Strength degradation of sandstone and granodiorite under uniaxial cyclic loading

Rashid Geranmayeh Vaneghi,Behnam Ferdosi,Achola D.Okoth,Barnabas Kuek

Department of Mining Engineering and Metallurgical Engineering,Western Australian School of Mines(WASM),Curtin University,Kalgoorlie,Australia

1.Introduction

In situ rock is basically subjected to monotonic and cyclic or dynamic loadings.A proper and detailed understanding of how the mechanical properties of rock change when subjected to different loading scenarios is required for the safe and proper design and construction of civil,mining and geotechnical engineering structures such as underground openings,tunnels,rock pillars,foundations and for better understanding of other related operations such as drilling and blasting.Cyclic loadings are generated by seismic events,earthquakes,blasting,repetitive loadings and explosions which affect either surface or underground rock structures(Fig.1).As shown in Fig.1,the stability of an underground excavation(openings like tunnels,galleries,caverns and shafts)is not only controlled by rock microstructures,geological features and in situ stress state,but also by the type of loading which could be static or dynamic.The period of cyclic loading,its frequency and stress level are important factors which govern the influence of cyclic loading on a rock body.Hence,the mechanical properties of rock under cyclic or dynamic loading should be different from those under static loading condition.

It has been widely acknowledged that a rock structure subjected to cyclic loading of ten fails prior to reaching its designed stress level or bearing capacity of its static uniaxial compressive strength(UCS).The mechanism is widely referred to as“fatigue”(Eberhardt et al.,1998).Fundamental rock structures,as mentioned above,are often subjected to cyclic loadings and their mechanical strengths experience degradation along with the loading period.Therefore,the effects of cyclic loading on stability and serviceability of rock structures cannot be neglected.

From the literature review,it was found that some researchers focused on the variation and degradation of intact or jointed rock properties under uniaxial and triaxial cyclic loadings and some others investigated the fatigue damage mechanism.It was first reported by Burdine(1963)that the pore pressure and confinement affected the cyclic response of sandstone,and rock fatigue strength decreased and increased at high pore pressure and confinement,respectively.Attewell and Farmer(1973)also examined the strength degradation of concrete,mortar and rock under cyclic loading.They revealed that the fatigue strengths of their tested materials decreased up to 50-70%compared to the static strength.Prost(1988)investigated the effect of pre-existing joints in Pikes Peak granite and Dakota sandstone on the crack initiation and propagation under compression-tension cyclic loading.He reported that the rocks generally failed at low number of cycles when loaded under higher stress levels and loading amplitudes.Macro tests conducted by Singh(1989)also concluded that cyclic loadings led to progressive weakening of rocks and in particular showed that there was a remarkable drop in the UCS of rocks following cyclic loading.

Tao and Mo(1990)attempted to correlate the experimental data of fatigue life to the mechanical properties of a rock specimen.They developed a constitutive equation to explain the stress-strain curves for cyclic loading.However,there is no single validated rule to describe the cyclic loading behavior of a rock.The equation developed by Tao and Mo(1990)only gives a best fit under given conditions.

The effects of cyclic loading and strain rate on the uniaxial strength of sandstone were studied by Ray et al.(1999).They reported that the degradation of rock strength is noticeable at higher maximum stress levels.According to their results,the axial failure strain was also relatively higher at higher stress levels.

Bagde and Petroš(2005a)reported that the fatigue strength and Young’s modulus of sandstone decreased and increased,respectively,with the loading frequency.Bagde and Petroš(2005b)reported that the loading machine showed sensitivity to high loading amplitude applied at high loading frequency,and found that the real applied loading amplitude was remarkably lower than the target loading amplitude.Bagde and Petroš(2005c)also revealed that the cyclic dynamic responses are different under different loading waveforms and loading rates.The sine waveform was found to have a stronger dynamic effect than a ramp(triangle)waveform.It was reported that damage accumulates most rapidly under square waveforms(Gong and Smith,2003);however,it is purely of academic interest.Because the loading rate of a square waveform is theoretically infinite in a quarter of a cycle,its dynamic effect is similar to an impact load(Xiao et al.,2008).The effects of loading amplitude and frequency on the strength degradation and deformation behavior of rocks under uniaxial cyclic compression were also studied by Bagde and Petroš(2009).They reported that the microstructure,texture and quartz content of the rock specimens affect the fatigue strength and cyclic dynamic response.It was found that the microfracturing is the main cause of fatigue failure.

