J. Cent. South Univ. (2012) 19: 252-261

DOI: 10.1007/s11771-012-0999-0

Creep properties and permeability evolution in triaxial rheological tests of hard rock in dam foundation

XU Wei-ya(徐卫亚)¹, WANG Ru-bin(王如宾)^{1, 2}, WANG Wei(王伟)¹,

ZHANG Zhi-liang(张治亮)¹, ZHANG Jiu-chang(张久长)¹, WANG Wen-yuan(王文远)³

1. Research Institute of Geotechnical Engineering, Hohai University, Nanjing 210098, China;

2. College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China;

3. Kunming Design and Research Institute, China Hydropower Consulting Group Co., Kunming 650051, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: Triaxial creep tests were carried out under seepage pressure by using rock servo-controlled triaxial rheology testing equipment. Based on experimental results, rock rheological properties influenced by seepage-stress coupling were studied, and variations of seepage rate with time in complete creep processes of rock were analyzed. It is shown that, when the applied stress is less than failure stress level, the creep deformation is not obvious, and its main form is steady-state creep. When applied stress level is greater than or less than but close to fracture stress, it is easier to see the increase of creep deformation and the more obvious accelerative creep characteristics. The circumferential creep deformation is obviously higher than the axial creep deformation. At the stage of steady-state creep, the average of seepage flow rate is about 4.7×10^{-9 m/s at confining pressure (σ}₃) of 2 MPa, and is about 3.9×10^{-9 m/s at σ}₃ of 6 MPa. It is seen that the seepage flow rate at σ₃ of 2 MPa in this case is obviously larger than that at σ₃ of 6 MPa. At the stage of creep acceleration, the seepage flow rate is markedly increased with the increase of time. The variation of rock permeability is directly connected to the growth and evolution of creep crack. It is suggested that the permeability coefficient in complete creep processes of rock is not a constant, but is a function of rock creep strain, confining pressure, damage variable and pore water pressure. The results can be considered to provide a reliable reference for the establishment of rock rheological model and parameter identification.

Key words: rock mechanics; creep properties; volcanic breccia; triaxial rheology test; permeability evolution; creep damage

1 Introduction

In recent years, it should be noted that fewer researches on creep properties and permeability evolution in complete creep processes of rock during triaxial compressive creep tests were conducted. More importantly, it was not easier to get quantitative data of the variation of permeability coefficient during the process of rock creep.

The triaxial compression tests of Inada granite to clarify permeability change with increasing stress up to failure were carried out. Coupling between crack growth and permeability change might be determined to fully understand the hydro-mechanical response of rocks subjected to non-hydrostatic stress [1]. The permeability of micro-cracked argillite was investigated and it was found that in case of water as flow liquid, swelling of clay particle led to additional closure of fractures [2]. In addition to the dependence on pressure, a time-dependent permeability reduction and thus crack closure at constant pressure was found, indicating creep compaction behavior of Opalinus clay, and the permeability reduction due to time-dependent stress variation could be used in long-term safety analyses [3]. Triaxial compression tests, with permeability measurements carried out on two different granites, provided a verification of the numerical implementation as a good agreement between experiments and predictions [4]. The viscoelastic-plastic creep experiments on soft ore-rock in Jinchuan Mine III were performed under circular increment step of load and unload, and the experimental data were analyzed according to instantaneous elastic strain, visco-elastic strain, instantaneous plastic strain and visco-plastic strain [5]. Micro-mechanical damage models were proposed, in which the kinetic equations of micro-cracks were characterized by the use of fracture mechanics stability criteria [6]. The deformation of rock salt damage and permeability variation were studied, and the results of deformation experiments focusing on the transport properties of rock salt and describing       the conditions for the transition from non-dilatants to dilatants deformation at the so-called dilatancy boundary were presented [7]. A flow-stress-damage coupling model for heterogeneous rocks taking into account of the growth of existing fractures and the formation of new fractures was proposed [8]. LI et al [9] studied the relation of complete creep and trixial stress-strain curves of rock. The results of laboratory tests on the time-dependent behavior of three rocks characterized by high proportion of clay particles were presented by FABRE and PELLET [10], and the viscosity of these sedimentary rocks was studied under different loading conditions in uniaxial compression. Static or cyclic creep tests and quasistatic tests (low-loading strain rate) were performed across various orientations of fabric planes.

