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Effects of the ring-cut method as a settlement deterrent in a soft ground tunnel
Tunnelling and Underground Space Technology 28 (2012) 90–97
Contents lists available at SciVerse ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Effects of the ring-cut method as a settlement deterrent in a soft ground tunnel Masayasu Hisatake ⇑, Shiro Ohno, Tatsuaki Katayama, Yukihiro Ohmae Department of Civil and Environmental Engineering, Faculty of Science and Engineering, Kinki University, Kowakae 3-4-1, Higashi-Osaka, Osaka 577-8502, Japan
a r t i c l e
i n f o
Article history: Received 14 January 2011 Received in revised form 15 September 2011 Accepted 26 September 2011 Available online 3 November 2011 Keywords: Settlements Centrifugal model tests Excavation robot Excavation method 3D-FEM
a b s t r a c t This paper presents the results of centrifugal model tests and three-dimensional elasto-plastic finite element analyses carried out to clarify the effects of the ring-cut method on the restraint of the ground settlements ahead of a tunnel face. A model tunnel is excavated in a soft ground by a robot under a centrifugal loading state, and the ground settlements are measured during the progress of the face by a picture analysis system with high accuracy. The settlements generated by the full-face excavation method are compared with those generated by the ring-cut method for two kinds of grounds with different mechanical properties. The maximum settlement caused by the ring-cut method becomes about 36% of that caused by the full-face excavation method for the ground with low strength and about 58% for the ground with high strength. Considerations regarding these phenomena are given by conducting threedimensional elasto-plastic finite element analyses. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Recently, the New Austrian Tunneling Method (NATM) has been adopted for the construction of urban tunnels in soft grounds with shallow depths. The reason for the adoption of NATM is mainly the low cost of tunnel construction in comparison with the shield tunneling method and its flexible application to several types of ground conditions. Settlements generated by tunnel construction in a soft ground may cause serious damage to nearby structures and existing services. The construction environment of tunneling beneath urban areas is becoming increasingly severe. Since a significant amount of disturbance is induced ahead of the excavation front (Farias et al., 2004), the stability of the face and the restriction of the ground settlements ahead of the face should be achieved during construction. For this purpose, certain auxiliary methods, such as pipe roof supports, face bolting, umbrella vaults, and so on, are often applied at the face (ITA Working Group ‘‘Research’’, 2007). Bernaud et al. (2009) investigated the state of reinforcement by horizontal anchors installed ahead of the excavation face. Shin et al. (2008) performed a series of large-scale model experiments for a pipe-reinforced tunnel heading in granular soil. Aksoy and Onargan (2010) studied the effect of umbrella arch and face bolt applications as settlement deterrents using a numerical analysis and in situ measurements at Izmir Metro, Turkey. The application of auxiliary methods is effective for difficult ground conditions in limiting ground settlements; however, it is obvious that the application of auxiliary methods, ⇑ Corresponding author. Tel.: +81 6 6721 2332; fax: +81 6 6730 1320. E-mail address: [email protected] (M. Hisatake). 0886-7798/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2011.09.008
such as the umbrella arch method, involves extra costs (Ocak, 2008). In order to conduct NATM economically, the ring-cut method is often adopted in urban areas where difficult ground conditions exist. The ring-cut method does not require any additional assistance, and it can be expected to increase the stability of the face and decrease the settlements ahead of the face. When the ringcut method is adopted, the elucidation of the displacement outbreak characteristics of the face front ground has been performed by Yoo (2009). He conducted elasto-plastic 3D finite element analyses of the performance of a multi-faced NATM tunneling work in a soft ground, and showed the effect of the ring-cut method on the settlement outbreak characteristics. Soft grounds are likely to show such mechanical characteristics as nonlinearity and the confining pressure dependency of stress–strain relationships, which affect the values of the ground settlements. An appropriate constitutive model is of the utmost importance for a proper displacement prediction (Farias et al., 2004). Since centrifugal model tests can take into account the above-mentioned mechanical characteristics, the tests are expected to enable the effective grasping of the outbreak mechanism of settlements. Hisatake and Ohno (2008) conducted centrifugal model tests to clarify the effects of the ring-cut method combined with pipe roof supports on the decrease in displacements at the face front ground. Hisatake et al. (2009) investigated the effects of the ring-cut method itself on the decrease in settlements and the increase in face stability by centrifugal model tests. In this study, three-dimensional elasto-plastic finite element analyses were also conducted for experimental grounds, which showed that a plastic region was not produced at the face. If the stress
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conditions at the face reach the failure criterion, the effectiveness of the ring-cut method to decrease settlements may be different from that obtained by Hisatake et al. (2009). In order to clarify this point experimentally, centrifugal model tests are conducted in this study with an excavation robot for two kinds of grounds with different constitutive conditions. The quantity of the subsidence caused by the full-face excavation method is compared with that caused by the ring-cut method. Supplemental numerical analyses of the three-dimensional elasto-plastic finite element method are also performed for the experimental grounds, and the effect of the ring-cut method as a subsidence deterrent is examined. Fig. 1. Deviator stress (r1–r3)-axial strain (e) relationships for Case 1.
2. Centrifugal model experiments 2.1. Experimental system The devices employed in the centrifugal model experiments, namely, an excavation robot controlled by computer programs and a picture analysis system for measuring settlements, are the same ones that have already been used (Hisatake and Ohno, 2008; Hisatake et al., 2009).
