Degradation characteristics of shear strength of joints in three rock ...

Cold Regions Science and Technology 138 (2017) 91–97

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Degradation characteristics of shear strength of joints in three rock types due to cyclic freezing and thawing Jian-qiao Mu a,b,⁎, Xiang-jun Pei a,b,⁎⁎, Run-qiu Huang a,b, Niek Rengers b,c, Xue-qing Zou a,b a b c

College of Environment and Civil Engineering, Chengdu University of Technology, Chengdu 610059, China State Key Laboratory of Geo-Hazard Prevention and Geo-Environment Protection, Chengdu University of Technology, 610059, China Faculty of Geo-Information Science and Earth Observation (retired), University of Twente, Enschede 7500 AE, The Netherlands

a r t i c l e

i n f o

Article history: Received 30 September 2015 Received in revised form 17 February 2017 Accepted 24 March 2017 Available online 25 March 2017 Keywords: Rock joint Shear strength Freeze-thaw cycles Damage model

a b s t r a c t With massive engineering projects carried out in cold regions where freeze-thaw processes can affect the mechanical properties of rock material, the temporal variation of geotechnical stability is highly concerned. Three typical types of jointed rocks were selected to undergo a number of freeze-thaw cycles after which direct shear tests were conducted on samples of joints in the rock material. The degradation characteristics of the rock joints were examined by the changes of the shear parameters after increasing numbers of freeze-thaw cycles. The results show that the cohesion is more sensitive to cyclic freezing and thawing than the joint friction angle and that the influence on cohesion and joint friction angle is different between hard rocks and soft rocks. Based on the damage mechanics theory and the fact that the deterioration degree rises with increasing numbers of freeze-thaw cycles, the damage state variable was redefined to develop an exponential decay model of freezethaw cycles. The comparison of the fitting curves obtained by the proposed model with the experimental results shows that the model reasonably well reflects the degradation characteristics of the shear strength under cyclic freezing and thawing. The model can thus be used to predict the tendency of geotechnical strength degradation of rock masses in cold regions. © 2017 Elsevier B.V. All rights reserved.

1. Introduction For engineering projects in cold regions, it is of great importance to understand the influence of freeze-thaw cycles on the degradation of rock mass mechanical performance. Numerous authors have already published about the freeze-thaw damage issue of rock masses and its consequences for the safe construction and operation of projects (Weeks, 1969; Hutchinson, 1974; Li et al., 2014). The freeze- thaw damage is usually ascribed to the thermal expansion-contraction and frostvolume expansion forces caused by the volume increase of the pore water in the rock material and the rock joints when freezing to ice (Franssen and Spiers, 1990; Hori and Morihiro, 1998). It involves thermo-hydro-mechanical (THM) field coupling and ice-to-water phase changes (Neaupane et al., 1999; Kang et al., 2013). The earlier freeze-thaw studies of intact rock samples mainly focus on the physical-mechanical properties and failure characteristics of

⁎ Correspondence to: J. Mu, State Key Laboratory of Geo-Hazard Prevention and GeoEnvironment Protection, College of Environment and Civil Engineering, Chengdu University of Technology, Sichuan, Chengdu 610059, China. ⁎⁎ Corresponding author. E-mail addresses: [email protected] (J. Mu), [email protected] (X. Pei).

http://dx.doi.org/10.1016/j.coldregions.2017.03.011 0165-232X/© 2017 Elsevier B.V. All rights reserved.