The variation of permeability with the growth of micro-cracks is one of the most significant phenomena to be taken into account in many engineering applications such as the long-term stability of rock slopes, surrounding rock of underground caverns, and dam foundation. The most important research of permeability evolution of rock under complex stress state was the study on coupling characteristics of seepage and stress in rock. Based on the review of current research achievements, three types of the research methods in the field of coupled fluid flow and stress in rock were proposed [11] as follows.

1) The empirical formulas were obtained by coupled fluid flow and stress experiments directly.

2) According to existent empirical formulas, the function was established and the variable expression was deduced in the established functions by mechanical method and then the formulas were determined.

3) Based on various physical models, the established coupled relation expressions were used to simulate the seepage phenomena.

By means of seepage tests under transient triaxial compression, the permeability in full stress-strain process was studied [1, 12-16]. It was found that the rock permeability coefficient under triaxial compression was generally not a constant, but varied with the inner structure evolution of rock in full stress-strain process.

As typical rock for dam foundation, underground cavern group and high rock slopes of the major hydropower project, volcanic breccia was a kind of complex geological media, which contained many flaws such as joints, fissures, cracks, weak surfaces and faults. The creep property and seepage characteristics of volcanic breccia were important factors to influence the long-stability of rock engineering.

The main objective of this work was to study the creep properties and permeability evolution of the volcanic breccia by means of triaxial compressive creep tests under the condition of seepage pressure, to analyze the seepage laws in complete creep processes of rock specimen, and to establish the explicit equation between creep deformation and permeability changes, considering rock creep damage. The experimental results of this work can be considered to provide a reliable reference for the establishment of rock rheological model and parameter identification. It may help to analyze the long-stability of rock engineering.

2 Testing equipment and experimental procedure

Laboratory experiments were the main methods on investigation of time-dependent mechanical properties and seepage laws of rocks through long-term testing and observation. Compressive creep behavior, damage property and seepage laws in rock interior were the main mechanical properties when rock sample entered into its creep deformation stage under the condition of axial load. Taking into account of in situ stress state of rock mass, creep tests were carried out under conventional triaxial compression conditions (σ₁>σ₂=σ₃).

2.1 Experimental equipment

Creep tests for volcanic breccia specimens were carried out by using rock servo-controlled triaxial rheology equipment (Fig. 1), developed by Laboratory of Mechanics in Lille (LML) of Centre National de la Recherche Scientifique (CNRS) in France, University of Science and Technology of Lille (USTL) in France and Hohai University in China. Its main accessory was self-equilibrium triaxial pressure system (Fig. 2), which was made up of three high-precision pumps controlling axial pressure (p₁), confining pressure (p₂) and pore pressure (p₃), respectively. The computer robotized operations of this equipment was sure to perform the controlled tests safely, timely and precisely.

Fig. 1 Rock servo-controlled triaxial rheology equipment, developed by Laboratory of Mechanics in Lille of CNRS in France, University of Sciences and Technology of Lille in France and Hohai University in China

Fig. 2 Self-equilibrium triaxial pressure chamber system of servo-controlled rock triaxial rheology equipment

2.2 Experimental procedures

The volcanic breccia materials were obtained from the site of Huangdeng Hydropower Project in southwestern China, which were massive, brecciated texture of gray purple or purple-red. These mineralogical compositions included mainly feldspar, quartz, pyroxene, sericite, calcite, and a small amount of iron.

