Research ArticleMechanical Characteristics for Rocks under Different Paths andUnloading Rates under Confining Pressures
Bing Dai Guoyan Zhao Longjun Dong and Chen Yang
School of Resources and Safety Engineering Central South University Changsha 410083 China
Correspondence should be addressed to Longjun Dong rydong001csueducn
Received 9 December 2014 Accepted 27 January 2015
Academic Editor Alicia Gonzalez-Buelga
Copyright copy 2015 Bing Dai et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
To investigate mechanical characteristics of rocks under different unloading conditions triaxial tests are carried out with initialconfining pressures of 10 20 and 30MPa and unloading rates of 005sim1MPas in three stress paths Results show that the incrementof axial strain is far less than that of the lateral strain The unloading rates of confining pressures have less influence on variation ofstrain and lateral increment in path IThe variation of axial increment strain in the same time is slightly larger than the variation oflateral increment D-value is influenced by unloading rates of confining pressures in path IIThe variation of axial strain incrementdecreases firstly and then increases with the variation of confining pressures The relation decreases and then increases withunloading rates increases in path III The dilatancy angle decreases with initial confining pressures increases The vary rates ofdilatancy angle from initial point of dilatancy angle to peak point of dilatancy angle increase with the unloading rates of confiningpressures In the same rates the vary rates of dilatancy angle from the initial point of the dilatancy angle to peak point of thedilatancy angle in path I are greater than those in path II
1 Introduction
Rock masses at depth are under a triaxial stress equilibriumstate before an excavation Excavating an opening disturbs theoriginal in situ stress field which will lead to stress redistri-bution around the excavation With the increase of miningdepth the excavation becomes more and more serious andthe stability of the surrounding rock get weaker and weaker[1 2] It would lead to severe rock failure such as rockburstspalling collapse and other geological disasters [3ndash5] Thesebehaviors have been observed in hard rock mines and indeep civil tunnels around the world [6] Many studies haveshown that during the excavation of deep-buried tunnelsand caverns the surrounding rockmasses undergo unloadingprocess [7ndash9]
However investigations indicated that rock behaviorunder unloading is different from that under loading [10ndash12]To achieve a clear understanding of the rock behavior underunloading many experimental studies have been carried outR Q Huang and D Huang [13] obtained the determinationof Poissonrsquos ratio of rock material by changing the axial stressand unloading lateral stress test Huang et al [14] reveals that
rock bursts during tunneling in a high in situ stress area couldbe controlled or reduced by lowering the excavation speed orapplying precautionarymeasures to control the displacementof surrounding rocks Li et al [15] studied the fatigue damagebehavior of sandstone after high temperature under triaxialunloading
Many experts and scholars have made great effects on theresearch of factors such as anisotropy size effect shear andrheological behavior which have great influence on mechan-ical characteristics of unloading rock Besides the abovefactors unloading rates of rocks and unloading paths alsohave a significant impact on the mechanical characteristicsof unloading rock About stress path Li et al [5 6] discussedthe influence of stress path on excavation unloading responseby PFC and obtained the characteristics of the unloadingprocess of rocks under high initial stress Cai [16] studiedthe influence of stress path on tunnel excavation responsemdashnumerical tool selection and modeling strategy Guo et al[17 18] studied mechanical properties of Jintan mine rocksalt under complex stress paths and found that the strengthof rock salt was only slightly affected by loading strain ratewhich is different from other brittle rocks And it also made
Hindawi Publishing CorporationShock and VibrationVolume 2015 Article ID 578748 8 pageshttpdxdoiorg1011552015578748
2 Shock and Vibration
some effects on unloading rate Qiu et al [19] carried out true-triaxial unloading tests on granite specimens and obtainedthe degree of violence during failure and the associated AEenergy release in the strain burst process are dependent onthe unloading rate Gang et al [1] reported the deformationand strength characters of jointed rockmass under unloadingstress states Qiu et al [20] studied characteristics of strengthof rocks under different unloading rates and indicated thatthe strength of the rock will increase as the unloading rate ishigher
These theoretical studies help us to understand theinfluence of the unloading rate and unloading path on theexcavation stability However the influence of the unloadingrate and unloading path on mechanical characteristics hasnot been studied systematically in these tests It can beseen from the review above different unloading rates anddifferent unloading paths were not considered together toresearchmechanical characteristics of unloading rocksThusexperimental studies are needed to provide new insight intothe influence of unloading rates and unloading paths onmechanical characteristics of rocks
