- Email: [email protected]
Time effects in rock–support interaction: a case study in the construction of two road tunnels
Paper 3B 20 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
TIME EFFECTS IN ROCK–SUPPORT INTERACTION: A CASE STUDY IN THE CONSTRUCTION OF TWO ROAD TUNNELS L. Xu¹, H.W. Huang² ¹)Dept. Of Geotech. Engng., Tongji University,Shanghai, China [email protected] ²) Dept. Of Geotech. Engng., Tongji University,Shanghai, China [email protected]
Abstract: With the great development of China, more and more rock road tunnels will be constructed. During the design and construction, it is necessary to know how the tunnel structure will work as time goes on. Based on the measured records during the construction of Dafengyakou and No.1 Yuanjiang tunnel in Yunnan province of China, contact pressure between the initial and secondary lining and crown displacement of the initial lining were analyzed firstly, and then the time effect on the deformation and contact pressure was carefully investigated. For example, the change of contact pressure with time can be divided into two stages and, in either stage, the change with time satisfies the hyperbolic rule. And the relationship between the crown displacement and time satisfies the exponential rule. It was found that tunnel excavation, rock creep and time-dependent modulus of concrete can affect the change of the contact pressure greatly. The conclusions obtained will be helpful for the design and construction of rock road tunnels in China. Keywords: Rock tunnel
Deformation
Contact pressure
1. INTRODUCTION After NATM came into being in the mid-term of 20th century, rock tunnel construction has developed greatly. Many research achievements have been got, for example, Wang (1990) and Li (2002) summarized on how to measure, how to analyze measured data. Kang (1997), Huang and Xu (2004) analyzed the mechanics of surrounding rock and lining by actual tunnel projects. Yang (1996) determined characteristics of rock and guided the tunnel construction with the back analysis of monitoring data. Pan and Dong (1991), Pan and Huang (1994) presented new models to study the deformation of surrounding rock and lining. Dafengyakou and No.1 Yuanjiang tunnels are located at Yuan-Mo Express highway in Yunnan province of China. No.1 Yuanjiang tunnel, about 1000m long, is a one-way running and double lane tunnel with separate up and down lines. The net height and width is 7.2m and 10.90m. The weak surrounding rock is mainly slate and sandrock, with the main class of II and III according to Chinese road tunnel code, where rock is classified into 6 and the smaller class means the weaker rock. And a few faults exist. Dafengyakou tunnel, about 3300m long, is also a one-way running and double lane
Creep
Time-dependent
Time effect
tunnel with separate up and down lines. The net height and width is as same as that of No.1 Yuanjiang. The weak surrounding rock is mainly slate, limestone and sandrock, with the main class of II, III and IV. And there are many fissures. These two tunnels are constructed according to NATM. So the composite lining is adopted. The initial lining, about 20cm thick, is shotcrete, rockbolt and steel arch set. The secondary lining, about 50cm thick, is reinforced concrete. The top and bottom bench excavated method is adopted with the top bench nearly 6.29m high and the bottom bench nearly 4.07m high. There are mainly common measured items in these two projects, such as the convergence of initial and secondary lining, the contact pressure between surrounding rock and initial lining, the contact pressure between the initial and secondary lining, the internal displacement of surrounding rock, the internal force of the steel of initial and secondary lining and etc.
1
Paper 3B 20 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
2. CONTACT PRESSURE BETWEEN INITIAL AND SECONDARY LINING 2.1 General situation The selected section is located at No.1 Yuanjiang tunnel. The monitoring lasted 542 days. At the beginning 192 days , it was measured every 2 or 3 days. As time going on, because contact pressure came to be stable, it was measured every 1 month. The surrounding rock is sandrock, belonging to class III. This section was excavated on April 14, 2001. And 10 days later, the whole excavation of tunnel and the construction of secondary lining were finished.
and 33 days later, the second begins (see Fig.3). In the first stage, the contact pressure firstly increases quickly and then increases slowly. In the second stage, the contact pressure firstly increases quickly, then increases slowly and becomes almost stable. In Fig.2 and 3, the positive pressure means the lining is compressed and the negative pressure means the lining is tensioned. 1681 1654
1695
1634
initial lining
1.8
secondary lining
4.3
0.9 1.95
2.2 Analysis of data Fig.1 shows where the pressure cells were placed. The numbers in Fig.1, such as 1695, 1654 and etc. are the codes of pressure cells. From the change of contact pressure after the construction of secondary lining, it can be known that the whole process can be divided into two stages, of which the first stage is the begining 33 days (see Fig.2)
1690
inverted arch pressure cell
Figure 1. Positions of pressure cells.