2.2. Experimental conditions Fig. 2. Deviator stress (r1–r3)-axial strain (e) relationships for Case 2.
The experimental grounds which are not in situ grounds are prepared by the compaction method; they are made of silica sand, cement, kaolin, and water. The composition ratios of the experimental ground materials are shown in Table 1. Two kinds of care periods, 2 days and 4 days, are used for making the experimental grounds with different mechanical characteristics. The stress– strain relationships for each case are indicated in Figs. 1 and 2; they show strongly confining pressure dependency and nonlinearity. The strength characteristics of the two grounds are indicated in Figs. 3 and 4. Adhesive strength c and internal friction angle / are determined as shown in Figs. 3 and 4, and the ground density and strength characteristics are summarized in Table 2.
2.3. Experimental procedure The grounds are made in a soil tank and are set up in the centrifugal device after the predetermined care periods. The tunnel excavation is performed by the robot under a centrifugal acceleration of 36 G (G: gravity acceleration). The quantity of the subsidence during the excavation is measured by a picture analysis system (Hisatake and Ohno, 2008). This experiment considers the geometrical symmetry for the vertically longitudinal section through the tunnel center, and a half section of the tunnel ground is used. The ground observation positions for each case are different just a little, and those in Cases 1 and 2 are shown in Figs. 5 and 6, respectively. The measurement points, ‘‘a’’, ‘‘b’’, ‘‘c’’, and ‘‘d’’, are located 10 mm above the horizontal line through the tunnel crown from the tunnel portal.
Table 1 Composition ratios of experimental ground. Materials
Mass (g)
Composition ratios (%)
Silica (No. 5) Kaolin Cement Water
19,000 1000 187.5 600
91.4 4.8 0.90 2.90
2.4. Excavation methods Two kinds of excavation methods, the full-face excavation method and the ring-cut method, are adopted to examine the effect of the ring-cut method in decreasing the subsidence. 2.4.1. Full-face excavation method The ground is excavated from the portal with a full-face excavation, 5 mm at a time, in the order of r, s, and t, as shown in Fig. 7. These excavations are repeated eight times, so that the total excavation depth becomes 40 mm. The geometrical relationship for the full-face excavation is shown in Fig. 8a. 2.4.2. Ring-cut method Procedure r, with the excavation depth of 5 mm, is repeated eight times, so that the total excavation depth becomes 40 mm. The ground is excavated in the shape of a ring-cut section, and the core is left at the tunnel center. The ring-cut area is about 55% of the full-face excavation area; therefore, the area of the core that remains is about 45% (Yoo, 2009). The geometrical relationship for the ring cut is shown in Fig. 8b. 3. Experimental results and considerations 3.1. The difference in the subsidence characteristics due to the difference in the excavation methods 3.1.1. Case 1 The quantities of the subsidence caused by the full-face excavation and the ring cut are compared in Fig. 9. The change in subsidence by the excavation progress at measurement point ‘‘a’’ in Fig. 5 is shown in Fig. 9a. The quantity of the final subsidence by the ring cut is about 40% of that by the full-face excavation, so that a large effect in decreasing the subsidence can be recognized by the existence of the core.
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400
c
16kPa 36.7
100
200
τ (kPa)
300
200
100
0 0
300
400
500
600
700
800
900
1000
800
900
1000
σ (kPa) Fig. 3. Strength characteristics of the ground in Case 1.
400
c
25kPa 38.6
τ (kPa)
300
200
100
0 0
100
200
300
400
500
600
700
σ (kPa) Fig. 4. Strength characteristics of the ground in Case 2.
Table 2 Density and strength characteristics of applied ground.
119mm
Parameters
Case 1
Case 2
Unit
Care period Density q Cohesion C Angle of internal friction /
2 1.63 16 36.7
4 1.63 25 38.6
days g/cm3 kPa Degree
91mm 102mm
Ground height 252mm
Tunnel height 68.9mm
115mm
64mm
a
36mm
b
c
d
Distance between measurement points and tunnel crown is 10mm.
90mm 102mm
a
Ground height 252mm
81.1mm
65mm 40mm
b
c
d
Tunnel
Fig. 6. Measurement points for Case 2.
height 68.9mm
Distance between measurement points and tunnel crown is 10mm.
81.1mm
at measurement points ‘‘c’’ and ‘‘d’’ by the ring cut are about 15% and 10% of those by the full-face excavation, respectively. The quantities of the final subsidence by the ring cut are very small compared to those by the full-face excavation, when the measuring points are more distant from the face than the tunnel height.
Fig. 5. Measurement points for Case 1.
The settlements at measurement point ‘‘b’’ are shown in Fig. 9b. The quantity of the final subsidence by the ring cut is about 43% of that by the full-face excavation. The settlements at measurement points ‘‘c’’ and ‘‘d’’ are shown in Figs. 9c and d, respectively. The quantities of the final subsidence
3.1.2. Case 2 The quantities of the subsidence caused by the full-face excavation and the ring cut are compared in Fig. 10. The change in subsidence by the excavation progress at measurement point ‘‘a’’ in Fig. 6 is shown in Fig. 10a. Measurement point ‘‘a’’ exists 36 mm from the tunnel portal and the excavation is performed up to
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(a) Measurement point a (40mm from entrance)
Fig. 7. Figure showing excavation process.
(b) Measurement point b (65mm from entrance)
Fig. 8. Excavation regions of full-face excavation and ring-cut methods.