Different damage variables used to examine the damage evolution under cyclic loading were discussed by Xiao et al.(2009,2010).When the permanent strain was plotted against the number of cycles,it was observed that the three-stage inverted S-shaped model is well capable of describing the whole process of fatigue damage development.The curve can be divided into three phases.The shape of the curve is dependent on the rock properties and magnitude of stress applied to the rock.The three phases may be associated with the three stages that a crack undergoes,i.e.crack initiation,stable propagation and unstable propagation(Xiao et al.,2009).Bastian et al.(2014)conducted uniaxial and triaxial cyclic compressive tests on Hawkesbury sandstone to examine the variation in its mechanical properties under cyclic loading conditions.Rapid evolution of damage was observed as unloading initiation stress and unloading amplitude increased.The variations of mechanical parameters and failure mechanism of Lac du Bonnet granite under uniaxial cyclic loading were discussed by Ghazvinian(2015).He described the relationship between the critical stress thresholds(crack initiation and crack damage thresholds)and the fatigue damage pattern during the cyclic process.Taheri et al.(2016)also studied the change in mechanical properties of the Hawkesbury sandstone during various cyclic loading conditions using uniaxial and triaxial compression tests.They reported that the unstable crack propagation was observed at approximately 65%of the cumulative axial strain.

To date,most of previous works attempted to evaluate the change in mechanical properties of rocks under different cyclic loading conditions.Few studies,however,have addressed the question:Which of the maximum stress level and loading amplitude has a stronger cyclic effect?Moreover,the cyclic response of soft rocks and hard rocks is not fully understood.As mentioned previously,the fatigue behavior of hard rocks such as granodiorite and soft rocks such as sandstone,which are very common rocks in most rock structures,was always of great importance.The cyclic behaviors of these two kinds of rocks under constant frequency but with varying loading stress amplitude and stress level are presented in this study.

2.Experimental set-up

2.1.Rock specimens

Among the intrusive rocks,granite and granodiorite are the most common and frequently encountered ones in most under ground mining activities.In addition,as a result of the high strength of granitic rock,it is also widely used in the construction industry.Sandstone is also bedrock for rock structures and its behavior is different from a hard rock like granodiorite.The rock specimens were obtained from sandstone and Gosford granite/granodiorite outcrops quarry in New South Wales,Australia.Petrographic thin section analysis shows that granodiorite is weakly altered coarse grained leucocratic holocrystalline and it contains anhedral quartz(20-30%),orthoclase(～20%),subhedral,zoned plagioclase(20-30%)and medium-grained flakes biotite(～10%).Sandstone is fine-grained and well-sorted and dominated by sub-rounded to angular quartz(～80%).The matrix material consisting of clay and sericite accounts for around 10%of the specimen.The inter granular porosity of this sandstone is approximately 10%.Photographs of the analyzed specimens from these two rock types in cross polarized light(XPL)are shown in Fig.2.The typical specimens of granodiorite and sandstone are shown in Fig.3.The densities of tested sandstone and granodiorite specimens were 2204 kg/m3and 2524 kg/m3,respectively.

Specimens were available in two sizes:regular-size with diameter of about 54 mm and height of 131 mm and small-size with diameter of 42 mm and height of 102 mm.Seven(five smallsize and two regular-size)specimens of granodiorite and seven(four small-size and three regular-size)of sandstone were tested to determine their UCS values.The sandstone specimens were ovendried for 24 h so as to eliminate any moisture present therein.Since the average water content was determined to be very low(equal to 0.3%),the effect of water content on the obtained results was neglected.

2.2.Equipment

The tests were done using a GCTS uniaxial testing system UCT 1000,as shown in Fig.4.The machine is fitted with a computer controlled axial actuator and can load a specimen by controlling the loading rate or strain rate.The UCT 1000 is capable of performing both dynamic and static tests,and the data obtained from the tests are collected automatically using PC-based software.