rock material under cyclic freeze-thaw action. These studies show that temperature, presence of water, rock type, and number of freeze-thaw cycles play a role (Yamabe and Neaupane, 2001; Nicholson et al., 2000; Chen et al., 2004; Takarli et al., 2008; Matsuoka, 1990), and that the rock deterioration is caused by the formation of micro-cracks and the extension of existing cracks (Remy et al., 1994). To describe the mechanical behavior affected by discontinuities, damage mechanics is a proper method (Kawamoto et al., 1988), and many constitutive models and damage equations have been established (Mazars, 1982; Loland, 1980; Frantziskonis and Desai, 1987). Afterwards, the method was applied in freeze-thaw damage field to search for the evolution of mechanical damage and strain softening (Lai et al., 2009; Tan et al., 2011; Liu et al., 2015). As for the mechanical property and damage model of jointed rock, some studies on the samples with pre-existing cracks have been made (Li et al., 2003; Lu et al., 2014; Li et al., 2013). However, limited work has been done on the degradation of primary joint in rock, which is usually very important to the stability of rock engineering. The main objective of this work was to investigate the degradation characteristics of shear strength of rock joints due to cyclic freezing and thawing. A series of direct shear tests were carried out on rock joints in three typical rock types to determine the changes of cohesion and joint friction angle. Moreover, a damage evolution model was proposed

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J. Mu et al. / Cold Regions Science and Technology 138 (2017) 91–97

to describe the relations between the shear parameters and the number of cycles, and then extrapolated the damage evolution. In addition, two degradation modes were proposed to distinguish between the degradation behavior of soft and hard rocks. 2. Direct shear tests

Table 1 Physical properties of the three rock types. Sample

Dry density(g/cm3)

Porosity(%)

Water absorption(%)

Granite Sandstone Phyllite

2.59 2.55 2.76

0.82 2.71 1.21

0.32 1.06 0.44

2.1. Apparatus The equipment used for the direct shear tests is a portable shear box developed by our laboratory (Su, 2008), which can test samples with irregular form such as rock joints by corresponding pretreatment. It is composed of an upper and a lower shear box, normal and shear load systems and gauges. Before direct shear tests, the irregular samples need to be casted in the two parts of shear boxes by concrete to get a standard form, and a gap of approximately 1 cm is left between the upper and lower concrete casts, in such way that the rock joint to be tested is aligned in the middle of the gap (Fig. 1). 2.2. Test samples and sample preparation Three typical rock types: granite (hard rock), sandstone (mediumhard rock), and phyllite (soft rock) were selected for the cyclic freezethaw tests. The joint samples of these rock types were collected by cutting them from their outcrops of which the weathering degree is weak, and were then wrapped in tape to avoid them falling to pieces during transport. 60 Cubical samples (20 samples for each rock type) of approximately 9 cm × 9 cm × 9 cm in size were collected. Before the cyclic freeze-thaw tests, these samples were water-saturated. To achieve water-saturation, the samples were dried in an oven (at a temperature of 105 °C) for 48 h, until they reached a constant weight, and were then water-saturated. In order to avoid the influence of pore gas pressure, each sample was immersed first for a quarter of its volume, then half, and then for three quarters in water for two hours. Finally, all samples were immersed in water completely for 48 h. The amount of water increase due to suction was calculated. Physical properties of the three rock types are listed in Table 1.

These freeze-thaw cycles were carried out as follows: (1) The water-saturated samples were put into a thermostatic freezer at −30 °C for 4 h; (2) The samples were then taken out and immersed in water at room temperature to thaw for 4 h; (3) Step 1 and 2 were repeated. Each freeze-thaw cycle had a duration of 8 h in total, which possibly represents the freeze-thaw weathering process for one year in a cold region. 2.4. Shear test program All samples, after having undergone different numbers of freezethaw cycles, were casted in concrete in a standard block form of 15 cm × 15 cm × 15 cm (Fig. 2). The rock joint was aligned in the middle of the gap reserved between the two parts of the concrete casts. The direct shear tests were then conducted along the joint to determine its shear strength. During the shear test of the five sample groups, the stress normal to the shear plane was maintained at a fixed value of 0.4 MPa, 0.8 MPa, 1.2 MPa, 1.6 MPa and 2.0 MPa respectively. The shear stress was increased progressively. When the value of the shear stress (monitored on the pressure gauge) no longer increased or even decreased, we assumed that the sample had failed in shear (Fig. 3(a)). Each test took about 5–10 min. Finally, we recorded the values of normal and shear stress and measured the area of the sheared plane. In addition, several typical joint samples were selected after they had failed to measure their profiles by a stylus sensing system (Tan et al., 2014), and the calculated joint roughness coefficients (JRC) values are shown in Fig. 3(b), (c) and (d). 3. Direct shear test results of rock joints

2.3. Cyclic freeze-thaw test

3.1. Normal stress-shear stress relation

The 20 samples of each rock type were divided into four groups, with approximately 5 samples in each group. Freeze-thaw tests were then conducted on these groups for 0, 15, 30 and 50 freeze-thaw cycles.