The volcanic breccias were made into many cylindrical specimens, which were used in the laboratory tests. The specimen had a columnar shape with a diameter of 50 mm and a height of 100 mm. The typical altered-rock is shown in Fig. 3.

Fig. 3 Photos of typical volcanic breccias specimens

In order to study the creep mechanical properties of volcanic breccia materials in seepage environment, the rock saturation tests were preformed before the starting of the creep tests.

The creep tests were carried out on the saturated rock specimens, and the creep experiment procedures were described as follows [17].

1) The saturated specimen (wrapped with flexible membrane) in the test chamber with two linear variable displacement transducer (LVDT) sensors was installed.

2) The confining pressure was applied at a rate of 1.5 MPa/min until the required hydrostatic state.

3) After reaching the predefined confining pressure, the deviatoric stresses were applied using the stepwise loading method. Then, the seepage pressure was loaded to 1.5 MPa.

4) When the rock specimen was loaded to the first stress level at a constant rate of 1.5 MPa/min, the axial stress was kept at a constant value while recording deformation, confining pressure, and stress with time by the automatic data acquisition system.

5) After completing creep test under first stress level, the rock specimen was tested under the second, third, etc stress levels gradually. Under the last stress level, accelerated creep damage occurred, and the variations of mechanical parameters of rock specimen were measured with time.

3 Triaxial creep test results and analysis

For two kinds of volcanic breccia specimens, the triaxial creep tests were performed under seepage pressure condition with confining pressures of 2 and 6 MPa. During the creep tests, pre-determined multi-step stress levels (Table 1) were applied in steps under the specific confining pressure. Here q is the axial deviatoric stress σ₁-σ₃, σ₁ is the axial stress and σ₃ is the confining pressure. On the deviatoric stress level with * symbol, it is the mark of creep failure of the specimen. Deviatoric stress levels marked with underline were not applied to the specimen.

Each deviatoric stress level, before the final failure in deviatoric stress level, was maintained for no less than 48 h. The stress increment from one level to the next was 2.5-10.0 MPa. The creep tests were taken with 6-10 stress steps. The triaxial creep experimental results of volcanic breccia under different confining pressures are shown in Fig. 4. The variations of axial and circumferential strains of the specimens with time under different deviatoric stresses were analyzed.

3.1 Variation of axial strain with time

As shown in Fig. 4, it is found that the axial and circumferential strain curves versus time include initial strain, steady-state creep strain, and accelerated creep strain under confining pressures of 2 and 6 MPa.

Table 1 Pre-confirmed stress levels of specimens before creep tests according to short-term strengths

Fig. 4 Creep strain vs time for volcanic breccia under confining pressure of 2 MPa (a) and 6 MPa (b)

As shown in Fig. 4(a), when σ₃=2 MPa, the axial strain of specimen increases only by 44 με (1 με=10^-6) after creeping for 48 h under q^1st of 65 MPa. It is not very clear that the axial creep strain has a tendency to increase with the increase of stress level. At this time, the creep experiment does not induce clear damage on the rock sample. The results show that rock material undergoes micro-structural adjustment such as microscopic fracturing and pore closure at the low stress levels [17]. With the increase of stress level, the sample shows more and clearer creep deformation, micro-fissures in the sample start to propagate, and this is the stage of crack initiation and stable crack growth. From Fig.4, it is found that the irreversible nonlinear deformation occurs. The results show that rock material gradually becomes soft and plastic deformation increases due to a long-term accumulation action of creep effect.

When the stress level is close to be the failure stress level, microscopic fissures in the rock interior progress further. These microscopic fissures are to be combined, accumulated and finally the macroscopic cracks form. These macroscopic cracks extend towards the end of the sample until its final failure [17]. From Fig. 4, under   q^6th =100 MPa, the specimen shows an accelerated creep behavior, and the axial strain is increased to 900 με after creeping for 69 h, which is more than the summation of creep strain during all previous loading steps at different stress levels. At this moment, the corresponding axial strain is 3.0×10^-3 and failure of volcanic breccia specimen takes place. Creep failure of the specimens shows the characteristics of catastrophe and purification due to the rapid expansion and progress of microscopic cracks from the accumulation of creep damage.

