Uniaxial compression creep experiments were carried out for low-grade metamorphic slate samples (located in the southeastern area of Guizhou province, China) with different moisture contents, using an Instron electric-fluid servo-compression machine. Based on the experimental results, a detailed analysis was made of the effect of moisture content on the strength and deformation behaviour of the slate specimens. The three-parameter generalised Kelvin model was identified to describe the creep behaviour of the low-grade metamorphic slate with different moisture contents. There is an approximately linear negative correlation between the elastic modulus and the saturation degree, and the viscoelastic modulus and viscosity coefficient show a negative exponent correlation with the saturation degree. The Kelvin creep model considering the moisture degradation effect was established and a three-dimensional finite difference model was developed with the software
The influence of moisture on the strength and deformability of rock has been analysed by many researchers [
Tunnel entrance construction presents challenges and because of its complexity it could easily result in landslides or collapse [
In this study, uniaxial compression creep experiments were carried out for the low-grade metamorphic slate samples (the surrounding rock of the Ruipo tunnel portal, which is located in the southeastern area of Guizhou province, China) with different moisture contents using an Instron electric-fluid servo-compression machine. A detailed analysis was made of the effect of moisture content on the strength and deformation behaviour of slate specimens. Then a three-dimensional finite difference analysis was executed on expressway tunnel portal areas while considering tunnel excavation and the moisture degradation effects on creep characteristics of surrounding rocks. In addition, the results were compared with those obtained by common elastoplastic models.
Low-grade metamorphic slate, a quintessential rock of the Shui-Du expressway that was taken from the Ruipo tunnel portal, has a cataclastic texture. X-ray diffraction analysis reveals that, apart from the most common quartz, kaolinite and muscovite are present in the collected low-grade metamorphic slate (see Figure
X-ray diffraction figures of low-grade metamorphic slate: (a) Specimen 1; (b) Specimen 2.
3 specimens, S-1, S-2, and S-3, were used to obtain the degree of saturation at different times. Nature dry specimens were considered as the first degree of saturation, specimens submerged in water for 24 hours represented the second degree, and those that remained submerged in water for 240 hours represented the third degree of saturation. The specimen preparation process was as follows. First, all specimens were nature-dried for 48 hours, the weights of S-1, S-2, and S-3 were measured, and S-4 to S-9 were selected as the specimens at the first degree of saturation. Second, all specimens except S-4 to S-9 were submerged in water, and the weights of S-1, S-2, and S-3 were measured every 24 hours. After having been submerged in water for 24 hours, S-10 to S-15 were selected as the specimens at the second degree of saturation, and S-16 to S-21 were specimens at the third degree of saturation after having been submerged in water for 240 hours. In order to avoid water loss from the specimens during compression testing, S-10 to S-21 were sealed up with wax (see Figure
Specimen sealed up with wax.
Uniaxial creep experiments were performed on an Instron 1346 electronic hydraulic servo-controlled testing machine, the loading capacity of which is 2 MN. Before the creep tests, uniaxial compression tests were performed on two specimens at each degree of saturation, and triaxial compression experiments were also carried out at each degree of saturation for specimens under three different confining pressures
The degree of saturation of specimens at different times can be defined as
The experimental results showed that the degree of saturation increased with the time submerged in water (see Figure
Curves showing relation between saturation degree of specimens and time submerged in water.
Table
Mechanical parameters of specimens at three degrees of saturation.
