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Evaluation of interfacial properties between rock mass and shotcrete
Paper 1A 18 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
EVALUATION OF INTERFACIAL PROPERTIES BETWEEN ROCK MASS AND SHOTCRETE Gyu-Jin Bae¹, Soo-Ho Chang ², Seok-Won Lee3, Hae-Geun Park4 ¹) Korea Institute of Construction Technology, Korea [email protected] ²) Korea Institute of Construction Technology, Korea [email protected] 3 ) Korea Institute of Construction Technology, Korea [email protected] 4 ) Samsung Engineering & Construction, Korea [email protected]
Abstract: Interfacial properties between rock mass and shotcrete play a significant role in the transmission of loads from the ground to shotcrete. These properties have a major effect on the behaviours of rock mass and shotcrete. They, however, have merely been assumed in most of numerical analyses, and little care has been taken in identifying them. This paper aimed to identify interfacial properties including cohesion, tension, friction angle, shear stiffness, and normal stiffness, through direct shear tests as well as interface normal compression tests for shotcrete/rock cores obtained from a tunnel sidewall. Mechanical properties such as compressive strength and elastic modulus were also measured to compare them with the timedependent variation of interfacial properties. Based on experiments, interfacial properties between rock and shotcrete showed a significant time-dependent variation similar to those of its mechanical properties. In addition, the time-dependent behaviours of interfacial properties can be well regressed through exponential and logarithmic functions of time. Keywords: Shotcrete, Interfacial properties, Mechanical properties, Direct shear test, Normal compression test, Time-dependent
1. INTRODUCTION Shotcrete plays a key role in interactions with rock mass deformation as the primary support and shows strong time-dependent behaviours after installation. Recently, high performance shotcrete linings have been highly in-demand for increasing the stability and safety of various rock structures. Shotcrete linings with high levels of strength and durability have been especially crucial in apply ing single-shell tunnelling methods such as Norwegian Method of Tunnelling (NMT). Previous studies to develop high performance shotcrete lining, however, have focused only on the improvement of its mechanical properties, without considering the interaction between rock mass and shotcrete. Bae et al. (2003) applied the sensitivity analysis to the numerical results from the UDEC and reported that among the shotcrete properties, the elastic modulus of shotcrete had the most dominant influence on the behaviours of shotcrete and rock mass. They also pointed out that
interfacial shear stiffness played a significant role in the transmission of ground load to shotcrete lining. In addition, high cohesive shotcrete was found to be crucial for its stable behaviours. Although interfacial properties have major effects on the behaviours of rock mass and shotcrete lining, they have merely been assumed in most numerical studies, and little care has been taken in the ir identification. Note that the mechanical characteristics of shotcrete vary with time, and time-dependent interfacial properties are still unknown. Given such background, this study intended to identify interfacial properties through direct shear tests as well as interface normal compression tests for shotcrete/rock cores obtained from a tunnel sidewall. Based on the experiments, timedependent behaviours of interfaces were investigated using cores of varied ages. For purposes of comparison, mechanical properties of
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Paper 1A 18 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
2. FUNDAMENTALS OF INTERFACIAL BEHAVIOURS Except behaviours at an interface arising from the deformation and displacement of the two different materials (rock and shotcrete), the behaviour of an interface subjected to normal and shear stresses is the same as that of a rock joint. dσ K n = dτ 0
0 dv K s du
(1)
Kn = (dσ/dv)u and Ks = (dτ/du)v represent the normal and shear stiffnesses, respectively (Fig. 1). In its complete form, the stiffness matrix is not symmetrical, containing non-zero off-diagonal terms.
S
Rock Shotcrete
σn
U Eo
V+
τ
Kss
Knn σn
σn
A
dinterface = f i(σ σn)
σn
B
C
σσn
Rock
Shotcrete
d total = ft( σn)
Rock
drock = fr( σn)
Shotcrete
dshot = f s(σ σn)
25
B(rock)
Day 1
C(shotcrete )
20
Interface 15
10
A(total)
5
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Normal displacement (mm)
d interface = dtotal – d rock – dshot = f(σ σ n)
N
S
as well as uniaxial compressive tests of rock and shotcrete as shown in Fig. 2.
Normal stress (MPa)
shotcrete were also evaluated based on their varying hardening ages.
V-
τ
Figure 1. Fundamental components of interfacial behaviour. Using direct shear tests at different normal stresses, interfacial properties, except the normal stiffness, can be identified by applying the MohrCoulomb criterion. Goodman (1976) proposed the methodology for determining the normal stiffness of a rock joint using a normal compression test. Different deformation characteristics of rock and shotcrete, however, must be considered to determine the normal stiffness of an interface between rock and shotcrete. Based on the basic concept of the methodology proposed by Goodman (1976), interfacial normal stiffness can be obtained from the normal compression of a sample with a horizontal interface
Figure 2. Fundamental concept to determine interfacial normal stiffness from a normal compression test. Results from normal compression included total deformation induced in interface, rock, and shotcrete. Therefore, pure deformation in interface must be distinguished in order to determine interfacial normal stiffness. At a normal stress level, each deformation induced in rock and shotcrete must be subtracted from the total deformation of a sample with an interface (Fig. 2). The initial normal stiffness and final normal stiffness of an interface can be then identified from the plot of normal stress and pure interface deformation.