The specimens were loaded using a servo-controlled loading machine.The linear variable differential transformers(LVDTs)were used for simultaneous readings of axial,radial and volumetric strains.UCS values for all specimens were recorded for analysis.

2.3.Methodology

Some laboratory tests have been performed through use of uniaxial cyclic loading to investigate the mechanical fatigue behaviors of the tested rocks.The granodiorite and sandstone specimens,used for cyclic loading,were in the same size as those used for monotonic uniaxial compression loadings.

Fig.2.Photomicrographs of(a)granodiorite and(b)sandstone in XPL.Qtz,Plag,Orth and Biot stand for quartz,plagioclase,orthoclase and biotite,respectively.

Uniaxial monotonic compression tests were conducted on both rock types.The average UCS for the tested specimens was used as the guiding maximum possible strength of the rock and to define the maximum stress level of cyclic loading.Table 1 shows the average UCS for regular-and small-size granodiorite and sandstone specimens.The stress-strain curves of uniaxial tests on small-size specimens are illustrated in Fig.5.

The uniaxial cyclic tests were carried out in a stress control mode.The loading waveform was sine waveform which has already been found to have a strongerdynamic effect than a ramp(triangle)waveform(Bagde and Petroš,2005c).The loading amplitudes were varied yet frequency was kept constant at 1 Hz.Two types of cyclic loadings were considered in these uniaxial cyclic tests.These two types were constant mean stress level or constant cyclic loading(CCL),and increasing mean stress level or stepped cyclic loading(SCL).The cyclic loading path with respect to time is illustrated schematically in Fig.6.

The CCL was designed to examine the effects of loading amplitude and the maximum stress level on fatigue strength.The regular-size specimens were tested under a CCL condition while the testing for the small-size specimens was done in a SCL manner.

Fig.3.Typical specimens of(a)granodiorite and(b)sandstone before testing.

Under SCL conditions,the loading amplitude was kept constant whereas the maximum stress level was increased step by step.These tests were designed to find the fatigue stress of the tested rocks and to explore the effect of maximum stress level on the fatigue strength.For the SCL tests,the initial mean stress was set and the specimen was loaded at a set amplitude for a specific timet.If no failure occurred,the mean stress was raised and the amplitude was kept constant and again the loading was done for another period of timet.This stepwise increase of mean stress was done up tothe failure point.The maximum stress level was set as 75-90%of static strength(UCS)for the granodiorite specimens and 85-97%of UCS for the sandstone specimens.The amplitude stresses were set as 3-8 MPa and 5-10 MPa in cyclic tests conducted on sandstone and granodiorite specimens,respectively.The specimen was axially loaded up to the mean stress level(the average of the maximum and minimum stress levels,σmean)in the load control mode with loading rates of approximately1 kN/s and 0.23 kN/s for regular-and small-size sandstone specimens and 3.3 kN/s and 0.23 kN/s for regular-and small-size granodiorite specimens,respectively.Since the results of the cyclic tests on regular specimens were somewhat scattered,the loading rate on small-size specimens was set relatively low.However,for the cyclic tests,it was attempted to set the loading rate of the initial loading to be the same as that of the uniaxial monotonic tests.

3.Results and discussion

The effects of the maximum stress level and loading amplitude on fatigue life and strength degradation of the tested rocks were investigated by uniaxial cyclic tests.As mentioned earlier,two types of cyclic loadings with constant mean stress level,named CCL,and increasing mean stress level cyclic loading,named SCL,were considered in these tests.Table 2 shows the experimental scheme and obtained results of uniaxial compression cyclic tests for both granodiorite and sandstone specimens.It is noteworthy that some specimens(St.-R-9,G-R-3 and G-R-4)were reloaded when they did not fail after a large number of cycles during the first loading path of CCL tests.Therefore,the results for specimens St.-R-10,G-R-5 and G-R-6 were used to analyze the effect of cyclic loading history on their fatigue response.Although these three specimens were loaded at a higher mean stress level for the second time,they were put into the CCL category.

