J. Cent. South Univ. (2017) 24: 1684-1695

DOI: 10.1007/s11771-017-3575-9

Perturbation effect of rock rheology under uniaxial compression

GAO Yan-fa(高延法)¹, HUANG Wan-peng(黄万朋)^{2, 3}, QU Guang-long(曲广龙)^{2, 3},

WANG Bo(王波)⁴, CUI Xi-hai(崔希海)², FAN Qing-zhong(范庆忠)⁵

1. School of Mechanics and Civil Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China;

2. College of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao 266590, China;

3. State Key Laboratory of Mining Disaster Prevention and Control (Shandong University of Science and Technology), Qingdao 266590, China;

4. North China Institute of Science and Technology, Langfang 065201, China;

Central South University Press and Springer-Verlag Berlin Heidelberg 2017

Abstract: Soft and medium-hard rocks are subjected to high rheology under high stress, and they are prone to a relatively large-degree of deformation when perturbed by external impacting loads. The phenomenon where rock deformation is developed due to external impacting perturbation in the rheological state is defined as the rock rheological perturbation effect. This work presents a new experimental system for investigating the rock rheological perturbation effect with experiments on medium-hard red sandstone. Results from our analysis show that red sandstone changes under two mechanical mechanisms: deformation-hardening effects at low stress states, and damage-fracture effects at high stress states when impacted by certain external impacting loads. Red sandstone tested in our experiments has a strain threshold of about 90% of the ultimate strain under the perturbation effect; the red sandstone is sensitive to a perturbed load when its actual strain exceeds the threshold. The perturbed deformation process of the rock can be divided into three phases: decline, approximately constant speed and acceleration. The rock will be rapidly destroyed when the perturbed deformation accumulates to a certain degree. The perturbation effect of rock deformation under uniaxial compression is more obvious than that under axial compression. Based on our experiment, a constitutive relation of the rock rheological perturbation effect is developed.

Key words: rock rheology; perturbation effect; experimental system; strain threshold

1 Introduction

The deep roadway’s surrounding rock at rheological state is very sensitive to external perturbation loads. It is subjected to relatively large-degree deformation under the perturbation effect where tunneling and mining are conducted [1, 2]. Perturbation loads from above can be created by mining activities in adjacent coal faces, shooting vibrations from heading faces, the fracturing of roof strata and rock bursts, etc. Perturbation deformation of soft rock surrounding a deep roadway under rheology, forming an important part of significant deformation, needs to be investigated.

The mechanical behavior of a rock caused by outside impact load falls into the field of rock dynamics [3], and it has been previously investigated through theoretical and experimental studies [4]. However, the complexity of testing the dynamic mechanical behavior of a rock has resulted in the International Society for Rock Mechanics (ISRM) to be unable to provide a unified method and standard [5]. Current studies on rock dynamics have focused on impact experiments under uniaxial or triaxial compression by using, for example, split Hopkinson pressure bar (SHPB), light-gas guns and drop hammers. The strain rate provided by SHPB ranges from 100 to 10000 s^-1, which is suitable for testing at the high strain rate [6]. In 1968, KUMAR [7] first tested the dynamic strength of a rock by using SHPB. In 1972, CHRISTENSEN et al [8] successfully developed a triaxial SHPB that examined the dynamic impact of a rock at different confining pressures. DUFFY et al [9], NEMAT-NASSER et al [10] and FREW et al [11, 12], through investigations on the impact waves of SHPB, successfully reduced impact concussion, rendering it easier for rock specimens to attain equilibrium in dynamic mechanics.

