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Pre-nailing support for shallow soft-ground tunneling
Tunnelling and Underground Space Technology 42 (2014) 216–226
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Pre-nailing support for shallow soft-ground tunneling D.H. Seo a, T.H. Lee b, D.R. Kim b, J.H. Shin b,⇑ a b
Hyun Engineering & Construction Co., Ltd., Republic of Korea Department of Civil Engineering, Konkuk University, Seoul, Republic of Korea
a r t i c l e
i n f o
Article history: Received 12 September 2013 Received in revised form 27 January 2014 Accepted 10 March 2014
Keywords: Shallow tunnel Soft-ground tunnel Nail Pre-support Reinforcement
a b s t r a c t In tunneling, supports are usually installed after excavation. Thus, the risk of tunnel collapse is highest immediately after excavation at the tunnel face. This is one of the main problems faced when constructing shallow tunnels in soft ground. In this paper, a pre-support tunneling method using a pre-nailing technique is proposed to improve face stability and reduce tunnel deformation. By driving nails into the ground before excavation, it is possible to achieve mechanical advantages such as restricting the deformation of the ground and preserving the arching of the ground. A theoretical governing equation for the pre-installed nails was formulated, and the mechanism whereby the deformation is reduced was investigated. The mechanical advantages of the method were validated in terms of the ground reaction behavior by carrying out small-scale model tests. A parametric study of the main design factors showed that the distance between the nails is the most important factor. Finally, a case study whereby the method was applied in the field was conducted; the pre-nailing technique was found to be particularly useful for reducing surface settlement and is appropriate for shallow, soft-ground tunneling. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction When a soft ground tunnel with a thin soil cover is excavated, special efforts are required to reduce the degree of tunnel deformation and to ensure stability. In the case of urban tunnels particularly, ensuring safety and controlling settlement are the most important engineering problems (Peck, 1969). To overcome these problems, not only the ground reinforcement must be provided before the tunnel is excavated but longitudinal tunnel reinforcements such as multi-step steel pipe grouting must also be installed (Aksoy and Onargan, 2010; Juneja et al., 2010; Kamata and Mashimo, 2003). However, sometimes the structural advantages provided by these reinforcements cannot be attained because their support functions and installation time are limited. Because tunnel supports can be installed only after considerable deformation has occurred, it is not possible to use these supports as a means of preventing deformation before or immediately after the excavation. Furthermore, additional ground disruption caused by the installation of supports is unavoidable. Therefore, there are limitations to controlling the deformation of the ground with
⇑ Corresponding author. Address: Department of Civil Engineering, Konkuk University, 120 Neungdong-ro, Gwangjin-gu, Seoul 143-701, Republic of Korea. Tel./fax: +82 2 2049 6081. E-mail address: [email protected] (J.H. Shin). http://dx.doi.org/10.1016/j.tust.2014.03.010 0886-7798/Ó 2014 Elsevier Ltd. All rights reserved.
supports inside the tunnel. As shown in Fig. 1, the greatest risk of collapse is at the face. If supports could be installed prior to the excavation of the tunnel, the risk of collapse can be significantly reduced, as indicated by the dotted line in Fig. 1. Korbin and Brekke (1976), through model testing, reported that pre-reinforcement of the ground not only limits the deformation of the tunnel and increases the length of time that it can support itself, but also increases the level of safety. Bolts and nails are important reinforcing and/or supporting elements in tunneling (Ng and Lee, 2002; Oreste and Dias, 2012; Osgoui and Oreste, 2007). In this study, we investigated the prenailing technique, whereby nails that provide ground reinforcement and support are installed before the tunnel is excavated. In particular, we examined the technique from the viewpoints of mechanical principle, design factors, and field applicability. As shown in Fig. 2, pre-nailing refers to the insertion of steel bars or pipes by drilling from the ground surface to the peripheral-tunnel boundary before the start of excavation. By using pressure grouting to install nails, ground reinforcement and pre-support can be provided during excavation. Finally, the nails are connected to lattice girders and/or steel supports, which are installed immediately after the excavation; this allows the nails to act as part of a combined tunnel support system. Therefore, the nails function both as ground reinforcement and as support, similar to the rock bolts installed inside the tunnel. Because nailing is possible on the ground surface and can be performed before the tunnel is
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collapse potential
217
in convergence suppresses the settlement of the subsurface and surface. However, in practice it would not be easy to separate these effects, because both are achieved by taking advantage of the shear resistance between the nails and the soil.
risk reduction
2.2. Governing equation for nail movement pre-nailing pipe roofing excavation direction
ground reinforcement
Fig. 1. Potential of collapse at the tunnel face.
excavated, it is referred to as ‘‘pre-nailing support.’’ Thus, the development of the pre-nailing technique has been based on the concept of a pre-supported tunnel, which incorporates existing simple reinforcement into the support structure of the tunnel. In this study, the mechanical principle of the pre-nailing method was investigated theoretically and the design factors were analyzed through model testing and numerical analysis. Finally, the technique’s practical applicability was verified through an actual field project. 2. Theoretical background to nail behavior 2.1. Concept of pre-support The principle of the pre-nailing technique can be understood by referring to the concept of convergence confinement. Fig. 3 shows the ground reaction curves for pre-nailing. Because pre-nailing provides ground reinforcement, the ground reaction curve is considerably lower than that before reinforcement, which results in a reduction in the convergence (Fig. 3(a)). Additionally, because nails are already installed before the excavation, they can share the tunnel bearing pressure even before the excavation by shifting the support characteristic curve to the origin (Fig. 3(b)). Therefore, pre-nailing suppresses the overall displacement Du1 + Du2, where the ground reinforcement effect reduces displacement Du1 and the pre-support function reduces displacement Du2. The reduction
pre-nailing pressurized grouting
The principle whereby settlement is reduced through the use of pre-nailing can be examined by studying the behavior of a single nail installed at the center of a tunnel. Fig. 4(a) shows how tunneling affects the movement of the ground into which a nail has been installed. To derive the governing equation for the nail, it is assumed that the ground is homogeneous, isotropic, and elastic, and that there is no slippage between the nail and the ground. The nail is installed prior to the excavation and is in a ‘‘0’’ stress state. As the excavation face approaches the nail, however, the settlement of the ground causes the nail to go into tension. According to Fleming et al. (1985), the shear stress (s) at the boundary of the pile (nail) and ground is proportional to the ground displacement (S):
s
GS 4r 0
ð1Þ
where G, S, and r0 are the shear modulus of the ground, displacement at the boundary, and radius of the nail, respectively. The load P applied to the nail is transferred to the skin friction of the nail. If the equilibrium condition for an infinitesimal element of the nail is considered as shown in Fig. 4(b), the equilibrium equation is obtained as
P ¼ P dP þ 2pr 0 sdz
ð2Þ
If Eq. (1) is then added to Eq. (2),
dP p ¼ GS dz 2
ð3Þ
If the elastic modulus of the nail is E, the constitutive equation for the nail can be formulated as
ea ¼
dS 1 P ¼ dz E pr 20
ð4Þ
connecting
before excavation
excavation & support installation
(a) pre-nailing
(b) combined-supporting system
Fig. 2. Construction sequence of pre-nailing method.
p p0
p p0
p p0
reinforced
prenailing support
unreinforced
unnailing support
+ Δu r1
ur
(a) ground reinforcement
Δu r 2
ur
(b) pre-nailing support Fig. 3. Principle of pre-nailing support.
= ur Δu = Δu r 2 + Δu r1
(c) combined effect
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nail
S
P-dP
z A
nail 2r0 Sc
dz
P
P
element ‘A’
tunnel
Fig. 4. Nail behavior due to tunnel excavation.