3. EXPERIMENTS To minimize possible damage to the interface between rock and shotcrete, which may be induced by shock and vibration during boring, NX size samples were carefully bored from a tunnel sidewall using the double-barrel boring machine. Nevertheless, it was very difficult to obtain samples with enough length to carry out tests. Although rock mass was fairly conditioned gneiss with few discontinuities and RMR(Rock Mass Rating) was over 70, rock cores around the tunnel perimeter were crushed and fractured (Fig. 3). This may be due to the blasting-induced damage on the tunnel perimeter. In general, the maximum depth of
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Paper 1A 18 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
damage zone induced by controlled blasting is known to be over 30cm from a tunnel perimeter (Pusch and Stanfors, 1992).
The mechanical properties of gneiss and the mixing conditions for steel-fiber reinforced shotcrete, S(fr) are summarized in Table 1 and Table 2, respectively. Table 1. Mechanical properties of gneiss samples. P-wave UCS Young’s Poisson’s velocity (MPa) modulus ratio (m/sec) (GPa) 3,150 124 48.7 0.24
Figure 3. Typical Shotcrete/rock core after boring As a result, fewer samples were obtained than expected. Multi-staged direct shear tests were, therefore, carried out as an alternative in this study. Normal stress was increased after peak shear stress was observed in a normal stress level. Then, consecutive tests were repeated (Fig. 4). Constant normal stresses were set to 0.5, 1.0, 1.5 and 2.0 MPa under the Constant Normal Load (CNL) conditions. In the direct tests, the DR44 manufactured by the SBEL was used. The shear displacement rate of 2mm/min and normal stresses were servo-controlled by two vertical LVDTs and one horizontal LVDT. The interfacial roughness was relatively smooth with the JRC ranging from 7 to 10.
4. TIME-DEPENDENT PROPERTIES OF SHOTCRETE
1.6 τ
Shear stress, τ (MPa)
=1.352 MPa
max
1.4
(σn =2.0 MPa) τmax=1.063 MPa
1.2
4.1 Mechanical properties
(σ n=1.5 MPa) 1.0 τmax=0.725 MPa (σ =1.0 MPa)
0.8
n
0.6 0.4
Table 2 Mixing condition for wet-mixed shotcrete with alkali-free accelerator. Gmax (mm) 13 Slump (cm) 10 Air content (%) 2.5 W/C (%) 47.0 S/a (%) 65.8 Unit weight W 219 3 (kg/m ) C 466 S 1,036 G 557 3 Plasticizer (kg/m ) 3.262 Accelerator (MEYCO SA160) C x 10%
τmax=0.391 MPa (σ n=0.5 MPa)
Curing: 1st day (Sample #1-2)
0.2 0.0 0.0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
2.4
Shear displacement, u ( m m )
Figure 4. Multi-stage direct shear test for a oneday aged sample after spraying. Normal compression tests were displacementcontrolled at the rate of 0.01mm/sec. Uniaxial compressive tests for shotcrete and rock samples were also carried out. In each test, two cross-type strain gauges and two LVDTs were used to measure sample deformation. To determine the time-dependent behaviours of shotcrete, each test was carried out for 1, 2, 4, 7 and 28-day aged cores since shotcrete was sprayed on the tunnel perimeter.
As expected, the uniaxial compressive strength as well as the elastic modulus of shotcrete showed strong time-dependent behaviours (Figs. 5 and 6). The uniaxial compressive strength and the elastic modulus of the 28-day aged cores were approximately 1.7 and 3.7 times bigger than those of 1-day aged cores, respectively. Oreste (2003) suggested that time-dependent behaviours of the mechanical properties of shotcrete could be simulated by Eq. (2).
M t = M 0 (1 − e −α ⋅t ) (2) Where M t is a mechanical property at time t, M o is the asymptotic mechanical property for t=∞, and α is a time constant (t-1). In general, a linear relationship between the elastic modulus and the compressive strength of shotcrete is assumed, i.e., α is the same for the two mechanical properties. Nonetheless, the uniaxial compressive strength did not follow the regression function by Eq. (2) as
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Paper 1A 18 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
shown in Fig. 5. It showed that the same hardening constant α should not always be used for the uniaxial compressive strength and the elastic modulus. When a logarithm function defined in Eq. (3) was applied instead of Eq. (2), the timedependent behaviour of the uniaxial compressive strength could very well be regressed.