Investigations into the dynamic behavior of rock have also been undertaken. ROUGIER et al [13] established a three-dimensional finite-discrete element method by using experimental results of the SHPB test. DEMIRDAG et al [14] investigated the effects of porosity, unit volume weight and Schmidt hardness on the quasi-static and dynamic compressive behaviors of some carbonate rocks with a classical servo-hydraulic testing machine and SHPB. The dynamic deformation behavior of gneiss at intermediate and high strain rates were investigated by CADONI [15] using a light-gas gun, the results of which showed that the dynamic mechanical behavior of gneiss was responsive to the changes of strain rates. This investigation provided insight into the relationship between an increase in dynamic tensile strength and strain rate. By subjecting rock samples to simultaneously coupled static and dynamic stresses, LI et al [16-18] investigated the strength characteristics, the failure law and suction rate using an improved SHPB and INSTRON system. Complete dynamic stress—strain curves of marble and granite were obtained by SHAN et al [19] using SHPB. CAI et al [20] and DAI et al [21] using SHPB studied the dynamic compressive strength and dynamic tensile strength at higher loading rates, and addressed several critical issues that could affect the results, including the choice of slenderness ratio of the compressive specimen, and the effect of friction between the sample and the bars. FAN et al [22] studied the viscoelastic behavior of sedimentary rock under dynamic loading by using drop hammers, WU et al [23] and JAFARI et al [24] studied the mechanical responses of rock joints caused by cyclic load, such as normal and shear displacements with SHPB.

To outside impact loads, the dynamic mechanical response of rocks varies at different levels of static stresses. Currently, few investigations have provided experiments and theoretical studies on the dynamic characteristics of rocks at high static stress in the rheology phase. Therefore, studying the perturbation effect of rock rheology provides theoretical significance and a practical engineering value because it can expand the content of rock rheological theory and guide the supporting design of deep soft roadways.

This work examines the dynamic mechanical behavior of soft red sandstone using a self-developed rock rheological testing system (RRTS) by investigating the rock rheological perturbation effect. This system can achieve long-term dead load and exercise impact load in accordance with free falling steel rings. This investigation aims to obtain the deformation and failure characteristics of red sandstone, as well as the deformation law of its perturbation when it is affected by an impact load under uniaxial compress and rheological state, to establish a constitutive relation of perturbation effect of rock rheology.

2 Conception of perturbation effect of rock rheology

The rheological deformation of a rock is very sensitive to external impacting loads at a state of high stress. To describe this effect, a new mechanical concept “perturbation effect of rock rheology” is proposed which describes the mechanical phenomenon whereby the rheological deformation of a rock increases at a certain level of stress when effected by outside impact loads (such as shooting vibration) [25].

Rocks are a kind of anisotropic material (Fig. 1) which can be considered a whole unit composed of many small units. Each unit and the mechanical parameters of their faying surfaces are usually displayed in a certain probability distribution. When a rock perturbed under high stress enters into a rheological state, local deformation will appear at some weak units and faying surfaces. This may lead to evolution inside the stress field of the rock which, as a whole, will manifest itself by an increase in the appearance of rheological deformation caused by the perturbation effect of rock rheology.

Fig. 1 Anisotropic structure of a rock

3 New experimental system for rock rheological perturbation effect

The new experimental system for the rock rheological perturbation effect consists of two parts: a testing machine and a data monitoring system. The new machine is the RRTS-III which in comparison to the RRTS-II machine improves the force-amplification structure. The RRTS-III has an increased rate of force-amplification, from 60 times to 100-120 times; the stability control system of impact loading is also strengthened.

3.1 Force-amplification structure and principle of stress loading system

The RRTS-III testing machine is capable of subjecting rock specimens to axial stress through gravity loading of weights. This machine can carry out sustained and stable loading as it does not rely on electrical power. It is also suitable for performing long-term rock rheological experiments under static stress and rock rheological perturbation effect experiments [26]. The testing machine and a schematic diagram are shown in Fig. 2.

The gravity load applied to rock specimens derives from circular ring-shaped mass made of cast iron. Each mass can be 10, 15 or 20 kg. The machine uses two grades of force-amplification which can increase the original gravity load by 100-120 times. The first grade of force-amplification is achieved by the mechanical gear transmission structure, and the second grade is achieved by the hydraulic transmission structure.