Contact pressure (MPa)
0.12 1695 1654 1681 1634 1690 Fitting curve of 1695 Fitting curve of 1654 Fitting curve of 1681 Fitting curve of 1634 Fitting curve of 1690
0.1 0.08 0.06 0.04 0.02 0 0
10
20
30 Time (days)
40
50
Figure 2. The curve of contact pressure between the initial and secondary lining versus time. Fig.2 also shows that in the first stage contact pressure σ changes with time t as hyperbolic rule: σ=
t a 1 t + b1
(1)
achieve stable stiffness. In this project, the parameter td is 33 days. In Fig.2, the data of cell 1690 (located at the down part on the right side wall) has the best fitting result, as an example, the fitting curve is
Where t is less than and equal to td , a1 and b1 are constants which are larger than 0. The parameter td is mainly affected by tunnel excavation, rock creep and the time which is needed for tunnel concrete to
2
Paper 3B 20 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
σ=
The data of cell 1695 (located at the down part on the left side wall) has the best fitting result, as an example, the fitting curve is
t 17 .1246 t + 39 . 5779
(2)
From this formulation, the ultimate value is 0.0584MPa. On the 33rd day, the measured pressure is 0.0546MPa, 93.5% of the former. Fig.3 gives out the change curve of the increment of contact pressure in the second stage. It reveals that the increment of contact pressure also changes with the increment of time t as hyperbolic rule: ∆σ =
∆σ =
(4)
The ultimate value is 0.1086MPa, and when the increment of time is 119 days, the increment of contact pressure is 80% of the ultimate value. On the 33rd day, the measured datum is 0.1017MPa, so the increment in the second stage is 107% of that in the first stage.
∆t a 2 ∆t + b 2
∆t 9. 2095 ∆t + 219 . 1702
(3)
Increment of contact pressure (MPa)
in which ∆σ = σt - σtd , ∆t = t - td , a2 and b2 are constants which are larger than 0. 0.12 1695 1654 1681 1634 1690 Fitting curve of 1695
0.1 0.08 0.06 0.04
Fitting curve of 1654 Fitting curve of 1681 Fitting curve of 1634
0.02 0
Fitting curve of 1690
-0.02 0
100
200
300
400
500
600
700
800
Increment of time (days)
Figure 3. The curve of the increment of contact pressure versus the increment of time. From the above analysis, it can be seen that during the full stage the contact pressure changes with time as hyperbolic rule, which is: When t ≤ td σ=
t a 1 t + b1
(5)
When t >td σ=
td a1 t d + b1
+
t − td a 2 ( t − td ) + b2
(6)
2.3 Influencing factor of td The parameter td in formulation (1), (3), (5) and (6) is influenced by some factors, such as tunnel
excavation, rock creep, stiffness of tunnel lining and etc. Weber (1979) and Mahar (1975) show that the stiffness cannot form at once, and it will develop with time. At the beginning stage, the secondary lining is just constructed and tunnel excavation still continues, so the contact pressure increases quickly. Tunnel excavation stopped after 10 days, so the increase of contact pressure will decrease with the deformation of lining. And in this stage, the increasing stiffness plays a role. When the stiffness of lining is almost formed, rock creep still develops. Because it is significant, rock creep becomes the most important. Tunnel lining confines the deformation of rock more and more, so the contact pressure becomes larger again. Later,
3
Paper 3B 20 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
the contact pressure becomes stable as rock creep becomes stable. Weber (1979) and Mahar (1975) considered that the strength and Young’s modulus of shotcrete always increase with time. Weber (1979) presented the empirical formulation on the change of the Young’s modulus of shotcrete with time:
[ (
E c (t ) = E 28 exp − c t −0 .6 £- 28 −0 .6
)] (7)
In which E28 is Young’s modulus of shotcrete on 28th day, c is a material parameter of shotcrete, and t is elapsed time. Mahar (1975) considered parameter c is about 0.4-0.9. It is clear that when t and E28 don’t change, bigger c means bigger E28 and bigger increasing rate of the modulus on 28th day. So let c be 0.9, when t increases to infinity, Ec( ) is equal to 1.13 E28 . So Young’s modulus of shotcrete on 28th day E28 is 88.5% of the ultimate value. And on 28th day, the increasing rate of modulus is small, only 0.00261 E28 . In this project, td is 33 days, and just then the initial lining has been constructed for 38 days, so the stiffness has been mainly formed. Comite Euro-international du Beton (1993) presented the formula on the change of the modulus of concrete with time: E c (t ) = β t Ec