40 mm; thus, the face goes beyond measurement point ‘‘a’’. When the face reaches the final excavation distance, the quantity of the subsidence by the ring cut shows a value considerably close to that by the full-face excavation. When measurement point ‘‘a’’ is located ahead of the face, the effect by the core as a subsidence deterrent can be recognized, but the effect cannot be expected after the face passes measurement point ‘‘a’’. When the face reaches almost directly under measurement point ‘‘a’’, the quantity of the subsidence by the ring cut is about 79% of that by the fullface excavation. In other words, the effect of the ring cut as a subsidence deterrent in Case 2 is almost half of that in Case 1. It can be understood that the effect in Case 2 deteriorates greatly. The subsidence at measurement point ‘‘b’’ is shown in Fig. 10b. The quantity of the final subsidence by the ring cut is about 73% of that by the full-face excavation. The effect of the ring cut as a subsidence deterrent in Case 2 (73%) deteriorates in comparison with that in Case 1 (43%), as shown in Fig. 9b. The subsidence at measurement points ‘‘c’’ and ‘‘d’’ is shown in Figs. 10c and d, respectively. The final subsidence at measurement points ‘‘c’’ and ‘‘d’’ by the ring cut is about 54% and 63% of that by the full-face excavation, respectively.
(c) Measurement point c (90mm from entrance)
(d) Measurement point d (115mm from entrance) Fig. 9. Settlement characteristics by excavation progress in Case 1.
a subsidence deterrent is defined by Eq. (1), in order to clarify the effect quantitatively.
R¼
Uf Ur 100 % Uf
ð1Þ
3.2. Effect of the ring cut as a subsidence deterrent The final subsidence at the respective measurement points by the ring cut has been compared with that by the full-face excavation as shown in Section 3.1. In the following, the effect of the ring cut (R) as
where Uf: final subsidence by the full-face excavation, Ur: final subsidence by the ring cut The effect (R) as a subsidence deterrent is shown in Fig. 11. The value of R in Case 1 with low strength is larger than that in Case 2
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(a) Measurement point a (36mm from entrance) Fig. 11. Effect of ring cut ‘R’ as a subsidence deterrent defined by Eq. (1).
(b) Measurement point b (64mm from entrance)
Fig. 12. Non-dimensional settlements at measurement point d in Case 1. (Settlements are divided by the maximum settlement caused by the full-face excavation.)
(c) Measurement point c (91mm from entrance)
(d) Measurement point d (119mm from entrance)
progress of the face and the effect of the ring cut as a subsidence deterrent can be clarified from these results. Figs. 12 and 13 show the relationships between the subsidence at point ‘‘d’’ and the distance between the face and measurement point ‘‘d’’ for Cases 1 and 2, respectively. The horizontal and the vertical axes are shown in non-dimensional forms divided by the tunnel height and by the maximum subsidence caused by the full-face excavation, respectively. Fig. 12 (Case 1) shows that the maximum subsidence ratio by the ring cut is about 36% of that by the full-face excavation, and that the subsidence hardly occurs until the distance between the face and the measurement point reaches the tunnel height. The ground movement caused by the ring cut is greatly reduced in Case 1. Fig. 13 (Case 2) shows that the maximum subsidence ratio by the ring cut is about 58% of that by the full-face excavation. The abovementioned results indicate that the effect of the ring cut, as a subsidence deterrent, changes with the difference in the mechanical characteristics of the ground.
Fig. 10. Settlement characteristics by excavation progress in Case 2.
with high strength. In addition, the value of R is large at the measurement points which are farther from the portal.
3.3. Variation in maximum settlements due to the difference in excavation methods When the face reaches the position directly below measurement point ‘‘d’’, the quantity of the subsidence at point ‘‘d’’ can be calculated by accumulating the absolute subsidence measured at respective measurement points ‘‘a’’, ‘‘b’’, ‘‘c’’, and ‘‘d’’ (Hisatake et al., 2009). The tendency of the subsidence caused by the
4. Considerations by three-dimensional elasto-plastic finite element analyses Three-dimensional elasto-plastic finite element analyses are conducted and several considerations are added. The analytical input values, determined in reference to the results of the tri-axial compression tests, are shown in Table 3. The ground is supposed to be a complete elasto-plastic material conforming to the Mohr– Coulomb failure criterion together with the associated flow rule. The value of the modulus of elasticity in Table 3 is determined by the deformation coefficient in tri-axial compression tests with the confining pressure that corresponds to the horizontal stress at the tunnel center before the tunnel is excavated. Excavation
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Non-dimensional settlements
the core stabilizes the face and restrains the subsidence of the face front ground. Fig. 16 shows the analytical results for the ground conditions in Case 2. The plastic regions produced by the full-face excavation can be seen in the lower part of the ground behind the face, but not at the face (Fig. 16a). In addition, the plastic regions produced by the ring cut occur lightly in part of the core, but they do not occur elsewhere (Fig. 16b). In brief, plastic regions do not occur at the face front ground in the full-face excavation, and the effect of the core in suppressing the outbreak of plastic regions cannot be expected because the ground has sufficient strength. 4.2. Effects of the deformation coefficient on subsidence
Fig. 13. Non-dimensional settlements at measurement point d in Case 2. (Settlements are divided by the maximum settlement caused by the full-face excavation.)
Table 3 Values of ground parameters used in FEM. Parameters
Case 1
Case 2
Unit
Modulus of elasticity E Poisson’s ratio m Unit weight c Cohesion C Angle of internal friction /
10.5 0.3 16 16 36.7
33 0.3 16 25 38.6
MPa – kN/m3 kPa Degree
Fig. 17 shows the experimental values of non-dimensional deformation coefficient D, which are obtained by the tri-axial compression tests for the experimental ground. Here, D is defined by the following equation:
analyses for the ring-cut and the full-face excavation methods are performed in each case, and the expanse of the plastic region is examined. Fig. 14 is the analytical model for the experimental ground converted into the gravitational field. The tunnel geometry and the excavation process for the two analyses correspond to those employed in the experiments.