The first grade of mechanical force-amplification structure includes a transmitted rotary table, a shaft and a transmitted gear. Chains are located on the edge of the rotary table where masses are attached to provide a gravity load on the rotary table. The gravity load is then transferred to the transmitted gear connected to a transmitted rack. Due to the size differences of the rotary table and the gear, the gravity load achieves first grade amplification. The second grade of hydraulic force- amplification structure includes a transmitted rack, a small cylinder, a big cylinder and an oil transferring pipeline. The transmitted rack directly presses on the pressure axis of the small cylinder before the force is transferred to the big cylinder through the oil transferring pipeline. The piston on the top of the big cylinder is pushed upwards to apply the load to the rock specimen. Because of the size differences of the cylinders, the load achieves second grade amplification.

3.2 Loading mode of perturbation effect

The loading mode of the perturbation effect is achieved by the exerted perturbation effect on the rheologically deformed rock specimen, which occurs by using weights freely falling to impact the top bearing plate of the machine. The impacting load can then be transferred to the rheologically deformed rock specimen.

Fig. 2 RRTS-III testing machine designed to analyze rock rheological perturbation effect

The concrete method: this method uses steel-ring weights around the linkage of the top bearing plate of the machine. Each steel ring has three different masses (3 kg, 5 kg and 10 kg), the different weights of the steel rings can be combined to make different impacting blocks. The masses are released from different relative heights (100-400 mm) which exert various perturbation effects on the rock specimen. After rock deformation has been achieved in the rheological stage at a certain level of stress, the steel rings are raised to a set relative height before they are released again. When the steel rings fall on the top bearing plate, the generated impacting load will be transferred to the rock specimen (Fig. 3).

Fig. 3 Schematic diagram of testing structure for perturbation effect

According to impulse and energy theorem, if ignoring the energy loss, the geopotential energy of impacting weights can be completely transformed to the rock specimen. Therefore, the perturbed loading energy ΔW can be calculated as

                            (1)

where m refers to the mass of the steel ring, kg; g is the acceleration of gravity, and g=9.8 m/s²; h is the falling height, m; A is the cross sectional area of the rock specimen, m².

3.3 Data acquisition system

The testing machine was equipped with a specialized data acquisition system, comprising of SD-I-type displacement sensors, JC-4A intelligent static strain gauges, JC-II-type load sensors, UBOX blasting vibration recorders, and computers (Table 1). The UBOX blasting vibration recorders can automatically record the vibration magnitude and waveform graph of the perturbation load.

4 Rock rheology perturbation effect experiment under uniaxial compression

4.1 Rock specimen and testing methods

The rock specimen comprised of red sandstones mined to the east of Shandong province, China. The rocks were maroon in color with a fine structure, excellent integrity and uniformity. All of the testing rock specimens were drilled down from a large rock plate to ensure consistency. Defective specimens with cracks, bedding and surface stripes were rejected. Ultrasonic detection was performed on the rock specimens to select specimens of similar wave velocity. The selected rock specimens were then used in the perturbation effect experiment (Fig. 4).

Fig. 4 Red sandstone specimen

The first three specimens (1^#, 2^# and 3^#) were chosen to test the conventional uniaxial compressive strength and ultimate strain of the red sandstone; this analysis provided a complete stress-strain curve for the red sandstone (Fig. 5). The results indicate that uniaxial compressive strength is about 49.5 MPa, ultimate strain is about 0.683%, and the red sandstone could be classified as a medium- hard rock.

Three points of stress were selected on the complete

Fig. 5 Complete stress-strain curves of red sandstone

stress-strain curve, the static stress levels, to undertake the perturbation effect experiment (Fig. 6). The corresponding stress of Point A was 22.5 MPa, 45.5% of the specimen’s uniaxial compressive strength. This level of stress had not yet reached long-term strength, and the specimen was at a stage of attenuated rheological deformation. The corresponding stress of Point B was 39.2 MPa, 79.2% of the specimen’s uniaxial compressive strength. This level of stress exceeded the rock’s long-term strength, and the specimen was at a stage of steady rheological deformation. The corresponding stress of Point C was 42.5 MPa, 85.9% of the specimen’s uniaxial compressive strength. At this level of stress, the rock specimen will quickly fracture after a period of rheological deformation.