(8) th
In which Ec is modulus of concrete on 28 day, and
βt = e s (1−
28 / t
) (9)
In which t is elapsed time, and s is a material parameter on the kind of cement, which is equal to 0.25 for normal cement and rapid hardening cement, and 0.20 for rapid hardening cement with high strength. After the secondary lining is constructed, load acts on the lining and the lining deforms, then the contact pressure between initial and secondary lining changes. So the modulus of concrete is an important factor on the deformation of secondary lining and the contact pressure. The stiffness is not formed at once, and it will develop with time, so the changes of the deformation of secondary lining and the contact pressure become complex. Take normal cement and rapid hardening cement as an example, it can be seen from formulation (8) and (9), the modulus increases with time. When t increases to infinity, Ec(∞) is equal to 1.13 E28 ,
which is the ultimate value. So the modulus of concrete on 28th day E28 is 88.3% of the ultimate value. On 28th day, the increasing rate of modulus is small, only 0.00223 E28 , and it will become smaller as time going on. Guo (1999) presented that the strength and modulus of concrete are influenced by some factors, such as the kind and moisture content of cement, the quality of cement, admixture, curing condition, temperature and humidity content, and etc. Meanwhile, the strength changes under longterm load. So td is influenced by many factors, not just 28 days. In this project, td is 33 days, very near 28. Certainly, the effect of tunnel excavation is also important. If tunnel excavation is stopped earlier, after secondary lining is constructed, the contact pressure will be small. Though the stiffness of lining still increases, its effect will not be so clear, and the two obvious change stages will not occur. After secondary lining is constructed, if tunnel excavation goes on very long, the effect of excavation will be the most important. Though the stiffness of lining still increases, its effect will not be so clear, and the two obvious change stages will not occur. So only tunnel excavation lasts certain time near the section, the two obvious change stages and td will occur. Rock creep is also important. If creep is not significant, the contact pressure will not increase quickly at the beginning of the second stage. Only if rock creep is significant and lasts long, the two obvious stages and td will occur.
3. DEFORMATION OF INITIAL LINING 3.1 General situation Fig.4 shows the change curve of tunnel crown displacement with time after the excavation of top bench. This measured section is located at Dafengyakou tunnel. And inrush water current once occurred. The surrounding rock is violet red clay and black mudstone, belonging to class III. During the measurement time, the excavation face of top bench is 5m-48m before the section. In Fig.4, the positive crown displacement means that the displacement directs to the inside of tunnel, and the negative crown displacement means that the displacement directs to the outside of tunnel. Point G1 is at the left and near the crown, and Point G2 is just at the crown (see Fig.4). Because Point G3 is quickly damaged, there are only data of Point G1 and G2.
4
Paper 3B 20 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
3.2 Analysis of data
du
From Fig.4, the displacements at point G1and G2 with time satisfy exponential rule:
dt
b t
65 . 142 t
2
5. 64 t
exp −
(12)
So the following results can be drawn: Firstly, the ultimate displacement is 11.55mm. on 25th day, the displacement is 9.22mm, 80% of the ultimate. Secondly, on 25th day, the displacement rate is 0.1mm/day. From then on, it becomes smaller. Thus, after the excavation of top bench, though the ultimate diplacement is not big, surrounding rock needs a long time to be stable.
u =a × exp −
(10)
In which u is crown displacement (mm), t is time (day), a and b are constants which are larger than 0. The two displcements satisfy the same rule, so either can be selected to analyze. Take point G2 as an example, of which the fitting curve is:
5 .64 t
=
u =11 .55 × exp −
(11)
The displacement rate is:
14 Crown displacement mm
G2 G1
12
G3
10 8 G1 G2 Fitting curve of G1 Fitting curve of G2
6 4 2 0 0
10
20
30 Time
40
50
60
days
Figure 4. The curve of crown displacement versus time after the excavation of top bench.