4.1. Influence of plastic regions on subsidence The plastic regions at the final stage in Case 1 are shown in Fig. 15. The plastic regions produced by the full-face excavation can be seen at the face (Fig. 15a). On the other hand, the plastic regions produced by the ring cut can hardly be seen at the face front ground (Fig. 15b). The outbreak of plastic regions at the face front ground is suppressed by the core of the ring cut. As a result,
2220mm
1800mm
3805mm
1040mm
6302mm Fig. 14. FEM ground model.
4307mm Fig. 15. Plastic regions in Case 1.
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Fig. 18. Minimum principal stress on tunnel axis through tunnel center, obtained by 3D-FEM analysis in Case 1.
Fig. 18 shows the analytical values of the minimum principal stress on the tunnel axis through the tunnel center in Case 1. In the case of the full-face excavation, the value of the minimum principal stress becomes small with a decrease in the distance between the face and the measurement point. However, this phenomenon cannot be recognized in the case of the ring cut, which gives sufficient restriction pressure to the face front ground. By considering the results of Figs. 17 and 18, the value of the minimum principal stress at the face front ground deteriorates in the full-face excavation method, then the value of the deformation coefficient decreases, and finally the increase in subsidence is generated. On the other hand, the value of the minimum principal stress at the face front ground in the ring-cut method is sufficiently sustained by the existence of the core. This produces a situation such that the deformation coefficient does not decrease, so the outbreak of the subsidence is restrained in comparison to the full-face excavation method. It is possible to know the degree of the confining-pressure dependency of the deformation coefficient by a geological survey before the tunnel execution, and this value becomes a useful index when the applicability of the ring-cut method is examined. In the full-face excavation method, the value of the maximum principal stress at the face front ground increases and the value of the minimum principal stress decreases by the approach of the face, so it is easy for the ground to reach the Mohr–Coulomb failure criterion. The decrease in minimum principal stress is restrained by the existence of the core in the ring-cut method (cf. Fig. 18), so it is difficult for the ground ahead of the face to reach the failure criterion.
Fig. 16. Plastic regions in Case 2.
5. Conclusions The results provided in this study are as follows:
Fig. 17. Non-dimensional deformation coefficient D defined by Eq. (2). (Results of tri-axial compression tests.)
D ¼
Dðr3 Þ Dðr3 ¼ 1 kPaÞ
ð2Þ
where Dðr3 Þ: value of deformation coefficient under certain confining pressure r3 , Dðr3 ¼ 1 kPaÞ: value of deformation coefficient under confining pressure of r3 ¼ 1 kPa. Therefore, Fig. 17 shows the degree of the confining-pressure dependency of the deformation coefficient for each case, and indicates that the degree of confining-pressure dependency in Case 1 is greater than that in Case 2.
1. Centrifugal model experiments have been performed with an excavation robot for two kinds of ground conditions with different mechanical characteristics. The subsidence characteristics during the progress of the face by the ring-cut and the full-face excavation methods have been clarified. 2. The maximum subsidence produced by the ring cut was found to be about 36% of that produced by the full-face excavation in the ground of Case 1 with low strength. This shows that the effect of the ring-cut method in decreasing the subsidence is very effective. On the other hand, the above-mentioned value was found to be 58% in the ground of Case 2 with high strength. 3. Three-dimensional elasto-plastic finite element analyses have been conducted for centrifugal model experiments, and the areas of the plastic regions around the face have been compared between both methods. The relationships between the settlements measured by the model experiments and the analytical plastic regions are compared, and the following conclusions can be made.
M. Hisatake et al. / Tunnelling and Underground Space Technology 28 (2012) 90–97
(1) When a plastic region is produced at the face front ground in the full-face excavation method, the region can be reduced by adopting the ring-cut method, and the effect of the ring-cut method as a subsidence deterrent can be expected. (2) The existence of the core that remains in the ring-cut method prevents the decrease in minimum principal stress of the face front ground, and this also leads to the prevention of a decrease in the deformation coefficient value of the face front ground. The core helps to maintain the tunnel axial pressure in the excavation face. The effect of the core as a subsidence deterrent can be expected when the confining-pressure dependency of the deformation coefficient is high. In other words, the effect of the ring-cut method, as a subsidence deterrent, changes with the degree of the confining-pressure dependency of the deformation coefficient. This study clarifies the effects of the ring-cut method on the restraint of the ground settlements ahead of a tunnel face. The ratio between the ring-cut area and the full-face excavation area is used as 55%, in this study. The ring-cut effects, however, are affected not only by the ring-cut area ratio but also the core volume, the tunnel shape, and so on. So it is expected to clarify the ring-cut effects of the above mentioned factors on the restraint of the ground settlements in the future.