Fig. 6 Static stress levels (A-C) used in applying perturbation load

When the perturbation load was applied, the strain of the specimen was recorded after each impact; at certain times a continuous impact was recorded as one perturbation [27]. The recording data can reflect the increment of rheological deformation of the rock at certain strengths of perturbation.

4.2 Rock rheology perturbation effect experimental results

4.2.1 Point A static stress results

At Point A static stress, the axial stress on the rock specimen was 22.5 MPa, 45.5% of the uniaxial compressive strength. This axial stress was small and the rock specimen entered into the first stage of the rock rheology-rheological attenuating phase.

1) First perturbation

Rock rheology lasts for 72 h before the first perturbation. The axial strain was 3.849×10^-3, and the lateral strain was 1.195×10^-3 when rheology was steady before the first impact was applied to the specimens.

The initial impact mass was 5 kg. The upper bearing board was impacted to exert dynamic disturbance impact load by way of free fall from a height of 10 cm. The impact energy of each strike was ΔW=3565 J/(s·m²), calculated in accordance with Eq. (1). The impacting numbers of first perturbation are 10 at A-stress level, then the relationship between the impact times (N) and the cumulative disturbing strain (ε_a) is shown in Fig. 7(a).

As shown in Fig. 7, with the applied load, axial disturbance strain differs with the transverse strain. The axial disturbance strain has an initial rapid increase before the rate of increase declined and a stable rate is attained. Under the continuous impact loads, the disturbing strain caused by the previous impact load will affect the subsequent impact effect, thereby reducing the subsequent disturbing strain and hardening the impact occurring in the rock specimen. At the same time, the lateral disturbing strain increases almost linearly; the previous impact load does not affect the subsequent impact effect and the disturbance deformations caused by each continuous impact are almost equal.

Fig. 7 Relationship between the impact times (N) and cumulative disturbing strain (ε_a) at Point A static stress

2) Second perturbation

The rock specimen enters into the second perturbation two days after the first perturbation, and the disturbing load and static stress are the same with that of the first perturbation. Eight impacts occur during this perturbation (Fig 7(b)).

The disturbing strain in the second perturbation is obviously smaller than that of the first. In comparison to the first perturbation, the lateral disturbing strain is noticeably reduced, and it tends to be stable; after a certain strain, the rock specimen presents elastic response to the impact effect. This result also shows that even if the rock specimen is in the elastic stage, plastic disturbing strain will occur. The total cumulative axial disturbing strain during the first and second stages is 0.177×10^-3, and the cumulative lateral disturbing strain is 0.184×10^-3.

4.2.2 Point B static stress results

At Point B static stress, the axial stress on the rock specimen is 39.2 MPa, 79.2% of the uniaxial compressive strength, recording a medium level of axial stress. The rock specimen entered into the second stage of rock rheology, that is, the uniform rheological phase.

The rock rheology disturbing effect experiment at Point B static stress was after the experiment at Point A static stress. The rock specimen was the same but only the axial static stress was bigger.

(1) First perturbation

After the static stress rock rheology perturbation effect experiment at Point A, the static stress increases to 39.2 MPa at Point B; the rock specimen entered the uniform rheological phase. The disturbing load is placed on the rock specimen 48 h after rheology. Before the load is applied, the total axial strain is 5.967×10^-3 and the lateral strain is 1.940×10^-3. The impact time at Point B is 10, and the relationship between the impact times (N) and the cumulative disturbing strain (ε_a) is shown in Fig. 8(a).

As seen in Fig. 8, the developing law of disturbing strain is basically the same with the results for Point A (Fig. 7(a)), however, the disturbing deformation value is slightly bigger. One day after the disturbing effect ceases, the rheological strain halts before gradually recovering. The rheological rate takes three days to return to the previous rate before the occurrence of the disturbing effect.

(2) Second perturbation

After the rheological strain is recovered, the second perturbation is applied on the specimens at Point B static stress; this experiment lasts for 11 impacts (Fig. 8(b)). Although the level of static stress and the impact load did not change, the disturbing strain noticeably increases and shows no apparent decrease.

