Experimental study on creep characteristics of infiltrated coal-rock under load

A series of laboratory tests were conducted, analyzing the influence of stress level and infiltration time on the creep properties of the coal-rock. The total damage variable based on damage mechanics is defined based on the coupling of the infiltration damage variable based on macro-benchmark variable and the stress damage variable based on creep timeliness, by characterizing the pattern of the infiltration–stress coupling effect on the total damage variable. The study shows that coal-rock underwent a process from surface drying and shrinkage to water absorption and swelling to water-filled infiltration damage in the infiltration test. With the increase of infiltration time, the water content of coal-rock tended to increase and eventually stabilizes, while the uniaxial compressive strength was gradually decreased. With the increase in stress level and infiltration time, the stable creep strain of coal-rock kept increasing, which accelerated creep advance, and its internal damage continued to accumulate and eventually led to destabilization damage. At the same stress level, mechanical parameter continued to decrease. Comparing the theoretical model of infiltrated coal-rock creep with the experimental data, the model developed in this paper reflected the whole process of infiltrated coal-rock creep deformation and damage and can characterize the influence of infiltration time and stress level on coal-rock creep properties.


ε
Total strain of the infiltrated coal-rock ε 0 Instantaneous strain ε ve Viscoelastic strain ε 1 Viscosity strain ε p Plastic strain σ 0 Stress on the coal-rock E 0 Instantaneous modulus of elasticity E 1 Deceleration stage elastic modulus η 1 , η 2 Viscous hysteresis coefficient t Creep time S Total area S 1 Damaged part area S 2 Undamaged part area S w Infiltration damage area D w Infiltration damage variable S 3 Infiltration and stress coupling damage area S 4 Stress damage area D Stress damage variable D m Total damage variable σ 0 Stress level of coal-rock σ s Yield strength of the damaged body σ 1 Undamaged part stress E 2 Modulus of elasticity in the accelerated phase C, v Coal-rock material parameters t F Creep life R w Uniaxial compressive strength of the coal-rock specimen in the infiltrated state R d Uniaxial compressive strength of the coal-rock specimen in the dry state T Infiltration time

Introduction
Since the depletion of shallow resources and underground space, how to use deep resources and space more efficiently, safely, scientifically, and rationally has attracted widespread attention from scholars all over the world. In the process of construction of deep underground projects, the appearance of groundwater will affect the stability of the project, and the influence of groundwater infiltration become significantly. In coal mining, watertight isolated coal pillars are always in the state of groundwater infiltration and subjected to long-time effect of roof pressure, resulting in creep phenomenon. With the extension of infiltration time, the creep effect of coal pillar will become more and more obvious, which will lead to the instability of coal pillar and cause safety accidents. At present, researchers worldwide have gotten fruitful results on creep mechanical properties of coalrock under the effect of stress level, water content and other influencing factors. Baud et al. [1] analyzed by experimental results that changing the stress levels can influence the rate of strain change and creep of coal-rock. Kurita et al. [2], Ngwenya et al. [3] and Heap et al. [4][5][6] studied the relationship between stress levels and creep mechanical properties of coal-rocks, mainly in terms of effects on creep rate and accelerated creep damage. Schoenball et al. [7] used Abaqus to apply time-dependent brittle creep to a wellbore damage mechanics model to explain the cause of "V" fracture in situ tests. Brijes et al. [8] conducted uniaxial and triaxial creep tests on coal-bearing shales to investigate the causes of failure of coal-rock with time under complex stress conditions. Mao et al. [9] performed creep pre-damage on coal samples using the SAW-2000 rock servo test system and conducted uniaxial compression damage tests to analyze the relationship between the degree of damage and peak strength and elastic modulus. Hadiseh et al. [10] tested the creep properties of salt rocks and found that the creep deformation is more intense and the creep rate increases faster as the axial stress increases. Trzeciak et al. [11] conducted long-time creep tests on shale and showed that the rock exhibited a significant time dependence under constant loading, with the creep strain in shale reaching more than half of the instantaneous strain after two weeks with the extension of loading time. Zhao [12] tested uniaxial compression deformation and uniaxial compression creep on red sandstone specimens with fine-grained and medium-grained. Results show that the microstructure obviously influences creep deformation mechanism.