From Eqs. (3) and (4), the following governing equation for nail behavior is obtained: 2
d S 2
dz
¼
GS 2E r 20
ð5Þ
The solution to the above differential equation is
S ¼ C 1 ekz þ C 2 ekz where k ¼
ð6Þ
qffiffiffiffiffiffiffiffiffi
G . 2E r 20
1 fðSc St ekl Þekz þ ðSt ekl Sc Þekz g ekl ekl
ð7Þ
The nail stress is
rz ¼ E ez ¼ E ¼
ekl
dS dz
E fðSc St ekl Þkekz þ ðSc St ekl Þkekz g ekl
ð8Þ
The nail load is
Pn ¼ rz pr 20 ¼
pr20 E ekl ekl
fðSc St ekl Þkekz þ ðSc St ekl Þkekz g
ð9Þ
At the tunnel crown. z = l; rz = ry
Sc ¼
2St þ
St z0 r o P0 ¼1n Sc 2r o
ðekl ekl Þry E k
1 ekl þ ekl
ð10Þ
St
S
nail St : surface settlement S
nailed
Sc : crown settlement
z
Sc
kl ðe ekl Þry 1 ekl þ ekl 2a E k
ð12Þ
According to Ward and Pender (1981), it can be assumed that St/ Sc 0.25 for shallow tunnels in sandy soils, although there is significant scatter. For a tunnel with depth z0 = 10 m, we assumed that a nail with a radius r0 = 0.029 m and an elastic modulus E = 210,000 MPa was installed in the ground, which has a shear modulus G = 30–100 MPa. We assumed the yield strength of the nail to be 400 MPa. The settlement (displacement of the nail) along the nail length is shown in Fig. 6(a) for each of the ground conditions. This shows that the amount of settlement at the surface is slightly larger than that for the subsurface. The nail behavior can clearly be seen in Fig. 6(b). This shows that the tensile forces act in other directions on the basis of the zero stress points. This negative behavior results from the tension in the nail, and is reduced significantly as the stiffness of the ground falls, and as the stiffness, yield stress and sectional area of the nail increase. This effect results only from the nail and does not take the grouting effect into consideration. We performed a parametric study in which we varied the nail load, nail section, and nail yield stress. The results are shown in Fig. 6(c) and (d). Although it would be incorrect to assume elasticity after the completion of the excavation, the stress state existing before and immediately after the excavation would not deviate much from this assumption. Slippage between the nail and the ground may cause a reduction in the soil resistance and the failure of the nail, thus needs to be checked. As the nailing process involves pressurized grouting and the contact strength between the nail and the grout is generally greater than that of the soil, any surface failure will generally start at the nail-soil interface. However, in the area in the vicinity of the tunnel-excavation boundary, a large plastic deformation may cause some slippage at the grout-soil interface. The plastic range caused by the tunnel excavation can be evaluated using plastic deformation theory. According to Bray (1967), Fenner (1938) and Kastner (1962), the extent of the plastic range from the tunnel-excavation boundary, shown in Fig. 7(a),can be evaluated using
Re ¼ Ro Fig. 5. Displacement of ground surface and subsurface by tunnel excavation.
ð11Þ
where n is a measure of the dilatancy of the ground (large for dense sand; small for clay). If St = aSc, Eq. (10) can be rewritten as
Sc ¼
The boundary conditions can be set by considering the ground behavior due to tunneling, as shown in Fig. 5. If the settlement at depth z is S, the conditions can be set as z = 0; S = St at the ground surface, and z = l; S = Sc at the tunnel crown.
S¼
To check the validity of Eqs. (7) and (8) and determine the nail behavior, we conducted a simple parametric analysis. Atkinson and Potts (1977) derived a simple relationship between the maximum surface settlement and the crown settlement
rv o ð1 sin /Þ cðcos / cot /Þ p þ c cot /
K 11 p
ð13Þ
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0 0.1 0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.7
0.7
0.8
0.8
0.9
0.9
1.0
1.0 0
1
2
3
4
5
6
7
8
-100
100
200
300
400
Nail stress ( σ, MPa )
(a) effect of soil stiffness : settlement
(b) effect of soil stiffness : nail stress
P=1,131 kN P=3,142 kN P=6,158 kN
0.2
0.2
0.3
0.3
0.4
0.4
z / z0
0.1
0.5
0.5
0.6
0.6
0.7
0.7
0.8
0.8
0.9
0.9
1.0
1.0 2
4
6
8
10
12
14
P=1,131 kN P=3,142 kN P=6,158 kN
0
0.1
0
0
Settlement (S, mm)
0
z / z0
G= 30MPa G= 50MPa G=100MPa
0.1
z / z0
z / z0
0
G= 30MPa G= 50MPa G=100MPa
16
-50
0
50 100 150 200 250 300 350 400 450
Settlement (S, mm)
Nail stress (σ , MPa)
(c) effect of nail load : settlement
(d) effect of nail load : nail stress
Fig. 6. Parametric study on the nail behavior.
where Ro is the tunnel radius, rvo is the initial vertical stress, p is the support pressure, and Kp is the coefficient of passive earth pressure. Here, Re is inversely proportional to the supporting pressure. The relationship between the supporting pressure and Re is shown in Fig. 7(b). In fact, the supporting pressure can be controlled by introducing other supporting elements such as shotcrete, rock bolts, and steel supports. In shallow tunnels, these additional support elements can handle a considerable portion of any overburden. Numerical simulation has shown that about 40% of an overburden is borne by these supports. For the case considered in this study, the plastic range, (Re Ro), is less than 1 m, which is small compared to the tunnel depth. If plasticity occurs, the slippage can be considered by reducing the soil resistance by the same amount as the plastic range. However, basically, as the nailing is one of the support elements, the entire support system must be redesigned such that the failure conditions are not exceeded.
the ground stiffness and consequently reduce the amount of settlement. It is not easy to consider the grouting effect for an individual nail. A simple method for evaluating the modified stiffness of the mixed ground involves considering the equivalent stiffness which is proportional to the grouted area. Thus, the resulting nailing effect consists of the effect of the nail itself and that of the grouting. The combined effects of both the nail and grout can be conceptually presented as shown in Fig. 9. Although the use of the nail reduces tunnel deformation significantly, it also increases the surface settlement slightly. This negative effect was not found to be due to the ground modification effect of the grouting. Rather, the use of grouting significantly reduces the ground deformation.
2.3. Effect of pressurized grouting
In general, nails are installed as a group. The effect of a group of nails can be deduced from the behavior of a fully grouted rock bolt (Bernaud et al., 2009; Bobet and Einstein, 2011; Carranza-Torres, 2009). The tensile stress in each nail limits the deformation of the ground. Therefore, the installation of a nail causes the radial
The nailing process includes pressurized grouting (37 kg/cm2) which reinforces the ground. Fig. 8 shows the grouting profile around a nail. Ground reinforcement using grouting will increase
2.4. Movement and design variables of nail groups
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advantage is a maximum when the installation angle is identical to the direction of the ground displacement vector. However, the depth to which the nails are installed is much greater than that of the rock bolt. Thus, the installation angle should be determined by considering the aspect of the settlement reduction. Fig. 10(a) shows the direction of the representative displacement vectors at the surface as determined by measurement. It is generally held that these vectors are directed toward the center of the tunnel (Attwell, 1978; O’Reilly and New, 1982), but according to Taylor (1995) and Mair and Taylor (1997), the displacement vectors are directed toward a point much lower than the center. As shown in Fig. 10(b), the convergence is not uniform in an actual horseshoe-shaped (or non-circular) shallow tunnel, and is much greater at the tunnel crown. Therefore, in this case the nails can effectively contribute to deformation control when installed in a direction which is close to vertical to the surface. It is also often difficult to install the nails with a precise inclination, making the vertical installation preferable for convenience in the field.
σ σθ nail
σR σvo
σe pi
R0
R Re Plastic Zone
Pressure ratio ( p
vo ,%)
(a) plastic range around tunnel
50
2.5. Experimental study of ground reaction curve
40
Because it is difficult to consider tunnel behavior through theoretical analysis or a large-scale model-based simulation, the concept of pre-nailing was investigated by using a simple smallscale trapdoor model test. The similarity of the model to the original shape of the trapdoor can be obtained as follows, using the governing equation given in Eq. (5).