In this paper the specimens are studied in the presentstudy by means of conventional triaxial unloading testsat different unloading paths and different unloading ratesThe progressive stress-strain curves and the characteristicdeformation behavior were studiedThe experimental resultshave important significance for reasonable excavation andsupport scheme
2 Testing Apparatus
The study was conducted at the geomechanical test centeron the MTS815 compression machine under strict testconditions incorporated into the test programThe tester is arigidmachine thatMTSCo Ltd (USA) produced specificallyfor versatile rock testing The machine incorporates electro-hydraulic servo control with automatic pressure relief as wellas axis servo control and the measurement system
3 Specimen Preparation
The rock specimens used in this test were drilled from onerock block sampled in a gold mine The material of theinvestigated rock specimens is granitic rock Cylindrical rockspecimens were cored by a drill with an inner diameter of50mm along a direction perpendicular to the smooth rocksurface thus the diameter of the samples ranges between49 and 495mm The specimens were cut into pieces 110mmin height and showed no apparent cracks or fracturesThen both ends were finely ground until they measuredbetween 995 and 100mm The machining accuracy of thespecimens was in accordance with the International Societyfor Rock Mechanics (ISRM) recommended methods [21]The allowable variations of the end flatness and the devi-ation from perpendicularity to the longitudinal axis of thespecimens were less than 002mm and 0001 rad respectivelyRock specimens were granitic rock measuring 120593 50mm times100mm The specimens had a longitudinal wave velocity of
Table 1 Initial geostress condition of various rock samples
3200sim3800ms a density of 25 gcm3 and a uniaxial com-pressive strength of 80MPa
4 Testing Methodology
The specimens are put into three schemes for being testedunder different initial conditions as listed in Table 1 Theaxial pressure which is 80 of triaxial strength is appliedin a strain-controlled way The initial confining pressure isset to be three levels 10 20 and 30MPa respectively Theunloading rate is set to be four levels 005MPas 01MPas05MPas and 1MPas The test steps are as follows
Shock and Vibration 3
(1) Using hydrostatic pressure the axial stress 1205901is
increased to the initial lateral stress 1205903 maintaining
120590
1= 120590
3
(2) The axial stress 1205901is increased to 80 of the peak
intensity maintaining a constant 1205903
(3) The axial stress and lateral stress are varied at differentunloading rates until the specimen is destroyed Inthis step there are three schemes Scheme I main-taining a constant for axial pressure while decreas-ing confining pressure Scheme II increasing axialpressure while decreasing confining pressure SchemeIII decreasing axial pressure and confining pressureInitial condition of various specimens is shown inTable 1
5 Test Results
51 Characteristics of Stress Strain Curves Figure 1 showsthe relationship between the stress and strain of specimensunder unloading conditions Observations from Figure 1 canbe summarized as follows
(1) The axial strain increases slowly and the lateral strainincreases rapidly The increment of lateral strain is4sim15 times than that of axial strain during the processof unloading confining pressures in three paths Itshould be noted that the volume strain changedinto negative in Figure 1 which indicates that thedilatancy of specimens occur It shows the lateraltension The dilatancy of specimens in path II is notobvious this is because the deviatoric stress increasedin path II It provides more energy to the specimenswhich accelerated the damage of rock accelerated thecrack extension and accelerated the macro failure ofspecimens In path III the dilatancy of specimens ismost obvious Because the unloading time in path IIIis greater than that in path I and path II
(2) The increment of axial strain decreases with unload-ing rates of confining pressures increases Whenthe unloading rate is 005MPas 01MPas and05MPas in path III the increment of axial strainchanges into negative In addition it can be seenthat the increment of axial strain decreases withinitial confining pressures increases When the ini-tial confining pressures are 20MPa and 30MPathe increment of axial strain reduced approximately20 and 40 compared with 10MPa This indicatesthat the unloading rates of confining pressures andinitial confining pressures increases the brittle failurecharacteristics of specimens is more obvious
52 Deformation Characteristics To describe the deforma-tion characteristics of specimens in the process of unloadingit presents a description variable-variation of strain incre-ment The variation of the strain increment is the ratio of