Characteristics of all SCL paths are detailed in Table 3.As can be seen,in all SCL,the loading amplitudes(σα)were constant yet the mean stress levels were varied.According to this table,the mean stress level and loading amplitude of specimen St.-S-5,for instance,were set to 34.5 MPa and 3 MPa,respectively,for the first step.Then the specimen would be loaded for up to 30 min(1800 cycles).If it did not fail,the test would continue for another 1800 cycles within the second step in which the mean stress level would be increased to 37 MPa under the same loading amplitude(3 MPa).This procedure would be continued up to the failure point of the specimen.

Fig.4.(a)Machine set-up and(b)LVDTs configuration to measure the axial and radial deformations.

Fig.7 shows the stress-strain curves for the cyclic tests carried out on regular-and small-size specimens of granodiorite and sandstone.As displayed in Fig.7a,the sandstone specimens St.-R-5,St.-R-6,St.-R-8 and St.-R-10 failed at 30.92 MPa,30.89 MPa,32.84 MPa and 33.84 MPa,respectively.Fig.7b also presents that specimens St.-S-5,St.-S-6 and St.-S-7,which were loaded under 3 MPa,5 MPa and 6 MPa,failed at 39.47 MPa,38.03 MPa and 35.69 MPa,respectively.The greater the loading amplitude,the lower the fatigue strength.The regular-size granodiorite specimens G-R-5,G-R-6 and G-R-7 failed at 85.09 MPa,102.4 MPa and 93.11 MPa,respectively(Fig.7c).The small-size granodiorite specimens(G-S-6 and G-S-7),as illustrated in Fig.7d,failed at 83.33 MPa and 79.4 MPa,respectively.These two specimens failed at the first step of SCL even though it was planned to load them under different stress levels during the fatigue process.The results are explained in detail in the following sections.

Table 1Average UCS of small-and regular-size granodiorite and sandstone specimens.

3.1.Effect of maximum stress level

The analysis of fatigue behavior of specimens as well as strength characteristics under various maximum stress levels has been carried out.In Table 2,the maximum stress levels were inadequate to influence the fatigue behavior of some rock specimens,either for granodiorite or sandstone.

Fig.5.Stress-strain curves for monotonic uniaxial compression tests conducted on small-size(a)sandstone and(b)granodiorite specimens.

Fig.6.Schematic illustration of cyclic loading path with(a)CCL and(b)SCL.

As can be found in Table 2,the sandstone specimens St.-R-4 and St.-R-9 did not fail even after a large number of cycles when they were loaded under the maximum stress levels of 30 MPa(83.3%of UCS)and 32 MPa(88.8%of UCS),respectively.This was also observed during the cyclic tests on small-size sandstone specimens,St.-S-5 and St.-S-6,under the maximum stress levels of 85.2%of UCS(37.5 MPa)during the first step of SCL path.As the maximum stress level exceeded 90%of UCS,all sandstone specimens failed and fatigue life decreased as well.The specimens St.-S-5 and St.-S-6,as can be seen in Table 2,yielded when the applied maximum stress level increased to91%of UCS(40 MPa)during the second step of SCL.The effect of the maximum stress level on strength degradation of specimens St.-R-5 and St.-R-8 was more noticeable.They failed just after 65 cycles and 71 cycles(shorter fatigue life),respectively,since they were loaded under a higher maximum stress level of 94.4%of UCS(34 MPa).

Comparing the results of specimens St.-R-4 and St.-S-6 with that of St.-R-5,under the same loading amplitude of 5 MPa,it can be seen that the fatigue life of specimens decreased as the maximum stress level increased.The specimen St.-R-5 failed after 65 cycles under a maximum stress level of 34 MPa(94.4%of UCS),whereas both specimens St.-R-4 and St.-S-6 did not fail under the maximum stress of 83.3%and 85.2%of UCS,respectively,even after a large number of cycles.