30 20 10 0
-1
lp r op
plastic
elastic
0
1
2
3
4
5
6
Re-Ro (m)
(b) relationship between support pressure and plastic range Fig. 7. Slippage evaluation.
grouted area : A g nail section d = 29 mm
d = 76 ~ 105 mm d = 120 ~ 150 mm Fig. 8. Profile of grouted nail.
stress rr toward the tunnel center to decrease to Eq. (14):
r0r ¼ rr
T SL SA
r0r , as shown in ð14Þ
where T is the axial force of the nail and SL and SA are the lateral and longitudinal nail distances at the tunnel boundary, respectively. If the nails are to function as pre-supports, each should be installed at the same angle as the rock bolt because the mechanical
2
2 Gp lm Gm ¼ Ep r om Em
ð15Þ
where subscript ‘‘p’’ represents the prototype and ‘‘m’’ represents the model. In this experiment, the width of the trapdoor was set to 50 mm to replicate a tunnel with a diameter of approximately 2.0 m, according to the rule of similarity. A steel wire with a diameter of 0.8 mm was used to model the nail (r0 = 0.4 mm). To simulate the effect of the grout used in the installation of the nail, soil particles were attached to the surface of the nail beforehand, as shown in Fig. 11(b) (Tsukada et al., 2006). The nails were installed vertically, and the ground was formed by using a sand falling technique. The soil tank, installation profile of the nails, and material properties are shown in Fig. 11. Five nails were installed laterally (SA) with a 15-mm spacing, and three nails were installed longitudinally (SL) with a spacing of 5, 7, and 13 mm, respectively. By lowering the three trapdoors in the order of No. 1, No. 2, and then No. 3, the vertical movement (corresponding to the tunnel convergence) and the stress (corresponding to the bearing pressure) were measured. Fig. 12 shows the relationship between the pressure normalized by the initial static pressure and the normalized vertical displacement of the trapdoor in position No. 2. This relationship corresponds to the ground reaction curves caused by the tunnel excavation. When the nails were added for support, the ground reaction curve (GRC) moved to the left, which showed that the nails reduced the ground displacement by absorbing a portion of the ground stress. It was also shown that the magnitude of the deformation is strongly dependent on the nail spacing. As the distance between the installed nails is reduced, the amount of settlement is suppressed. This model test did not consider the combined effect of a support installed inside a tunnel. If it were to be considered, then the amount by which the settlement is suppressed would be more significant. 3. Numerical parametric study of design factors The design factors, which are reviewed at the time of pre-nailing design, are the installation length of the nails, installation angle
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effect of grouting only S
effect of nail only
combined effect
S
S
+
=
non-nailed
z
non-nailed
non-nailed
grouted
nail effect
z
z
Fig. 9. Nailing effects in terms of ground settlements.
A vertical nail
z0
inclined nail
B
0.175 z 0.325 0
A : Attewell, 1978; B : Taylor, 1995
O
(a) displacement vectors
(b) non-circular shallow tunnel
Fig. 10. Installation angles of group nails.
400 mm
sand grains nail
Tr : No.2 Tr : No.1
400 mm
H
soil A
Load cell
100 mm
Tr : No.3
50 50 mm mm
D=50 mm
nail
trap door
B
(a) plan of test soil tank
A
A
A GS = 2.63 γ = 15.17kN/m3 e = 0.734 Dr = 54.85% φ = 36.24˚
D
B
(b) section profiles of the trap door and model nail Fig. 11. Layout of model tests.
of the nails, spacing between the nails (vertical and horizontal), installation range of the nails, etc. A parametric study using a two-dimensional numerical model was carried out to investigate the effect of these design factors.
we used. For a qualitative study of the nail effect, the grouting is not considered in two-dimensional analyses. The nail design factors reviewed were the nail distance (SL), nail length (L), installation angle (h), and installation range (B), as shown in Fig. 14. The analysis cases are summarized in Table 1.
3.1. Analysis model and analysis cases 3.2. Results As shown in Fig. 13, a horseshoe-shaped tunnel with a width of 13 m and a height of 9 m, which is 15 m below the ground surface, was selected as the analysis model. To eliminate the effects of the model boundary conditions, the widths of the model boundaries were assumed to be more than four times the width of the tunnel. The ground reinforcement effect of the grouting was ignored and the nail and shotcrete were modeled by an elastic bar element. The ground behavior was simulated using linear elastic and Mohr-Coulomb models. Fig. 13 lists the material parameters that
The effects of the pre-nailing are mainly evaluated in terms of the amount of settlement at the crown of the tunnel. The amount of settlement was normalized by the ‘‘non-nailed’’ results. The settlement trends at the surface and at the crown were the same except for the case of the nail length. The effect of the nail spacing was investigated by varying the spacing between the nails from 1 m to 3 m. Fig. 15(a) shows the amount of crown settlement for different nail spacing. As the
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Table 1 Analysis cases.
non-nail
’0
SL = 15mm SL = 30mm
1
SL = 45mm
0.5
Design factor
Installation range
Nail distance (m)
Nail length (m)
Installation angle (°)
SL L
– –
1.0; 2.0; 3.0 1.0
– 90
h B
– 0.1D; 0.5D; 1.0D
1.0 –
7.0 6.0; 9.0; 12.0 9.0 9.0
60; 75; 90 90
increase in SL
settlement reduction
0 0.5
0
1
normalized Displacement (δ/δf) Fig. 12. Ground reaction curves (df: final displ).
H=15m
9m 4D D=13m
ground properties
shotcrete properties
γ = 19 kN/m3 c = 15 kPa φ = 30˚ E = 85 MPa ν = 0.35 K0 = 0.5
γ s = 25 kN/m3 Es1= 5,000 Mpa Es2= 15,000 MPa
4D
nail properties γ n = 78.5 kN/m3 E n= 210,000 Mpa d = 0.029m
The effect of the nail installation angle was investigated within a range of 60°–90°. As shown in Fig. 15(c), the amount of settlement was a minimum when the nail angle was 75°. Fig. 15(d) shows the effect of the horizontal nail installation range. The effect of installation range was not significant in the case of a shallow, horseshoe-shaped tunnel. The nail installation width contributed to a slight reduction in the surface settlement at a distance from the tunnel wall equal to 0.5 times the tunnel width (D). However, when the width value was exceeded, there was almost no structural advantage. The theoretical solution showed that tension in the nails could increase the amount of surface settlement. Thus, the nail length (or grouting length) is an important factor in the design of the prenailing. Although this effect is eliminated when the grouting effect is considered, the effect of the nail length is interesting and was investigated using numerical analysis. The results of this numerical analysis for different distances from the excavation boundary are presented in Fig. 16. This shows that the maximum amount of surface settlement increases as the nail length increases. This is identical to the theoretical solution, and indicates that it is not necessary to install (or grout) nails that extend to the ground surface in terms of reducing the amount of settlement at the surface. 4. Field application The pre-nailing method was applied to an actual tunnel project in which a shallow tunnel was constructed in decomposed granite soil and weathered rock. Practically, because the effect of construction using pre-nailing cannot be compared to the construction of an actual tunnel under the same conditions, the effect of pre-nailing was predicted by carrying out a three-dimensional numerical analysis. The results were then compared with measurements of the settlement of the crown, taken in the field.
Fig. 13. Analysis model.
S L´
L
4.1. Project description
B
D
L : nail length B : installation range S L : nail distance : installation angle
Fig. 14. Design parameter of pre-nailing method.
distance between the nails was reduced, the amount of settlement fell considerably, but once the distance exceeded 3 m, the effect of the nails on reducing the amount of settlement decreased. The effect of the nail length on tunnel deformation was investigated by changing the distance of the nail installation from the tunnel boundary (6–12 m). As shown in Fig. 15(b), for nail lengths of up to 6 m, the greater the distance of the nail from the tunnel, the more the settlement was reduced. Once the distance exceeded 9 m, however, the settlement reduction effect was lessened.
Fig. 17(a) shows the ground profile and tunnel cross-section to which the pre-nailing was applied. The project consisted of a largesection, horseshoe-shaped tunnel, 10.14 m high and approximately 20 m wide, with 12.5 m of soil cover. The tunnel face presented decomposed granite soil (see Table 2). Nails were installed vertically with a 1.5-m spacing relative to the tunnel axis and a 1.0-m lateral spacing, as shown in Fig. 17(b). The nails were combined with the steel supports and shotcrete lining immediately after the tunnel was excavated. The thickness of the shotcrete was 0.25 m, which was applied in two layers, first of 0.1 m and then of 0.15 m (see Table 3). 4.2. Three-dimensional modeling and analysis results The length of the model was set to 40 m relative to the tunnel axis. Within this range, modeling of a 20-m length of excavation was carried out. The ground movement and the lining were modeled using the elastic and Mohr-Coulomb models. The nails were modeled using elastic bar elements. To account for the effect of
223
, %)
100
normalized dispacement (
95 90 85 80 75 70 1
2
3
100 95 90 85 80 75 70 3
6
9
12
nail length (m)
(a) effect of nail spacing
(b) effect of nail lengths , %)
nail spacing (m)
100 (-)θ
95 90 85 80 75 70 60
75
90
15
100
(+)θ
95
normalized dispacement (
normalized dispacement (
, %)
normalized dispacement (
, %)
D.H. Seo et al. / Tunnelling and Underground Space Technology 42 (2014) 216–226
90 85 80 75 70 0.1B 0.2B 0.3B 0.4B 0.5B 0.6B 0.7B 0.8B 0.9B 1.0B
nail angle (degree)
nail installation range
(c) effect of installation angle
(d) effect of installation range
Fig. 15. Effect of installation on tunnel deformation.