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References Aksoy, C.O., Onargan, T., 2010. The role of umbrella arch and face bolt as deformation preventing support system in preventing building damages. Tunnelling and Underground Space Technology 25, 553–559. Bernaud, D., Maghous, S., de Buhan, P., Couto, E., 2009. A numerical approach for design of bolt-supported tunnels regarded as homogenized structures. Tunnelling and Underground Space Technology 24 (5), 533–546. Farias, M.M., Moraes Junior, A.H., Assis, A.P., 2004. Displacement control in tunnel excavated in the NATM: 3-D numerical simulations. Tunnelling and Underground Space Technology 19, 283–294. Hisatake, M., Ohno, S., 2008. Effects of pipe roof supports and the excavation method on the displacements above a tunnel face. Tunnelling and Underground Space Technology 23, 120–127. Hisatake, M., Ohno, S., Katayama, T., Ohmae, Y., Sano, S., 2009. Effects of the ring-cut excavation method on the restraint of displacements ahead of a tunnel face. Tunnelling and Underground Space Technology 24, 547–554. ITA Working Group ‘‘Research’’, 2007. Settlement induced by tunneling in soft ground. Tunnelling and Underground Space Technology 22 (2), 119–149. Ocak, I., 2008. Control of surface settlements with umbrella arch method in second stage excavations of Istanbul Metro. Tunnelling and Underground Space Technology 23 (6), 674–681. Shin, J.H., Choi, Y.K., Kwon, O.Y., Lee, S.D., 2008. Model testing for pipe-reinforced tunnel heading in a granular soil. Tunnelling and Underground Space Technology 23 (3), 241–250. Yoo, C., 2009. Performance of multi-faced tunnelling – a 3D numerical investigation. Tunnelling and Underground Space Technology 24, 562–573.
Contents lists available at SciVerse ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Effects of the ring-cut method as a settlement deterrent in a soft ground tunnel Masayasu Hisatake ⇑, Shiro Ohno, Tatsuaki Katayama, Yukihiro Ohmae Department of Civil and Environmental Engineering, Faculty of Science and Engineering, Kinki University, Kowakae 3-4-1, Higashi-Osaka, Osaka 577-8502, Japan
a r t i c l e
i n f o
Article history: Received 14 January 2011 Received in revised form 15 September 2011 Accepted 26 September 2011 Available online 3 November 2011 Keywords: Settlements Centrifugal model tests Excavation robot Excavation method 3D-FEM
a b s t r a c t This paper presents the results of centrifugal model tests and three-dimensional elasto-plastic finite element analyses carried out to clarify the effects of the ring-cut method on the restraint of the ground settlements ahead of a tunnel face. A model tunnel is excavated in a soft ground by a robot under a centrifugal loading state, and the ground settlements are measured during the progress of the face by a picture analysis system with high accuracy. The settlements generated by the full-face excavation method are compared with those generated by the ring-cut method for two kinds of grounds with different mechanical properties. The maximum settlement caused by the ring-cut method becomes about 36% of that caused by the full-face excavation method for the ground with low strength and about 58% for the ground with high strength. Considerations regarding these phenomena are given by conducting threedimensional elasto-plastic finite element analyses. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Recently, the New Austrian Tunneling Method (NATM) has been adopted for the construction of urban tunnels in soft grounds with shallow depths. The reason for the adoption of NATM is mainly the low cost of tunnel construction in comparison with the shield tunneling method and its flexible application to several types of ground conditions. Settlements generated by tunnel construction in a soft ground may cause serious damage to nearby structures and existing services. The construction environment of tunneling beneath urban areas is becoming increasingly severe. Since a significant amount of disturbance is induced ahead of the excavation front (Farias et al., 2004), the stability of the face and the restriction of the ground settlements ahead of the face should be achieved during construction. For this purpose, certain auxiliary methods, such as pipe roof supports, face bolting, umbrella vaults, and so on, are often applied at the face (ITA Working Group ‘‘Research’’, 2007). Bernaud et al. (2009) investigated the state of reinforcement by horizontal anchors installed ahead of the excavation face. Shin et al. (2008) performed a series of large-scale model experiments for a pipe-reinforced tunnel heading in granular soil. Aksoy and Onargan (2010) studied the effect of umbrella arch and face bolt applications as settlement deterrents using a numerical analysis and in situ measurements at Izmir Metro, Turkey. The application of auxiliary methods is effective for difficult ground conditions in limiting ground settlements; however, it is obvious that the application of auxiliary methods, ⇑ Corresponding author. Tel.: +81 6 6721 2332; fax: +81 6 6730 1320. E-mail address: [email protected] (M. Hisatake). 0886-7798/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2011.09.008
such as the umbrella arch method, involves extra costs (Ocak, 2008). In order to conduct NATM economically, the ring-cut method is often adopted in urban areas where difficult ground conditions exist. The ring-cut method does not require any additional assistance, and it can be expected to increase the stability of the face and decrease the settlements ahead of the face. When the ringcut method is adopted, the elucidation of the displacement outbreak characteristics of the face front ground has been performed by Yoo (2009). He conducted elasto-plastic 3D finite element analyses of the performance of a multi-faced NATM tunneling work in a soft ground, and showed the effect of the ring-cut method on the settlement outbreak characteristics. Soft grounds are likely to show such mechanical characteristics as nonlinearity and the confining pressure dependency of stress–strain relationships, which affect the values of the ground settlements. An appropriate constitutive model is of the utmost importance for a proper displacement prediction (Farias et al., 2004). Since centrifugal model tests can take into account the above-mentioned mechanical characteristics, the tests are expected to enable the effective grasping of the outbreak mechanism of settlements. Hisatake and Ohno (2008) conducted centrifugal model tests to clarify the effects of the ring-cut method combined with pipe roof supports on the decrease in displacements at the face front ground. Hisatake et al. (2009) investigated the effects of the ring-cut method itself on the decrease in settlements and the increase in face stability by centrifugal model tests. In this study, three-dimensional elasto-plastic finite element analyses were also conducted for experimental grounds, which showed that a plastic region was not produced at the face. If the stress
M. Hisatake et al. / Tunnelling and Underground Space Technology 28 (2012) 90–97
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conditions at the face reach the failure criterion, the effectiveness of the ring-cut method to decrease settlements may be different from that obtained by Hisatake et al. (2009). In order to clarify this point experimentally, centrifugal model tests are conducted in this study with an excavation robot for two kinds of grounds with different constitutive conditions. The quantity of the subsidence caused by the full-face excavation method is compared with that caused by the ring-cut method. Supplemental numerical analyses of the three-dimensional elasto-plastic finite element method are also performed for the experimental grounds, and the effect of the ring-cut method as a subsidence deterrent is examined. Fig. 1. Deviator stress (r1–r3)-axial strain (e) relationships for Case 1.
