It is important to confirm the longterm strength of rock materials for the purpose of evaluating the longterm stability of rock engineering. In this study, a series of triaxial creep tests were conducted on granite gneiss under different pore pressures. Based on the test data, we proposed two new quantitative methods, tangent method and intersection method, to confirm the longterm strength of rock. Meanwhile, the isochronous stressstrain curve method was adopted to make sure of the accuracy and operability of the two new methods. It is concluded that the new methods are suitable for the study of the longterm strength of rock. The effect of pore pressure on the longterm strength of rock in triaxial creep tests is also discussed.
Longterm strength is a key and typical mechanical parameter in rock creep behavior. The creep mechanical behavior of rock is very important to evaluate the stability and safety of rock engineering, such as high slope rock engineering, underground cavern rock engineering, dam base rock engineering, and underground oil storage project [
Granite gneiss, a kind of metamorphic rock derived from igneous rocks, is commonly and widely distributed in engineering. Due to its low permeability and relatively high mechanical strength, granite gneiss is envisaged as one of the potential materials for underground oil storage, CO_{2} and shale gas storage, and radioactive waste disposal [
As the relatively convenient and direct method, creep tests are usually used to characterize creep rate, identify different creep phases, and determine the longterm strength. Large numbers of investigations have been made through uniaxial and triaxial creep tests [
In this paper, we have performed the triaxial creep tests on granite gneiss under different pore pressures. Based on the test data, the longterm strength of the rock is investigated. Two new methods, tangent method and intersection method, of steady creep rate are put forward to confirm the longterm strength of rock in the quantitative way. The isochronous stressstrain curve method is also adopted to verify the results of the new methods. In the end, we discuss the effect of pore pressure on the longterm strength of rock in triaxial creep tests.
A rock servocontrolled triaxial rheology test system is used to perform the triaxial compression tests and creep tests. It can apply the confining pressure up to 60 MPa and the maximum axial deviatoric stress of 500 MPa. The hydraulic pressures at the inlet and outlet can be automatically adjusted between 0 and 50 MPa with an accuracy of 0.1 MPa. The test data of stress, strain, and permeability changes are automatically and accurately recorded at 5 s intervals and then transferred to a computer for further analysis.
The rock cores are granite gneiss, originally drilled from the early Cretaceous stratum of underground oil storage at a depth of 120 m. The mineral components of the rock specimens are 33% plagioclase, 32% Kfeldspar, 30% quartz, and 5% biotite. The microstructure surface morphologies of the samples were obtained as shown in Figure
Mean value of porosity and density.
Specimen  Porosity (%)  Density (g cm^{−3}) 

Granite gneiss  1.79  2.61 
SEM photomicrographs of granite gneiss: (a) enlarged 250 times; (b) enlarged 2000 times; (c) enlarged 5000 times.
The tested specimens were prepared as cylindrical samples with a diameter of 50 mm and a length of 100 mm in accordance with the ISRM standard [
Typical rock specimens of granite gneiss.
Taking into account the longterm strength of rock, it is necessary and significant to identify the timedependent mechanical behavior of rock. Therefore, the triaxial creep tests were carried out for saturated granite gneiss under different pore pressures. Table
Triaxial creep test conditions and preconfirmed deviatoric stress levels of the specimens.
Specimens number  Confining pressure  Pore pressure  Stress level  Deviatoric stress  Creep duration 

(MPa)  (MPa)  (MPa)  (h)  
A1  4  1  1  130  72 
2  140  72  
3  150  72  
4  160  72  
5  170  52  


