (UTD situation), and Fig. 12b illustrates that the UCS decreases from the central layer (CTS situation). The highest rock UCS is 200 MPa and the lowest is 20 MPa. The results of the performance indexes are shown in Fig. 13. It can be seen that f1 and f2 are higher while f3 and f4 are lower for the CTS situation than the UTD situation, respectively. This is because that for multi-layer conditions, more disc cutters were located in the layers closer to the cutterhead centre, as shown in Fig. 13, and the stronger rock in the centre can bring in lower eccentric force and overturning moment, as described in Section 3.2. f3 and f4 decrease dramatically from 2-layer condition to 3-layer (or 4-layer) condition and then generally keep stable. This illustrates that the adverse effects of eccentric loads will not increase with the number of rock layers. However, for tunnel projects, more layers may result in the instability of the tunnel face. As
Please cite this article in press as: Geng, Q., et al. Mechanical performance of TBM cutterhead in mixed rock ground conditions. Tunnel. Underg. Space Technol. (2016), http://dx.doi.org/10.1016/j.tust.2016.02.012
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Fig. 10. Cutterhead mechanical performance indexes in three-layer LBR condition (a) thrust f1; (b) torque f2; (c) eccentric moment f3; and (d) overturning moment f4.
Fig. 11. Schematic representation of the multi-layer LBR condition (a) 2 layers; (b) 3 layers; (c) 4 layers; (d) 5 layers; (e) 6 layers; (f) 7 layers; (g) 8 layers; and (h) 9 layers.
Fig. 12. Rock UCS definition of each layer for different layer conditions (a) rock UCS decrease from the side layer; and (b) rock UCS decrease from the central layer.
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Fig. 13. Cutterhead mechanical performance indicators in multi-layer LBR condition (a) thrust f1; (b) torque f2; (c) eccentric moment f3; and (d) overturning moment f4.
Fig. 14. Cutterhead mechanical performance indicators in RDR condition (a) thrust f1; (b) torque f2; (c) eccentric moment f3; and (d) overturning moment f4.
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a result, the 3-layer or 4-layer situations are optimal considering the cutterhead mechanical performance and engineering practices. 3.4. Mechanical performance analysis in RDR condition As is illustrated in Section 2.1, the final mechanical performance indexes are the average values of each index during a revolution. As a result, influence of the enveloping circle’s (representing the inserted rock or cave on the tunnel face) polar angle (Fig. 2d) is not necessary to study. Setting the UCS of the rocks inside and outside the enveloping circle to be 200 MPa and 20 MPa respectively, the calculations were conducted by setting parameters r1 and r2 to be 1, 2, 3, 4 and 5 m respectively. Fig. 14a and b shows that f1 and f2 generally decrease with r1 and the changing speed increases with r2. This is because that the number of cutters in the enveloping circle decreases with the circle polar radius since the distribution density of the cutters on the cutterhead decreases with the polar radius. It is also shown that f1 and f2 increase with r2 since the rock inside the enveloping circle is defined to be hard rock. As illustrated in Fig. 14c and d, the highest f3 and f4 values generally occur when r1 is equal to r2. The values of f3 and f4 are relatively low when r2 is low. Fig. 14 shows the calculated results for the hard rock inserted RDR condition. For the hollow (or soft rock) inserted RDR condition, the only difference is that f1 and f2 generally increase with r1 and the results will not be discussed in detail. The analysis on the cutterhead mechanical performance suggests that in TBM tunnel projects, the inserted rocks or hollows should be planned closer to cutterhead centre by micro-adjusting the boring direction if the rocks or hollows are detected in advance. 4. Conclusions In the present paper, a calculation model has been built to study the mechanical performance of TBM cutterhead in mixed rock ground conditions using the ray intersection algorithm. The model has been verified to be feasible using a designed experiment in the three-layer LBR condition. The calculations were conducted in the (two-layer, three-layer and multi-layer) LBR and RDR conditions considering the rock strength, rock locations, area percentages of different rock layers and number of rock layers. The following conclusions were drawn. (1) For the two-layer LBR condition, the eccentric force and overturning moment are high when the percentages of soft and hard rocks are close to each other, which can produce damages in the cutterhead and main bearing. (2) For the three-layer and multi-layer LBR condition, lower eccentric force and overturning moment will be obtained if the strongest rock layer is in the middle of the tunnel face, though the cutterhead thrust and torque will be higher.