M t = a + b ln( t + c ) (3) Where a, b and c are regression constants. 28 26 24 22 20 18
4.0
16
1st day 2nd day 4th day 7th day 28th day
3.5
14
Experimental results
UCS = 13.301+3.080 ln( t-0.025)
12
2
(R =0.999)
10 0
5
10
15
20
25
30
Curing time, t (days)
Figure 5. Time-dependent behaviour of uniaxial compressive strength of shotcrete.
Peak shear stress, τ (MPa)
Uniaxial compressive strength (MPa)
30
bond between shotcrete and rock was low. In the latter ages, however, shotcrete was observed to be bonded firmly to rock pieces. It showed an increase in bond strength as shotcrete hardened. Peak friction angle at the interface of the oneday aged samples was only 33.61o . On the first day, peak friction angle was believed to be close to the basic friction angle at the interface. In the early ages, when shotcrete was not well-hardened, the shotcrete material as well as the interfacial roughness might be severely damaged during shearing. After the second day, peak friction angle ranged from 40.83o to 43.74o , regardless of curing time. The possible reason for this was that shotcrete had hardened enough to endure shearing, and peak friction angle after hardening was governed by the interface roughness.
3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5
18
1.0
1.5
2.0
2.5
Normal stress, σn (MPa)
16
Figure 7. Relationships between peak shear stress and normal stress of interfaces at different curing time.
14 12 10 8 6 4
Experimental results
2
K s = 14.474 (1-e ) (R =0.960) K s = -0.829+4.483 ln(t +1.289) (R 2=0.990)
-0.1436t
0 0
5
10
15
2
20
25
30
Curing time, t (days)
Figure 6. Time-dependent behaviour of elastic modulus of shotcrete.
4.2 Interfacial properties Fig. 7 shows experimental results from direct shear tests on shotcrete/rock cores. The results were approximated by the Mohr-Coulomb failure criterion. Based on these results, cohesion and peak friction angle were estimated as shown in Figs. 8 and 9. Cohesion at interface showed a strong timedependent behaviour close to that of the mechanical properties of shotcrete. From the early ages until the fourth day, shotcrete was often detached from rock pieces after boring since the
Cohesion in S(fr)/rock interface, C (MPa)
Elastic modulus of shotcrete, E (GPa)
20
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
Experimental results
C = 0.797 (1-e -0.112t ) (R 2=0.987)
0.1 0.0 0
5
10
15
20
25
30
Curing time, t (days)
Figure 8. Time-dependent behaviour of cohesion at interface. Using the Mohr-Coulomb failure envelope, tensile strength can be estimated from Eq. (4).
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Paper 1A 18 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
St =
c sin φ tan φ (1 + sin φ )
(4)
48
4.5
46 44
Shear stiffness, Ks (GPa/m)
Friction in S(fr)/rock interface, φ (degrees)
Where S t denotes tensile strength at interface, c cohesion, and φ peak friction angle. Since shotcrete hardening increased the bond strength of interface, tensile strength at interface showed a time-dependent behavior close to cohesion (Fig. 10). Nonetheless, tensile strength at interface was approximately two times smaller than cohesion at interface. This result coincided with the recommendation for selecting interfacial properties, explaining that friction angle is high due to very low normal stress, and cohesion is bigger than tensile strength at interface (Chryssanthakis et al, 1997).
The increasing rates of normal stresses may have an effect on interfacial shear stiffnesses. From normal compressive tests on interfaces, initial and final normal stiffnesses can be determined as explained in Fig. 2. Initial normal stiffness at interface showed a strong timedependent behaviour (Fig. 12). In constrast, final normal stiffnesses measured after the second day were close to each other (Fig. 12). The reason may be that initial normal stiffness obtained during interface becomes mated might be more dominated by the mechanical properties and hardening states of shotcrete. On the other hand, the final normal stiffness after interface is perfectly mated might be controlled more by rock stiffness rather than shotcrete. As a result, final normal stiffnesses at interface were close to those of rock joints.
42 40 38 36 Experimental results
34
φ = 42.672 (1-e
-1.553t
)
2
(R =0.959)
32 30 0
5
10
15
20
25
3.5
3.0 Experimental results
Ks = 3.559 (1-e
2.5
-1.125t
)
2
(R =0.965)
Ks = 3.179+0.170 ln( t-0.985)
30
Curing time, t ( d a y s )
2
(R =0.983)
2.0
Figure 9. Time-dependent behaviour of peak friction angle at interface. 0.40
0
5
10
15
20
25
30
Curing time, t (days)
Figure 11.Time-dependent behaviour of interfacial shear stiffness.
0.35
100 0.30 0.25 0.20 0.15 0.10 Experimental results σ t = 0.336 (1-e
0.05
-0.122t
)
2
(R =0.989)
0.00 0
5
10
15
20
25
30
Curing time, t ( d a y s )
Figure 10.Time-dependent behavior of tensile strength at interface.