The above creep test results of coal-rock offer a foundation for the construction of creep models of coalrock. In recent years, Tan et al. [13] performed a micro-rheological analysis of the deformation properties of rocks and concluded that creep and confining stress are two fundamental factors in the mechanical properties of rocks, whereby the intrinsic equations of rocks under the action of confining stress, creep and dilation were established. Wang [14] used the internal variable damage factor and its corresponding rheological deformation to characterize the macroscopic features of the creep-damage continuum of rock salt and developed a new constitutive model of creep damage in rock salt. Yang [15] et al. developed a nonlinear short-term creep damage constitutive model for coal under triaxial compression conditions based on elastic-plasticity theory combined with damage evolution equations and validated it by experiments. Kang et al. [16] considered the relationship between viscoelastic-plastic properties of coal-rock and damage, described the creep properties of coal with a fractional-order nonlinear model, and verified the validity of the model by uniaxial creep tests with different axial stresses applied. Wang et al. [17] considered different degrees of initial damage as well as new damage caused by loading of coal-rock in creep constitutive model. Yuan et al. [18] analyzed the effect of changing stress levels on strain-time curves under different surrounding pressures by triaxial consolidation creep tests. Choens et al. [19] performed creep tests on sandstone specimens from the Zenifim strata by low-to-medium confining pressure divisions and developed a continuous damage pore-elastic constitutive model for sandstone considering the effect of gradual accumulation of rock damage.
With the depth of research, some scholars introduced the effect of water on coal-rock into the creep constitutive equation. Wang et al. [20] studied the mechanical properties of soft rocks under water corrosion and concluded that the fracture effect of soft rock damage under water action is time-dependent. He et al. [21,22] investigated the creep-percolation coupling effect and established a creep damage criterion based on the maximum tensile stress theory. Huang et al. [23] established a rock damage constitutive model considering variable water content by combining the results of experimental studies on creep of muddy siltstone under different water content states. Wang et al. [24] conducted triaxial creep tests with oil shale as the research object, introduced the nonlinear relationship presented by the damage inside the rock into the model, and constructed a creep constitutive model of oil shale under different water content change rates. Chen et al. [25] approximated the internal water content of the rock as a switch, while introducing creep damage thresholds into the rock creep constitutive model. Yang et al. [26] conducted triaxial creep tests on soft rocks under different water-bearing states to analyze the effect of changes in water content on the creep properties of rocks and their damage mechanisms, and obtained an improved Nishihara model. Xu et al. [27] studied in depth the creep change mechanism under different stress levels and water content and established an time-effect creep damage model. Hashiba [28] considered rock strength and creep life theory under the influence of moisture and obtained the relationship between rock strength and creep life under dry and wet conditions. Zhang et al. [29] subjected the filling body of the goaf to graded loading creep tests under different water pressures. The results showed that the mechanical properties of the filling body decreased with increasing water injection pressure.
In general, most of the studies on creep properties of rocks in the above results take different stress levels and different water content conditions as influencing factors, while relatively few studies on creep properties of coal-rock under the combined effect of different stress levels and infiltration time. In fact, the change of water content after saturation of coal-rock infiltration is weak, but with the increase of infiltration time, the cumulative effect of damage is obvious, and the friction coefficient of its internal structural particles decreases after the continuous lubrication effect of water, which will further aggravate the deterioration of coal-rock body and lead to the decrease of bearing capacity. Therefore, this paper studies the creep mechanical properties of coal-rock under the combined action of stress level and infiltration time, analyzes the creep law of infiltrated coal-rock, and reveals the mechanism of creep deformation of coal-rock. To provide some theoretical basis for the prevention and control of soaked coal pillar instability.