The axial strain of the volcanic breccia specimen at σ₃=6 MPa versus time shows similar behavior as that   at σ₃=2 MPa. When the failure stress level of         q^cf (=120 MPa) is reached, the specimen shows an accelerated creep behavior and the axial strain is increased to 1 670 με after creeping for 41 h under confining pressure σ₃ of 6 MPa. Moreover, it is shown in Fig. 4 that the confining pressure has a strong influence on the creep deformation of volcanic breccia at the same stress level. The higher the confining pressure, the smaller the corresponding axial creep strain, i.e., there is less creep deformation. Table 2 summarizes the test durations, starting deviatoric stresses, final failure deviatoric stresses and short-term strengths of volcanic breccia specimens.

Table 2 Test durations, starting deviatoric stresses, last failure deviatoric stresses and short-term strengths [18]

From Table 2, the first deviatoric stress level q^1st reaches 47.6%-61.3% of corresponding short-term strength σ_c. The objective of this work is to assure that the specimen shows attenuation and steady-state creep under the first stress level q^1st, which will provide more experimental data to model delayed creep damage and failure of rock.

3.2 Variation of circumferential strain with time

As shown in Fig. 4(b), compared with the axial creep strain curves, the circumferential strain curves are relatively smooth, and the phenomenon of strain mutation is not found. The results indicate that the effect of the heterogeneity, local weakening and damage, and rupture of rock on the circumferential strains are relatively small.

The circumferential strains also show initial, steady-state, accelerated creep stages under the confining pressures of 2 and 6 MPa. Compared with the axial creep deformation, the circumferential creep deformation is not obvious at low stress levels under confining pressures of 2 and 6 MPa. When the deviatoric stress level reaches or exceeds the long-term strength, there is a large amount of circumferential deformation, even under the condition of restriction on confining pressure. The circumferential strain curve versus time at σ₃ of 6 MPa is taken as an example in the following analysis.

At σ₃=6 MPa, when reaching the failure stress level of q^cf=120 MPa, the specimen shows the accelerated creep behavior. It is found that the circumferential strain is increased to 3 507 με after loading for 41 h, which is more than two times of the total creep strain during all former loading steps. Under q^9th=117.5 MPa, the loading lasts for 120 h at the constant stress. As shown in     Fig. 4(b), before the deviatoric stress level q^9th=117.5 MPa is applied, the circumferential deformation is relatively small, but the circumferential creep deformation becomes larger after q^9th=117.5 MPa. The circumferential strain versus time at σ₃=2 MPa shows a similar behavior as that at σ₃=6 MPa.

Based on the above analysis, it is considered that the creep deformation puts emphasis on the axial strain before the failure stress level is applied, and the circumferential strain is the integral part of creep deformation during the failure stress level load. Therefore, circumferential creep deformation can reflect the deformation characteristics of rock from another point of view, and the results should be drawn sufficient attention.

3.3 Analysis of steady-state creep rate and accelerated creep mechanical behavior

Steady-state creep rate is defined as the slope of straight line at the stage of steady-state creep, which is strongly dependent on deviatoric stress, confining pressure, etc. In recent years, some typical experimental results on the steady-state creep rate of salt rock, argillite rock and tuff were proposed [10, 19-20]. From the results of creep tests of brittle rocks, it was concluded that circumferential strain could be used as a condition- insensitive damage indicator of rock in creep tests as well as in constant strain rate tests [21].