A similar result was also obtained for granodiorite specimens.Specimens G-R-3 and G-R-4 did not fail after 1 h(about 3600 cycles)and 2 h(about 7200 cycles)of loading under the maximum stress levels of 90 MPa(75%of UCS)and 94 MPa(78.3%of UCS),respectively,however,they failed when the maximum stress levels increased to 82.5%and 88.3%of UCS(results of G-R-5 and G-R-6),respectively.The fatigue life and strength(σf)of specimen G-S-7 under a maximum stress level of 85 MPa(81%of UCS)were compared with those of G-R-5 and G-R-6 under higher maximum stress levels of 99 MPa and 106 MPa(82.5%and 88.3%of UCS),respectively.It was found that the loading history had a great effect on cyclic response even though the loading amplitude was equal to 10 MPa for all specimens.Since G-R-5 and G-R-6 failed under a larger number of cycles compared to G-S-7,the strain-hardening behavior is clear,because they have already been loaded under cyclic conditions and experienced the fatigue process.As can be seen,specimen G-R-6,which had already been loaded under the maximum stress level of 78.3%of UCS,failed after 217 cycles,while specimen G-R-5,which had already experienced loading under a maximum stress level of 75%of UCS,failed after 313 cycles.Thus it can be stated that when a rock experienced a higher loading level at previous loading stages,yet less than the fatigue stress threshold,a shorter fatigue life would be resulted in.

A similar finding was also reported by other researchers.According to Singh(1989)and Momeni et al.(2015),the rock material tends to fail at a low number of cycles and has a shorter fatigue life as the maximum stress level increases(Fig.8).As can be seen in Fig.8,when the maximum stress level exceeded 90%of monotonic compressive strengths of granodiorite and graywacke,they failed at a number of cycles less than 200.Whereas when the graywacke,for instance,was loaded at 88%of UCS,it sustained more than 6000 cycles.It can be concluded that every rock material has a strength threshold,named as fatigue strength,and the rock fails at a lownumber of cycles when the maximum stress level is more than this threshold,if other testing conditions remain constant.Thus the maximum applied stress level is of great importance in assessing the mechanical parameters of rock and design of any structure which will be operated under a cyclic loading condition.

Table 2Experimental scheme of uniaxial compression cyclic tests for both granodiorite and sandstone specimens.

Table 3Detail of loading path for specimens loaded under SCL tests.

3.2.Effect of loading amplitude

Fig.7.Stress-strain curves for uniaxial cyclic tests conducted on(a)regular-and(b)small-size sandstone specimens,and(c)regular-and(d)small-size granodiorite specimens.

Fig.8.Effect of the maximum stress level on fatigue life of granodiorite and graywacke.Data obtained from Singh(1989)and Momeni et al.(2015)under loading frequency of 1 Hz.

Amplitude is a key factor when analyzing the cyclic loading,as it is an indicator of how much the maximum and minimum stresses vary from the mean stress and it also determines the values expected for the maximum stress reached.Even with a slightly lower initial loading stress,the specimens subjected to higher magnitudes of amplitude failed sooner than those under low amplitudes.

Comparing the fatigue life and strength of small-size sandstone specimens,St.-S-5 and St.-S-6,under the same maximum stress level,it is clear that the fatigue life and strength of sandstone decreased as the loading amplitude increased from 3 MPa to 5 MPa.Specimen St.-S-5 with loading amplitude of 3 MPa failed after 2153 cycles during the second stage of SCL when the maximum stress level was 40 MPa.Specimen St.-S-6,whereas,with loading amplitude of 5 MPa,failed after 1930 cycles during the second stage of SCL when the maximum stress level was 40 MPa.The fatigue strength of specimen St.-S-6 loaded under a higher loading amplitude was 38.03 MPa(86.4%of UCS),lower than that of specimen St.-S-5,which was 39.47 MPa(89.7%of UCS).