After test data processing, the peak shear stresses and normal stresses act on the joints of each rock type after different numbers of freeze-thaw cycles were shown in Table 2, and the scatter diagrams

Fig. 1. Shear box used to test the structural planes.


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Table 3. The data of the 0-cycle time represent the samples which did not undergo a freeze-thaw cycle.

3.2. Damage variables for shear strength degradation Based on the classical damage formula proposed by Lemaitre (Lemaitre, 1984), the damage variables for cohesion and joint friction angle can be defined as follows:

Fig. 2. Casted joint samples.

were plotted. The Mohr failure criteria fitting on the points with different numbers of freeze-thaw cycles were drawn in different colors as well, as shown in Fig. 4. From Fig. 4, the cohesion and the joint friction angle for different numbers of freeze-thaw cycles can be obtained, and are shown in

Dc ¼ 1−

cn c0

ð1aÞ

Dϕ ¼ 1−

φn φ0

ð1bÞ

Where, cn and φn are the cohesion c(kPa) and the joint friction angle φ(°) after n freeze-thaw cycles; c0 and φ0 are the initial strength. From Eq. (1a) and Eq. (1b), the freeze-thaw damage variables Dc and Dφ after different numbers of cycles can be calculated, and the results are shown in Table 4. Table 4 shows that the cohesion is more sensitive and shows greater damage than the joint friction angle. And during the first 15 freeze-thaw cycles, both the cohesion and the joint friction angle of each rock type are seriously affected. Moreover, it is worth noting that the degradation degrees of cohesion and joint friction angle show significant differences between hard rock and soft rock: at the same number of freeze-thaw cycles, the Dφ of granite and sandstone are greater than that of phyllite. Contrary to this, the cohesion of phyllite decreases faster than that of granite and sandstone. After 50 freeze-thaw cycles, the Dc of phyllite has already reached 65%, which in the case of granite and sandstone are 44% and 50%.

Fig. 3. Representative joint samples and their JRC values.

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Table 2 Peak shear stresses versus normal stresses act on the rock joints. 0 Sample Granite

Sandstone

Phyllite

1 2 3 4 5 1 2 3 4 5 6 1 2 3 4 5

15

30

50

σ(MPa)

τ(MPa)

σ(MPa)

τ(MPa)

σ(MPa)

τ(MPa)

σ(MPa)

τ(MPa)

0.08 0.21 0.24 0.27 0.41 0.07 0.15 0.20 0.31 0.32 0.38 0.09 0.14 0.15 0.22 0.42

0.20 0.38 0.42 0.47 0.62 0.15 0.20 0.32 0.30 0.40 0.44 0.17 0.17 0.28 0.39 0.49

0.08 0.16 0.20 0.24 0.37 0.07 0.11 0.21 0.28 0.31

0.18 0.28 0.27 0.38 0.51 0.10 0.15 0.23 0.23 0.33

0.11 0.20 0.23 0.39 0.51 0.06 0.11 0.24 0.26 0.29

0.16 0.29 0.32 0.58 0.56 0.08 0.15 0.23 0.22 0.24

0.11 0.19 0.24 0.37 0.49 0.07 0.14 0.20 0.27 0.31

0.18 0.25 0.32 0.38 0.58 0.08 0.14 0.20 0.22 0.25

0.07 0.13 0.20 0.27 0.31

0.13 0.21 0.28 0.27 0.42

0.06 0.15 0.23 0.26 0.35

0.09 0.22 0.31 0.31 0.36

0.08 0.13 0.22 0.27 0.36

0.11 0.15 0.23 0.27 0.38

4. Proposed damage evolution model 4.1. Definition of the damage state variable According to the damage mechanics theory, and considering the strength before the freeze-thaw cycles as initial state and after undergoing freeze-thaw cycles as damaged state, the basic equation of strength damage can be described as follows: Sn ¼ S0 ð1−DÞ ð2Þ Where, S0 is the strength of the rock mass at the initial state; Sn is the strength of the rock mass at the damaged state; and D is the damage variable. If a rock joint is considered as a kind of natural material, with variable mineral composition and cementation, it can be possible assumed