Table 2 Properties of soil. Property
Decomposed granite soil (dgs)
Grouted dgs
Soft rock
Hard rock
E (MPa) v / (°) c (kPa) c (kN/ m3)
85 0.35 30 15 19
380 0.35 30 43 19
350 0.30 33 300 21
1500 0.27 35 800 23
distance from crown (m)
15 12
6.0m 9.0m 12.0m
y
9 6 3 0 -12
-14
-16
Table 3 Properties of ground support. Shot.1
Shot.2
-20
-22
-24
-26
E (MPa) c (kN/m3)
210,000 78.5
5000 25
15,000 25
the grouting, the reinforced range was set as a composite body of the grout bulb and the original ground. The material properties of the reinforced range were evaluated by applying the area ratio as a weighted value to the stiffness of each element such as the ground and grout bulb, and by calculating the equivalent elastic coefficient and equivalent cohesion intercept. For instance, the stiffness of the grouted ground was evaluated by considering
ð16Þ
where Ag is the grouted area (volume), Ao is the ungrouted area, Eg is the stiffness of grout material, E0 is the stiffness of original ground (Fig. 8). Fig. 18 shows the 3D analysis model and the installation mode of the nails. By setting the first excavation length to 1.0 m, the
(a) settlement profile , %)
Nail
normalized dispacement (
Property
Ag Ao Eeq ¼ Eg þ E0 Ag þ Ao Ag þ Ao
-18
displacement (m)
100
95
90
85
80 3
6
9
12
15
nail length (m)
(b) maximum surface settlement Fig. 16. Effect of nail length.
analysis was done based on the actual field construction process. The analysis was carried out for both the non-nailed and pre-nailed conditions.
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decomposed granite soil (dgs) soft rock
shotcrete hard rock
10.14m
19.56m
(a) ground and tunnel profile tunnel driving nails nail diameter, d=0.029m 1.5m
nails 1.5m
excavation 1.0m
Plan
section
connection details
(b) nail installation
Fig. 19 shows a comparison of the analysis results for the surface settlement and the subsurface displacement. Because of the inclined ground profile and surface geometry, the maximum settlement occurred slightly to the right of the tunnel crown. Additionally, it can be seen that pre-nailing reduced the ground surface settlement by a maximum of approximately 43%. This is relatively large in comparison with the results of the parametric study. The main difference between the analyses is the consideration of grouting. We can see that the ground reinforcement effect of the pre-nailing is also considerable. For non-nailing, the subsurface settlement increased exponentially close to the tunnel crown; however, when pre-nailing was applied, it exhibited a linear increase. Compared to non-nailing, the crown settlement was
surface displacement (mm)
Fig. 17. Field application of pre-nailing.
0 -4 -8
nailed (nail + pressurized grouting)
-12
non-nail
-16 -20 -80
-60
-40
-20
0
20
40
60
80
distance from the tunnel center (m)
(a) surface settlements distance from crown (m)
14 y
12 10 non-nail
8
nailed
6
(nail + pressurized grouting)
4 2 0 -5
-10
-15
-20
-25
-30
-35
displacement (mm)
(a) 3D model
(b) nail model
Fig. 18. 3D analysis model.
(b) subsurface settlements Fig. 19. Numerical results from 20 m ahead of tunnel portal.
-40
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distance from tunnel face 0
0.5D
1.0D
1.5D
2.0D
2.5D 0
measured (mm)
measured
4
8
8
12 16
12
predicted longitudinal settlement profile with nails
16
20 24
20
predicted (mm)
4
0
28
24 28 measured estimated
32 0
20
predicted longitudinal profile without nails
32 36
40
60
80
40 100
Elapsed time (day) Fig. 20. Comparison of field measurements and numerical predictions.
reduced by approximately 62.5%, which is approximately 10% more than the rate of reduction in the surface settlement. Fig. 20 compares the measured results for ‘‘settlement-time’’ and the analysis results for ‘‘settlement-face distance’’ at the crown. The measured value for the tunnel crown was approximately 7 mm, which does not include any initial displacement before the installation of the measurement device. Based on the numerical analysis and considering the prior displacement, the total crown displacement was estimated to be approximately 12 mm including the measured 7 mm, as shown in Fig. 20. The settlement of the crown was 35 mm with no nailing and 13 mm when nailing was applied. The predicted value was a little higher than the measured value. If this is compared with the non-nailed case, we can estimate that the settlement of the crown is reduced by approximately 50% as a result of pre-nailing.
5. Conclusions The risk of collapse in tunnel excavation is highest at the excavation face. However, because supports are not installed until after the excavation, there is a fundamental limit to the degree that tunnel safety can be improved and settlement reduced by using supports inside the tunnel. To overcome such problems, the prenailing support method, which works not only as ground reinforcement but also as a support during excavation, has been proposed. The behavior of a nail during tunneling was identified by deriving the governing equation for the nail. It was found that the effect of deformation control was large, provided the ground exhibited a large relative displacement between the surface and the crown. Through model-based tests of the use of pre-nailing, it was shown that the ground supports shifted the GRC to the left and caused the characteristic curve of the supports to originate from the excavation, thereby reducing the amount of settlement. From the results of a numerical parametric study of the design factors, the factors governing the pre-nailing were found to be the installation distance and angle and the installation range. We showed that the installation distance was the main factor governing the reduction of the settlement. For a non-circular tunnel with thin soil cover, a vertical installation can greatly reduce surface settlement and improve the ease of construction without a large structural loss. From the results of the field application and a three-dimensional numerical analysis, we showed that pre-nailing reduces the ground deformation by approximately 50%. We can thus
conclude that this technology is useful for reducing surface settlement and improving the stability of the tunnel face during excavation in soft ground with a thin soil cover.
Acknowledgement This study was supported by the National Research Foundation of Korea under Research Project 2012R1A2A1A01002326. The authors greatly appreciate the support provided.
References Aksoy, C.O., Onargan, T., 2010. The role of umbrella arch and face bolt as deformation preventing support system in preventing building damages. Tunn. Undergr. Space Technol. 25 (5), 553–559. Atkinson, J.H., Potts, D.M., 1977. Stability of a shallow circular tunnel in cohesionless soil. Géotechnique 27 (2), 203–215. Attwell, P.B., 1978. Ground movements caused by tunnelling in soil. In: Geddes, J.D. (Ed.), Int: Proc. Conf. on Large Movements and Structures. Pentech Press, London, pp. 812–948. Bernaud, D., Maghous, S., De Buhan, P., Couto, E., 2009. A numerical approach for design of bolt-supported tunnels regarded as homogenized structures. Tunn. Undergr. Space Technol. 24 (5), 533–546. Bobet, A., Einstein, H.H., 2011. Tunnel reinforcement with rock bolts. Tunn. Undergr. Space Technol. 26 (1), 100–123. Bray, J.W., 1967. A study of jointed and fractured rock, II. Theory of limiting equilibrium. Rock Mech. Eng. Geol. 5, 197–216. Carranza-Torres, C., 2009. Analytical and numerical study of the mechanics of rock bolt reinforcement around tunnels in rock masses. Rock Mech. Rock Eng. 42 (2), 175–228. Fenner, R., (1938). Untersuchungen zur erkenntnis des gebirgsdruckes. Gluückauf. Fleming et al., 1985. Piling Engineering. Surrey University Press, Glasgow and John Wiley, New York. Juneja, A., Hegde, A., Lee, F.H., Yeo, C.H., 2010. Centrifuge modelling of tunnel face reinforcement using forepoling. Tunn. Undergr. Space Technol. 25 (4), 377–381. Kamata, H., Mashimo, H., 2003. Centrifuge model test of tunnel face reinforcement by bolting. Tunn. Undergr. Space Technol. 18 (2–3), 205–212. Kastner, H., 1962. Statik des Tunnel- and Stollenbaues. Springer, Berlin. Korbin, G.E., Brekke, T.L., 1976. Model Study of Tunnel pre-reinforcement. ASCE J. Geotech. Eng. 4, 895–908. Mair, R.J., Taylor, R.N., (1997). Bored tunnelling in the urban environment. In: Proc.14th Int. Conf. Soil Mech. Found. Eng., Hamburg, vol. 4, pp. 2353–2385. Ng, C.W.W., Lee, G.T.K., 2002. A three-dimensional parametric study of the use of soil nails for stabilizing tunnel faces. Comput. Geotech. 29, 673–697. O’Reilly, M.P., New, B.M., (1982). Settlements above tunnels in the United Kingdom – their magnitude and prediction. In: Proc. Tunnelling 82, IMM, London, pp. 173–181. Oreste, P.P., Dias, D., 2012. Stabilization of the excavation face in shallow tunnels using fiberglass dowels. Rock Mech. Rock Eng. 45 (4), 499–517. Osgoui, R.R., Oreste, P., 2007. Convergence-control approach for rock tunnels reinforced by grouted bolts, using the homogenization concept. Geotech. Geol. Eng. 25 (4), 431–440.