3.3 Effect of hydrologic condition and support From the above study, it has been known that at this measured section the deformation needs a long time to be stable. It is mainly affected by hydrologic condition and support. Inrush water current once occurs. Surrounding rock is weak with many fissures and abundant underground water. Supporting wall with the height of 3m was constructed after the occurrence of inrush water. Advanced grouting, central drainage, the steel arch set with the clearance of 60cm, and shotcrete with the thickness of 20cm were adopted. So the tunnel lining resists the deformation more than ever, which can be known from that the ultimate displacement is only 11.55mm. But because of the characteristic of weak rock and abundant underground water, the effect of tunnel excavation
on rock will last a long period and then the deformation will become stable, which should be paid attention to in the future design and construction of rock tunnel.
4. CONCLUSIONS At No.1 Yuanjiang tunnel, the change of the contact pressure between initial and secondary lining is mainly affected by tunnel excavation, rock creep and time-dependent modulus of lining. The change phrase can be divided into two stages. The first stage is some time after constructing the secondary lining, the change of pressure is mainly on tunnel excavation, rock creep and timedependent modulus of lining. The pressure changes with time as hyperbolic rule. In the second stage, the change of pressure is mainly on rock creep. The
5
Paper 3B 20 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
increment of pressure changes with the increment of time also as hyperbolic rule. In the change of contact pressure, the parameter td is the time that the first stage lasts. It is considered that td is on the time which is needed for the stiffness of tunnel lining to become stable, tunnel excavation and rock creep. In this project, td is 33 days, which is very near 28 days when the modulus of concrete has become stable from the change rule for the modulus of concrete with time. At Dafengyakou tunnel, for the section where inrush water occurred, the crown displacement after the excavation of top bench changes with time as exponential rule. The reinforcement adopted decreases the ultimate value, but because of the inherent characteristic of the weak rock and abundant underground water, the deformation will need a long period to be stable.
5. REFERENCES Comite Euro-International du Beston. 1993. Bulletin D’ information NO.213/214 CEB-FIP Model Code 1990 (Concrete Structures). Lausanne. Guo, Zh.H. 1999. Theory of reinforcement concrete structure. Beijing: Qinghua University Press. Huang,H.W. & Xu, L. 2004, Study on the deformation and internal force of the surrounding rock and initial lsupport in Da Feng Ya Kou rock road tunnel. Chinese Journal of Rock mechanics and Engineering 24(1): pp. 19. Kang,N. 1997, Construction monitoring of Donggang tunnel. Chinese Journal of Rock mechanics and Engineering 17(2): pp. 140-147.
Li, X.H. 2002. NATM and measurement technology of tunnel. Beijing: Science Press. Lu, Ch.Y. & He, Ch.Y. 1998. Concrete structure and bricking-up structure. Chongqin: Chongqin University Press. Mahar,J.W. 1975. Shotcrete practice in underground construction: Final report. Dept. of Civil Engrg. Univ. of Illinois at UrbanChampaign, Springfield, VA. Pan,Y.W. & Dong, J.J. 1991. Time –dependent tunnel convergence – . Formulation of the model. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 28(5): pp. 469-475. Pan,Y.W. & Dong, J.J. 1991. Time –dependent tunnel convergence – . Advance rate and tunnel-support interaction. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 28(5): pp. 477488. Pan,Y.W. & Huang, Z.L. 1994. A model of the time-dependent interaction between rock and shotcrete support in a tunnel. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 31(3): pp. 213219. Wang,J.Y. 1990. Principles of monitoring and informational design in tunnel construction. Beijing: Chinese Railway Press. Weber,J.W. 1979. Empirische formeln zur beschreibung der festigkeitsentwicklung und der entwicklung des e-moduls von beton betonwerk und fertigtechbik. Yang,L.D. 1996. Theory of inversion on geotechnical engineering and construction experience. Beijing: Science Press.