that the rock joint is composed of micro-units with different material strength. Statistical methods can then be used to study the micro-damage caused by cyclic freezing and thawing. By combination of the continuous damage theory and the statistical strength theory, Krajcinovic and Silva (1982) proposed the following statistical damage model: Nf σ ¼ Eε 1− N

ð3Þ

Where, E is elastic modulus; ε is strain; Nf is the number of failed micro-units, and N is the total number of micro-units. Combining Eq. (2) with Eq. (3), the damage variable D can be defined as the ratio of the Nf to the N. Further assuming that the damage probability density function due to damage force F is P[F], the damage

Fig. 4. Relationships between peak shear stress and normal stress for all shear tests after different numbers of freeze-thaw cycles.

J. Mu et al. / Cold Regions Science and Technology 138 (2017) 91–97 Table 3 Shear parameters for three rock types after different number of freeze-thaw cycles. 0

15

30

50

Sample

c(kPa)

φ(°)

c(kPa)

φ(°)

c(kPa)

φ(°)

c(kPa)

φ(°)


105.8 86.3 94.5

52.3 42.2 45.2

80.9 55.9 69.0

49.0 38.3 44.3

71.5 49.8 56.3

47.0 35.4 43.8

59.5 43.4 33.6

45.1 34.0 42.9

variable D is becoming: Z Nf ¼ D¼ N

F 0

NP ½xdx

ð4Þ

N

The density function suitable for the micro-damage is the Weibull distribution (Weibull, 1951). Therefore, it is possible to express the damage probability density function P[F] as follows: m P½ F ¼ F0

F F0

m−1

m F exp − F0

ð5Þ

After replacing Eq. (5) into Eq. (4), the damage variable D based on the Weibull distribution is defined: D ¼ 1− exp −ð F=F 0 Þm

ð6Þ

Where, m and F0 are the parameters of the Weibull distribution for materials. Eq. (6) shows the damage constitutive relation between the damage state variable D and the damage force F, but it is static and valid only when the damage force F is determined. For the dynamic process due to cyclic freezing and thawing, the damage state variable D should be combined with the freeze-thaw cycles.

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At lower numbers of cycles, the damage force F leads to limited destruction of the weak micro-units (see Fig. 5(a)). With an increase in the number of freeze-thaw cycles, further damage is caused to the weak micro-units, which causes macroscopic deterioration of the material (see Fig. 5(b)). Based on Fig. 5, it is assumed that a linear relationship exists between the freeze-thaw damage force F and the number of freeze-thaw cycles n, (when n is 0, the F is also 0), thus F = an. The linear coefficient a is the growth rate of F with the increase in the number of cycles n. Therefore, the damage probability density function P[F] and the damage variable D can be transformed as follows: P½ F ¼

m m an m−1 an exp − F0 F0 F0

D ¼ 1− exp −ðan= F 0 Þm

ð7Þ ð8Þ

Taking the number of freeze-thaw cycles as independent variable, in Eq. (8), the equation of damage evolution rate P(n), which represents the damage probability density influenced by freeze-thaw cycles n, can be written as follows: P ðnÞ ¼

m dD m an m−1 an ¼a exp − dn F0 F0 F0

ð9Þ

After replacing Eq. (8) into Eq. (2), a damage evolution model, which describes the relation between the decreased strength Sn and the initial strength S0 with the number of freeze-thaw cycles n, can be proposed: Sn ¼ S0 ð1−DÞ ¼ S0 exp −ðan= F 0 Þm

ð10Þ

According to Eq. (10), we can calculate the Sn for any number of freeze-thaw cycles when the material parameters F0/a and m are confirmed, and the equation has a certain physical significance.