strain increment at any time point and strain increment inall process of unloading They are defined below
119863ax =(Δ120576ax)119894sumΔ120576ax
119863lat =(Δ120576lat)119894sumΔ120576lat
(1)
where 119863ax and 119863lat are the variation of strain increment ofaxial and lateral respectively 120576ax and 120576lat are the axial andlateral respectively and 119894 is any time point in the process ofunloading
According to the equation mentioned above the respec-tive 119863ax and 119863lat are calculated and then the evolution ofthem is analyzed Figure 2 shows the relationship between thevariation of unloading confining pressure 30MPa incrementand the two variables As shown in Figure 2 the evolution ofvariables may be summarized as follows
(1) Firstly the curve shows the linear steady evolutionstage in which there are linear increases of thevariation of strain increment of axial and lateraluntil the variation of unloading confining pressureis between 05 and 06 in path I Additionally thevariation of strain increment of axial and lateral isabout 20 of the variation of total strain incrementIt indicates that the damage of specimens growsslowly with the variation of unloading confiningpressure increases in this stage suggesting that themicrocracks have initiated and increased steadilywhile no interaction has occurred among the cracksThen the curve shows the nonlinear evolution stageAbout 80of the variation of strain increment of axialand lateral occurs in this stage This indicates thatlots of microcracks are produced and opened rapidlyresulting in fast increases of strain Also it can be seenfrom the Figure 2 the unloading rates have a littleinfluence on the variation of strain increment of axialand lateral in whole unloading process
(2) The variation of strain increment of axial is slightlylarger than that of lateral at same time in path II Andthe difference between them is affected by unload-ing rates When the unloading rate increases from005MPas to 1MPas the difference between themincreases firstly and then decreases Additionallyabout 60sim80 of the variation of strain incrementoccurs with the variation of unloading confiningpressure change from 08 to 10 Also the variationof strain increment increases with unloading ratesincreases
(3) In path III the variation of the strain increment ofaxial decreases firstly and then increases with thevariation of unloading confining pressure increasesAnd the rule decreases firstly and then increases withthe unloading rates increases These results indicatethat the axial strain is rebound with the unloadingof axial in the initial stage When the variation ofunloading confining pressure is larger than 04 or so
Figure 1 Complete stress-strain curves of rock under different paths and unloading rates of confining pressures
Shock and Vibration 5
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 005MPas
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 01MPas
12
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 05MPas 12
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 1MPas
1
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 005MPas1
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 01MPas
1
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 05MPas
1
12
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 1MPas
1
12
08
06
04
02
0
minus02
D
minus01minus01
01 03 05 07 09 11
Δ1205909984003Δ1205903
Path III v1205903 = 005MPas
1
12
08
06
04
02
0
minus02
D
01 03 05 07 09 11
Δ1205909984003Δ1205903
Path III v1205903 = 01MPas
DlatDax
DlatDax
Figure 2 Continued
6 Shock and Vibration
1
12
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
DlatDax
DlatDax
Path III v1205903 = 05MPas
1
12
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path III v1205903 = 1MPas
Figure 2 The evolution of variation of axial strain increment with unloading confining pressures
the variation of strain increment of axial graduallyincreases It indicates that interaction has occurredamong cracks resulting in rapid increases of strainand the dilatancy of specimens has occurred obvi-ously in path III
53 Analysis of Dilation Characteristics In the theory ofrock mechanics the dilatancy angle 120595 is usually used todescribe the dilation characteristics Vermeer and de Borst[22] defined the dilatancy angle as follows
120595 = arcsin(120576
1015840
V
minus2120576
1015840
1+ 120576
1015840
V) (2)
where 12057610158401and 1205761015840V are the strain increment of axial and
volumetric respectivelyFigure 3 shows the evolution of dilatancy angle120595with the
variation of strain increment lateral in process of unloadingconfining pressures
(1) From Figure 3 it can be seen that the initial confiningpressure has an important influence on the dilatancyangle 120595 which decreases with the initial confiningpressure increases This indicates that the initial con-fining pressure hinders the dilatancy angle to extend