Interfacial normal stiffness, Kn (GPa/m)
Tensile strength in S(fr)/rock interface, σ t (MPa)
4.0
Kn final = 82.755 (1-e
90
-0.369t
2
)
(R =0.947)
80 70
Kn initial = 3.495 (1-e
60
-0.186t
)
2
(R =0.982)
3 2 I n i t i a l n o r m a l s t i f f n e s s , K n initial
1
F i n a l n o r m a l s t i f f n e s s , K n final
0 0
5
10
15
20
25
30
Curing time, t (days)
As shotcrete hardened, interfacial shear stiffness also increased (Fig. 11). After the second day, however, stiffness values were within their error bounds. Therefore, based on statistics, they were not significantly different. These results might be influenced by increasing normal stresses on the next steps during a multi-stage direct shear test.
Figure 12.Time-dependent behaviour of interfacial normal stiffnesses. In summary, interfacial properties obtained in this study were compared with those assumed in previous numerical studies, where the UDEC-BB model was mainly used to consider the interface
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Paper 1A 18 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
between rock mass and shotcrete lining (Chryssanthakis et al, 1997; Chryssanthakis et al, 1998). Interfacial properties assumed in previous studies were very close to those from experiments on 28-day aged samples. Since shotcrete is a highly time-dependent material as verified in this study, however, transient behaviours of shotcrete lining cannot be exactly simulated from the assumed properties. Futher numerical studies to simulate the time-dependent chracteristics of shotcrete and the interface between rock mass and shotcrete lining may be necessary. Table 3. Summary of interfacial properties Properties Experiments Previous (28th day) numerical studies Peak friction 40, 60 43.74 ± 2.42 angle (degrees) Cohesion (MPa) 0.77 ± 0.07 0.25, 0.86 Tensile strength 0.33 ± 0.02 0.43, 0.50 (MPa) Interface shear 3.69 ± 0.37 stiffness (GPa/m) Interface normal 3.54 ± 0.31 stiffness (initial) (GPa/m) 83.20 ± 7.66 (final)
5. CONCLUSIONS In this study, the time-dependent interfacial properties as well as mechanical properties of shotcrete were identified through direct shear tests, normal compressive tests and uniaxial compressive tests for shotcrete/rock cores bored from the tunnel perimeter. Since the bond between rock and shotcrete increases dependently with time as shotcrete hardens, interfacial cohesion and tensile strength related to bond strength also show strong timedependent behaviours. Peak friction angle at an early age is as close as basic friction angle due to severe damage on interface during shearing. Since the friction angles in the latter ages are governed mainly by interface roughness, however, they are relatively constant ranging from 40o to 44o . Interfacial shear stiffnesses after the fourth day stabilize to values between 3.5 GPa/m and 3.7 GPa/m. Initial normal stiffness at interface shows a highly time-dependent behaviour close to the mechanical properties. Final normal stiffness at
interface is dominated by rock stiffness rather than by shotcrete. In summary, most of interfacial properties between rock and shotcrete shows time-dependent characteristics like its mechanical properties. Since they play a significant role in the interaction between rock mass and shotcrete lining, it is recommended that not only the mechanical properties such as compressive strength but also interfacial properties should be quality-controlled. Multi-staged shear test, however, were carried out in this study since core samples were very limited due to blasting-induced damage to rock mass around a tunnel. Therefore, further studies on the residual properties of interface as well as scale effects of sample size are necessary. Variations of interfacial properties with different mixing conditions of shotcrete should also be further identified.
6. ACKNOWLEDGEMENTS This work is a part of results from the research project of Development of High Performance Shotcrete Lining funded by Samsung Engineering & Construction, Korea.
7. REFERENCES Bae, Gyu-Jin, Lee, Du-Hwa, Chang, Soo-Ho, KimYoung-Geun, 2003. Sensitivity Analysis on Shotcrete Input Parameters Influencing Its Behaviors. KSCE (Korean Society of Civil Engineers) Journal of Civil Engineering 23(5C): pp. 345 – 356. Chryssanthakis, P., Barton, N., Lorig, L., Christianson, M. 1997. Numerical simulation of fiber reinforced shotcrete in a tunnel using the discrete element method. Int. J. Rock. Mech. Min. Sci. 34(3-4): Paper No. 054. Chryssanthakis, P., Barton, N. Luet, F., Dallas, A., Mitsotakis, K. 1998. Application of Norwegian Method of Tunnelling (NMT) in weak rocks in Western Greece. Int. J. Rock Mech. Min. Sci. 35(4-5): Paper No. 129. Goodman, R.E. 1976. Methods of Geological Engineering in Discontinuous Rocks: pp. 170173. New York: West Publishing Company. Oreste, P.P. 2003. A Procedure for Determining the Reaction Curve of Shotcrete Lining Considering
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Paper 1A 18 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
Transient Conditions. Rock Mech. Rock Engng. 36(3): pp. 209 – 236. Pusch, R. & Stanfors, R. 1992. The zone of disturbance around blasted tunnels at depth. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr 29(5): pp. 447 – 456.