2. Centrifugal model experiments 2.1. Experimental system The devices employed in the centrifugal model experiments, namely, an excavation robot controlled by computer programs and a picture analysis system for measuring settlements, are the same ones that have already been used (Hisatake and Ohno, 2008; Hisatake et al., 2009).
2.2. Experimental conditions Fig. 2. Deviator stress (r1–r3)-axial strain (e) relationships for Case 2.
The experimental grounds which are not in situ grounds are prepared by the compaction method; they are made of silica sand, cement, kaolin, and water. The composition ratios of the experimental ground materials are shown in Table 1. Two kinds of care periods, 2 days and 4 days, are used for making the experimental grounds with different mechanical characteristics. The stress– strain relationships for each case are indicated in Figs. 1 and 2; they show strongly confining pressure dependency and nonlinearity. The strength characteristics of the two grounds are indicated in Figs. 3 and 4. Adhesive strength c and internal friction angle / are determined as shown in Figs. 3 and 4, and the ground density and strength characteristics are summarized in Table 2.
2.3. Experimental procedure The grounds are made in a soil tank and are set up in the centrifugal device after the predetermined care periods. The tunnel excavation is performed by the robot under a centrifugal acceleration of 36 G (G: gravity acceleration). The quantity of the subsidence during the excavation is measured by a picture analysis system (Hisatake and Ohno, 2008). This experiment considers the geometrical symmetry for the vertically longitudinal section through the tunnel center, and a half section of the tunnel ground is used. The ground observation positions for each case are different just a little, and those in Cases 1 and 2 are shown in Figs. 5 and 6, respectively. The measurement points, ‘‘a’’, ‘‘b’’, ‘‘c’’, and ‘‘d’’, are located 10 mm above the horizontal line through the tunnel crown from the tunnel portal.
Table 1 Composition ratios of experimental ground. Materials
Mass (g)
Composition ratios (%)
Silica (No. 5) Kaolin Cement Water
19,000 1000 187.5 600
91.4 4.8 0.90 2.90
2.4. Excavation methods Two kinds of excavation methods, the full-face excavation method and the ring-cut method, are adopted to examine the effect of the ring-cut method in decreasing the subsidence. 2.4.1. Full-face excavation method The ground is excavated from the portal with a full-face excavation, 5 mm at a time, in the order of r, s, and t, as shown in Fig. 7. These excavations are repeated eight times, so that the total excavation depth becomes 40 mm. The geometrical relationship for the full-face excavation is shown in Fig. 8a. 2.4.2. Ring-cut method Procedure r, with the excavation depth of 5 mm, is repeated eight times, so that the total excavation depth becomes 40 mm. The ground is excavated in the shape of a ring-cut section, and the core is left at the tunnel center. The ring-cut area is about 55% of the full-face excavation area; therefore, the area of the core that remains is about 45% (Yoo, 2009). The geometrical relationship for the ring cut is shown in Fig. 8b. 3. Experimental results and considerations 3.1. The difference in the subsidence characteristics due to the difference in the excavation methods 3.1.1. Case 1 The quantities of the subsidence caused by the full-face excavation and the ring cut are compared in Fig. 9. The change in subsidence by the excavation progress at measurement point ‘‘a’’ in Fig. 5 is shown in Fig. 9a. The quantity of the final subsidence by the ring cut is about 40% of that by the full-face excavation, so that a large effect in decreasing the subsidence can be recognized by the existence of the core.
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400
c
16kPa 36.7
100
200
τ (kPa)
300
200
100
0 0
300
400
500
600
700
800
900
1000
800
900
1000
σ (kPa) Fig. 3. Strength characteristics of the ground in Case 1.
400
c
25kPa 38.6
τ (kPa)
300
200
100
0 0
100
200
300
400
500
600
700
σ (kPa) Fig. 4. Strength characteristics of the ground in Case 2.
Table 2 Density and strength characteristics of applied ground.
119mm
Parameters
Case 1
Case 2
Unit
Care period Density q Cohesion C Angle of internal friction /
2 1.63 16 36.7
4 1.63 25 38.6
days g/cm3 kPa Degree
91mm 102mm
Ground height 252mm
Tunnel height 68.9mm
115mm
64mm
a
36mm
b
c
d
Distance between measurement points and tunnel crown is 10mm.
90mm 102mm
a
Ground height 252mm
81.1mm
65mm 40mm
b
c
d
Tunnel
Fig. 6. Measurement points for Case 2.
height 68.9mm
Distance between measurement points and tunnel crown is 10mm.
81.1mm
at measurement points ‘‘c’’ and ‘‘d’’ by the ring cut are about 15% and 10% of those by the full-face excavation, respectively. The quantities of the final subsidence by the ring cut are very small compared to those by the full-face excavation, when the measuring points are more distant from the face than the tunnel height.
Fig. 5. Measurement points for Case 1.
The settlements at measurement point ‘‘b’’ are shown in Fig. 9b. The quantity of the final subsidence by the ring cut is about 43% of that by the full-face excavation. The settlements at measurement points ‘‘c’’ and ‘‘d’’ are shown in Figs. 9c and d, respectively. The quantities of the final subsidence
3.1.2. Case 2 The quantities of the subsidence caused by the full-face excavation and the ring cut are compared in Fig. 10. The change in subsidence by the excavation progress at measurement point ‘‘a’’ in Fig. 6 is shown in Fig. 10a. Measurement point ‘‘a’’ exists 36 mm from the tunnel portal and the excavation is performed up to
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(a) Measurement point a (40mm from entrance)
Fig. 7. Figure showing excavation process.