Fig. 8 Relationship between impact times (N) and cumulative disturbing strain (ε_a) under Point B static stress

According to the failure strain in the follow-up experiments, at the beginning of the first perturbation, the total axial strain accounts for 85% of the failure strain; at the beginning of the second perturbation, the total axial strain accounts for 88% of the failure strain. This result indicates that, under the condition of rheology, it is suitable to use strain as a parameter to measure the sensitivity of the rock to a disturbing load. For the applied disturbing load, when the strain reaches 90% of the failure strain, the disturbing deformation has no obvious decrease. This point could be used as the dividing point between the disturbing sensitivity area and the disturbing non-sensitivity area.

4.2.3 Point C static stress results

After experiment tests at Point B, the rock rheology under the action of static stress still need 3 h to stagnate, which is noticeably less than the time recorded after the Point A experiment. After stagnation, the static stress increases by one degree and Point C raises to the static stress level. After 24 h, the total axial strain attains 6.225×10^-3, accounting for 96% of the failure strain. With the same impact load, when the specimen is impacted for the 8th time, it is destroyed and the axial failure strain is 6.484×10^-3. The relationship between the impact times (N) and the cumulative disturbing strain (ε_a) at Point C static stress is shown in Fig. 9.

Fig. 9 Relationship between impact times (N) and cumulative disturbing strain (ε_a) at Point C static stress

Results from this experiment show that when the rock specimens are close to being destroyed, the axial and lateral disturbing strains noticeably increase with the time of impact, which differs from those in the previous attenuation.

4.3 Analysis of rock rheology perturbation effect

The experimental results for Points A-C show that, under a certain impact load, there is a strain threshold for the occurrence of the rock rheology perturbation effect. If the strain of the specimen is less than this threshold, under continuous impact loads, the disturbing deformation induced by impact loads will obviously weaken with an increasing number of impacts. If the strain of the specimen is larger than the threshold, the disturbing deformation will continue to increase until the specimen fails. This threshold could be used as the dividing point between the disturbing sensitivity area and the disturbing non-sensitivity area. It can be concluded that the threshold of a medium-hard red sandstone accounts for about 90% of its ultimate failure strain.

Further experiments are undertaken to examine the general law of rock rheology disturbing effect and to further investigate this threshold. The experimental method was the same as the previous experiments, and the disturbing loads are applied when the strain is above 80% of the ultimate failure strain.

(1) Specimen C-D-1 under the impact load of 30 N

Specimen C-D-1 is loaded on a static stress of 35.7 MPa; 48 h after rheology its strain reaches 5.463×10^-3, suggesting that it enters into a stable creep stage. The disturbing load is then attached. The relationship between impact times (N) and the single disturbing strain (ε_r) induced by each impact load is shown in Fig. 10(a). The relationship between impact times (N) and the cumulative disturbing strain (ε_a) is shown in Fig. 10(b).

From Fig. 10, it can be seen that, compared with the curve of the cumulative disturbing strain (Fig. 10(b)), the curve of the single time disturbing strain (Fig. 10(a)) more clearly reflects the response of the rock specimen to the impact load. The axial disturbing strain induced by the single impact consistently weakens, except for the first impact, and it tends to stabilize more quickly than the lateral strain. The curve of the cumulative disturbing strain is roughly similar with that of the previous experiments. However, compared with the previous experiments, there are more impacts on the rock specimens and the lateral disturbing strain also tends to stabilize gradually.

Fig. 10 Impact deformation of C-D-1

Twenty-four hours after the first perturbation, the second perturbation is loaded on the specimen; the interval of subsequent disturbing loads is also 24 h. Five perturbations are undertaken with the specimen being destroyed when the 5th perturbation is loaded. The curves of the disturbing strain of specimen C-D-1 under the second, third, fourth and fifth impact are shown in Figs. 11-14.