(2) The evolution of dilatancy angle first increases slowlyto about 15 times of the initial dilatancy angle thenmaintain approximate the same dilatancy angle untilthe rock failureswith 005MPas of unloading rate Asthe unloading rate adds up to 01MPas the dilatancyangle quickly enhances and reaches a limit value thendecreases a bit and ultimately reaches a fixed valueWhen the unloading rate ranges from 05MPas to1MPas the dilatancy angle reaches a limit valuemorerapidly that is 2sim5 times of the initial dilatancy anglethen reduced to a fixed level until the rock failures
(3) It is particularlyworth noting that the rate of dilatancyangle from initial value to limit value increases withthe unloading rates increases as shown in Figure 3It indicates that when the unloading rate is rapidthe strain energy quickly releases resulting in many
microcracks produced and expanded It leads to anincrease of the lateral strains occur and propagatebut the axial strains have less time to expandedgenerating the process of dilatancy angle increasesfast Then with the unloading the strain energy isconsumed by extending of microcracks the dilatancyangle decreases slowly to a stable state until the rockfailures
(4) Comparedwith the rate of dilatancy angle from initialvalue to limit value in path I and path II the rateof dilatancy angle from initial value to limit value inpath I is greater than that in path II with the sameunloading rates The result indicates that loadingof axial in path II provides more energy to rocksome microcracks expanded rapidly resulting in thedilatancy angle increasing rapidly
6 Conclusions
(1) The axial strain increases slowly and the lateral strainincreases rapidly in the process of unloading the dila-tancy of specimens occurs In path III the dilatancyof specimens is the most obvious The unloadingrates of confining pressures and initial confiningpressures increase the brittle failure characteristics ofspecimens are more obvious
(2) A description variable-variation of strain increment ispresented in this paper According to the relationshipsbetween variation of strain increment and variationof the confining pressure there are linear increases ofthe variation of strain increment of axial and lateraluntil the variation of unloading confining pressure isbetween 05 and 06 in path I The variation of strainincrement of axial is slightly larger than that of lateralat same time in path II The difference between themis affected by unloading rates In path III the variationof strain increment of axial decreases firstly and thenincreases with the variation of unloading confiningpressure increases The rule decreases firstly and thenincreases with the unloading rates increases
Shock and Vibration 7
minus01 01 03 05 07 09 11
80
70
60
50
40
30
Dlat
Path I 1205903 = 005MPas120595
(∘)
30
35
40
45
50
55
60
minus01 01 03 05 07 09
Dlat
11
Path I 1205903 = 01MPas
120595(∘
)30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path I 1205903 = 05MPas
30
40
50
60
70
80
minus01 01 03 05 07 09 11Dlat
120595(∘
)
Path I 1205903 = 1MPas
10
20
30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 005MPas
20
25
30
35
40
45
50
55
60
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 01MPas
0
10
20
30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 05MPas
1015202530354045505560
Dlat
120595(∘
)
minus01 01 03 05 07 09 11
Path II v1205903 = 1MPas
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
Figure 3 The evolution of dilatancy angle with variation of lateral strain increment
(3) According to the analysis of the evolution of dilatancyanglewith the variation of strain increment lateral theinitial confining pressure has an important influenceon the dilatancy angle 120595 which decreases with theinitial confining pressure increases The rate of dila-tancy angle from initial value to limit value increaseswith the unloading rates increases The rate of thedilatancy angle from the initial value to the limit value
in path I is greater than that in path II under the sameunloading rates
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
8 Shock and Vibration
References
[1] W Gang S Jun and W Zhong-ru ldquoDamage mechanicalanalysis of unloading failure of intact rock under complex stressstaterdquo Journal of Hehai University vol 25 no 3 pp 44ndash49 1997
[2] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission source location for cuboid monitoringnetwork without pre-measured wave velocityrdquo Transactions ofNonferrous Metals Society of China vol 25 no 1 pp 293ndash3022015
[3] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission or microseismic source location undercube monitoring networkrdquo Transactions of Nonferrous MetalsSociety of China vol 22 no 12 pp 3087ndash3094 2012
[4] L-J Dong and X-B Li ldquoA microseismicacoustic emissionsource location method using arrival times of PS waves forunknown velocity systemrdquo International Journal of DistributedSensor Networks vol 2013 Article ID 307489 8 pages 2013
[5] L-J Dong X-B Li and G Xie ldquoAn analytical solution foracoustic emission source location for known P wave velocitysystemrdquoMathematical Problems in Engineering vol 2014 Arti-cle ID 290686 6 pages 2014
[6] X Li W Cao Z Zhou and Y Zou ldquoInfluence of stress path onexcavation unloading responserdquo Tunnelling and UndergroundSpace Technology vol 42 pp 237ndash246 2014