Submerged |
Degree of |
Uniaxial compressive strength/MPa | Poisson’s ratio | Elasticity modulus/GPa | Triaxial compressive strength |
Cohesion |
Internal friction angle |
||||
---|---|---|---|---|---|---|---|---|---|---|---|
Confining |
Peak | ||||||||||
0 (nature dry) | 41.5 | 88.80 | 0.30 | 50.56 | 2 | 97.12 | 25.44 | 31.84 | |||
95.42 | 0.32 | 54.83 | 5 | 106.61 | |||||||
Average | 92.11 | Average | 0.31 | Average | 52.70 | 10 | 124.53 | ||||
|
|||||||||||
24 | 80.1 | 68.92 | 0.41 | 17.64 | 2 | 73.84 | 21.32 | 26.91 | |||
70.78 | 0.41 | 19.86 | 5 | 82.69 | |||||||
Average | 69.85 | Average | 0.41 | Average | 18.75 | 10 | 96.21 | ||||
|
|||||||||||
240 | 93.5 | 58.34 | 0.46 | 8.32 | 2 | 62.18 | 18.91 | 24.07 | |||
59.13 | 0.47 | 8.73 | 5 | 69.95 | |||||||
Average | 58.74 | Average | 0.47 | Average | 8.53 | 10 | 82.40 |
For the triaxial test, the linear Mohr-Coulomb criterion, which can be expressed simply as a linear relationship between peak axial stress
Relationships between the peak strength parameters and saturation degree of specimens: (a)
Uniaxial experimental creep results for specimens are shown in Figure
Curves showing relation between strain and time of specimens with different saturation degrees: (a)
From the compression and creep tests results, it can be seen that the moisture has a great effect on the strength and deformability of the low-grade metamorphic slate. Hawkins and McConnell [
From Figure
The three-parameter generalized Kelvin model.
For the creep test, in general, the least square method is used to statistically process the test data [
Creep parameters of specimens with different moisture contents.
Submerged time/hours | Degree of saturation/% | Elastic modulus |
Viscoelastic modulus |
Viscosity coefficient |
---|---|---|---|---|
0 (nature dry) | 41.5 | 39.01 | 1536.43 | 2339.84 |
24 | 80.1 | 20.46 | 148.60 | 229.78 |
240 | 93.5 | 6.20 | 76.24 | 161.62 |
Parameters of generalized Kelvin model with the degrees of saturation: (a)
The viscoelastic modulus
It can be seen that all the Kelvin model parameters,
In the same way, the damage variables of the viscoelastic modulus
To validate the Kelvin creep model considering the moisture degradation effect, a three-dimensional finite difference model is developed with
Due to the limitations of the Kelvin model in dealing with the plastic characteristic of rock material, a Mohr-Coulomb model is then used. The viscoelastic and plastic strain rate components are assumed to act in series. The viscoelastic constitutive law corresponds to the Kelvin model, and the plastic constitutive law corresponds to the Mohr-Coulomb model. The creep model is developed by using a user subroutine, which is an option provided by
The calculated results for the specimens are shown in Figure
Comparison between numerical data and laboratory test data of specimens with different saturation degrees: (a)
The Shui-Du (Shuikou to Duyun city in Guizhou province, China) expressway is one of the most difficult sections in the construction of the Xiamen to Chengdu highway, which is the number 16 east-west expressway of the National Trunk Highway System. 58 tunnels were designed on the Shui-Du expressway, with a total length of 71,988 m (34.6% of the whole line) and more than 200 tunnel portals. Almost all of the rocks surrounding the tunnel portals are broken and have poor stability. About half of the portals are shallow buried and unsymmetrically loaded, such as the Laozhai tunnel portal [
Ruipo tunnel portal on the Shui-Du expressway.
The Ruipo tunnel is located in AT11 section of the Shui-Du expressway, with starting and ending milestones of ZK49+865 and ZK51+395. The surrounding rocks of the tunnel portal section (ZK49+865 and ZK50+000) were composed mainly of strong-weathered slate and completely weathered slate, which have very poor stability. The tunnel portal section was seriously shallow buried (the depth was 0–38 m) and unsymmetrically loaded (the transversal gradient was about 40°). According to design, the excavation in the tunnel portal section was to be performed by the CRD method. Before excavation the surrounding rocks were reinforced by a grouting method and a 108 mm diameter steel pipeline shed was installed along the tunnel outline, for which the intervals of steel were 50 cm. In order to mitigate the influence of an unsymmetrical load, seven antislide piles were installed in the shallow buried side. The support system and excavation sequence are shown in Figure
The support system and excavation sequence: (a) support system at ZK49+899; (b) excavation sequence with CRD method (length unit: cm).
During excavation rain began to fall and lasted for nearly 3 days, and then the portal suffered severe damage. Cracks first appeared in the slope, initial support, and landfills behind the antislide piles, and more cracks appeared and spread in the next few days (see Figure
Damage in Ruipo tunnel portal: (a) cracks in slope at the beginning; (b) cracks expanded and instability of the slope; (c) cracks in landfills behind the antislide pile.