Model development
In order to describe the whole process of coal-rock creep deformation under load, the Hooke body, Kelvin body, Newtonian body and elastic-plastic damage body are used to describe the instantaneous stage, decelerating creep stage and the accelerated creep stage of coal-rock, respectively. The total strain ε of coal-rock consists of the instantaneous strain ε 0 of coal-rock simulated by the spring, the viscoelastic strain ε ve simulated by the Kelvin body, the viscosity strain ε 1 simulated by the Newtonian body, and the plastic strain ε p simulated by the damaged elastic-plastic body, and the schematic diagram is shown in Fig. 1.
The total strain of the infiltrated coal-rock can be expressed as: The instantaneous strain ε 0 expressed by the Hooke body is: where σ 0 is the stress on the coal-rock; E 0 is the instantaneous modulus of elasticity. The viscoelastic strain expressed by Kelvin body is where E 1 is the viscoelastic modulus also called the deceleration stage elastic modulus; η 1 is the viscous hysteresis coefficient; t is the creep time. The viscoelastic strain expressed by the Newtonian body is where η 2 is the viscous hysteresis coefficient. The plastic strain is described by the elastic-plastic damage body, and the micro-element of the damaged body is taken, as shown in Fig. 2. It is assumed that the total area S of the micro-element consists of two parts, the damaged part and the undamaged part, and the areas are S 1 and S 2 , respectively.
After the coal-rock is infiltrated by water, the infiltration damage area is S w , which defines the infiltration damage variable: Coal-rock that has undergone infiltration is further damaged by stress. Suppose the stress damage area is S 4 , and the infiltration and stress coupling damage area are S 3 . Therefore, the stress damage variable of infiltrated coal-rock is defined: In fact, the total damage variable D m of infiltrated loaded coal-rock can also be directly defined according to its final damage degree: The total damage variable can be obtained from the simultaneous Eqs. (5)~(7) It can be seen from Eq. (8) that infiltration and stress promote the continuous expansion of internal fractures in coal-rock by different mechanisms. The interaction and influence of the two kinds of damages induced show significant nonlinear characteristics, and the coupling effect weakens the total damage, where DD w represents the coupling term.
According to the characteristics of the damaged elastoplastic body, stress level of coal-rock σ 0 is greater than the yield strength of the damaged body σ s before starting work, the actual damage to the elastic body of the stress needs to overcome the yield strength of coal-rock, σ 0 − σ s , set the force on the undamaged part of the coal-rock to S 2 . It can be obtained by the balance principle of force Based on the relationship between the damaged area and the total area of coal-rock, the total damage variable is defined, which gives The stress-strain relationship obeys Hooke's law, defining the strain of the micro-unit and the undamaged part as ε p and ε p1 . E 2 is the deformation modulus of the damaged elastoplastic body, which called the modulus of elasticity in the accelerated phase, then According to the coordination principle of internal deformation of coal-rock, we can get Thus, simultaneous Eqs. (11) and (12) Substituting Eq. (13) into (10), we can get Equation (14) is the damage elastic-plastic stress-strain relationship of coal-rock subjected to water infiltration and stress.
Kachanov expression for creep damage of coal-rock under stress [30], obtained after Rabotnov generalization, is defined as follows: (15) where C and v are both the inherent properties of the coal-rock material which are called coal-rock material parameters. Solving Eq. (15) yields the expression for the creep damage variable D under stress as where t F is the creep life, also known as coal-rock creep damage time.
When the stress is less than the yield strength σ s , the coal-rock does not produce damage, and vice versa, produce damage, and the model is expressed as follows: where α 1/(v + 1).