6
TIME EFFECTS IN ROCK–SUPPORT INTERACTION: A CASE STUDY IN THE CONSTRUCTION OF TWO ROAD TUNNELS L. Xu¹, H.W. Huang² ¹)Dept. Of Geotech. Engng., Tongji University,Shanghai, China [email protected] ²) Dept. Of Geotech. Engng., Tongji University,Shanghai, China [email protected]
Abstract: With the great development of China, more and more rock road tunnels will be constructed. During the design and construction, it is necessary to know how the tunnel structure will work as time goes on. Based on the measured records during the construction of Dafengyakou and No.1 Yuanjiang tunnel in Yunnan province of China, contact pressure between the initial and secondary lining and crown displacement of the initial lining were analyzed firstly, and then the time effect on the deformation and contact pressure was carefully investigated. For example, the change of contact pressure with time can be divided into two stages and, in either stage, the change with time satisfies the hyperbolic rule. And the relationship between the crown displacement and time satisfies the exponential rule. It was found that tunnel excavation, rock creep and time-dependent modulus of concrete can affect the change of the contact pressure greatly. The conclusions obtained will be helpful for the design and construction of rock road tunnels in China. Keywords: Rock tunnel
Deformation
Contact pressure
1. INTRODUCTION After NATM came into being in the mid-term of 20th century, rock tunnel construction has developed greatly. Many research achievements have been got, for example, Wang (1990) and Li (2002) summarized on how to measure, how to analyze measured data. Kang (1997), Huang and Xu (2004) analyzed the mechanics of surrounding rock and lining by actual tunnel projects. Yang (1996) determined characteristics of rock and guided the tunnel construction with the back analysis of monitoring data. Pan and Dong (1991), Pan and Huang (1994) presented new models to study the deformation of surrounding rock and lining. Dafengyakou and No.1 Yuanjiang tunnels are located at Yuan-Mo Express highway in Yunnan province of China. No.1 Yuanjiang tunnel, about 1000m long, is a one-way running and double lane tunnel with separate up and down lines. The net height and width is 7.2m and 10.90m. The weak surrounding rock is mainly slate and sandrock, with the main class of II and III according to Chinese road tunnel code, where rock is classified into 6 and the smaller class means the weaker rock. And a few faults exist. Dafengyakou tunnel, about 3300m long, is also a one-way running and double lane
Creep
Time-dependent
Time effect
tunnel with separate up and down lines. The net height and width is as same as that of No.1 Yuanjiang. The weak surrounding rock is mainly slate, limestone and sandrock, with the main class of II, III and IV. And there are many fissures. These two tunnels are constructed according to NATM. So the composite lining is adopted. The initial lining, about 20cm thick, is shotcrete, rockbolt and steel arch set. The secondary lining, about 50cm thick, is reinforced concrete. The top and bottom bench excavated method is adopted with the top bench nearly 6.29m high and the bottom bench nearly 4.07m high. There are mainly common measured items in these two projects, such as the convergence of initial and secondary lining, the contact pressure between surrounding rock and initial lining, the contact pressure between the initial and secondary lining, the internal displacement of surrounding rock, the internal force of the steel of initial and secondary lining and etc.
1
Paper 3B 20 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
2. CONTACT PRESSURE BETWEEN INITIAL AND SECONDARY LINING 2.1 General situation The selected section is located at No.1 Yuanjiang tunnel. The monitoring lasted 542 days. At the beginning 192 days , it was measured every 2 or 3 days. As time going on, because contact pressure came to be stable, it was measured every 1 month. The surrounding rock is sandrock, belonging to class III. This section was excavated on April 14, 2001. And 10 days later, the whole excavation of tunnel and the construction of secondary lining were finished.
and 33 days later, the second begins (see Fig.3). In the first stage, the contact pressure firstly increases quickly and then increases slowly. In the second stage, the contact pressure firstly increases quickly, then increases slowly and becomes almost stable. In Fig.2 and 3, the positive pressure means the lining is compressed and the negative pressure means the lining is tensioned. 1681 1654
1695
1634
initial lining
1.8
secondary lining
4.3
0.9 1.95
2.2 Analysis of data Fig.1 shows where the pressure cells were placed. The numbers in Fig.1, such as 1695, 1654 and etc. are the codes of pressure cells. From the change of contact pressure after the construction of secondary lining, it can be known that the whole process can be divided into two stages, of which the first stage is the begining 33 days (see Fig.2)
1690
inverted arch pressure cell
Figure 1. Positions of pressure cells.