Fig. 11 Curve of disturbing strain of specimen C-D-1 under 2nd perturbation

Fig. 12 Curve of disturbing strain of specimen C-D-1 under 3rd perturbation

Fig. 13 Curve of disturbing strain of specimen C-D-1 under 4th perturbation

Fig. 14 Curve of disturbing strain of specimen C-D-1 under 5th perturbation

Figures 11-14 indicate that the deformation rules for the rock in the second and third perturbation are basically the same as the first perturbation. Although the axial strain is basically stable after being impacted 6 or 7 times, the lateral deformations differ slightly. The disturbing strain becomes stable after being impacted 15 times in the first perturbation; the second and third disturbing strains are stable after being impacted 12 and 7 times, respectively. The impact time of the lateral strain becomes stable decreased gradually, indicating that this strain stage does not enter the sensitivity zone for a given impact strength.

After perturbation for three times and 72 h of static-load rheology, the total axial strain reached 5.940×10^-3. With the forth perturbation, the cumulative disturbing strain increases and the impact time needs the strain to stabilize increased by a small amount; the lateral strain also increases by a small amount, even when the axial strain is stable. The increase of the cumulative disturbing strain shows that the deformation of the rock has entered into the perturbation-sensitivity zone.

During the fifth perturbation, the basic law of strain is generally the same as that for the previous 8 or 9 impacts. In other words, the disturbing strain attenuates, which is induced by a single impact; the cumulative disturbing strain is similar to that of the previous impact. However, the value of the disturbing strain is obviously larger. After this, the single disturbing strain developed with fluctuations and the cumulative disturbing strain continuously increases. The specimen fails at the 21st impact; after the 20th impact the total strain is 6.407×10^-3, which is the ultimate failure strain ε_s, making this strain as the ultimate failure strain is conservative. The results from this experiment are shown in Table 1.

2) C-D-2 and C-D-3 specimens under impact loads of 60 N and 90 N

To examine the effect, an increase in load, on the rock specimens, the mass of impact material on the C-D-2 specimen is set at 6 kg, and the mass of impact material on the C-D-3 specimen is 9 kg. For both experiments, the impact height is set at 10 cm. The strain at the beginning of perturbation is 80% of ultimate failure strain, 6.407×10^-3. The interval of the adjacent two perturbations is 24 h. During each perturbation, the specimen is applied with a series of impact loads until the axial strain is stable. The experimental results show that the deformation law is the same with that from the previous experiment (C-D-1 specimen). The experimental results of C-D-2 and C-D-3 are shown in Tables 2 and 3.

During the fourth perturbation, the C-D-2 specimen fails when the 15th impact load is implemented. After the 14th impact, the maximum strain is 6.268×10^-3. This strain can be used as the ultimate failure strain of the specimen. During the 4th perturbation, the C-D-3 specimen fails when the 8th impact load is implemented. After the 7th impact, the maximum strain is 6.198×10^-3. This strain can be used as the ultimate failure strain of this specimen.

Comprehensive comparison of the disturbance response of the three specimens under different stages clearly shows the law of the response of the rock specimens to impact loads (Fig. 15). The x-coordinate is the perturbation sequence, Nr, and the y-coordinate is the axial cumulative disturbing strain (ε_aa) and the lateral cumulative disturbing strain (ε_al).

Table 1 Rock rheology perturbation effect experimental results of C-D-1

Table 2 Rock rheology perturbation effect experimental results of C-D-2

Table 3 Rock rheology perturbation effect experimental results of C-D-3

Fig. 15 Comparison of disturbance responses of three specimens

As the ultimate failure strain for each specimen is the maximum strain recorded in the experiment, the fractions of the strain at the dividing point between the sensitivity zone and non-sensitivity zone are similar. However, compared with the absolute total strain for the three specimens when they enter the sensitivity zone and their ultimate failure strains, it can be seen that, with an increase of impact force, the strains at the dividing point and ultimate failure strains decreas, but the differences are not significant. There are two reasons for these results: the discreteness of the mechanical properties of the rock; and the difference of impact load is little, thus the different response of the rocks to different perturbation strengths is not clear. Therefore, our experiments provide information for qualitative research of rock perturbation responses, but they do not contain enough information for quantitative research of rock perturbation responses. Further experiments are therefore needed to quantitatively investigate rock perturbation responses.