In the creep process of the infiltration coal-rock, in addition to the role of stress, there also exists the infiltration of water, which will lead to the softening of coal-rock. Define the creep damage variable of coalrock under infiltration is where R w is the uniaxial compressive strength of the coal-rock specimen in the infiltrated state; R d is the uniaxial compressive strength of the coal-rock specimen in the dry state. From Eqs. (8), (17) and (18), the total damage variable is: Substituting Eq. (19) into Eq. (14), the constitutive model of the damaged elastic-plastic body under stress-infiltration is obtained as: Substituting Eqs. (2), (3), (4) and (20) into Eq. (1), we can obtain the damage creep constitutive model of coal-rock considering infiltration time and stress level 3 Overview of the experiment and analysis of results

Specimen preparation and test protocol
The fresh coal blocks retrieved from the mine site are processed into 50mm × 100 mm cylindrical international standard rock samples according to ISRM recommendations, after core sampling from the set of holes and cutting and grinding processes. The specimens with obvious defects are removed before the test, and then, the specimens with similar wave speed are selected for the test by ultrasonic detector, so as to reduce the influence of coal-rock discreteness on the test results.
In order to study the creep law of coal-rock under the long-time action of water infiltration and stress, the following test procedure is designed: (1) The specimens were subjected to a water continuous infiltration test, and the specimens were taken out without infiltration, saturated with infiltration and after 120 d of infiltration for SEM to obtain their mesoscopic structural features. (2) Three specimens were selected for uniaxial compression tests to obtain the average compressive strength value σ c of the coal-rock, which was then used to classify the stress levels for uniaxial creep tests as 30%σ c , 40%σ c , 50%σ c , 60%σ c , 70%σ c and 80%σ c , respectively.
(3) Put the coal-rock specimens in the natural state into the drying oven and to ensure that the coal samples are completely dried, remove the coal samples from the oven every 0.5 h and weigh them on a high-precision balance until the mass no longer changes; measure the mass of the specimens under different infiltration time, and obtain the water content of the specimens with infiltration time of 0, 1, 3, 7, 15 and 30 d, respectively. (4) Uniaxial creep tests with stress levels of 30%σ c , 40%σ c , 50%σ c , 60%σ c , 70%σ c , and 80%σ c were performed simultaneously on specimens infiltrated for 0, 1, 3, 7, 15, and 30 d.

Mesoscopic structural properties of infiltrated coal-rock
The coal-rocks under vacuum were scanned using COXEM EM-30 Plus SEM in dry condition, natural water absorption saturated condition and after 120 d of infiltration water with a magnification of 500 times. The results are shown in Fig. 3.
As can be seen in Fig. 3, it can be seen that the mesoscopic structure of coal-rocks has been greatly changed under the action of water infiltration. As shown in Fig. 3a, the clay particles in the dry state are cemented together to form a larger lamellar structure. The units are assembled into larger particles with fine particles, and the pores are relatively uniformly distributed between the particles. As shown in Fig. 3b, water is infiltrated in coal-rock and the open pores and fissures are filled by water body. The reason is that a large number of clay minerals absorb water and swell, resulting in the narrowing of the pores between the coal-rock, while in Fig. 3c, the connection between coal-rock particles became looser after 120 d of infiltration, and the initial tight, high-strength structure was gradually transformed into a porous, loose structure by the infiltration time. Meanwhile, more larger pores can be detected in the coal-rock, and flocculent material can be seen locally, and the mineral particles are basically distributed in a flaky or flocculent structure. It indicates that the damage to the rock accumulated throughout the infiltration process, which is consistent with the scanning electron microscopy results in the literature [31,32].
Scanning electron microscopy results show that water infiltration causes internal damage to coal-rock. The coal-rock undergoes a process from surface drying and shrinkage to water absorption and swelling to water-saturated infiltration damage during the infiltration process. In the dry state, the surface of coal-rock is rough and prone to dry shrinkage, and the micro-features show that the microstructure of internal minerals is sharp and angular. After infiltration and water absorption, the minerals swell with water, and the surface bulges minerals especially so, so that the original cemented skeletal structure becomes softened and full, and the surface of coal-rock is more rounded and smooth. As the infiltration time continues to increase, the cement gradually dilutes, the internal volume of the coal-rock expands, the pores increase and new cracks are created, and the infiltration action continues to accumulate damage to the coal-rock.