Comparing the fatigue life and strength of specimen St.-S-7 with those of specimens St.-S-5 and St.-S-6,it suggests that the effect of loading amplitude is stronger than that of the maximum stress level.Specimen St.-S-7 loaded under a maximum stress level of 85.2%of UCS with higher loading amplitude of 6 MPa failed during the first step of SCL,after just 470 cycles(shorter fatigue life)and lower fatigue stress(81.1%of UCS)compared to St.-S-5 and St.-S-6 that did not fail during the first step(at the same maximum stress level of 85.2%of UCS).These two specimens failed during the second stage when the maximum stress level increased to 91%of UCS.Thus it can be concluded that the rock would more easily yield at a lower maximum stress level with higher loading amplitude than at a high maximum stress level with low loading amplitude.This finding,however,needs to be validated by more experimental data.The importance of loading amplitude has also been stated by Attewell and Farmer(1973)when they compared the cyclic response of rocks under different loading amplitudes and frequencies.They believed that failure of rock occurs more easily at low-frequency dynamic stress with higher amplitude than at high-frequency dynamic stress with low loading amplitude.

As can be found in Table 2,if the fatigue strengths of granodiorite specimens G-S-6 and G-S-7 are compared,the fatigue strength of G-S-6 with loading amplitude of 7.5 MPawas 83.33 MPa(79.3%of UCS)compared to that of 79.4 MPa(75.6%of UCS)for G-S-7 with higher loading amplitude of 10 MPa.

The effect of loading amplitude on fatigue life was also reported by Singh(1989),He et al.(2016)and Taheri et al.(2016).The more the loading amplitude,the shorter the fatigue life.As shown in Fig.9,the graywacke specimens sustained 10,189 cycles under loading amplitude of 50 MPa,while they failed at 287 cycles when the loading amplitude increased to 83 MPa(Singh,1989).As illustrated in this figure,this trend was also reported by He et al.(2016)and Taheri et al.(2016)for their tested sandstone specimens.The sandstone specimens were loaded more than 100 cycles under loading amplitude of 40 MPa,whereas they failed just after 2 cycles as the loading amplitude increased to 47 MPa(Taheri et al.,2016).The sandstone specimens tested by He et al.(2016)showed a similar result.Specimens sustained loading up to 233 cycles when the loading amplitude was less than 10 MPa,while they failed after 20 cycles when the loading amplitude was more than 60 cycles.

3.3.Fatigue strength

The fatigue strength of the tested rocks can be determined from the results discussed above.As previously mentioned,each type of rock has a strength threshold at which it can sustain loading under a large number of cycles if the loading level is less than this threshold.According to Table 2 and based on the discussion in previous sections,the fatigue strengths of sandstone and granodiorite specimens can be taken as 90%and 80%of their UCS values,respectively.Thus the fatigue strengths of regular-and small-size sandstone specimens are 32 MPa and 40 MPa,respectively.These amounts were found equal to be 96 MPa and 85 MPa for regularand small-size granodiorite,respectively.

Based on the fatigue strengths of sandstone and granodiorite,it can be concluded that the fatigue strength of hardrocks is relatively lower than that of soft rocks.Thus the brittle rocks are more prone to be weakened under cyclic loading than ductile rocks.The more brittle the rock,the more the strength degradation,and the less the fatigue strength.

3.4.Failure modes of the tested rock specimens

Damage mechanism was always an interesting topic to figure out how solid materials fail by fracturing and cracking.Identifying crack development through laboratory tests would improve our understanding of the real failure process in practice(Eberhardt,1998).The failure modes of the tested sandstone and granodiorite specimens are presented in Fig.10.As can be seen in this figure,there were more fractured planes observed on both sandstone and granodiorite specimens after cyclic loading compared to static loading tests.The main shearing plane(named 1)is accompanied by axial tensile cracks(named 2)for both specimens under cyclic loading.More tensile splitting cracks were observed under a cyclic loading condition.Since the granodiorite rock is more brittle,there was more powder on the fracture planes after the cyclic tests,which is an indication of fatigue failure.This pattern was also observed by Wang et al.(2013).Similar failure modes for sandstone specimens under triaxial monotonic and cyclic tests were also reported by Liu et al.(2011,2012)and Yang et al.(2015).

Fig.9.Effect of loading amplitude on fatigue life of rock material under cyclic loading.Data obtained from Singh(1989),He et al.(2016)and Taheri et al.(2016).