[7] Y Ming-qing and H An-zeng ldquoTri-axial confining depressuretest of rock samplerdquo Chinese Journal of Rock Mechanics andEngineering vol 17 no 1 pp 24ndash29 1998
[8] Q-R Huang and D Huang ldquoExperimental research on affec-tion laws unloading rates on mechanical properties of Jinpingmarble under high geostressrdquoChinese Journal of RockMechanicsand Engineering vol 29 no 1 pp 21ndash33 2010
[9] L-J Dong X-B Li and K Peng ldquoPrediction of rockburstclassification using Random Forestrdquo Transactions of NonferrousMetals Society of China (English Edition) vol 23 no 2 pp 472ndash477 2013
[10] M C Torres-Suarez A Alarcon-Guzman and R Berdugo-DeMoya ldquoEffects of loading-unloading and wetting-drying cycleson geomechanical behaviors of mudrocks in the ColombianAndesrdquo Journal of Rock Mechanics and Geotechnical Engineer-ing vol 6 no 3 pp 257ndash268 2014
[11] H Q Yang Y Y Zeng Y F Lan and X P Zhou ldquoAnalysisof the excavation damaged zone around a tunnel accountingfor geostress and unloadingrdquo International Journal of RockMechanics and Mining Sciences vol 69 pp 59ndash66 2014
[12] L F Fan and L N Y Wong ldquoStress wave transmissionacross a filled joint with different loadingunloading behaviorrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 60 pp 227ndash234 2013
[13] R Q Huang and D Huang ldquoEvolution of rock cracks underunloading conditionrdquo Rock Mechanics and Rock Engineeringvol 47 no 2 pp 453ndash466 2014
[14] R Q Huang X N Wang and L S Chan ldquoTriaxial unloadingtest of rocks and its implication for rock burstrdquo Bulletin ofEngineering Geology and the Environment vol 60 no 1 pp 37ndash41 2001
[15] J Li X Chen L Dang Y Dong Z Cheng and J Guo ldquoTriaxialunloading test of sandstone after high temperaturerdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 8 pp1587ndash1595 2011
[16] M Cai ldquoInfluence of stress path on tunnel excavationresponsemdashnumerical tool selection and modeling strategyrdquo
Tunnelling andUnderground Space Technology vol 23 no 6 pp618ndash628 2008
[17] Y-T Guo C-H Yang andH-JMao ldquoMechanical properties ofJintan mine rock salt under complex stress pathsrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 56 pp 54ndash61 2012
[18] Y-T Guo C-H Yang and J-J Fu ldquoExperimental research onmechanical characteristics of salt rock under triaxial unloadingtestrdquo Rock and Soil Mechanics vol 33 no 3 pp 725ndash738 2012
[19] S-L Qiu X-T Feng J-Q Xiao and C-Q Zhang ldquoAn exper-imental study on the pre-peak unloading damage evolution ofmarblerdquoRockMechanics and Rock Engineering vol 47 no 2 pp401ndash419 2014
[20] S-L Qiu X-T Feng and C-Q Zhang ldquoExperimental researchon mechanical properties of deep-buried marble under differ-ent unloading rates of confining pressuresrdquo Chinese Journal ofRock Mechanics and Engineering vol 29 no 9 pp 1807ndash18172010
[21] R Ulusay and J A Hudson The Complete ISRM SuggestedMethods for Rock Characterization Testing and Monitoring1974ndash2006 International Society for Rock Mechanics 2007
[22] P A Vermeer and R de Borst ldquoNon-associated plasticity forsoils concrete and rockrdquo Heron vol 29 3 pp 1ndash64 1984
some effects on unloading rate Qiu et al [19] carried out true-triaxial unloading tests on granite specimens and obtainedthe degree of violence during failure and the associated AEenergy release in the strain burst process are dependent onthe unloading rate Gang et al [1] reported the deformationand strength characters of jointed rockmass under unloadingstress states Qiu et al [20] studied characteristics of strengthof rocks under different unloading rates and indicated thatthe strength of the rock will increase as the unloading rate ishigher
These theoretical studies help us to understand theinfluence of the unloading rate and unloading path on theexcavation stability However the influence of the unloadingrate and unloading path on mechanical characteristics hasnot been studied systematically in these tests It can beseen from the review above different unloading rates anddifferent unloading paths were not considered together toresearchmechanical characteristics of unloading rocksThusexperimental studies are needed to provide new insight intothe influence of unloading rates and unloading paths onmechanical characteristics of rocks
In this paper the specimens are studied in the presentstudy by means of conventional triaxial unloading testsat different unloading paths and different unloading ratesThe progressive stress-strain curves and the characteristicdeformation behavior were studiedThe experimental resultshave important significance for reasonable excavation andsupport scheme
2 Testing Apparatus
The study was conducted at the geomechanical test centeron the MTS815 compression machine under strict testconditions incorporated into the test programThe tester is arigidmachine thatMTSCo Ltd (USA) produced specificallyfor versatile rock testing The machine incorporates electro-hydraulic servo control with automatic pressure relief as wellas axis servo control and the measurement system
3 Specimen Preparation