Contact pressure (MPa)
0.12 1695 1654 1681 1634 1690 Fitting curve of 1695 Fitting curve of 1654 Fitting curve of 1681 Fitting curve of 1634 Fitting curve of 1690
0.1 0.08 0.06 0.04 0.02 0 0
10
20
30 Time (days)
40
50
Figure 2. The curve of contact pressure between the initial and secondary lining versus time. Fig.2 also shows that in the first stage contact pressure σ changes with time t as hyperbolic rule: σ=
t a 1 t + b1
(1)
achieve stable stiffness. In this project, the parameter td is 33 days. In Fig.2, the data of cell 1690 (located at the down part on the right side wall) has the best fitting result, as an example, the fitting curve is
Where t is less than and equal to td , a1 and b1 are constants which are larger than 0. The parameter td is mainly affected by tunnel excavation, rock creep and the time which is needed for tunnel concrete to
2
Paper 3B 20 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
σ=
The data of cell 1695 (located at the down part on the left side wall) has the best fitting result, as an example, the fitting curve is
t 17 .1246 t + 39 . 5779
(2)
From this formulation, the ultimate value is 0.0584MPa. On the 33rd day, the measured pressure is 0.0546MPa, 93.5% of the former. Fig.3 gives out the change curve of the increment of contact pressure in the second stage. It reveals that the increment of contact pressure also changes with the increment of time t as hyperbolic rule: ∆σ =
∆σ =
(4)
The ultimate value is 0.1086MPa, and when the increment of time is 119 days, the increment of contact pressure is 80% of the ultimate value. On the 33rd day, the measured datum is 0.1017MPa, so the increment in the second stage is 107% of that in the first stage.
∆t a 2 ∆t + b 2
∆t 9. 2095 ∆t + 219 . 1702
(3)
Increment of contact pressure (MPa)
in which ∆σ = σt - σtd , ∆t = t - td , a2 and b2 are constants which are larger than 0. 0.12 1695 1654 1681 1634 1690 Fitting curve of 1695
0.1 0.08 0.06 0.04
Fitting curve of 1654 Fitting curve of 1681 Fitting curve of 1634
0.02 0
Fitting curve of 1690
-0.02 0
100
200
300
400
500
600
700
800
Increment of time (days)
Figure 3. The curve of the increment of contact pressure versus the increment of time. From the above analysis, it can be seen that during the full stage the contact pressure changes with time as hyperbolic rule, which is: When t ≤ td σ=
t a 1 t + b1
(5)
When t >td σ=
td a1 t d + b1
+
t − td a 2 ( t − td ) + b2
(6)
2.3 Influencing factor of td The parameter td in formulation (1), (3), (5) and (6) is influenced by some factors, such as tunnel
excavation, rock creep, stiffness of tunnel lining and etc. Weber (1979) and Mahar (1975) show that the stiffness cannot form at once, and it will develop with time. At the beginning stage, the secondary lining is just constructed and tunnel excavation still continues, so the contact pressure increases quickly. Tunnel excavation stopped after 10 days, so the increase of contact pressure will decrease with the deformation of lining. And in this stage, the increasing stiffness plays a role. When the stiffness of lining is almost formed, rock creep still develops. Because it is significant, rock creep becomes the most important. Tunnel lining confines the deformation of rock more and more, so the contact pressure becomes larger again. Later,
3
Paper 3B 20 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
the contact pressure becomes stable as rock creep becomes stable. Weber (1979) and Mahar (1975) considered that the strength and Young’s modulus of shotcrete always increase with time. Weber (1979) presented the empirical formulation on the change of the Young’s modulus of shotcrete with time:
[ (
E c (t ) = E 28 exp − c t −0 .6 £- 28 −0 .6
)] (7)
In which E28 is Young’s modulus of shotcrete on 28th day, c is a material parameter of shotcrete, and t is elapsed time. Mahar (1975) considered parameter c is about 0.4-0.9. It is clear that when t and E28 don’t change, bigger c means bigger E28 and bigger increasing rate of the modulus on 28th day. So let c be 0.9, when t increases to infinity, Ec( ) is equal to 1.13 E28 . So Young’s modulus of shotcrete on 28th day E28 is 88.5% of the ultimate value. And on 28th day, the increasing rate of modulus is small, only 0.00261 E28 . In this project, td is 33 days, and just then the initial lining has been constructed for 38 days, so the stiffness has been mainly formed. Comite Euro-international du Beton (1993) presented the formula on the change of the modulus of concrete with time: E c (t ) = β t Ec