Fig.10.Failure modes of tested(a)sandstone and(b)granodiorite specimens under static and cyclic loadings.Cracks named 1 are shearing cracks and the ones named 2 are axial tensile cracks.

3.5.Rock nonhomogeneity and response to cyclic loadings

During laboratory testing of granodiorite and sandstone specimens subjected to uniaxial cyclic loadings,there were some disparities observed in the fatigue failure of rock specimens.Some specimens developed immediate failure and premature yielding though the loading amplitude was minimal and the maximum stresses were not significantly high.However,a few specimens have shown no yielding or axial strain and lateral strain as a result of dynamic deformation failure.One significant observation noted is that fatigue characteristics are dependent on geological condition,in situ stress and depth of core extraction as well as chemical composition of the rock micro structure formation.The unlikely variability in cyclic failure is an obvious heterogeneity of the rock specimens due to changes in in situ stress distribution,which might have altered the mechanical properties of the intact rock,i.e.strength,deform ability and especially permeability initiated due to development of network of stress relief cracks.These conditions could have created stress corrosion phenomena and plenty of weakening mechanical actions,i.e.weak strain bonds around the crack tips thus facilitating crack propagation at lower stress levels.

Moreover,the perceived nonhomogeneity is a result of microscale heterogeneity of the rock specimens.It is believed that the presence of microstructures has created an additional dimension on the nonhomogeneous specimen.There is room for expansion of one or more individual micro-fractures into cleavage fractures(splitting/extension mode)and a dramatic drop of load-bearing capacity to abrupt failure.

4.Conclusions

The main objectives for this study were to investigate the effects of loading amplitude and stress on the mechanical properties of sandstone and granodiorite and to understand how the cyclic response differs from soft rock of sandstone to hard rock of granodiorite.From the conducted tests and obtained results,the following conclusions were drawn:

(1)The increasing mean stress level tests(SCL path)provides a decent way to not only explore the effect of the maximum stress level and loading amplitude on cyclic response of rocks but also to investigate the effect of loading history on their fatigue behavior.

(2)The fatigue life decreased with an increase in the maximum stress level if the cyclic loading amplitude remained constant.

(3)The decreases in the fatigue life and strength were evident with increasing loading amplitude.

(4)The effect of loading amplitude is stronger than that of the maximum stress level.The rock would more easily yield at a lower maximum stress level with higher loading amplitude than at high maximum stress level with lower loading amplitude.

(5)The fatigue strength of hard/brittle rocks seems to be less than that of soft/ductile rocks.The more brittle the rock,the more the strength degradation,and the less the fatigue strength.

(6)It is observed that more local cracks are formed after cyclic loading tests compared to static loading tests.

Further experimental work,however,is required to be carried out to validate that the loading amplitude has more cyclic effect than the maximum stress level.Different rock types are suggested to be tested under cyclic loading to precisely explore the difference between fatigue response of hard rocks and soft rocks.It would also be interesting to assess the effects of rock fabric and its heterogeneity on the fatigue response.

Conflicts of interest

The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

We would like to express our sincere gratitude to Department of Mining Engineering and Metallurgical Engineering of Western Australian School of Mines(WASM),Curtin University for the provided laboratory equipment at Geomechanics Laboratory,Mining Research Institute of Western Australia(MRIWA)for the financial support and also special appreciation to Dr.Takahiro Funatsu forhis technical support to undertake the laboratory tests.

Attewell PB,Farmer IW.Fatigue behaviour of rock.International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts 1973;10(1):1-9.

Bagde MN,Petroš V.Fatigue properties of intact sandstone samples subjected to dynamic uniaxial cyclical loading.International Journal of Rock Mechanics and Mining Sciences 2005a;42(2):237-50.

Bagde MN,Petroš V.The effect of machine behaviour and mechanical properties of intact sandstone under static and dynamic uniaxial cyclic loading.Rock Mechanics and Rock Engineering 2005b;38(1):59-67.

Bagde MN,Petroš V.Waveform effect on fatigue properties of intact sandstone in uniaxial cyclical loading.Rock Mechanics and Rock Engineering 2005c;38(3):169-96.