The rock specimens used in this test were drilled from onerock block sampled in a gold mine The material of theinvestigated rock specimens is granitic rock Cylindrical rockspecimens were cored by a drill with an inner diameter of50mm along a direction perpendicular to the smooth rocksurface thus the diameter of the samples ranges between49 and 495mm The specimens were cut into pieces 110mmin height and showed no apparent cracks or fracturesThen both ends were finely ground until they measuredbetween 995 and 100mm The machining accuracy of thespecimens was in accordance with the International Societyfor Rock Mechanics (ISRM) recommended methods [21]The allowable variations of the end flatness and the devi-ation from perpendicularity to the longitudinal axis of thespecimens were less than 002mm and 0001 rad respectivelyRock specimens were granitic rock measuring 120593 50mm times100mm The specimens had a longitudinal wave velocity of
Table 1 Initial geostress condition of various rock samples
3200sim3800ms a density of 25 gcm3 and a uniaxial com-pressive strength of 80MPa
4 Testing Methodology
The specimens are put into three schemes for being testedunder different initial conditions as listed in Table 1 Theaxial pressure which is 80 of triaxial strength is appliedin a strain-controlled way The initial confining pressure isset to be three levels 10 20 and 30MPa respectively Theunloading rate is set to be four levels 005MPas 01MPas05MPas and 1MPas The test steps are as follows
Shock and Vibration 3
(1) Using hydrostatic pressure the axial stress 1205901is
increased to the initial lateral stress 1205903 maintaining
120590
1= 120590
3
(2) The axial stress 1205901is increased to 80 of the peak
intensity maintaining a constant 1205903
(3) The axial stress and lateral stress are varied at differentunloading rates until the specimen is destroyed Inthis step there are three schemes Scheme I main-taining a constant for axial pressure while decreas-ing confining pressure Scheme II increasing axialpressure while decreasing confining pressure SchemeIII decreasing axial pressure and confining pressureInitial condition of various specimens is shown inTable 1
5 Test Results
51 Characteristics of Stress Strain Curves Figure 1 showsthe relationship between the stress and strain of specimensunder unloading conditions Observations from Figure 1 canbe summarized as follows
(1) The axial strain increases slowly and the lateral strainincreases rapidly The increment of lateral strain is4sim15 times than that of axial strain during the processof unloading confining pressures in three paths Itshould be noted that the volume strain changedinto negative in Figure 1 which indicates that thedilatancy of specimens occur It shows the lateraltension The dilatancy of specimens in path II is notobvious this is because the deviatoric stress increasedin path II It provides more energy to the specimenswhich accelerated the damage of rock accelerated thecrack extension and accelerated the macro failure ofspecimens In path III the dilatancy of specimens ismost obvious Because the unloading time in path IIIis greater than that in path I and path II
(2) The increment of axial strain decreases with unload-ing rates of confining pressures increases Whenthe unloading rate is 005MPas 01MPas and05MPas in path III the increment of axial strainchanges into negative In addition it can be seenthat the increment of axial strain decreases withinitial confining pressures increases When the ini-tial confining pressures are 20MPa and 30MPathe increment of axial strain reduced approximately20 and 40 compared with 10MPa This indicatesthat the unloading rates of confining pressures andinitial confining pressures increases the brittle failurecharacteristics of specimens is more obvious
52 Deformation Characteristics To describe the deforma-tion characteristics of specimens in the process of unloadingit presents a description variable-variation of strain incre-ment The variation of the strain increment is the ratio of
strain increment at any time point and strain increment inall process of unloading They are defined below
119863ax =(Δ120576ax)119894sumΔ120576ax
119863lat =(Δ120576lat)119894sumΔ120576lat
(1)
where 119863ax and 119863lat are the variation of strain increment ofaxial and lateral respectively 120576ax and 120576lat are the axial andlateral respectively and 119894 is any time point in the process ofunloading
According to the equation mentioned above the respec-tive 119863ax and 119863lat are calculated and then the evolution ofthem is analyzed Figure 2 shows the relationship between thevariation of unloading confining pressure 30MPa incrementand the two variables As shown in Figure 2 the evolution ofvariables may be summarized as follows