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Peck, R.B., (1969). Deep excavation and tunneling in soft ground – State of the Art Volume. In: Proc. 7th Int. Conf. Soil Mechanics and Foundation Engineering, pp. 225–290. Taylor, R.N., 1995. Tunnelling in soft ground in the UK. In: Fujita, K., Kusakabe, O. (Eds.), Underground Construction in Soft Ground. Balkema, Rotterdam, pp. 123–126.
Tsukada et al., 2006. Mechanism of bearing capacity of spread footings reinforced with micropiles. J. Soils Found. 46 (3), 267–276. Ward, W.H., Pender, M.J., (1981). Tunnelling in soft ground: general report. In: Proceedings of the 10th International Conference on Soil Mechanics and Foundation Engineering, Stockholm, vol. 4.
Contents lists available at ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Pre-nailing support for shallow soft-ground tunneling D.H. Seo a, T.H. Lee b, D.R. Kim b, J.H. Shin b,⇑ a b
Hyun Engineering & Construction Co., Ltd., Republic of Korea Department of Civil Engineering, Konkuk University, Seoul, Republic of Korea
a r t i c l e
i n f o
Article history: Received 12 September 2013 Received in revised form 27 January 2014 Accepted 10 March 2014
Keywords: Shallow tunnel Soft-ground tunnel Nail Pre-support Reinforcement
a b s t r a c t In tunneling, supports are usually installed after excavation. Thus, the risk of tunnel collapse is highest immediately after excavation at the tunnel face. This is one of the main problems faced when constructing shallow tunnels in soft ground. In this paper, a pre-support tunneling method using a pre-nailing technique is proposed to improve face stability and reduce tunnel deformation. By driving nails into the ground before excavation, it is possible to achieve mechanical advantages such as restricting the deformation of the ground and preserving the arching of the ground. A theoretical governing equation for the pre-installed nails was formulated, and the mechanism whereby the deformation is reduced was investigated. The mechanical advantages of the method were validated in terms of the ground reaction behavior by carrying out small-scale model tests. A parametric study of the main design factors showed that the distance between the nails is the most important factor. Finally, a case study whereby the method was applied in the field was conducted; the pre-nailing technique was found to be particularly useful for reducing surface settlement and is appropriate for shallow, soft-ground tunneling. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction When a soft ground tunnel with a thin soil cover is excavated, special efforts are required to reduce the degree of tunnel deformation and to ensure stability. In the case of urban tunnels particularly, ensuring safety and controlling settlement are the most important engineering problems (Peck, 1969). To overcome these problems, not only the ground reinforcement must be provided before the tunnel is excavated but longitudinal tunnel reinforcements such as multi-step steel pipe grouting must also be installed (Aksoy and Onargan, 2010; Juneja et al., 2010; Kamata and Mashimo, 2003). However, sometimes the structural advantages provided by these reinforcements cannot be attained because their support functions and installation time are limited. Because tunnel supports can be installed only after considerable deformation has occurred, it is not possible to use these supports as a means of preventing deformation before or immediately after the excavation. Furthermore, additional ground disruption caused by the installation of supports is unavoidable. Therefore, there are limitations to controlling the deformation of the ground with
⇑ Corresponding author. Address: Department of Civil Engineering, Konkuk University, 120 Neungdong-ro, Gwangjin-gu, Seoul 143-701, Republic of Korea. Tel./fax: +82 2 2049 6081. E-mail address: [email protected] (J.H. Shin). http://dx.doi.org/10.1016/j.tust.2014.03.010 0886-7798/Ó 2014 Elsevier Ltd. All rights reserved.
supports inside the tunnel. As shown in Fig. 1, the greatest risk of collapse is at the face. If supports could be installed prior to the excavation of the tunnel, the risk of collapse can be significantly reduced, as indicated by the dotted line in Fig. 1. Korbin and Brekke (1976), through model testing, reported that pre-reinforcement of the ground not only limits the deformation of the tunnel and increases the length of time that it can support itself, but also increases the level of safety. Bolts and nails are important reinforcing and/or supporting elements in tunneling (Ng and Lee, 2002; Oreste and Dias, 2012; Osgoui and Oreste, 2007). In this study, we investigated the prenailing technique, whereby nails that provide ground reinforcement and support are installed before the tunnel is excavated. In particular, we examined the technique from the viewpoints of mechanical principle, design factors, and field applicability. As shown in Fig. 2, pre-nailing refers to the insertion of steel bars or pipes by drilling from the ground surface to the peripheral-tunnel boundary before the start of excavation. By using pressure grouting to install nails, ground reinforcement and pre-support can be provided during excavation. Finally, the nails are connected to lattice girders and/or steel supports, which are installed immediately after the excavation; this allows the nails to act as part of a combined tunnel support system. Therefore, the nails function both as ground reinforcement and as support, similar to the rock bolts installed inside the tunnel. Because nailing is possible on the ground surface and can be performed before the tunnel is
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collapse potential
217
in convergence suppresses the settlement of the subsurface and surface. However, in practice it would not be easy to separate these effects, because both are achieved by taking advantage of the shear resistance between the nails and the soil.
risk reduction
2.2. Governing equation for nail movement pre-nailing pipe roofing excavation direction
ground reinforcement
Fig. 1. Potential of collapse at the tunnel face.
excavated, it is referred to as ‘‘pre-nailing support.’’ Thus, the development of the pre-nailing technique has been based on the concept of a pre-supported tunnel, which incorporates existing simple reinforcement into the support structure of the tunnel. In this study, the mechanical principle of the pre-nailing method was investigated theoretically and the design factors were analyzed through model testing and numerical analysis. Finally, the technique’s practical applicability was verified through an actual field project. 2. Theoretical background to nail behavior 2.1. Concept of pre-support The principle of the pre-nailing technique can be understood by referring to the concept of convergence confinement. Fig. 3 shows the ground reaction curves for pre-nailing. Because pre-nailing provides ground reinforcement, the ground reaction curve is considerably lower than that before reinforcement, which results in a reduction in the convergence (Fig. 3(a)). Additionally, because nails are already installed before the excavation, they can share the tunnel bearing pressure even before the excavation by shifting the support characteristic curve to the origin (Fig. 3(b)). Therefore, pre-nailing suppresses the overall displacement Du1 + Du2, where the ground reinforcement effect reduces displacement Du1 and the pre-support function reduces displacement Du2. The reduction
pre-nailing pressurized grouting
The principle whereby settlement is reduced through the use of pre-nailing can be examined by studying the behavior of a single nail installed at the center of a tunnel. Fig. 4(a) shows how tunneling affects the movement of the ground into which a nail has been installed. To derive the governing equation for the nail, it is assumed that the ground is homogeneous, isotropic, and elastic, and that there is no slippage between the nail and the ground. The nail is installed prior to the excavation and is in a ‘‘0’’ stress state. As the excavation face approaches the nail, however, the settlement of the ground causes the nail to go into tension. According to Fleming et al. (1985), the shear stress (s) at the boundary of the pile (nail) and ground is proportional to the ground displacement (S):
s
GS 4r 0
ð1Þ
where G, S, and r0 are the shear modulus of the ground, displacement at the boundary, and radius of the nail, respectively. The load P applied to the nail is transferred to the skin friction of the nail. If the equilibrium condition for an infinitesimal element of the nail is considered as shown in Fig. 4(b), the equilibrium equation is obtained as
P ¼ P dP þ 2pr 0 sdz
ð2Þ
If Eq. (1) is then added to Eq. (2),
dP p ¼ GS dz 2
ð3Þ
If the elastic modulus of the nail is E, the constitutive equation for the nail can be formulated as
ea ¼
dS 1 P ¼ dz E pr 20
ð4Þ
connecting
before excavation
excavation & support installation
(a) pre-nailing
(b) combined-supporting system
Fig. 2. Construction sequence of pre-nailing method.
p p0
p p0
p p0
reinforced
prenailing support
unreinforced
unnailing support
+ Δu r1
ur
(a) ground reinforcement
Δu r 2
ur
(b) pre-nailing support Fig. 3. Principle of pre-nailing support.