Bagde MN,Petroš V.Fatigue and dynamic energy behaviour of rock subjected to cyclical loading.International Journal of Rock Mechanics and Mining Sciences 2009;46(1):200-9.

Bastian T,Connelly B,Lazo Olivares C,Yfantidis N,Taheri A.Progressive damage of Hawkesbury sandstone subjected to systematic cyclic loading.Journal of Research Projects Review 2014;3(1):7-14.

Burdine NT.Rock failure under dynamic loading conditions.Society of Petroleum Engineers Journal 1963;3(1).https://doi.org/10.2118/481-PA.

Eberhardt E.Brittle rock fracture and progressive damage in uniaxial compression.PhD Thesis.Saskatoon,Canada:University of Saskatchewan;1998.

Eberhardt E,Stead D,Stimpson B,Read RS.Identifying crack initiation and propagation thresholds in brittle rock.Canadian Geotechnical Journal 1998;35(2):222-33.

Ghazvinian E.Fracture initiation and propagation in low porosity crystalline rocks:implications for excavation damage zone(EDZ)mechanics.PhD Thesis.Kingston,Ontario,Canada:Queen’s University;2015.

Gong M,Smith I.Effect of waveform and loading sequence on low-cycle compressive fatigue life of spruce.Journal of Materials in Civil Engineering 2003;15(1):93-9.

He MM,Li N,Chen YS,Zhu CH.Strength and fatigue properties of sandstone under dynamic cyclic loading.Shock and Vibration 2016.https://doi.org/10.1155/2016/9458582.

Liu EL,He SM,Xue XH,Xu J.Dynamic properties of intact rock samples subjected to cyclic loading under confining pressure conditions.Rock Mechanics and Rock Engineering 2011;44(5):629-34.

Liu EL,Huang RQ,He SM.Effects of frequency on the dynamic properties of intact rock samples subjected to cyclic loading under confining pressure conditions.Rock Mechanics and Rock Engineering 2012;45(1):89-102.

Momeni A,Karakus M,Khanlari GR,Heidari M.Effects of cyclic loading on the mechanical properties of a granite.International Journal of Rock Mechanics and Mining Sciences 2015;77:89-96.

Prost GL.Jointing at rock contacts in cyclic loading.International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts 1988;25(5):263-72.

Ray SK,Sarkar M,Singh TN.Effect of cyclic loading and strain rate on the mechanical behaviour of sandstone.International Journal of Rock Mechanics and Mining Sciences 1999;36(4):543-9.

Singh SK.Fatigue and strain hardening behaviour of graywacke from the flagstaff formation,New South Wales.Engineering Geology 1989;26(2):171-9.

Taheri A,Yfantidis N,Olivares C,Connelly B,Bastian T.Experimental study on degradation of mechanical properties of sandstone under different cyclic loadings.Geotechnical Testing Journal 2016;39(4):673-87.

Tao ZY,Mo HH.An experimental study and analysis of the behaviour of rock under cyclic loading.International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts 1990;27(1):51-6.

Wang Z,Li S,Qiao L,Zhao J.Fatigue behavior of granite subjected to cyclic loading under triaxial compression condition.Rock Mechanics and Rock Engineering 2013;46(6):1603-15.

Xiao JQ,Ding DX,Jiang FL,Xu G.Fatigue damage variable and evolution of rock subjected to cyclic loading.International Journal of Rock Mechanics and Mining Sciences 2010;47(3):461-8.

Xiao JQ,Ding DX,Xu G,Jiang FL.Waveform effect on quasi-dynamic loading condition and the mechanical properties of brittle materials.International Journal of Rock Mechanics and Mining Sciences 2008;45(4):621-6.

Xiao JQ,Ding DX,Xu G,Jiang FL.Inverted S-shaped model for nonlinear fatigue damage of rock.International Journal of Rock Mechanics and Mining Sciences 2009;46(3):643-8.

Yang SQ,Ranjith PG,Huang YH,Yin PF,Jing HW,Gui YL,Yu QL.Experimental investigation on mechanical damage characteristics of sandstone under triaxial cyclic loading.Geophysical Journal International 2015;201(2):662-82.