(1) Firstly the curve shows the linear steady evolutionstage in which there are linear increases of thevariation of strain increment of axial and lateraluntil the variation of unloading confining pressureis between 05 and 06 in path I Additionally thevariation of strain increment of axial and lateral isabout 20 of the variation of total strain incrementIt indicates that the damage of specimens growsslowly with the variation of unloading confiningpressure increases in this stage suggesting that themicrocracks have initiated and increased steadilywhile no interaction has occurred among the cracksThen the curve shows the nonlinear evolution stageAbout 80of the variation of strain increment of axialand lateral occurs in this stage This indicates thatlots of microcracks are produced and opened rapidlyresulting in fast increases of strain Also it can be seenfrom the Figure 2 the unloading rates have a littleinfluence on the variation of strain increment of axialand lateral in whole unloading process
(2) The variation of strain increment of axial is slightlylarger than that of lateral at same time in path II Andthe difference between them is affected by unload-ing rates When the unloading rate increases from005MPas to 1MPas the difference between themincreases firstly and then decreases Additionallyabout 60sim80 of the variation of strain incrementoccurs with the variation of unloading confiningpressure change from 08 to 10 Also the variationof strain increment increases with unloading ratesincreases
(3) In path III the variation of the strain increment ofaxial decreases firstly and then increases with thevariation of unloading confining pressure increasesAnd the rule decreases firstly and then increases withthe unloading rates increases These results indicatethat the axial strain is rebound with the unloadingof axial in the initial stage When the variation ofunloading confining pressure is larger than 04 or so
Figure 1 Complete stress-strain curves of rock under different paths and unloading rates of confining pressures
Shock and Vibration 5
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 005MPas
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 01MPas
12
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 05MPas 12
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 1MPas
1
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 005MPas1
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 01MPas
1
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 05MPas
1
12
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 1MPas
1
12
08
06
04
02
0
minus02
D
minus01minus01
01 03 05 07 09 11
Δ1205909984003Δ1205903
Path III v1205903 = 005MPas
1
12
08
06
04
02
0
minus02
D
01 03 05 07 09 11
Δ1205909984003Δ1205903
Path III v1205903 = 01MPas
DlatDax
DlatDax
Figure 2 Continued
6 Shock and Vibration
1
12
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
DlatDax
DlatDax
Path III v1205903 = 05MPas
1
12
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path III v1205903 = 1MPas
Figure 2 The evolution of variation of axial strain increment with unloading confining pressures
the variation of strain increment of axial graduallyincreases It indicates that interaction has occurredamong cracks resulting in rapid increases of strainand the dilatancy of specimens has occurred obvi-ously in path III
53 Analysis of Dilation Characteristics In the theory ofrock mechanics the dilatancy angle 120595 is usually used todescribe the dilation characteristics Vermeer and de Borst[22] defined the dilatancy angle as follows
120595 = arcsin(120576
1015840
V
minus2120576
1015840
1+ 120576
1015840
V) (2)
where 12057610158401and 1205761015840V are the strain increment of axial and
volumetric respectivelyFigure 3 shows the evolution of dilatancy angle120595with the
variation of strain increment lateral in process of unloadingconfining pressures
(1) From Figure 3 it can be seen that the initial confiningpressure has an important influence on the dilatancyangle 120595 which decreases with the initial confiningpressure increases This indicates that the initial con-fining pressure hinders the dilatancy angle to extend
(2) The evolution of dilatancy angle first increases slowlyto about 15 times of the initial dilatancy angle thenmaintain approximate the same dilatancy angle untilthe rock failureswith 005MPas of unloading rate Asthe unloading rate adds up to 01MPas the dilatancyangle quickly enhances and reaches a limit value thendecreases a bit and ultimately reaches a fixed valueWhen the unloading rate ranges from 05MPas to1MPas the dilatancy angle reaches a limit valuemorerapidly that is 2sim5 times of the initial dilatancy anglethen reduced to a fixed level until the rock failures
(3) It is particularlyworth noting that the rate of dilatancyangle from initial value to limit value increases withthe unloading rates increases as shown in Figure 3It indicates that when the unloading rate is rapidthe strain energy quickly releases resulting in many
microcracks produced and expanded It leads to anincrease of the lateral strains occur and propagatebut the axial strains have less time to expandedgenerating the process of dilatancy angle increasesfast Then with the unloading the strain energy isconsumed by extending of microcracks the dilatancyangle decreases slowly to a stable state until the rockfailures