Influence of infiltration time on water content and strength of coal-rock
The results of water content of the specimens and their uniaxial compressive strength under the influence of infiltration time are shown in Fig. 4.
From Fig. 4, it can be seen that the infiltration time increased from 0 to 1 d and the water content of coal-rock increased from 0 to 6.375%. The infiltration time increased from 1 to 3 d and the water content of coal-rock increased from 6.375% to 8.258%, an increase of 29.96%. The infiltration time increased from 3 to 7 d and increase in coal-rock water content from 8.258% to 8.481%, an increase of 2.70%. The infiltration time increased from 7 to 15 d and the water content of coal-rock increased from 8.481% to 8.492%, an increase of 0.13%. The infiltration time increased from 15 to 30 d, and the water content of coal-rock increased from 8.492% to 8.518%, an increase of 0.31%. It can be seen that, with the increase of infiltration time, the water content of coal-rock is increasing but its change rate gradually decreases and stabilizes, and the water content of coal-rock is 8.481% at 7 d of infiltration, compared with the water content of 8.518% at 30 d of infiltration, almost no change occurs.
The analysis shows that with the extension of infiltration time, the water content after infiltration saturation, although maintaining the same but the uniaxial compressive strength of coal-rock decreases, and the mechanical properties continue to weaken. As shown in Fig. 3, the prolonged infiltration of water molecules in coal-rock fissures reduces the cohesion between coal-rock particles, causing its overall structure to become porous, loose and soft, which leads to the weakening of the overall macroscopic mechanical properties. Therefore, the infiltration time is an important influence factor for the mechanical properties of coal-rock.  There are two main factors that affect the creep properties of coal-rock. Under the action of water infiltration for a long time and stress level, the original pores and cracks exist inside the coal-rock, which will extend to cause new damage. Therefore, it is important to study the influence of infiltration time and stress level on creep mechanical properties of coal-rock for theoretical guidance of engineering.
The creep test result curves of coal-rock at different infiltration times and different stress levels were obtained from the uniaxial creep test of infiltrated coal-rock, and the results are shown in Figs. 5 and 6.
It is easy to see from Figs. 5 and 6 that when the stress levels are 11.1 MPa, 14.8 MPa, and 18.5 MPa, respectively, the creep curves go through the deceleration creep phase, the isokinetic creep phase, but there is no accelerated creep phase. This is due to the fact that the strain in the stable creep phase increases with the prolongation of infiltration time, but when the stress level acting on the coal-rock specimen is low, the accumulated damage is not enough to cause damage to the coal-rock. Its deformation eventually tends to a stable value, so the coal-rock does not produce an accelerated creep phase. When the coal-rock stress level is equal to 22.2 MPa and 25.9 MPa, an accelerated creep phase appears in part of the creep curve; when the coal-rock stress level is equal to 29.6 MPa, an accelerated creep phase appears in each of the creep curves. It can be seen that when the applied stress is close to the ultimate stress of the coal-rock, the specimen undergoes a short period of stable creep or even directly enters the accelerated creep phase and undergoes rapid fracturing.
When the infiltration time is fixed 0 d, and stable creep strain reaches 4.85 × 10 −3 at a stress of 11.1 MPa and 5.46 × 10 −3 at a stress of 14.8 MPa, with an increase of 12.57%, 6.00 × 10 −3 at a stress of 18. In summary, the generation of total creep process in coal-rocks depends on the nature of coal-rock themselves on the one hand and is closely related to the environment in which coal-rock is stored on the other hand. Both stress level and infiltration time can change the creep mechanical properties of coal-rock. According to the scanning electron microscope results, the coal-rock is transformed from an initial relatively dense, high- strength flaky and dense structure to a loose and porous flocculent and crumbly structure under the long-time infiltration of water, and the infiltration of the water body makes the internal damage of the coal-rock accumulate continuously. When the infiltration time and stress level reach a specific value, the combination of both causes the accumulation of damage inside the coal-rock to increase and the deformation to intensify, which eventually makes the coal-rock destabilized and ruptured. Compared with the infiltration time, the coal-rock reflects more sensitive to the stress level and has more significant effect.