In the starting creep failure, the axial creep strain rate shows a different behavior compared with that under the former stress levels. From Figs. 5(a) and (b), it can be seen that the axial and circumferential strains under the failure stress load undergo three stages of attenuation creep, steady-state creep and accelerated creep. The attenuation creep rate, steady-state creep rate and accelerated creep rate are proposed. At the stage of attenuation creep, the strain rate is found to decrease quickly with the increase of time. At the stage of steady-state creep, the strain rate is basically constant. At the stage of accelerated creep, the strain rate increases sharply with time, and the failure of rock specimen is found at this time. As shown in Fig. 5(a), the average of steady-state axial creep rate under confining pressure of 2 MPa is 36 με/h. Under confining pressure of 6 MPa, the axial creep rate undergoes three stages of 17 με/h, 29 με/h, and 40 με/h, respectively.

Fig. 5 Complete axial accelerative creep curves of volcanic breccia and relation between axial creep rate and time under confining pressures of 2 and 6 MPa: (a) Axial accelerative creep curves; (b) Circumferential accelerative creep curves  

As shown in Fig. 5(b), similarly, under the failure stress load, the average of steady-state circumferential creep rate of the rock specimen is about 16 με/h under confining pressure of 2 MPa. Under confining pressure of 6 MPa, the circumferential creep rate also undergoes three stages of 8 με/h, 40 με/h, and 238 με/h, respectively. With the increase of time, the circumferential deformation of the rock specimen is found to accelerate into the stage of accelerated creep. Therefore, from    Fig. 5, it can also be seen that, under confining pressures of 2 and 6 MPa, the circumferential deformation is earlier for entering into the phase of accelerated creep than the axial before the rock failure. In summary, the accelerated creep characteristics are relatively prominent in complete creep processes.

4 Seepage laws in complete creep stress- strain process of rock

Due to the complexity of rock structure, the pore structure of nature rock is in disorder and unsystematic state. The progressive deterioration of rock configuration and mechanical performance due to underground seepage flow is found, so that the long-term safety is threatened seriously. Therefore, the study on rock seepage flow laws and coupling property of stress and seepage under complex stress is one of the key problems for many fields of rock mechanics and engineering.

During the rheological tests, the specimens are considered as continuous media, for which seepage flow law is consistent with Darcy’s law in the complete creep processes of rock sample. The seepage pressure difference between the upper and bottom of the specimen is 1.5 MPa. The test data of seepage flow are collected with auto-controlled computer.

In order to compute seepage flow rate, the formula of permeability coefficient in complete processes of the specimen is described as

                            (1)

where K_i is the seepage flow rate during the interval between the i-th and (i+1)-th recording data; Q_i , Q_i+1 are the seepage quantities of the i-th and (i+1)-th recording interval, respectively; Δt_i is the interval between the i-th and (i+1)-th recording data; Δp_i is the seepage pressure difference between the upper and bottom of the specimen within; H is the height of specimen.

According to the collected test data, the relations between seepage rate and time are analyzed in complete creep processes, and the permeability evolution laws of volcanic breccia specimens are studied. Based on the creep curves, the complete creep processes are divided into four stages, including transient strain stage under instantaneous load, attenuation creep stage, steady-state creep stage and accelerated creep stage.

4.1 Variation of seepage flow rate with time at stage of transient strain

The relation between seepage flow rate and time at the stage of transient strain under instantaneous load is shown in Fig. 6.

Fig. 6 Relation between seepage flow rate and time at stage of instantaneous strain under preloading

From Fig. 6, it can be seen that the deformation of volcanic breccia specimen is nonlinear under the initial loading. In the process of nonlinear deformation, the natural pore and fracture in rock interior are gradually closed with the increase of axial stress, and the seepage flow rate is gradually decreased with time. When it is at the stage of elastic deformation, the variation of permeability is really little although the permeability of rock specimen is decreased, and it is found that the seepage flow rate tends to be stable with loading time.