(b) Measurement point b (65mm from entrance)
Fig. 8. Excavation regions of full-face excavation and ring-cut methods.
40 mm; thus, the face goes beyond measurement point ‘‘a’’. When the face reaches the final excavation distance, the quantity of the subsidence by the ring cut shows a value considerably close to that by the full-face excavation. When measurement point ‘‘a’’ is located ahead of the face, the effect by the core as a subsidence deterrent can be recognized, but the effect cannot be expected after the face passes measurement point ‘‘a’’. When the face reaches almost directly under measurement point ‘‘a’’, the quantity of the subsidence by the ring cut is about 79% of that by the fullface excavation. In other words, the effect of the ring cut as a subsidence deterrent in Case 2 is almost half of that in Case 1. It can be understood that the effect in Case 2 deteriorates greatly. The subsidence at measurement point ‘‘b’’ is shown in Fig. 10b. The quantity of the final subsidence by the ring cut is about 73% of that by the full-face excavation. The effect of the ring cut as a subsidence deterrent in Case 2 (73%) deteriorates in comparison with that in Case 1 (43%), as shown in Fig. 9b. The subsidence at measurement points ‘‘c’’ and ‘‘d’’ is shown in Figs. 10c and d, respectively. The final subsidence at measurement points ‘‘c’’ and ‘‘d’’ by the ring cut is about 54% and 63% of that by the full-face excavation, respectively.
(c) Measurement point c (90mm from entrance)
(d) Measurement point d (115mm from entrance) Fig. 9. Settlement characteristics by excavation progress in Case 1.
a subsidence deterrent is defined by Eq. (1), in order to clarify the effect quantitatively.
R¼
Uf Ur 100 % Uf
ð1Þ
3.2. Effect of the ring cut as a subsidence deterrent The final subsidence at the respective measurement points by the ring cut has been compared with that by the full-face excavation as shown in Section 3.1. In the following, the effect of the ring cut (R) as
where Uf: final subsidence by the full-face excavation, Ur: final subsidence by the ring cut The effect (R) as a subsidence deterrent is shown in Fig. 11. The value of R in Case 1 with low strength is larger than that in Case 2
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(a) Measurement point a (36mm from entrance) Fig. 11. Effect of ring cut ‘R’ as a subsidence deterrent defined by Eq. (1).
(b) Measurement point b (64mm from entrance)
Fig. 12. Non-dimensional settlements at measurement point d in Case 1. (Settlements are divided by the maximum settlement caused by the full-face excavation.)
(c) Measurement point c (91mm from entrance)
(d) Measurement point d (119mm from entrance)
progress of the face and the effect of the ring cut as a subsidence deterrent can be clarified from these results. Figs. 12 and 13 show the relationships between the subsidence at point ‘‘d’’ and the distance between the face and measurement point ‘‘d’’ for Cases 1 and 2, respectively. The horizontal and the vertical axes are shown in non-dimensional forms divided by the tunnel height and by the maximum subsidence caused by the full-face excavation, respectively. Fig. 12 (Case 1) shows that the maximum subsidence ratio by the ring cut is about 36% of that by the full-face excavation, and that the subsidence hardly occurs until the distance between the face and the measurement point reaches the tunnel height. The ground movement caused by the ring cut is greatly reduced in Case 1. Fig. 13 (Case 2) shows that the maximum subsidence ratio by the ring cut is about 58% of that by the full-face excavation. The abovementioned results indicate that the effect of the ring cut, as a subsidence deterrent, changes with the difference in the mechanical characteristics of the ground.
Fig. 10. Settlement characteristics by excavation progress in Case 2.
with high strength. In addition, the value of R is large at the measurement points which are farther from the portal.
3.3. Variation in maximum settlements due to the difference in excavation methods When the face reaches the position directly below measurement point ‘‘d’’, the quantity of the subsidence at point ‘‘d’’ can be calculated by accumulating the absolute subsidence measured at respective measurement points ‘‘a’’, ‘‘b’’, ‘‘c’’, and ‘‘d’’ (Hisatake et al., 2009). The tendency of the subsidence caused by the
4. Considerations by three-dimensional elasto-plastic finite element analyses Three-dimensional elasto-plastic finite element analyses are conducted and several considerations are added. The analytical input values, determined in reference to the results of the tri-axial compression tests, are shown in Table 3. The ground is supposed to be a complete elasto-plastic material conforming to the Mohr– Coulomb failure criterion together with the associated flow rule. The value of the modulus of elasticity in Table 3 is determined by the deformation coefficient in tri-axial compression tests with the confining pressure that corresponds to the horizontal stress at the tunnel center before the tunnel is excavated. Excavation
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Non-dimensional settlements
the core stabilizes the face and restrains the subsidence of the face front ground. Fig. 16 shows the analytical results for the ground conditions in Case 2. The plastic regions produced by the full-face excavation can be seen in the lower part of the ground behind the face, but not at the face (Fig. 16a). In addition, the plastic regions produced by the ring cut occur lightly in part of the core, but they do not occur elsewhere (Fig. 16b). In brief, plastic regions do not occur at the face front ground in the full-face excavation, and the effect of the core in suppressing the outbreak of plastic regions cannot be expected because the ground has sufficient strength. 4.2. Effects of the deformation coefficient on subsidence
Fig. 13. Non-dimensional settlements at measurement point d in Case 2. (Settlements are divided by the maximum settlement caused by the full-face excavation.)