Validation of damage creep constitutive model
In order to analyze the variation law of coal-rock creep constitutive model parameters with different stress levels and infiltration time, the parameters of the test model were identified by the least-square method; the results are shown in Table 1.
Based on the results of parameter identification in Table 1, different parameter curves were plotted with infiltration time for six stress levels.
Under the same stress level, the modulus of elasticity in the decelerating creep phase and the modulus of elasticity in the accelerating creep phase of coal-rock decrease gradually with the extension of infiltration time. As shown in Fig. 7, due to the softening and dissolution of the cementing material, it shows a decreasing trend of the viscosity coefficient, and the creep life of the coal-rock becomes shorter and shorter, making the accelerated destruction time earlier. As shown by the coefficient α 1/(v + 1), the coal-rock material parameter ν decreases with the increase of infiltration time.
The theoretical curve of coal-rock creep constitutive model was obtained based on the experimental data and Eq. (21), and compared with the experimental curve as shown in Fig. 8. As can be seen from Fig. 8, the overall agreement between the theoretical curve of the creep constitutive model of coal-rock and the experimental curve is good, which can reflect the whole process of creep deformation and damage of infiltrated coal-rock. The influence of stress level and infiltration time on creep properties of coal-rock can also be characterized, thus verifying the rationality of the creep constitutive model of coal-rock developed in this paper.

Mechanical properties of creep damage of coal-rock
Study the evolution path of total damage of coal-rock under the coupling action of infiltration and stress, and to reveal the law of coal-rock damage expansion. In this paper, the total damage variable of coal-rock with different infiltration days at the stress level of 29.6 MPa is taken as an example. Calculated according to the total damage variable in Eq. (20) and the test data, when the stress level is 29.6 MPa, the evolution curve of the total damage variable of coal-rock under different soaking days is obtained, as shown in Fig. 9.
As shown in Fig. 9, when t 0, the total damage of coal-rock corresponds to infiltration damage. The total damage variables of coal-rock after infiltration by water in the creep test process are as follows: (1) In the initial development stage, corresponding to the near-horizontal section of the total damage evolution curve, under the action of constant stress, some micro-fractures inside the coal-rock are compacted and closed without expanding, and the total damage variable is almost unchanged; (2) in the slow development stage, corresponding to the gently rising section of the total damage evolution curve, the coal-rock begins to deform, and the total damage variable increases slightly; (3) in the rapid deterioration stage, corresponding to the upper concave section of the total damage evolution curve, the deformation of coal-rock continues to intensify, its internal fractures begin to expand and develop, and the total damage variable rises rapidly; (4) in the failure stage, corresponding to the nearly vertical section of the total damage evolution curve, coal-rock forms through fractures, and the total damage variable reaches 1.
With the prolongation of the soaking time, especially after the soaking is saturated for 7 d, the initial development stage is very short, and the damage deterioration trend of the coal-rock increases rapidly. After 30 d of infiltration, its initial damage has reached 0.4, and it almost enters the rapid deterioration stage without going through the initial development stage. This shows that under the influence of long-term water infiltration, the internal structure of coal-rock is seriously damaged, which aggravates the degree of creep damage, which is extremely unfavorable for the stability of engineering rock mass.