A2  4  2  1  125  72 
2  135  72  
3  145  72  
4  155  72  
5  165  54  


A3  4  3  1  120  72 
2  130  72  
3  140  72  
4  150  72  
5  160  58 
Triaxial creep test curves of granite gneiss: (a)
As can be seen from Figure
Based on the creep curves, the axial modulus and the ratio of lateral to axial strain in the complete creep test are obtained. The axial modulus is calculated by the ratio of the total axial deviatoric stress to the total axial strain. In the three groups of specimens numbered A1, A2, and A3 as shown in Table
The isochronous stressstrain curve method is an approach that has been used extensively for the creep evaluation of materials [
In this study, the specimens were allowed to creep for a time interval of 72 h in each stress level. As a result, 10 h, 20 h, 30 h, 40 h, and 50 h in each stress level are determined as the time parameter in the isochronous stressstrain curves. Compared with the isochronous stressaxial strain and stressvolumetric strain curves, it is more obvious and convenient to find the inflection point in the isochronous stresslateral strain curves (Figure
Isochronous stresslateral strain curves of granite gneiss: (a)
With time, the isochronous curves show obvious nonlinear characteristics and then the inflection point occurs. When the deviatoric stress exceeds the stress value of the inflection point, the strain difference between the two immediate isochronous curves increases largely under high deviatoric stress.
As mentioned before, the steady creep rate plays an important role in the confirmation of the longterm strength. In the steady creep rate curves, the longterm strength corresponds to the stress of the inflection point. However, in practice, it is difficult to quantify the longterm strength just relying on the visual observation and furthermore sometimes the inflection point of the curves is vague. In order to solve the problem, we introduce the tangent of the steady creep rate curves. The acute angles (
The lateral steady creep rate is also chosen as the research subject. All the specimens experience five stress levels before the failure. The steady creep rate curves are obtained through the fitting of exponential function on the five points. In the curves (shown in Figure
Curves of tangent method of steady creep rate: (a)
In Figure
For the rock specimens under other pore pressures, the angles between 50° and 60° are also suitable for the confirmation of the longterm strength. This is shown in Figures
In the process of triaxial creep test, granite gneiss experiences not only the volumetric compression, but also the volumetric dilatancy. At low level of stress, the rock deformation is in compression while the axial steady creep rate is greater than the volumetric steady creep rate. Under high stress, the volumetric steady creep rate increases sharply and becomes greater than the axial steady creep rate. The rock samples experience significant volumetric dilatancy and exhibit creep failure quickly. Therefore, the axial and volumetric curves of steady creep rate exhibit an intersection point. It is the critical point of rock compression and volumetric dilatancy. Based on the actual deformation characteristics of the samples, the longterm strength is defined by the stress at the intersection point.
The steady creep rate curves are obtained in the same manner with the tangent method. The exponential function is also used for the curves fitting. In the curves (Figure
Curves of intersection method of steady creep rate: (a)
Based on the triaxial creep test data, isochronous stressstrain curve method, tangent method, and intersection method of steady creep rate are used to confirm the longterm strength of the rock specimens under different pore pressures. The results of isochronous stressstrain curve method are used as the reference, as the method is most commonly used. The two new proposed quantitative methods are compared on the basis of the reference. In Table
Results comparison of the three methods to confirm the longterm strength.
Specimen number  Isochronous stressstrain curve method  Tangent method of steady creep rate  Intersection method of steady creep rate  







A1  157.8  156.8~158.6  −0.6~0.5  158.4  0.4 
A2  152.4  151.6~153.4  −0.5~0.7  153.2  0.5 
A3  147.6  146.4~148.2  −0.8~0.4  148.4  0.5 
According to Table
In conclusion, the tangent method and intersection method of steady creep rate are very precise and suitable for the confirmation of the longterm strength of granite gneiss, which may be applied in the longterm stability analysis of rock engineering.
It is also apparent from Table
It can also be noticed from Figure
Granite gneiss, taken from underground oil storage, was tested in a series of triaxial creep tests under different pore pressures. The longterm strength of rock is investigated and studied in this paper experimentally. Based on the results obtained, conclusions can be made as follows:
The tangent method of steady creep rate is proposed to confirm the longterm strength of rock in the quantitative way. The acute angles (
Based on the deformation characteristics of the samples, the stress at the intersection point of the axial and volumetric steady creep rate curves is defined as the longterm strength of rock. This new method is more convenient to obtain the longterm strength of rock.
The common isochronous stressstrain curve method is also adopted and used as the reference. Through the results comparison, the results ranges of the tangent method are precise with the fluctuation between −0.8% and 0.7% of the reference values. Moreover, the results of the intersection method are very close to that of the isochronous curve method with the maximum difference of 0.5% of the reference values.
The two new proposed methods, tangent method and intersection method, are very precise and suitable for the determination of longterm strength of rock in the quantitative way. It is also apparent that pore pressure has influence on the longterm strength of the rock specimens.
Nevertheless, the two methods are proposed and implemented based on the rock specimens of granite gneiss. In the future, the two new methods are to be validated by more test data with various rocks and loading conditions to show the generalization ability in the study of the longterm strength of rock.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The work was supported by the National Natural Science Foundation of China (nos. 11172090, 51209075, 11272113, and 51479049).