5 Constitutive relationship of rock rheological perturbation effects under axial compression

To examine the constitutive relationship of rock rheological perturbation effects under axial compression, the stress state of the rock needs to be considered. Moreover, there are three independent variables [28, 29] including:1) the difference between the stress level of the rock under axial compression and its ultimate strength, δ; 2) the energy of the perturbation load, ΔW; 3) the impact times of the perturbation load, N.

The preliminary result of the rock rheological perturbation experiment under axial compression, i.e. the relationship between the increment of perturbation deformation, Δε, and the energy of the perturbation load, ΔW, is linear. Therefore, the constitutive relationship, which is also termed the incremental function of rheology induced by each impact load, is given by

                       (5)

where Δε is the increment of perturbation deformation in a certain period, and there is no dimension; F(δ, Δσ₁, N) is the function of rheological perturbation obtained from the experiments; N is the perturbation time; Δσ₁ is the interval compression strength of rock on the perturbation sensitivity, also called perturbation sensitivity zone, MPa; K is the modulus of rheological perturbation; ΔW is the perturbation load, which is represented by vibration energy density, J/(s·m²); and δ is the difference between the stress level of rock under axial compression and its ultimate strength, δ=σ₀-σ, MPa.

To ensure the constitutive relationship of the rock rheological perturbation effect, it is important to build up the function F(δ, Δσ₁, N). According to the curving shape from our experimental results, the following assumptions are made:

1) When the stress is far away from the ultimate strength of the rock, the function of rock rheological perturbation, F(δ, Δσ₁, N), is an attenuation function. Namely, its second derivative is negative;

2) When the stress is close to the ultimate strength of the rock, the function of rock rheological perturbation, F(δ, Δσ₁, N), is an increment function. Namely, its second derivative is positive;

3) When the stress is in the middle of the rock’s perturbation sensitivity zone, δ=Δσ₁/2, the function of rock rheological perturbation, F(δ, Δσ₁, N), is linear.

So, under the axial compression stress state, the function of rock rheological perturbation is

Then,    (6)

So, the constitutive relationship, which is also termed the incremental function of rheological, induced by each impact is

          (7)

6 Conclusions

1) The magnitude and rising tendency of perturbation deformation for red sandstone reflect the mechanical response characteristics of the rock under a rheological state to the external impacting load, also known as the rock rheological perturbation effect. This mechanical effect of rock has a hardening mechanism under a low-axial stress state and a damaging mechanism under a high-axial stress state.

2) Measuring the sensitivity degree of rock to external impacting perturbation should use strain as a parameter. A strain threshold exists which could be used as the dividing point between the perturbation sensitivity area and the perturbation non-sensitivity area. The experimental results show that a strain threshold of the medium-hard red sandstone specimen is 90% of its ultimate failure strain.

3) The magnitude of perturbation load plays an important role in the development of perturbation deformation. Under equivalent strain levels, increasing the perturbation load will result in an increase of perturbation deformation at the initial stage, cumulative perturbation deformation at steady state, and increasing the rate of perturbation deformation.

4) The constitutive relationship of the rock rheological perturbation effect induced by each impact load, also termed the incremental function of rheology, is built-up.

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(Edited by FANG Jing-hua)

Cite this article as: GAO Yan-fa, HUANG Wan-peng, QU Guang-long, WANG Bo, CUI Xi-hai, FAN Qing-zhong. Perturbation effect of rock rheology under uniaxial compression [J]. Journal of Central South University, 2017, 24(7): 1684-1695. DOI: 10.1007/s11771-017-3575-9.

Foundation item: Projects(51474218, 51304127, 50474029) supported by the National Natural Science Foundation of China; Project(2016M590646) supported by China Postdoctoral Science Foundation; Project(2016121) supported by Qingdao Postdoctoral Applied Research Foundation, China

Received date: 2015-10-27; Accepted date: 2016-01-30

Corresponding author: HUANG Wan-peng, PhD; Tel: +86-18753226508; E-mail: hwp20033@sdust.edu.cn