= ur Δu = Δu r 2 + Δu r1
(c) combined effect
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nail
S
P-dP
z A
nail 2r0 Sc
dz
P
P
element ‘A’
tunnel
Fig. 4. Nail behavior due to tunnel excavation.
From Eqs. (3) and (4), the following governing equation for nail behavior is obtained: 2
d S 2
dz
¼
GS 2E r 20
ð5Þ
The solution to the above differential equation is
S ¼ C 1 ekz þ C 2 ekz where k ¼
ð6Þ
qffiffiffiffiffiffiffiffiffi
G . 2E r 20
1 fðSc St ekl Þekz þ ðSt ekl Sc Þekz g ekl ekl
ð7Þ
The nail stress is
rz ¼ E ez ¼ E ¼
ekl
dS dz
E fðSc St ekl Þkekz þ ðSc St ekl Þkekz g ekl
ð8Þ
The nail load is
Pn ¼ rz pr 20 ¼
pr20 E ekl ekl
fðSc St ekl Þkekz þ ðSc St ekl Þkekz g
ð9Þ
At the tunnel crown. z = l; rz = ry
Sc ¼
2St þ
St z0 r o P0 ¼1n Sc 2r o
ðekl ekl Þry E k
1 ekl þ ekl
ð10Þ
St
S
nail St : surface settlement S
nailed
Sc : crown settlement
z
Sc
kl ðe ekl Þry 1 ekl þ ekl 2a E k
ð12Þ
According to Ward and Pender (1981), it can be assumed that St/ Sc 0.25 for shallow tunnels in sandy soils, although there is significant scatter. For a tunnel with depth z0 = 10 m, we assumed that a nail with a radius r0 = 0.029 m and an elastic modulus E = 210,000 MPa was installed in the ground, which has a shear modulus G = 30–100 MPa. We assumed the yield strength of the nail to be 400 MPa. The settlement (displacement of the nail) along the nail length is shown in Fig. 6(a) for each of the ground conditions. This shows that the amount of settlement at the surface is slightly larger than that for the subsurface. The nail behavior can clearly be seen in Fig. 6(b). This shows that the tensile forces act in other directions on the basis of the zero stress points. This negative behavior results from the tension in the nail, and is reduced significantly as the stiffness of the ground falls, and as the stiffness, yield stress and sectional area of the nail increase. This effect results only from the nail and does not take the grouting effect into consideration. We performed a parametric study in which we varied the nail load, nail section, and nail yield stress. The results are shown in Fig. 6(c) and (d). Although it would be incorrect to assume elasticity after the completion of the excavation, the stress state existing before and immediately after the excavation would not deviate much from this assumption. Slippage between the nail and the ground may cause a reduction in the soil resistance and the failure of the nail, thus needs to be checked. As the nailing process involves pressurized grouting and the contact strength between the nail and the grout is generally greater than that of the soil, any surface failure will generally start at the nail-soil interface. However, in the area in the vicinity of the tunnel-excavation boundary, a large plastic deformation may cause some slippage at the grout-soil interface. The plastic range caused by the tunnel excavation can be evaluated using plastic deformation theory. According to Bray (1967), Fenner (1938) and Kastner (1962), the extent of the plastic range from the tunnel-excavation boundary, shown in Fig. 7(a),can be evaluated using
Re ¼ Ro Fig. 5. Displacement of ground surface and subsurface by tunnel excavation.
ð11Þ
where n is a measure of the dilatancy of the ground (large for dense sand; small for clay). If St = aSc, Eq. (10) can be rewritten as
Sc ¼
The boundary conditions can be set by considering the ground behavior due to tunneling, as shown in Fig. 5. If the settlement at depth z is S, the conditions can be set as z = 0; S = St at the ground surface, and z = l; S = Sc at the tunnel crown.
S¼
To check the validity of Eqs. (7) and (8) and determine the nail behavior, we conducted a simple parametric analysis. Atkinson and Potts (1977) derived a simple relationship between the maximum surface settlement and the crown settlement
rv o ð1 sin /Þ cðcos / cot /Þ p þ c cot /
K 11 p
ð13Þ
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0 0.1 0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.7
0.7
0.8
0.8
0.9
0.9
1.0
1.0 0
1
2
3
4
5
6
7
8
-100
100
200
300
400
Nail stress ( σ, MPa )
(a) effect of soil stiffness : settlement
(b) effect of soil stiffness : nail stress
P=1,131 kN P=3,142 kN P=6,158 kN
0.2
0.2
0.3
0.3
0.4
0.4
z / z0
0.1
0.5
0.5
0.6
0.6
0.7
0.7
0.8
0.8
0.9
0.9
1.0
1.0 2
4
6
8
10
12
14
P=1,131 kN P=3,142 kN P=6,158 kN
0
0.1
0
0
Settlement (S, mm)
0
z / z0
G= 30MPa G= 50MPa G=100MPa
0.1
z / z0
z / z0
0
G= 30MPa G= 50MPa G=100MPa
16
-50
0
50 100 150 200 250 300 350 400 450
Settlement (S, mm)
Nail stress (σ , MPa)
(c) effect of nail load : settlement
(d) effect of nail load : nail stress
Fig. 6. Parametric study on the nail behavior.
where Ro is the tunnel radius, rvo is the initial vertical stress, p is the support pressure, and Kp is the coefficient of passive earth pressure. Here, Re is inversely proportional to the supporting pressure. The relationship between the supporting pressure and Re is shown in Fig. 7(b). In fact, the supporting pressure can be controlled by introducing other supporting elements such as shotcrete, rock bolts, and steel supports. In shallow tunnels, these additional support elements can handle a considerable portion of any overburden. Numerical simulation has shown that about 40% of an overburden is borne by these supports. For the case considered in this study, the plastic range, (Re Ro), is less than 1 m, which is small compared to the tunnel depth. If plasticity occurs, the slippage can be considered by reducing the soil resistance by the same amount as the plastic range. However, basically, as the nailing is one of the support elements, the entire support system must be redesigned such that the failure conditions are not exceeded.
the ground stiffness and consequently reduce the amount of settlement. It is not easy to consider the grouting effect for an individual nail. A simple method for evaluating the modified stiffness of the mixed ground involves considering the equivalent stiffness which is proportional to the grouted area. Thus, the resulting nailing effect consists of the effect of the nail itself and that of the grouting. The combined effects of both the nail and grout can be conceptually presented as shown in Fig. 9. Although the use of the nail reduces tunnel deformation significantly, it also increases the surface settlement slightly. This negative effect was not found to be due to the ground modification effect of the grouting. Rather, the use of grouting significantly reduces the ground deformation.
2.3. Effect of pressurized grouting
In general, nails are installed as a group. The effect of a group of nails can be deduced from the behavior of a fully grouted rock bolt (Bernaud et al., 2009; Bobet and Einstein, 2011; Carranza-Torres, 2009). The tensile stress in each nail limits the deformation of the ground. Therefore, the installation of a nail causes the radial
The nailing process includes pressurized grouting (37 kg/cm2) which reinforces the ground. Fig. 8 shows the grouting profile around a nail. Ground reinforcement using grouting will increase
2.4. Movement and design variables of nail groups
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advantage is a maximum when the installation angle is identical to the direction of the ground displacement vector. However, the depth to which the nails are installed is much greater than that of the rock bolt. Thus, the installation angle should be determined by considering the aspect of the settlement reduction. Fig. 10(a) shows the direction of the representative displacement vectors at the surface as determined by measurement. It is generally held that these vectors are directed toward the center of the tunnel (Attwell, 1978; O’Reilly and New, 1982), but according to Taylor (1995) and Mair and Taylor (1997), the displacement vectors are directed toward a point much lower than the center. As shown in Fig. 10(b), the convergence is not uniform in an actual horseshoe-shaped (or non-circular) shallow tunnel, and is much greater at the tunnel crown. Therefore, in this case the nails can effectively contribute to deformation control when installed in a direction which is close to vertical to the surface. It is also often difficult to install the nails with a precise inclination, making the vertical installation preferable for convenience in the field.