4.2. Damage state variable incorporating freeze-thaw cycles 4.3. Calibration of the material parameters and model verification In many studies (Bayram, 2012; Si et al., 2014; Wang et al., 2015), the mechanical properties of rock material decreased with increasing numbers of freeze-thaw cycles, and the freeze-thaw damage acting on rock material is explained as the force formed by pore water that freezes to ice and by temperature changes. In this approach, the micro-damage process due to cyclic freezing and thawing can be described as follows: Table 4 Damage variables for the three rock types after different numbers of freeze-thaw cycles. 0

15

30

50

Sample

Dc

Dφ

Dc

Dφ

Dc

Dφ

Dc

Dφ


0.00 0.00 0.00

0.00 0.00 0.00

0.24 0.35 0.27

0.06 0.09 0.02

0.32 0.42 0.40

0.10 0.16 0.03

0.44 0.50 0.65

0.14 0.19 0.05

The method to obtain the material parameters, F0/a and m, only relies on data fitting. After making a simple transform of Eq. (10) and taking a logarithm on both sides of the equation, Eq. (10) is becoming: − ln ðSn =S0 Þ ¼

m n ð F 0 =aÞ

ð11Þ

The power function of Eq. (11) can be fitted with the shear test results in Table 3. The values of the F0/a and the m are then obtained, and are shown in Table 5. The correlation coefficients R2 of the fitting curves in Table 5 are all above 0.959. It shows that the derived freeze-thaw damage evolution model is reliable. After entering the fitting results of (F0/a)c,φ and mc,φ into Eq. (10), the resulting fitting curves are shown in Fig. 6.

Fig. 5. Damage process due to freeze-thaw cycles.

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Table 5 Fitting Results of F0/a and m. φ

c Sample

(F0/a)c

mc

R2

(F0/a)φ

mφ

R2


117.88 134.50 49.29

0.6568 0.3865 1.121

0.992 0.995 0.978

848.62 579.48 1675.5

0.673 0.6145 0.8448

0.999 0.959 0.987

As mentioned in Section 2.3, the degradation degrees of cohesion and joint friction angle due to freeze-thaw cycles are different between hard rocks and soft rocks, which can also be seen in Fig. 7. The damage rate of cohesion of phyllite is generally higher than that of granite and sandstone. While the damage rates of joint friction angles are the opposite. For this case, two degradation modes (Mu et al., 2013) could be used to describe the difference: (1) Hard rocks.

Since the sensitivities of cohesion and joint friction angle to cyclic freezing and thawing are different, it is possible to define the following damaged shear strength by replacing Eq. (10) into the Mohr-Coulomb strength criterion: τn ¼ c0 ð1−Dc Þ þ σ tan φ0 1−Dφ "

Dc;φ

n ¼ 1− exp − ð F 0 =aÞc;φ

ð12aÞ

!mc;φ # ð12bÞ

In conclusion, the derived model works reasonably well and we assume that it has universal theoretical and practical applicability. However, the curve fitting by only four points for each line is not convincing enough, so the applicability of the model still needs to be further verified.

Crack extension caused by frost-volume expansion forces is the main degradation mode for hard rocks, such as granite and sandstone. The joint friction angle φ is influenced by this mode. It can lead to failure along the expanded discontinuities at lower values of shear stress. (2) Soft rocks. Particle disintegration is the main degradation mode for soft rocks, such as phyllite. The temperature changes destroy the bonds between the micro-particles, which weakens the cementation degree. The decrease of cohesion c is mainly due to this mode. It should be noted that the two degradation modes act on rock material at the same time, only with different intensities. Therefore, the values of cohesion c and joint friction angle φ are both affected by freeze-thaw cycles. 6. Discussion

5. Degradation characteristics and trends in damage evolution The high degrees of correlation between the fitting curves and the experimental results give the reason to assume that the derived model can correctly describe the degradation characteristics which lead to the following trends in the damage evolution: (1) The degradation of the shear strength of joints in three rock types under cyclic freezing and thawing are nonlinear in trend, and the material parameters F0/a and m control the characteristics of the degradation. (2) With Eq. (9), the damage evolution rates of cohesion c and joint friction angle φ, in dependence from the number of freezethaw cycles can be obtained. As shown in Fig. 7, the damage rates of cohesion and joint friction angle for each rock type are high during the first freeze-thaw cycles, which means the initial freeze-thaw behavior acting on the material is serious. Comparison shows that the cohesion is more sensitive to cyclic freezing and thawing than the joint friction angle and leads to greater damage. However, with increasing numbers of freeze-thaw cycles, the damage rate decreases gradually which means that the influence of freeze-thaw cycles tends to level off.