7
EVALUATION OF INTERFACIAL PROPERTIES BETWEEN ROCK MASS AND SHOTCRETE Gyu-Jin Bae¹, Soo-Ho Chang ², Seok-Won Lee3, Hae-Geun Park4 ¹) Korea Institute of Construction Technology, Korea [email protected] ²) Korea Institute of Construction Technology, Korea [email protected] 3 ) Korea Institute of Construction Technology, Korea [email protected] 4 ) Samsung Engineering & Construction, Korea [email protected]
Abstract: Interfacial properties between rock mass and shotcrete play a significant role in the transmission of loads from the ground to shotcrete. These properties have a major effect on the behaviours of rock mass and shotcrete. They, however, have merely been assumed in most of numerical analyses, and little care has been taken in identifying them. This paper aimed to identify interfacial properties including cohesion, tension, friction angle, shear stiffness, and normal stiffness, through direct shear tests as well as interface normal compression tests for shotcrete/rock cores obtained from a tunnel sidewall. Mechanical properties such as compressive strength and elastic modulus were also measured to compare them with the timedependent variation of interfacial properties. Based on experiments, interfacial properties between rock and shotcrete showed a significant time-dependent variation similar to those of its mechanical properties. In addition, the time-dependent behaviours of interfacial properties can be well regressed through exponential and logarithmic functions of time. Keywords: Shotcrete, Interfacial properties, Mechanical properties, Direct shear test, Normal compression test, Time-dependent
1. INTRODUCTION Shotcrete plays a key role in interactions with rock mass deformation as the primary support and shows strong time-dependent behaviours after installation. Recently, high performance shotcrete linings have been highly in-demand for increasing the stability and safety of various rock structures. Shotcrete linings with high levels of strength and durability have been especially crucial in apply ing single-shell tunnelling methods such as Norwegian Method of Tunnelling (NMT). Previous studies to develop high performance shotcrete lining, however, have focused only on the improvement of its mechanical properties, without considering the interaction between rock mass and shotcrete. Bae et al. (2003) applied the sensitivity analysis to the numerical results from the UDEC and reported that among the shotcrete properties, the elastic modulus of shotcrete had the most dominant influence on the behaviours of shotcrete and rock mass. They also pointed out that
interfacial shear stiffness played a significant role in the transmission of ground load to shotcrete lining. In addition, high cohesive shotcrete was found to be crucial for its stable behaviours. Although interfacial properties have major effects on the behaviours of rock mass and shotcrete lining, they have merely been assumed in most numerical studies, and little care has been taken in the ir identification. Note that the mechanical characteristics of shotcrete vary with time, and time-dependent interfacial properties are still unknown. Given such background, this study intended to identify interfacial properties through direct shear tests as well as interface normal compression tests for shotcrete/rock cores obtained from a tunnel sidewall. Based on the experiments, timedependent behaviours of interfaces were investigated using cores of varied ages. For purposes of comparison, mechanical properties of
1
Paper 1A 18 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
2. FUNDAMENTALS OF INTERFACIAL BEHAVIOURS Except behaviours at an interface arising from the deformation and displacement of the two different materials (rock and shotcrete), the behaviour of an interface subjected to normal and shear stresses is the same as that of a rock joint. dσ K n = dτ 0
0 dv K s du
(1)
Kn = (dσ/dv)u and Ks = (dτ/du)v represent the normal and shear stiffnesses, respectively (Fig. 1). In its complete form, the stiffness matrix is not symmetrical, containing non-zero off-diagonal terms.
S
Rock Shotcrete
σn
U Eo
V+
τ
Kss
Knn σn
σn
A
dinterface = f i(σ σn)
σn
B
C
σσn
Rock
Shotcrete
d total = ft( σn)
Rock
drock = fr( σn)
Shotcrete
dshot = f s(σ σn)
25
B(rock)
Day 1
C(shotcrete )
20
Interface 15
10
A(total)
5
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Normal displacement (mm)
d interface = dtotal – d rock – dshot = f(σ σ n)
N
S
as well as uniaxial compressive tests of rock and shotcrete as shown in Fig. 2.
Normal stress (MPa)
shotcrete were also evaluated based on their varying hardening ages.
V-
τ
Figure 1. Fundamental components of interfacial behaviour. Using direct shear tests at different normal stresses, interfacial properties, except the normal stiffness, can be identified by applying the MohrCoulomb criterion. Goodman (1976) proposed the methodology for determining the normal stiffness of a rock joint using a normal compression test. Different deformation characteristics of rock and shotcrete, however, must be considered to determine the normal stiffness of an interface between rock and shotcrete. Based on the basic concept of the methodology proposed by Goodman (1976), interfacial normal stiffness can be obtained from the normal compression of a sample with a horizontal interface
Figure 2. Fundamental concept to determine interfacial normal stiffness from a normal compression test. Results from normal compression included total deformation induced in interface, rock, and shotcrete. Therefore, pure deformation in interface must be distinguished in order to determine interfacial normal stiffness. At a normal stress level, each deformation induced in rock and shotcrete must be subtracted from the total deformation of a sample with an interface (Fig. 2). The initial normal stiffness and final normal stiffness of an interface can be then identified from the plot of normal stress and pure interface deformation.