σ σθ nail
σR σvo
σe pi
R0
R Re Plastic Zone
Pressure ratio ( p
vo ,%)
(a) plastic range around tunnel
50
2.5. Experimental study of ground reaction curve
40
Because it is difficult to consider tunnel behavior through theoretical analysis or a large-scale model-based simulation, the concept of pre-nailing was investigated by using a simple smallscale trapdoor model test. The similarity of the model to the original shape of the trapdoor can be obtained as follows, using the governing equation given in Eq. (5).
30 20 10 0
-1
lp r op
plastic
elastic
0
1
2
3
4
5
6
Re-Ro (m)
(b) relationship between support pressure and plastic range Fig. 7. Slippage evaluation.
grouted area : A g nail section d = 29 mm
d = 76 ~ 105 mm d = 120 ~ 150 mm Fig. 8. Profile of grouted nail.
stress rr toward the tunnel center to decrease to Eq. (14):
r0r ¼ rr
T SL SA
r0r , as shown in ð14Þ
where T is the axial force of the nail and SL and SA are the lateral and longitudinal nail distances at the tunnel boundary, respectively. If the nails are to function as pre-supports, each should be installed at the same angle as the rock bolt because the mechanical
2
2 Gp lm Gm ¼ Ep r om Em
ð15Þ
where subscript ‘‘p’’ represents the prototype and ‘‘m’’ represents the model. In this experiment, the width of the trapdoor was set to 50 mm to replicate a tunnel with a diameter of approximately 2.0 m, according to the rule of similarity. A steel wire with a diameter of 0.8 mm was used to model the nail (r0 = 0.4 mm). To simulate the effect of the grout used in the installation of the nail, soil particles were attached to the surface of the nail beforehand, as shown in Fig. 11(b) (Tsukada et al., 2006). The nails were installed vertically, and the ground was formed by using a sand falling technique. The soil tank, installation profile of the nails, and material properties are shown in Fig. 11. Five nails were installed laterally (SA) with a 15-mm spacing, and three nails were installed longitudinally (SL) with a spacing of 5, 7, and 13 mm, respectively. By lowering the three trapdoors in the order of No. 1, No. 2, and then No. 3, the vertical movement (corresponding to the tunnel convergence) and the stress (corresponding to the bearing pressure) were measured. Fig. 12 shows the relationship between the pressure normalized by the initial static pressure and the normalized vertical displacement of the trapdoor in position No. 2. This relationship corresponds to the ground reaction curves caused by the tunnel excavation. When the nails were added for support, the ground reaction curve (GRC) moved to the left, which showed that the nails reduced the ground displacement by absorbing a portion of the ground stress. It was also shown that the magnitude of the deformation is strongly dependent on the nail spacing. As the distance between the installed nails is reduced, the amount of settlement is suppressed. This model test did not consider the combined effect of a support installed inside a tunnel. If it were to be considered, then the amount by which the settlement is suppressed would be more significant. 3. Numerical parametric study of design factors The design factors, which are reviewed at the time of pre-nailing design, are the installation length of the nails, installation angle
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effect of grouting only S
effect of nail only
combined effect
S
S
+
=
non-nailed
z
non-nailed
non-nailed
grouted
nail effect
z
z
Fig. 9. Nailing effects in terms of ground settlements.
A vertical nail
z0
inclined nail
B
0.175 z 0.325 0
A : Attewell, 1978; B : Taylor, 1995
O
(a) displacement vectors
(b) non-circular shallow tunnel
Fig. 10. Installation angles of group nails.
400 mm
sand grains nail
Tr : No.2 Tr : No.1
400 mm
H
soil A
Load cell
100 mm
Tr : No.3
50 50 mm mm
D=50 mm
nail
trap door
B
(a) plan of test soil tank
A
A
A GS = 2.63 γ = 15.17kN/m3 e = 0.734 Dr = 54.85% φ = 36.24˚
D
B
(b) section profiles of the trap door and model nail Fig. 11. Layout of model tests.
of the nails, spacing between the nails (vertical and horizontal), installation range of the nails, etc. A parametric study using a two-dimensional numerical model was carried out to investigate the effect of these design factors.
we used. For a qualitative study of the nail effect, the grouting is not considered in two-dimensional analyses. The nail design factors reviewed were the nail distance (SL), nail length (L), installation angle (h), and installation range (B), as shown in Fig. 14. The analysis cases are summarized in Table 1.
3.1. Analysis model and analysis cases 3.2. Results As shown in Fig. 13, a horseshoe-shaped tunnel with a width of 13 m and a height of 9 m, which is 15 m below the ground surface, was selected as the analysis model. To eliminate the effects of the model boundary conditions, the widths of the model boundaries were assumed to be more than four times the width of the tunnel. The ground reinforcement effect of the grouting was ignored and the nail and shotcrete were modeled by an elastic bar element. The ground behavior was simulated using linear elastic and Mohr-Coulomb models. Fig. 13 lists the material parameters that
The effects of the pre-nailing are mainly evaluated in terms of the amount of settlement at the crown of the tunnel. The amount of settlement was normalized by the ‘‘non-nailed’’ results. The settlement trends at the surface and at the crown were the same except for the case of the nail length. The effect of the nail spacing was investigated by varying the spacing between the nails from 1 m to 3 m. Fig. 15(a) shows the amount of crown settlement for different nail spacing. As the
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Table 1 Analysis cases.
non-nail
’0
SL = 15mm SL = 30mm
1
SL = 45mm
0.5
Design factor
Installation range
Nail distance (m)
Nail length (m)
Installation angle (°)
SL L
– –
1.0; 2.0; 3.0 1.0
– 90
h B
– 0.1D; 0.5D; 1.0D
1.0 –
7.0 6.0; 9.0; 12.0 9.0 9.0
60; 75; 90 90
increase in SL
settlement reduction
0 0.5
0
1
normalized Displacement (δ/δf) Fig. 12. Ground reaction curves (df: final displ).
H=15m
9m 4D D=13m
ground properties
shotcrete properties
γ = 19 kN/m3 c = 15 kPa φ = 30˚ E = 85 MPa ν = 0.35 K0 = 0.5
γ s = 25 kN/m3 Es1= 5,000 Mpa Es2= 15,000 MPa
4D
nail properties γ n = 78.5 kN/m3 E n= 210,000 Mpa d = 0.029m
The effect of the nail installation angle was investigated within a range of 60°–90°. As shown in Fig. 15(c), the amount of settlement was a minimum when the nail angle was 75°. Fig. 15(d) shows the effect of the horizontal nail installation range. The effect of installation range was not significant in the case of a shallow, horseshoe-shaped tunnel. The nail installation width contributed to a slight reduction in the surface settlement at a distance from the tunnel wall equal to 0.5 times the tunnel width (D). However, when the width value was exceeded, there was almost no structural advantage. The theoretical solution showed that tension in the nails could increase the amount of surface settlement. Thus, the nail length (or grouting length) is an important factor in the design of the prenailing. Although this effect is eliminated when the grouting effect is considered, the effect of the nail length is interesting and was investigated using numerical analysis. The results of this numerical analysis for different distances from the excavation boundary are presented in Fig. 16. This shows that the maximum amount of surface settlement increases as the nail length increases. This is identical to the theoretical solution, and indicates that it is not necessary to install (or grout) nails that extend to the ground surface in terms of reducing the amount of settlement at the surface. 4. Field application The pre-nailing method was applied to an actual tunnel project in which a shallow tunnel was constructed in decomposed granite soil and weathered rock. Practically, because the effect of construction using pre-nailing cannot be compared to the construction of an actual tunnel under the same conditions, the effect of pre-nailing was predicted by carrying out a three-dimensional numerical analysis. The results were then compared with measurements of the settlement of the crown, taken in the field.