(8) th
In which Ec is modulus of concrete on 28 day, and
βt = e s (1−
28 / t
) (9)
In which t is elapsed time, and s is a material parameter on the kind of cement, which is equal to 0.25 for normal cement and rapid hardening cement, and 0.20 for rapid hardening cement with high strength. After the secondary lining is constructed, load acts on the lining and the lining deforms, then the contact pressure between initial and secondary lining changes. So the modulus of concrete is an important factor on the deformation of secondary lining and the contact pressure. The stiffness is not formed at once, and it will develop with time, so the changes of the deformation of secondary lining and the contact pressure become complex. Take normal cement and rapid hardening cement as an example, it can be seen from formulation (8) and (9), the modulus increases with time. When t increases to infinity, Ec(∞) is equal to 1.13 E28 ,
which is the ultimate value. So the modulus of concrete on 28th day E28 is 88.3% of the ultimate value. On 28th day, the increasing rate of modulus is small, only 0.00223 E28 , and it will become smaller as time going on. Guo (1999) presented that the strength and modulus of concrete are influenced by some factors, such as the kind and moisture content of cement, the quality of cement, admixture, curing condition, temperature and humidity content, and etc. Meanwhile, the strength changes under longterm load. So td is influenced by many factors, not just 28 days. In this project, td is 33 days, very near 28. Certainly, the effect of tunnel excavation is also important. If tunnel excavation is stopped earlier, after secondary lining is constructed, the contact pressure will be small. Though the stiffness of lining still increases, its effect will not be so clear, and the two obvious change stages will not occur. After secondary lining is constructed, if tunnel excavation goes on very long, the effect of excavation will be the most important. Though the stiffness of lining still increases, its effect will not be so clear, and the two obvious change stages will not occur. So only tunnel excavation lasts certain time near the section, the two obvious change stages and td will occur. Rock creep is also important. If creep is not significant, the contact pressure will not increase quickly at the beginning of the second stage. Only if rock creep is significant and lasts long, the two obvious stages and td will occur.
3. DEFORMATION OF INITIAL LINING 3.1 General situation Fig.4 shows the change curve of tunnel crown displacement with time after the excavation of top bench. This measured section is located at Dafengyakou tunnel. And inrush water current once occurred. The surrounding rock is violet red clay and black mudstone, belonging to class III. During the measurement time, the excavation face of top bench is 5m-48m before the section. In Fig.4, the positive crown displacement means that the displacement directs to the inside of tunnel, and the negative crown displacement means that the displacement directs to the outside of tunnel. Point G1 is at the left and near the crown, and Point G2 is just at the crown (see Fig.4). Because Point G3 is quickly damaged, there are only data of Point G1 and G2.
4
Paper 3B 20 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
3.2 Analysis of data
du
From Fig.4, the displacements at point G1and G2 with time satisfy exponential rule:
dt
b t
65 . 142 t
2
5. 64 t
exp −
(12)
So the following results can be drawn: Firstly, the ultimate displacement is 11.55mm. on 25th day, the displacement is 9.22mm, 80% of the ultimate. Secondly, on 25th day, the displacement rate is 0.1mm/day. From then on, it becomes smaller. Thus, after the excavation of top bench, though the ultimate diplacement is not big, surrounding rock needs a long time to be stable.
u =a × exp −
(10)
In which u is crown displacement (mm), t is time (day), a and b are constants which are larger than 0. The two displcements satisfy the same rule, so either can be selected to analyze. Take point G2 as an example, of which the fitting curve is:
5 .64 t
=
u =11 .55 × exp −
(11)
The displacement rate is:
14 Crown displacement mm
G2 G1
12
G3
10 8 G1 G2 Fitting curve of G1 Fitting curve of G2
6 4 2 0 0
10
20
30 Time
40
50
60
days
Figure 4. The curve of crown displacement versus time after the excavation of top bench.