It can be seen from Fig. 9 that when the creep time is 300 min, and the infiltration time increases from 0 to 1, 3, 7, 15, and 30 d, the total damage variables are 0.0111, 0.1442, 0.2335, 0.2761, 0.5147, and 1, respectively. Under the same creep time, with the increase of infiltration time, the corresponding total damage variable Table 1 Coal and rock creep constitutive model parameters after different infiltration time under six sets of stress levels  developed from a slow increase to a sharp increase with the water saturation for 7 d of infiltration as the cutoff point. It shows that the dissolution of coal-rock particles caused by water saturation and the degree of damage and deterioration continue to increase, and macroscopically, the creep deformation of coal-rock increases and the strength decreases. The total damage variable was 0.45, and the creep time was 1320 min, 1134 min, 814 min, 630 min, 262 min, and 59 min when the infiltration time increased from 0 to 1, 3, 7, 15, and 30 d, respectively. With the increase of infiltration time, the creep time corresponding to the same total damage variable developed from a sharp shortening to a slow shortening, taking the water saturation at 7 d after the infiltration as the cutoff point. It shows that the accelerated creep stage of coal-rock is advanced after water infiltration, and the deformation characteristics are more significant.
Taking the total damage variable of coal-rock under different stress levels for 15 d of infiltration as an example, according to the total damage variable in Eq. (19) and the test data, it is calculated that after infiltration for 15 d, the evolution curve of the total damage variable of coal-rock under different stress levels is obtained, as shown in Fig. 10.
It can be seen from Fig. 10 that the total damage variable at time 0 under different stress levels for 15 d of infiltration is 0.32, which is due to the initial damage caused by infiltration. Under the condition of constant infiltration time, taking the stress level of 18.5 MPa as the turning point, the total damage curves almost overlapped when the stress level was lower than 18.5 MPa. This is because the applied stress level is low, the coal-rock does not undergo plastic deformation, and some of the internal micro-cracks are compressed and closed and then slowly expanded. The total damage variable D m is in a slowly rising state, and there is no near-vertical segment, and the corresponding creep curve does not have an accelerated creep stage, and the final creep strain tends to be stable and no damage occurs. When the stress is higher than 18.5 MPa, the plastic deformation of coal-rock increases continuously, and the total damage variable D m increases rapidly, corresponding to the accelerated creep stage of the creep curve, and the creep strain increases rapidly until failure.
As can be seen from Fig. 10 With the increase of the stress level, taking the stress of 18.5 MPa as the dividing point, the creep time corresponding to the same total damage variable developed from a slow shortening to a rapid shortening. It shows that the higher the stress level, the shorter the creep time of coal-rock and the faster the failure process.

Conclusions
In this paper, the influence of stress level and infiltration time on the creep properties of coal-rock was systematically studied after the water infiltration test, electron microscope scanning test, water content test, uniaxial compressive strength test and creep mechanical properties test.
Creep tests of coal-rock were conducted at six infiltration times and six stress levels, respectively. The results show that the higher the stress level, the greater the amount of stable creep and the more likely to have an accelerated creep phase. The longer the coal-rock is infiltrated, the greater the amount of stable creep, and the accelerated creep phase will appear earlier at low stress levels. Coal-rock creep is more sensitive to the magnitude of stress levels compared to the length of infiltration time. According to the results of parameter identification, at the same stress level, E 0 , E 1 , η 1 , η 2 , t F , E 2 and ν show a general decreasing trend. The analysis shows that water infiltration has a weakening effect on the creep properties of coal-rock.
Describing the whole process of coal-rock creep by connecting Hooke body, Kelvin body, Newtonian body and elastic-plastic damage body in series. The total damage variable is used to represent the weakening effect of the coupling effect of stress and water infiltration on the mechanical properties of coal-rock, and a creep constitutive model of coal-rock under the stress-infiltration effect is established.
The damage evolution pathway of coal-rock reflects the alignment of microscopic mechanical response with the macroscopic deformation damage process. Water infiltration changes the fine structure of coal-rock; thus, its damage deterioration degree increases with the extension of infiltration time, and the macroscopic manifestation is more obvious as creep deformation and damage characteristics; at the same time, with the increase of stress level, the damage degree of coal-rock increases, creep time shortens, and plastic characteristics gradually increase.
However, it must be noted that the present model does not account for the size effect that exists during localization of damage, and so the parameters obtained for tests on specimens of one single size cannot be expected to be valid for specimens of whole sizes. This size effect will need to be incorporated into future extensions of our creep model.