The experimental results show that the variation of deformation at the stage of transient strain is obvious with the increase of confining pressure, which has influences on seepage flow rate of rock at this stage. The pore and fracture in rock are gradually reduced with the increase of confining pressure, and the rock permeability also decreases with it. As shown in Fig. 6, the seepage flow rate under confining pressure of 6 MPa is less than that under confining pressure of 2 MPa. However, at the stage of elastic deformation, the seepage flow rate trends to be stable with increasing time.

4.2 Variation of seepage flow rate with time at stages of attenuation creep and steady-state creep under lower stress levels

The relations of seepage flow rate with loading time at the stages of attenuation creep, steady-state creep and accelerated creep under confining pressures of 2 and    6 MPa are shown in Fig. 7.

Fig. 7 Relation between seepage rate and time under different grading stress levels

During the stage of attenuation creep, it is found that the seepage flow rate is fluctuated prominently because of its short time of attenuation creep, and its variation law is not obvious. Therefore, the seepage flow rate cannot be considered temporarily in this stage. When the stress loading is kept constant, it is found that the creep rate attenuates to a constant quickly. If the loading stress level is lower than the final failure stress, the characteristics of steady-state creep are exhibited on creep curves. Because of the crack initiation and stable crack growth of rock specimen at the stages of attenuation creep and steady-state creep, the steady-state creep rate is close to zero on the whole. When entering into the stage of elastic deformation, the seepage flow is in the steady state, and the variation of seepage flow rate with the increase of time under lower stress levels is not obvious.

From the experimental results, it can be seen that the average of seepage flow rate at the stage of steady-state creep is about 4.7×10^{-9 m/s under confining pressure of 2 MPa, and is about 3.9×10-9 m/s under confining pressure of 6 MPa. The seepage flow rate under confining pressure of 2 MPa in this case is obviously larger than that under confining pressure of   6 MPa. The experimental results show that the variation of seepage rate of this stage is obvious with the increase of confining pressure.}

4.3 Variation of seepage flow rate with time at stage of creep deformation under failure stress level

When the loading stress reaches the final failure stress level, the typical creep curve is shown in Fig. 8. From Fig. 8, it can be seen that the creep curve includes three stages: attenuation creep, steady-state creep and accelerated creep.

At the stage of the steady-state creep under the failure stress level, the experimental results show that the micro-cracks are developed further, combined and accumulated. In this stage, the steady-state creep deformation is increased steadily, and the rock permeability also remains stable mainly with time.

Fig. 8 Complete creep curve of rock with three classical stages of attenuation creep, steady-state creep and accelerated creep

The seepage flow rate versus time is shown in Fig. 9. From Fig. 9(a), it is concluded that the seepage flow rate is increased significantly. The seepage flow rate under confining pressure of 2 MPa is about 5.0×10^{-9 m/s, and about 5.2×10-9 m/s under confining pressure of 6 MPa, which is slightly larger than that under confining pressure of 2 MPa.}

Fig. 9 Relation of seepage flow rate (a) and acceleration     (b) versus time under final deviatoric stress level

At the stage of accelerated creep, a lot of microscopic fissures of rock specimen are developed further during the accelerated creep process, expanded, combined and accumulated, and finally formed macroscopic cracks. The macro-cracks extend towards the ends of rock specimens until final failure. In this stage, the seepage flow rate is also increased significantly with the crack growth.

The seepage acceleration curve versus time under the final deviatoric stress level is shown in Fig. 9(b). From Fig. 9(b), it can be seen that the seepage flow acceleration is relatively larger under confining pressure of 2 MPa, and the duration of increasing phase is shorter than that under confining pressure of 6 MPa. Because of rapid expanding and progressing of micro-cracks due to creep damage accumulation, the variation of permeability is directly connected to the crack growth and evolution of rock.