3. EXPERIMENTS To minimize possible damage to the interface between rock and shotcrete, which may be induced by shock and vibration during boring, NX size samples were carefully bored from a tunnel sidewall using the double-barrel boring machine. Nevertheless, it was very difficult to obtain samples with enough length to carry out tests. Although rock mass was fairly conditioned gneiss with few discontinuities and RMR(Rock Mass Rating) was over 70, rock cores around the tunnel perimeter were crushed and fractured (Fig. 3). This may be due to the blasting-induced damage on the tunnel perimeter. In general, the maximum depth of
2
Paper 1A 18 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
damage zone induced by controlled blasting is known to be over 30cm from a tunnel perimeter (Pusch and Stanfors, 1992).
The mechanical properties of gneiss and the mixing conditions for steel-fiber reinforced shotcrete, S(fr) are summarized in Table 1 and Table 2, respectively. Table 1. Mechanical properties of gneiss samples. P-wave UCS Young’s Poisson’s velocity (MPa) modulus ratio (m/sec) (GPa) 3,150 124 48.7 0.24
Figure 3. Typical Shotcrete/rock core after boring As a result, fewer samples were obtained than expected. Multi-staged direct shear tests were, therefore, carried out as an alternative in this study. Normal stress was increased after peak shear stress was observed in a normal stress level. Then, consecutive tests were repeated (Fig. 4). Constant normal stresses were set to 0.5, 1.0, 1.5 and 2.0 MPa under the Constant Normal Load (CNL) conditions. In the direct tests, the DR44 manufactured by the SBEL was used. The shear displacement rate of 2mm/min and normal stresses were servo-controlled by two vertical LVDTs and one horizontal LVDT. The interfacial roughness was relatively smooth with the JRC ranging from 7 to 10.
4. TIME-DEPENDENT PROPERTIES OF SHOTCRETE
1.6 τ
Shear stress, τ (MPa)
=1.352 MPa
max
1.4
(σn =2.0 MPa) τmax=1.063 MPa
1.2
4.1 Mechanical properties
(σ n=1.5 MPa) 1.0 τmax=0.725 MPa (σ =1.0 MPa)
0.8
n
0.6 0.4
Table 2 Mixing condition for wet-mixed shotcrete with alkali-free accelerator. Gmax (mm) 13 Slump (cm) 10 Air content (%) 2.5 W/C (%) 47.0 S/a (%) 65.8 Unit weight W 219 3 (kg/m ) C 466 S 1,036 G 557 3 Plasticizer (kg/m ) 3.262 Accelerator (MEYCO SA160) C x 10%
τmax=0.391 MPa (σ n=0.5 MPa)
Curing: 1st day (Sample #1-2)
0.2 0.0 0.0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
2.4
Shear displacement, u ( m m )
Figure 4. Multi-stage direct shear test for a oneday aged sample after spraying. Normal compression tests were displacementcontrolled at the rate of 0.01mm/sec. Uniaxial compressive tests for shotcrete and rock samples were also carried out. In each test, two cross-type strain gauges and two LVDTs were used to measure sample deformation. To determine the time-dependent behaviours of shotcrete, each test was carried out for 1, 2, 4, 7 and 28-day aged cores since shotcrete was sprayed on the tunnel perimeter.
As expected, the uniaxial compressive strength as well as the elastic modulus of shotcrete showed strong time-dependent behaviours (Figs. 5 and 6). The uniaxial compressive strength and the elastic modulus of the 28-day aged cores were approximately 1.7 and 3.7 times bigger than those of 1-day aged cores, respectively. Oreste (2003) suggested that time-dependent behaviours of the mechanical properties of shotcrete could be simulated by Eq. (2).
M t = M 0 (1 − e −α ⋅t ) (2) Where M t is a mechanical property at time t, M o is the asymptotic mechanical property for t=∞, and α is a time constant (t-1). In general, a linear relationship between the elastic modulus and the compressive strength of shotcrete is assumed, i.e., α is the same for the two mechanical properties. Nonetheless, the uniaxial compressive strength did not follow the regression function by Eq. (2) as
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Paper 1A 18 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
shown in Fig. 5. It showed that the same hardening constant α should not always be used for the uniaxial compressive strength and the elastic modulus. When a logarithm function defined in Eq. (3) was applied instead of Eq. (2), the timedependent behaviour of the uniaxial compressive strength could very well be regressed.
M t = a + b ln( t + c ) (3) Where a, b and c are regression constants. 28 26 24 22 20 18
4.0
16
1st day 2nd day 4th day 7th day 28th day
3.5
14
Experimental results
UCS = 13.301+3.080 ln( t-0.025)
12
2
(R =0.999)
10 0
5
10
15
20
25
30
Curing time, t (days)
Figure 5. Time-dependent behaviour of uniaxial compressive strength of shotcrete.