Fig. 13. Analysis model.
S L´
L
4.1. Project description
B
D
L : nail length B : installation range S L : nail distance : installation angle
Fig. 14. Design parameter of pre-nailing method.
distance between the nails was reduced, the amount of settlement fell considerably, but once the distance exceeded 3 m, the effect of the nails on reducing the amount of settlement decreased. The effect of the nail length on tunnel deformation was investigated by changing the distance of the nail installation from the tunnel boundary (6–12 m). As shown in Fig. 15(b), for nail lengths of up to 6 m, the greater the distance of the nail from the tunnel, the more the settlement was reduced. Once the distance exceeded 9 m, however, the settlement reduction effect was lessened.
Fig. 17(a) shows the ground profile and tunnel cross-section to which the pre-nailing was applied. The project consisted of a largesection, horseshoe-shaped tunnel, 10.14 m high and approximately 20 m wide, with 12.5 m of soil cover. The tunnel face presented decomposed granite soil (see Table 2). Nails were installed vertically with a 1.5-m spacing relative to the tunnel axis and a 1.0-m lateral spacing, as shown in Fig. 17(b). The nails were combined with the steel supports and shotcrete lining immediately after the tunnel was excavated. The thickness of the shotcrete was 0.25 m, which was applied in two layers, first of 0.1 m and then of 0.15 m (see Table 3). 4.2. Three-dimensional modeling and analysis results The length of the model was set to 40 m relative to the tunnel axis. Within this range, modeling of a 20-m length of excavation was carried out. The ground movement and the lining were modeled using the elastic and Mohr-Coulomb models. The nails were modeled using elastic bar elements. To account for the effect of
223
, %)
100
normalized dispacement (
95 90 85 80 75 70 1
2
3
100 95 90 85 80 75 70 3
6
9
12
nail length (m)
(a) effect of nail spacing
(b) effect of nail lengths , %)
nail spacing (m)
100 (-)θ
95 90 85 80 75 70 60
75
90
15
100
(+)θ
95
normalized dispacement (
normalized dispacement (
, %)
normalized dispacement (
, %)
D.H. Seo et al. / Tunnelling and Underground Space Technology 42 (2014) 216–226
90 85 80 75 70 0.1B 0.2B 0.3B 0.4B 0.5B 0.6B 0.7B 0.8B 0.9B 1.0B
nail angle (degree)
nail installation range
(c) effect of installation angle
(d) effect of installation range
Fig. 15. Effect of installation on tunnel deformation.
Table 2 Properties of soil. Property
Decomposed granite soil (dgs)
Grouted dgs
Soft rock
Hard rock
E (MPa) v / (°) c (kPa) c (kN/ m3)
85 0.35 30 15 19
380 0.35 30 43 19
350 0.30 33 300 21
1500 0.27 35 800 23
distance from crown (m)
15 12
6.0m 9.0m 12.0m
y
9 6 3 0 -12
-14
-16
Table 3 Properties of ground support. Shot.1
Shot.2
-20
-22
-24
-26
E (MPa) c (kN/m3)
210,000 78.5
5000 25
15,000 25
the grouting, the reinforced range was set as a composite body of the grout bulb and the original ground. The material properties of the reinforced range were evaluated by applying the area ratio as a weighted value to the stiffness of each element such as the ground and grout bulb, and by calculating the equivalent elastic coefficient and equivalent cohesion intercept. For instance, the stiffness of the grouted ground was evaluated by considering
ð16Þ
where Ag is the grouted area (volume), Ao is the ungrouted area, Eg is the stiffness of grout material, E0 is the stiffness of original ground (Fig. 8). Fig. 18 shows the 3D analysis model and the installation mode of the nails. By setting the first excavation length to 1.0 m, the
(a) settlement profile , %)
Nail
normalized dispacement (
Property
Ag Ao Eeq ¼ Eg þ E0 Ag þ Ao Ag þ Ao
-18
displacement (m)
100
95
90
85
80 3
6
9
12
15
nail length (m)
(b) maximum surface settlement Fig. 16. Effect of nail length.
analysis was done based on the actual field construction process. The analysis was carried out for both the non-nailed and pre-nailed conditions.
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decomposed granite soil (dgs) soft rock
shotcrete hard rock
10.14m
19.56m
(a) ground and tunnel profile tunnel driving nails nail diameter, d=0.029m 1.5m
nails 1.5m
excavation 1.0m
Plan
section
connection details
(b) nail installation
Fig. 19 shows a comparison of the analysis results for the surface settlement and the subsurface displacement. Because of the inclined ground profile and surface geometry, the maximum settlement occurred slightly to the right of the tunnel crown. Additionally, it can be seen that pre-nailing reduced the ground surface settlement by a maximum of approximately 43%. This is relatively large in comparison with the results of the parametric study. The main difference between the analyses is the consideration of grouting. We can see that the ground reinforcement effect of the pre-nailing is also considerable. For non-nailing, the subsurface settlement increased exponentially close to the tunnel crown; however, when pre-nailing was applied, it exhibited a linear increase. Compared to non-nailing, the crown settlement was
surface displacement (mm)
Fig. 17. Field application of pre-nailing.
0 -4 -8
nailed (nail + pressurized grouting)
-12
non-nail
-16 -20 -80
-60
-40
-20
0
20
40
60
80
distance from the tunnel center (m)
(a) surface settlements distance from crown (m)
14 y
12 10 non-nail
8
nailed
6
(nail + pressurized grouting)
4 2 0 -5
-10
-15
-20
-25
-30
-35
displacement (mm)
(a) 3D model
(b) nail model
Fig. 18. 3D analysis model.
(b) subsurface settlements Fig. 19. Numerical results from 20 m ahead of tunnel portal.
-40
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distance from tunnel face 0
0.5D
1.0D
1.5D
2.0D
2.5D 0
measured (mm)
measured
4
8
8
12 16
12
predicted longitudinal settlement profile with nails
16
20 24
20
predicted (mm)
4
0
28
24 28 measured estimated
32 0
20
predicted longitudinal profile without nails
32 36
40
60
80
40 100
Elapsed time (day) Fig. 20. Comparison of field measurements and numerical predictions.
reduced by approximately 62.5%, which is approximately 10% more than the rate of reduction in the surface settlement. Fig. 20 compares the measured results for ‘‘settlement-time’’ and the analysis results for ‘‘settlement-face distance’’ at the crown. The measured value for the tunnel crown was approximately 7 mm, which does not include any initial displacement before the installation of the measurement device. Based on the numerical analysis and considering the prior displacement, the total crown displacement was estimated to be approximately 12 mm including the measured 7 mm, as shown in Fig. 20. The settlement of the crown was 35 mm with no nailing and 13 mm when nailing was applied. The predicted value was a little higher than the measured value. If this is compared with the non-nailed case, we can estimate that the settlement of the crown is reduced by approximately 50% as a result of pre-nailing.
5. Conclusions The risk of collapse in tunnel excavation is highest at the excavation face. However, because supports are not installed until after the excavation, there is a fundamental limit to the degree that tunnel safety can be improved and settlement reduced by using supports inside the tunnel. To overcome such problems, the prenailing support method, which works not only as ground reinforcement but also as a support during excavation, has been proposed. The behavior of a nail during tunneling was identified by deriving the governing equation for the nail. It was found that the effect of deformation control was large, provided the ground exhibited a large relative displacement between the surface and the crown. Through model-based tests of the use of pre-nailing, it was shown that the ground supports shifted the GRC to the left and caused the characteristic curve of the supports to originate from the excavation, thereby reducing the amount of settlement. From the results of a numerical parametric study of the design factors, the factors governing the pre-nailing were found to be the installation distance and angle and the installation range. We showed that the installation distance was the main factor governing the reduction of the settlement. For a non-circular tunnel with thin soil cover, a vertical installation can greatly reduce surface settlement and improve the ease of construction without a large structural loss. From the results of the field application and a three-dimensional numerical analysis, we showed that pre-nailing reduces the ground deformation by approximately 50%. We can thus
conclude that this technology is useful for reducing surface settlement and improving the stability of the tunnel face during excavation in soft ground with a thin soil cover.
Acknowledgement This study was supported by the National Research Foundation of Korea under Research Project 2012R1A2A1A01002326. The authors greatly appreciate the support provided.
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