Table 3 Values of ground parameters used in FEM. Parameters
Case 1
Case 2
Unit
Modulus of elasticity E Poisson’s ratio m Unit weight c Cohesion C Angle of internal friction /
10.5 0.3 16 16 36.7
33 0.3 16 25 38.6
MPa – kN/m3 kPa Degree
Fig. 17 shows the experimental values of non-dimensional deformation coefficient D, which are obtained by the tri-axial compression tests for the experimental ground. Here, D is defined by the following equation:
analyses for the ring-cut and the full-face excavation methods are performed in each case, and the expanse of the plastic region is examined. Fig. 14 is the analytical model for the experimental ground converted into the gravitational field. The tunnel geometry and the excavation process for the two analyses correspond to those employed in the experiments.
4.1. Influence of plastic regions on subsidence The plastic regions at the final stage in Case 1 are shown in Fig. 15. The plastic regions produced by the full-face excavation can be seen at the face (Fig. 15a). On the other hand, the plastic regions produced by the ring cut can hardly be seen at the face front ground (Fig. 15b). The outbreak of plastic regions at the face front ground is suppressed by the core of the ring cut. As a result,
2220mm
1800mm
3805mm
1040mm
6302mm Fig. 14. FEM ground model.
4307mm Fig. 15. Plastic regions in Case 1.
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Fig. 18. Minimum principal stress on tunnel axis through tunnel center, obtained by 3D-FEM analysis in Case 1.
Fig. 18 shows the analytical values of the minimum principal stress on the tunnel axis through the tunnel center in Case 1. In the case of the full-face excavation, the value of the minimum principal stress becomes small with a decrease in the distance between the face and the measurement point. However, this phenomenon cannot be recognized in the case of the ring cut, which gives sufficient restriction pressure to the face front ground. By considering the results of Figs. 17 and 18, the value of the minimum principal stress at the face front ground deteriorates in the full-face excavation method, then the value of the deformation coefficient decreases, and finally the increase in subsidence is generated. On the other hand, the value of the minimum principal stress at the face front ground in the ring-cut method is sufficiently sustained by the existence of the core. This produces a situation such that the deformation coefficient does not decrease, so the outbreak of the subsidence is restrained in comparison to the full-face excavation method. It is possible to know the degree of the confining-pressure dependency of the deformation coefficient by a geological survey before the tunnel execution, and this value becomes a useful index when the applicability of the ring-cut method is examined. In the full-face excavation method, the value of the maximum principal stress at the face front ground increases and the value of the minimum principal stress decreases by the approach of the face, so it is easy for the ground to reach the Mohr–Coulomb failure criterion. The decrease in minimum principal stress is restrained by the existence of the core in the ring-cut method (cf. Fig. 18), so it is difficult for the ground ahead of the face to reach the failure criterion.
Fig. 16. Plastic regions in Case 2.
5. Conclusions The results provided in this study are as follows:
Fig. 17. Non-dimensional deformation coefficient D defined by Eq. (2). (Results of tri-axial compression tests.)
D ¼
Dðr3 Þ Dðr3 ¼ 1 kPaÞ
ð2Þ
where Dðr3 Þ: value of deformation coefficient under certain confining pressure r3 , Dðr3 ¼ 1 kPaÞ: value of deformation coefficient under confining pressure of r3 ¼ 1 kPa. Therefore, Fig. 17 shows the degree of the confining-pressure dependency of the deformation coefficient for each case, and indicates that the degree of confining-pressure dependency in Case 1 is greater than that in Case 2.
1. Centrifugal model experiments have been performed with an excavation robot for two kinds of ground conditions with different mechanical characteristics. The subsidence characteristics during the progress of the face by the ring-cut and the full-face excavation methods have been clarified. 2. The maximum subsidence produced by the ring cut was found to be about 36% of that produced by the full-face excavation in the ground of Case 1 with low strength. This shows that the effect of the ring-cut method in decreasing the subsidence is very effective. On the other hand, the above-mentioned value was found to be 58% in the ground of Case 2 with high strength. 3. Three-dimensional elasto-plastic finite element analyses have been conducted for centrifugal model experiments, and the areas of the plastic regions around the face have been compared between both methods. The relationships between the settlements measured by the model experiments and the analytical plastic regions are compared, and the following conclusions can be made.
M. Hisatake et al. / Tunnelling and Underground Space Technology 28 (2012) 90–97
(1) When a plastic region is produced at the face front ground in the full-face excavation method, the region can be reduced by adopting the ring-cut method, and the effect of the ring-cut method as a subsidence deterrent can be expected. (2) The existence of the core that remains in the ring-cut method prevents the decrease in minimum principal stress of the face front ground, and this also leads to the prevention of a decrease in the deformation coefficient value of the face front ground. The core helps to maintain the tunnel axial pressure in the excavation face. The effect of the core as a subsidence deterrent can be expected when the confining-pressure dependency of the deformation coefficient is high. In other words, the effect of the ring-cut method, as a subsidence deterrent, changes with the degree of the confining-pressure dependency of the deformation coefficient. This study clarifies the effects of the ring-cut method on the restraint of the ground settlements ahead of a tunnel face. The ratio between the ring-cut area and the full-face excavation area is used as 55%, in this study. The ring-cut effects, however, are affected not only by the ring-cut area ratio but also the core volume, the tunnel shape, and so on. So it is expected to clarify the ring-cut effects of the above mentioned factors on the restraint of the ground settlements in the future.
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