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(3) Three or four is the optimal layer number for multi-layer LBR condition considering the cutterhead eccentric loads and stability of the tunnel face. (4) For the RDR condition, the inserted rock or hollow should be arranged closer to the cutterhead centre, while the situation that the distance from the hollow (or inserted rock) centre to cutterhead centre equalling to the hollow radius should be avoided. The conclusions drawn from the calculation results revealed some preferred and adverse situations in mixed rock ground conditions considering cutterhead mechanical performance indexes and tunnel face stability. According to these suggestions, the tunnel line can be planed adaptively or micro-adjusted by controlling the TBM boring direction. This relies much on the distance and accuracy of the advance detection to the ground. Acknowledgment This work is supported by the Major State Basic Research Development Program of China (the 973 program) (Granted No. 2013CB035402). References Bruland, A., 2000. Hard rock tunnel boring. Geology and Site Investigations, vol. 5. Doctoral thesis. Chen, L., Liu, J., Wang, C., Liu, J., Su, R., Wang, J., 2014. Characterization of damage evolution in granite under compressive stress condition and its effect on permeability. Int. J. Rock Mech. Min. Sci. 71, 340–349. Darrag, A., 1999. Ground stabilization for tunnel construction in mixed-face conditions. Tunn. Undergr. Space Technol. 14, 319–326. Delisio, A., Zhao, J., Einstein, H., 2013. Analysis and prediction of TBM performance in blocky rock conditions at the Lötschberg base tunnel. Tunn. Undergr. Space Technol. 33, 131–142. Huang, C.-W., Shih, T.-Y., 1997. On the complexity of point-in-polygon algorithms. Comput. Geosci. 23, 109–118. Rostami, J., 2008. Hard rock TBM cutterhead modeling for design and performance prediction. Geomech. Tunnelling 1, 18–28. Steingrimsson, J., GRV, E., Nilsen, B., 2002. The significance of mixed-face conditions for TBM performance. Mixed Face TBM Performance. World Tunnelling, Sydney, pp. 435–441. Tóth, Á., Gong, Q., Zhao, J., 2013. Case studies of TBM tunneling performance in rock–soil interface mixed ground. Tunn. Undergr. Space Technol. 38, 140–150. Xiaoxing, Z., Haidong, Y., Hao, W., Xinmin, L., Kaizhi, Z., 2010. Equivalent load model on the cutterheads of TBM excavating in heterogeneous geologic strata. Rock Soil Mech. 31, 1199–1203. Xingjian, Z., Puqing, L., Fei, H., 2013. Development of TBM boring test bench. Tunnel Construction 33, 615–618 (in Chinese). Zhang, D.-M., Huang, H.-W., Hu, Q.-F., Jiang, F., 2015. Influence of multi-layered soil formation on shield tunnel lining behavior. Tunn. Undergr. Space Technol. 47, 123–135. Zhang, K., Yu, H., Liu, Z., Lai, X., 2010. Dynamic characteristic analysis of TBM tunnelling in mixed-face conditions. Simul. Model. Pract. Theory 18, 1019–1031. Zhao, J., Gong, Q.M., Eisensten, Z., 2007. Tunnelling through a frequently changing and mixed ground: a case history in Singapore. Tunn. Undergr. Space Technol. 22, 388–400. Zhongsheng, T., Kairong, H., Jianglin, W., Mengshu, W., 2006. Study on composite shield and construction technique in complex uneven strata. Chin. J. Rock Mech. Eng. 2, 3945–3952.
Please cite this article in press as: Geng, Q., et al. Mechanical performance of TBM cutterhead in mixed rock ground conditions. Tunnel. Underg. Space Technol. (2016), http://dx.doi.org/10.1016/j.tust.2016.02.012