5 Discussion of correlation between rock creep deformation and damage-induced permeability changes

In recent years, based on the method to measure the rock permeability in axial load direction, many experimental studies are implemented to quantify the changes in permeability induced by micro-crack growth during the process of rock deformation, and to grasp the relationship between rock stress-strain and damage- induced permeability changes. According to the current studies, it is concluded that the damage induced crack growth is the important factor leading to the variation of rock permeability, which results in a change of the seepage flow and the stress field in the affected zone. The variation of permeability is directly connected to the mechanical damage of rock material. However, fewer researches on correlation between creep properties and permeability evolution in process of creep deformation of rock are conducted. Therefore, it is very important to examine the correlation between the creep damage- induced permeability variations and creep deformation of rock.

5.1 Correlation between creep deformation and creep damage property

The initiation and propagation of all kinds of micro-cracks in rock result in the weakness of physical-mechanical properties on rock, which is the effect of damage on rock. The pseudo-damage variable is defined according to the effect of fissure propagation of rock during its rupture process.

Based on the experimental results in this work, the relationships between stress and strain, and between damage factors and pseudo-damage are derived. According to the analysis of damage evolution in the process of instantaneous stress-strain, it is found that new micro-cracks of specimen basically have no extension at the stages of crack compaction and elastic deformation, and the rock damage does not occur basically at the stages of attenuation creep and steady-state creep.

With the increase of time of axial loading, the creep deformation of rock is found to enter into the stage of crack extension and macro-rupture, in which the damage begins to set and then continues to accumulate, until the rock fractures. Therefore, the rock damage should be closely related not only with rock creep deformation, but also with axial load. In other words, rock creep damage is deemed to possess obvious deformation effect and time-dependent effect.

From Figs. 5 and 8, under the creep failure stress level, the characteristics of the microscopic cracks of rock expand rapidly and progress with the increase of loading time, and then the occurrence and development of accelerated creep are shown. The rock damage tends to be aggravated continuously, and finally induces rock failure. The rock failure is a process of damage accumulation, in which rock mechanical properties are deteriorated continuously. Acoustic emission energy can be described comprehensively as the occurrence intensity of micro-cracks in rock. The frequency, strength and energy of acoustic emission are concerned with rock fracturing. The characteristic curve of acoustic emission event versus time for salt rock under uniaxial creep test was obtained by Szcepanik [22]. As shown in Fig. 10, during the stage of accelerated creep, the acoustic emission increases dramatically with time. It is shown that the accelerated growth of rock damage leads to the sharp increase of creep rate.

Fig. 10 Characteristic shape curve of acoustic emission event vs time for salt rock under uniaxial creep test [22]

As the effective method to solve the correlation between creep deformation and damage property, the triaxial rheological tests of rock specimens under seepage pressure loading are carried out by using stepwise loading levels. Therefore, according to the creep results, it is necessary that the next researches are pointed out, in which creep damage variable and damage evolution equation are studied, and the relation of damage variable with creep strain of rock is analyzed.

5.2 Relationship equation between permeability evolution and rock creep deformation

It is very important that the relationship equation between permeability evolvement and creep deformation of rock is studied. Based on the results of Section 4, it is found that the variation of permeability coefficient of rock specimen is more obvious in the processes of instantaneous load and attenuation creep, and the permeability coefficient and seepage rate are relatively steady in the process of steady-state creep. Under the failure stress level, due to the cumulation of creep damage, it is shown that the permeability coefficient and seepage velocity trend to increase with the creep deformation.

Based on the above analysis, it is very necessary that the relationship between rock permeability evolution and creep stress-strain is studied. The objective is to establish the relation between damage-induced creep strain and rock seepage flow rate, permeability coefficient, and seepage acceleration.

Before the occurrence of accelerated creep of rock specimens, the permeability coefficient of rock is described as follows [23]:

             (2)

where f₀ is the porosity when the initial pore water pressure is p₀; K₀ is the permeability coefficient when the initial pore water pressure is p₀; ε_v is the volumetric strain; p is pore water pressure.