Peak shear stress, τ (MPa)
Uniaxial compressive strength (MPa)
30
bond between shotcrete and rock was low. In the latter ages, however, shotcrete was observed to be bonded firmly to rock pieces. It showed an increase in bond strength as shotcrete hardened. Peak friction angle at the interface of the oneday aged samples was only 33.61o . On the first day, peak friction angle was believed to be close to the basic friction angle at the interface. In the early ages, when shotcrete was not well-hardened, the shotcrete material as well as the interfacial roughness might be severely damaged during shearing. After the second day, peak friction angle ranged from 40.83o to 43.74o , regardless of curing time. The possible reason for this was that shotcrete had hardened enough to endure shearing, and peak friction angle after hardening was governed by the interface roughness.
3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5
18
1.0
1.5
2.0
2.5
Normal stress, σn (MPa)
16
Figure 7. Relationships between peak shear stress and normal stress of interfaces at different curing time.
14 12 10 8 6 4
Experimental results
2
K s = 14.474 (1-e ) (R =0.960) K s = -0.829+4.483 ln(t +1.289) (R 2=0.990)
-0.1436t
0 0
5
10
15
2
20
25
30
Curing time, t (days)
Figure 6. Time-dependent behaviour of elastic modulus of shotcrete.
4.2 Interfacial properties Fig. 7 shows experimental results from direct shear tests on shotcrete/rock cores. The results were approximated by the Mohr-Coulomb failure criterion. Based on these results, cohesion and peak friction angle were estimated as shown in Figs. 8 and 9. Cohesion at interface showed a strong timedependent behaviour close to that of the mechanical properties of shotcrete. From the early ages until the fourth day, shotcrete was often detached from rock pieces after boring since the
Cohesion in S(fr)/rock interface, C (MPa)
Elastic modulus of shotcrete, E (GPa)
20
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
Experimental results
C = 0.797 (1-e -0.112t ) (R 2=0.987)
0.1 0.0 0
5
10
15
20
25
30
Curing time, t (days)
Figure 8. Time-dependent behaviour of cohesion at interface. Using the Mohr-Coulomb failure envelope, tensile strength can be estimated from Eq. (4).
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Paper 1A 18 — SINOROCK2004 Symposium Int. J. Rock Mech. Min. Sci. Vol. 41, No. 3, CD-ROM, © 2004 Elsevier Ltd.
St =
c sin φ tan φ (1 + sin φ )
(4)
48
4.5
46 44
Shear stiffness, Ks (GPa/m)
Friction in S(fr)/rock interface, φ (degrees)
Where S t denotes tensile strength at interface, c cohesion, and φ peak friction angle. Since shotcrete hardening increased the bond strength of interface, tensile strength at interface showed a time-dependent behavior close to cohesion (Fig. 10). Nonetheless, tensile strength at interface was approximately two times smaller than cohesion at interface. This result coincided with the recommendation for selecting interfacial properties, explaining that friction angle is high due to very low normal stress, and cohesion is bigger than tensile strength at interface (Chryssanthakis et al, 1997).
The increasing rates of normal stresses may have an effect on interfacial shear stiffnesses. From normal compressive tests on interfaces, initial and final normal stiffnesses can be determined as explained in Fig. 2. Initial normal stiffness at interface showed a strong timedependent behaviour (Fig. 12). In constrast, final normal stiffnesses measured after the second day were close to each other (Fig. 12). The reason may be that initial normal stiffness obtained during interface becomes mated might be more dominated by the mechanical properties and hardening states of shotcrete. On the other hand, the final normal stiffness after interface is perfectly mated might be controlled more by rock stiffness rather than shotcrete. As a result, final normal stiffnesses at interface were close to those of rock joints.
42 40 38 36 Experimental results
34
φ = 42.672 (1-e
-1.553t
)
2
(R =0.959)
32 30 0
5
10
15
20
25
3.5
3.0 Experimental results
Ks = 3.559 (1-e
2.5
-1.125t
)
2
(R =0.965)
Ks = 3.179+0.170 ln( t-0.985)
30
Curing time, t ( d a y s )
2
(R =0.983)
2.0
Figure 9. Time-dependent behaviour of peak friction angle at interface. 0.40
0
5
10
15
20
25
30
Curing time, t (days)
Figure 11.Time-dependent behaviour of interfacial shear stiffness.
0.35
100 0.30 0.25 0.20 0.15 0.10 Experimental results σ t = 0.336 (1-e
0.05
-0.122t
)
2
(R =0.989)
0.00 0
5
10
15
20
25
30
Curing time, t ( d a y s )
Figure 10.Time-dependent behavior of tensile strength at interface.