3.3 Effect of hydrologic condition and support From the above study, it has been known that at this measured section the deformation needs a long time to be stable. It is mainly affected by hydrologic condition and support. Inrush water current once occurs. Surrounding rock is weak with many fissures and abundant underground water. Supporting wall with the height of 3m was constructed after the occurrence of inrush water. Advanced grouting, central drainage, the steel arch set with the clearance of 60cm, and shotcrete with the thickness of 20cm were adopted. So the tunnel lining resists the deformation more than ever, which can be known from that the ultimate displacement is only 11.55mm. But because of the characteristic of weak rock and abundant underground water, the effect of tunnel excavation
on rock will last a long period and then the deformation will become stable, which should be paid attention to in the future design and construction of rock tunnel.
4. CONCLUSIONS At No.1 Yuanjiang tunnel, the change of the contact pressure between initial and secondary lining is mainly affected by tunnel excavation, rock creep and time-dependent modulus of lining. The change phrase can be divided into two stages. The first stage is some time after constructing the secondary lining, the change of pressure is mainly on tunnel excavation, rock creep and timedependent modulus of lining. The pressure changes with time as hyperbolic rule. In the second stage, the change of pressure is mainly on rock creep. The
5
Paper 3B 20 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
increment of pressure changes with the increment of time also as hyperbolic rule. In the change of contact pressure, the parameter td is the time that the first stage lasts. It is considered that td is on the time which is needed for the stiffness of tunnel lining to become stable, tunnel excavation and rock creep. In this project, td is 33 days, which is very near 28 days when the modulus of concrete has become stable from the change rule for the modulus of concrete with time. At Dafengyakou tunnel, for the section where inrush water occurred, the crown displacement after the excavation of top bench changes with time as exponential rule. The reinforcement adopted decreases the ultimate value, but because of the inherent characteristic of the weak rock and abundant underground water, the deformation will need a long period to be stable.
5. REFERENCES Comite Euro-International du Beston. 1993. Bulletin D’ information NO.213/214 CEB-FIP Model Code 1990 (Concrete Structures). Lausanne. Guo, Zh.H. 1999. Theory of reinforcement concrete structure. Beijing: Qinghua University Press. Huang,H.W. & Xu, L. 2004, Study on the deformation and internal force of the surrounding rock and initial lsupport in Da Feng Ya Kou rock road tunnel. Chinese Journal of Rock mechanics and Engineering 24(1): pp. 19. Kang,N. 1997, Construction monitoring of Donggang tunnel. Chinese Journal of Rock mechanics and Engineering 17(2): pp. 140-147.
Li, X.H. 2002. NATM and measurement technology of tunnel. Beijing: Science Press. Lu, Ch.Y. & He, Ch.Y. 1998. Concrete structure and bricking-up structure. Chongqin: Chongqin University Press. Mahar,J.W. 1975. Shotcrete practice in underground construction: Final report. Dept. of Civil Engrg. Univ. of Illinois at UrbanChampaign, Springfield, VA. Pan,Y.W. & Dong, J.J. 1991. Time –dependent tunnel convergence – . Formulation of the model. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 28(5): pp. 469-475. Pan,Y.W. & Dong, J.J. 1991. Time –dependent tunnel convergence – . Advance rate and tunnel-support interaction. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 28(5): pp. 477488. Pan,Y.W. & Huang, Z.L. 1994. A model of the time-dependent interaction between rock and shotcrete support in a tunnel. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr. 31(3): pp. 213219. Wang,J.Y. 1990. Principles of monitoring and informational design in tunnel construction. Beijing: Chinese Railway Press. Weber,J.W. 1979. Empirische formeln zur beschreibung der festigkeitsentwicklung und der entwicklung des e-moduls von beton betonwerk und fertigtechbik. Yang,L.D. 1996. Theory of inversion on geotechnical engineering and construction experience. Beijing: Science Press.
6