As shown in Eq. (2), the permeability coefficient is the function of rock porosity, volumetric strain and pore water pressure. During accelerated creep deformation and failure of rock, the expansion of pore and fissure of rock specimens from macroscopic viewpoint is considered to reflect the variation of volumetric strain. In this stage, it is found that the variation of permeability coefficient has a direct relationship not only with volumetric strain of rock specimen, but also with rock creep damage. Therefore, in order to study the relation of rock permeability versus creep damage evolution, the creep damage variable is used to analyze the variation of permeability coefficient at the stage of accelerated creep deformation.

In brief, during accelerated creep deformation and until rock failure, the permeability coefficient is mainly the function of rock creep strain, confining pressure, creep damage variable and pore water pressure. The correlation function expression is described as

                          (3)

where ε is the creep strain; σ₃ is the confining pressure; f is the function of ε, σ₃, D and p; D represents the creep damage variable; A is the parameter determined by creep tests.

The specific expression of Eq. (3) during accelerated creep deformation can be obtained from the results of multi-group of creep tests.

By combining Eq. (2) and Eq. (3), the relation equation between creep damage-induced permeability coefficient and creep strain in complete process of rock creep is described as

      (4)

Equation (4) shows that the variation of rock creep damage-induced permeability coefficient is closely related not only to the creep strain, but also to the creep damage-induced crack growth. This equation is considered to describe the variation of the permeability coefficient of rock specimens in complete range of creep tests. To sum up, such relationship equation is very important for predicting the long-term stability of rock engineering.

6 Conclusions

1) Under the applied stress level which is considerably less than failure stress, it is shown that the creep deformation of rock is not obvious, and the main creep form is steady state creep. When the applied stress level is greater than or close to the failure stress, the creep deformation and accelerative creep characteristics become more obvious. Based on the experimental  results, the confining pressure has a strong influence on the creep deformation at the same stress level. The higher the confining pressure, the smaller the corresponding axial creep strain, i.e., there is less creep deformation. It is also considered that the circumferential creep deformation can reflect the deformation characteristics of rock from another point of view, and the results should be drawn sufficient attention.

2) At the stage of transient strain, the deformation is obvious with the increase of confining pressure, which has influences on seepage flow rate of rock. During the attenuation creep, the seepage flow rate is fluctuated prominently. During the process of steady-state creep, it is seen that the seepage flow rate is decreased obviously with the increase of confining pressure. During the process of acceleration creep, the seepage flow rate is increased significantly with the crack growth. It can be also seen that the seepage flow acceleration relatively becomes larger. The variation of permeability is directly connected to the damage growth in complete creep processes of rock specimen.

3) Under the axial load, the creep failure characteristics of catastrophe and purification of rock specimens are shown due to the rapid expansion and progress of microscopic cracks from the accumulation of creep damage. Based on the analysis of relation between creep deformation and damage property, it is considered that the rock damage should be closely related not only to the rock creep deformation, but also to the creep damage-induced crack growth. During accelerated creep deformation and failure of rock, the permeability coefficient is mainly considered to be the function of rock creep strain, confining pressure, damage variable and pore water pressure. The relation equation between creep damage-induced permeability coefficient and creep strain in complete process of rock creep is established, and such relationship equation is very important for predicting the long-term stability of rock engineering.

Acknowledgements

Thanks are given to W. Y. Wang and D. F. Huang for kindly help in obtaining and shipping experimental materials, who come from Kunming Design and Research Institute, China Hydropower Consulting Group Co. The authors also thank Prof. W. X. Huang for help to English improvement of this work, who comes from the College of Water Conservancy and Hydropower Engineering of Hohai University, China.

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(Edited by YANG Bing)

Foundation item: Projects(11172090, 51009052, 51109069) supported by the National Natural Science Foundation of China; Project(2011CB013504) supported by the National Basic Research Program of China

Received date: 2010-12-16; Accepted date: 2011-05-12

Corresponding author: WANG Ru-bin, PhD; Tel: +86-25-83787738; E-mail: rbwang_hhu@foxmail.com