Interfacial normal stiffness, Kn (GPa/m)
Tensile strength in S(fr)/rock interface, σ t (MPa)
4.0
Kn final = 82.755 (1-e
90
-0.369t
2
)
(R =0.947)
80 70
Kn initial = 3.495 (1-e
60
-0.186t
)
2
(R =0.982)
3 2 I n i t i a l n o r m a l s t i f f n e s s , K n initial
1
F i n a l n o r m a l s t i f f n e s s , K n final
0 0
5
10
15
20
25
30
Curing time, t (days)
As shotcrete hardened, interfacial shear stiffness also increased (Fig. 11). After the second day, however, stiffness values were within their error bounds. Therefore, based on statistics, they were not significantly different. These results might be influenced by increasing normal stresses on the next steps during a multi-stage direct shear test.
Figure 12.Time-dependent behaviour of interfacial normal stiffnesses. In summary, interfacial properties obtained in this study were compared with those assumed in previous numerical studies, where the UDEC-BB model was mainly used to consider the interface
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between rock mass and shotcrete lining (Chryssanthakis et al, 1997; Chryssanthakis et al, 1998). Interfacial properties assumed in previous studies were very close to those from experiments on 28-day aged samples. Since shotcrete is a highly time-dependent material as verified in this study, however, transient behaviours of shotcrete lining cannot be exactly simulated from the assumed properties. Futher numerical studies to simulate the time-dependent chracteristics of shotcrete and the interface between rock mass and shotcrete lining may be necessary. Table 3. Summary of interfacial properties Properties Experiments Previous (28th day) numerical studies Peak friction 40, 60 43.74 ± 2.42 angle (degrees) Cohesion (MPa) 0.77 ± 0.07 0.25, 0.86 Tensile strength 0.33 ± 0.02 0.43, 0.50 (MPa) Interface shear 3.69 ± 0.37 stiffness (GPa/m) Interface normal 3.54 ± 0.31 stiffness (initial) (GPa/m) 83.20 ± 7.66 (final)
5. CONCLUSIONS In this study, the time-dependent interfacial properties as well as mechanical properties of shotcrete were identified through direct shear tests, normal compressive tests and uniaxial compressive tests for shotcrete/rock cores bored from the tunnel perimeter. Since the bond between rock and shotcrete increases dependently with time as shotcrete hardens, interfacial cohesion and tensile strength related to bond strength also show strong timedependent behaviours. Peak friction angle at an early age is as close as basic friction angle due to severe damage on interface during shearing. Since the friction angles in the latter ages are governed mainly by interface roughness, however, they are relatively constant ranging from 40o to 44o . Interfacial shear stiffnesses after the fourth day stabilize to values between 3.5 GPa/m and 3.7 GPa/m. Initial normal stiffness at interface shows a highly time-dependent behaviour close to the mechanical properties. Final normal stiffness at
interface is dominated by rock stiffness rather than by shotcrete. In summary, most of interfacial properties between rock and shotcrete shows time-dependent characteristics like its mechanical properties. Since they play a significant role in the interaction between rock mass and shotcrete lining, it is recommended that not only the mechanical properties such as compressive strength but also interfacial properties should be quality-controlled. Multi-staged shear test, however, were carried out in this study since core samples were very limited due to blasting-induced damage to rock mass around a tunnel. Therefore, further studies on the residual properties of interface as well as scale effects of sample size are necessary. Variations of interfacial properties with different mixing conditions of shotcrete should also be further identified.
6. ACKNOWLEDGEMENTS This work is a part of results from the research project of Development of High Performance Shotcrete Lining funded by Samsung Engineering & Construction, Korea.
7. REFERENCES Bae, Gyu-Jin, Lee, Du-Hwa, Chang, Soo-Ho, KimYoung-Geun, 2003. Sensitivity Analysis on Shotcrete Input Parameters Influencing Its Behaviors. KSCE (Korean Society of Civil Engineers) Journal of Civil Engineering 23(5C): pp. 345 – 356. Chryssanthakis, P., Barton, N., Lorig, L., Christianson, M. 1997. Numerical simulation of fiber reinforced shotcrete in a tunnel using the discrete element method. Int. J. Rock. Mech. Min. Sci. 34(3-4): Paper No. 054. Chryssanthakis, P., Barton, N. Luet, F., Dallas, A., Mitsotakis, K. 1998. Application of Norwegian Method of Tunnelling (NMT) in weak rocks in Western Greece. Int. J. Rock Mech. Min. Sci. 35(4-5): Paper No. 129. Goodman, R.E. 1976. Methods of Geological Engineering in Discontinuous Rocks: pp. 170173. New York: West Publishing Company. Oreste, P.P. 2003. A Procedure for Determining the Reaction Curve of Shotcrete Lining Considering
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Transient Conditions. Rock Mech. Rock Engng. 36(3): pp. 209 – 236. Pusch, R. & Stanfors, R. 1992. The zone of disturbance around blasted tunnels at depth. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr 29(5): pp. 447 – 456.
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