Measurement results of pressure between landfills and antislide piles: (a) 2 # antislide pile; (b) 4 # antislide pile; (c) 6 # antislide pile.
In order to analyse the moisture degradation effect on creep characteristics of surrounding rocks, a three-dimensional finite difference analysis was performed by using the program
Three-dimensional analysis model.
Before excavation, the system was brought to elastic equilibrium (time 0 of modelling) under gravity. Boundary and initial conditions were set. Referring to Figure
Part A was excavated once with a length of 2 m.
Parts A and B were excavated once with lengths of 2 m.
Parts A, B, and C were excavated once with lengths of 2 m.
Parts A, B, C, and D were excavated once with lengths of 2 m, until the tunnel excavation was completed.
Based on the actual situation of tunnel excavation and support implementation, no matter which part was excavated, the lining and anchors corresponding to that part should be activated before the creep time of 12 hours had passed. And the next excavation stage was performed 24 hours after the support implementation.
For comparison, another condition, where the influences of rainfall and creep were not considered, was also simulated. The lining and anchors corresponding to the excavated part should be activated simultaneously to simulate the support of the tunnel.
The constitutive models used in the numerical calculation are as follows: elastic model for all of the support system, including the tunnel liners, steel pipeline shed, horizontal support, median septum, and antislide piles; the Kelvin-MC model established in Section
The evaluation of the rock mass quality has been carried out through detailed geomechanical field surveys according to the ISRM suggested method [
Physical and mechanical properties of the rock mass and support.
Properties | Strong-weathered |
Completely weathered |
Initial lining | Second lining | Antislide pile | Landfills |
---|---|---|---|---|---|---|
Bulk volume |
23 | 18 | 22 | 25 | 25 | 22 |
Elastic modulus/MPa |
|
|
|
|
|
|
Poisson’s ratio | 0.35 | 0.4 | 0.2 | 0.2 | 0.2 | 0.2 |
Cohesion |
0.25 | 0.10 | — | — | — | — |
Friction angle |
30 | 20 | — | — | — | — |
Elastic bulk modulus |
327.1 | 32.3 | — | — | — | — |
Elastic shear modulus |
158.5 | 15.2 | — | — | — | — |
Viscoelastic shear modulus |
6108.1 | 593.4 | — | — | — | — |
Viscosity coefficient |
9072.3 | 889.0 | — | — | — | — |
During excavation, a heavy rainfall lasted for 3 days. Based on the relationship between saturation degree and time submerged in water (Section
The excavation section ZK49+883, which was in the middle portion of the freshly constructed tunnel, was chosen as the subject for the research. Large surface subsidence happened after ZK49+883 was excavated (see Figure
Displacements at section ZK49+883 when the influences of rainfall and creep were considered: (a) vertical displacement; (b) horizontal displacement.
The vertical and horizontal displacements at section ZK49+883, where the influences of rainfall and creep were not considered, are shown in Figure
Displacements at section ZK49+883 when the influences of rainfall and creep were not considered: (a) vertical displacement; (b) horizontal displacement.
In this study, laboratory experiments were performed to understand the compression and creep characteristics of the low-grade metamorphic slate with different moisture states. Then a three-dimensional analysis on the Ruipo tunnel portal was performed while considering tunnel excavation and the moisture degradation effect on creep characteristics of surrounding rocks. The laboratory tests showed that the moisture has a great effect on the strength and deformability of the low-grade metamorphic slate, and the mathematical relation between the creep parameters and degree of saturation was established. The simulation results show that the tunnel excavation is safe without considering the influence of rainfall and creep, whereas with these being considered large surface subsidence and displacement would appear. Therefore, a three-dimensional analysis that considers the influence of moisture and creep of the surrounding rocks is needed for estimating the deformation of complex tunnel portals.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the National Natural Science Foundation of China (no. 51408464), the Foundation of Shaanxi Educational Committee (no. 14JK1413), and the Foundation for the Talents of Xian University of Architecture and Technology (no. RC1365).