The damage to rock joints due to cyclic freezing and thawing brings potential safety hazards to engineering projects in cold regions. Until recently, a simple method used for describing the tendency in strength degradation is statistical analysis. The disadvantage of this method is that it needs a large number of test data and cannot be used to describe the freeze-thaw damage process in-depth. In this study, a new method is proposed to describe the degradation evolution due to freeze-thaw cycles. However, it is still difficult to measure the magnitude of the freezethaw damage force, as the relation between the damage force and the number of freeze-thaw cycles remains to be solved, and the confirmation of the material parameters F0/a and m still requires more test results. 7. Conclusions The shear strength degradation of the joint planes in three rock types with different characteristics were investigated by a series of direct shear tests, and the trends in damage evolution were analyzed with a derived model of freeze-thaw cycles.

Fig. 6. Fitting curves obtained with the damage evolution model.


97

Fig. 7. Freeze-thaw damage evolution rates of the three rock types.

The conclusions from this research are as follows: (1) The shear strength of joint plane decreases with increasing numbers of freeze-thaw cycles, but shows an obvious nonlinear behavior. In most cases, the cohesion decreases more seriously than the joint friction angle. (2) The developed damage model, incorporating freeze-thaw cycles, works reasonably well and reflects the degradation characteristics of three rock types. It can be used to predict the tendency of damage evolution with increasing numbers of freeze-thaw cycles. (3) Two degradation modes, one characterized by crack extension and the other by particle disintegration are used to describe the different influences of freeze-thaw process on the cohesion and joint friction angle degradations for hard rocks and soft rocks. Acknowledgements We would like to thank the reviewers, whose constructive comments were helpful for improving this paper. This research was funded by the Creative Research Groups of China under Grant No. 41521002, and by the National Natural Science Foundation of China under Grant No 41572283. Appendix A Supplementary data. Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.coldregions.2017.03.011. These data include the Google map of the most important areas described in this article. References Bayram, F., 2012. Predicting mechanical strength loss of natural stones after freeze-thaw in cold regions. Cold Reg. Sci. Technol. 83–84, 98–102. Chen, T.C., Yeung, M.R., Mori, N., 2004. Effect of water saturation on deterioration of welded tuff due to freeze-thaw action. Cold Reg. Sci. Technol. 38, 127–136. Franssen, R.C.M.W., Spiers, C.J., 1990. Deformation of Polycrystalline Salt in Compression and in Shear at 250–300 °C. Geological Society London Publications 54 (1), 201–213. Frantziskonis, G., Desai, C.S., 1987. Constitutive model with strain softening. Int. J. Solids Struct. 23 (6), 733–750. Hori, M., Morihiro, H., 1998. Micromechanical analysis on deterioration due to freezing and thawing in porous brittle materials. Int. J. Eng. Sci. 36 (4), 511–522. Hutchinson, J.N., 1974. Periglacial solifluction: an approximate mechanism for clay soil. Geotechnique 24, 438–443. Kang, Y.S., Liu, Q.S., Huang, S.B., 2013. A fully coupled thermo-hydro-mechanical model for rock mass under freezing/thawing condition. Cold Reg. Sci. Technol. 95, 19–26. Kawamoto, T., Ichikawa, Y., Kyoya, T., 1988. Deformation and fracturing behavior of discontinuous rock mass and damage mechanics theory. Int. J. Numer. Anal. Methods Geomech. 12, 1–30. Krajcinovic, D., Silva, M.A.G., 1982. Statistical aspects of the continuous damage theory. Int. J. Solids Struct. 18 (7), 551–562.

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