(4) Comparedwith the rate of dilatancy angle from initialvalue to limit value in path I and path II the rateof dilatancy angle from initial value to limit value inpath I is greater than that in path II with the sameunloading rates The result indicates that loadingof axial in path II provides more energy to rocksome microcracks expanded rapidly resulting in thedilatancy angle increasing rapidly
6 Conclusions
(1) The axial strain increases slowly and the lateral strainincreases rapidly in the process of unloading the dila-tancy of specimens occurs In path III the dilatancyof specimens is the most obvious The unloadingrates of confining pressures and initial confiningpressures increase the brittle failure characteristics ofspecimens are more obvious
(2) A description variable-variation of strain increment ispresented in this paper According to the relationshipsbetween variation of strain increment and variationof the confining pressure there are linear increases ofthe variation of strain increment of axial and lateraluntil the variation of unloading confining pressure isbetween 05 and 06 in path I The variation of strainincrement of axial is slightly larger than that of lateralat same time in path II The difference between themis affected by unloading rates In path III the variationof strain increment of axial decreases firstly and thenincreases with the variation of unloading confiningpressure increases The rule decreases firstly and thenincreases with the unloading rates increases
Shock and Vibration 7
minus01 01 03 05 07 09 11
80
70
60
50
40
30
Dlat
Path I 1205903 = 005MPas120595
(∘)
30
35
40
45
50
55
60
minus01 01 03 05 07 09
Dlat
11
Path I 1205903 = 01MPas
120595(∘
)30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path I 1205903 = 05MPas
30
40
50
60
70
80
minus01 01 03 05 07 09 11Dlat
120595(∘
)
Path I 1205903 = 1MPas
10
20
30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 005MPas
20
25
30
35
40
45
50
55
60
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 01MPas
0
10
20
30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 05MPas
1015202530354045505560
Dlat
120595(∘
)
minus01 01 03 05 07 09 11
Path II v1205903 = 1MPas
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
Figure 3 The evolution of dilatancy angle with variation of lateral strain increment
(3) According to the analysis of the evolution of dilatancyanglewith the variation of strain increment lateral theinitial confining pressure has an important influenceon the dilatancy angle 120595 which decreases with theinitial confining pressure increases The rate of dila-tancy angle from initial value to limit value increaseswith the unloading rates increases The rate of thedilatancy angle from the initial value to the limit value
in path I is greater than that in path II under the sameunloading rates
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
8 Shock and Vibration
References
[1] W Gang S Jun and W Zhong-ru ldquoDamage mechanicalanalysis of unloading failure of intact rock under complex stressstaterdquo Journal of Hehai University vol 25 no 3 pp 44ndash49 1997
[2] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission source location for cuboid monitoringnetwork without pre-measured wave velocityrdquo Transactions ofNonferrous Metals Society of China vol 25 no 1 pp 293ndash3022015
[3] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission or microseismic source location undercube monitoring networkrdquo Transactions of Nonferrous MetalsSociety of China vol 22 no 12 pp 3087ndash3094 2012
[4] L-J Dong and X-B Li ldquoA microseismicacoustic emissionsource location method using arrival times of PS waves forunknown velocity systemrdquo International Journal of DistributedSensor Networks vol 2013 Article ID 307489 8 pages 2013
[5] L-J Dong X-B Li and G Xie ldquoAn analytical solution foracoustic emission source location for known P wave velocitysystemrdquoMathematical Problems in Engineering vol 2014 Arti-cle ID 290686 6 pages 2014
[6] X Li W Cao Z Zhou and Y Zou ldquoInfluence of stress path onexcavation unloading responserdquo Tunnelling and UndergroundSpace Technology vol 42 pp 237ndash246 2014
[7] Y Ming-qing and H An-zeng ldquoTri-axial confining depressuretest of rock samplerdquo Chinese Journal of Rock Mechanics andEngineering vol 17 no 1 pp 24ndash29 1998
[8] Q-R Huang and D Huang ldquoExperimental research on affec-tion laws unloading rates on mechanical properties of Jinpingmarble under high geostressrdquoChinese Journal of RockMechanicsand Engineering vol 29 no 1 pp 21ndash33 2010
[9] L-J Dong X-B Li and K Peng ldquoPrediction of rockburstclassification using Random Forestrdquo Transactions of NonferrousMetals Society of China (English Edition) vol 23 no 2 pp 472ndash477 2013
[10] M C Torres-Suarez A Alarcon-Guzman and R Berdugo-DeMoya ldquoEffects of loading-unloading and wetting-drying cycleson geomechanical behaviors of mudrocks in the ColombianAndesrdquo Journal of Rock Mechanics and Geotechnical Engineer-ing vol 6 no 3 pp 257ndash268 2014
[11] H Q Yang Y Y Zeng Y F Lan and X P Zhou ldquoAnalysisof the excavation damaged zone around a tunnel accountingfor geostress and unloadingrdquo International Journal of RockMechanics and Mining Sciences vol 69 pp 59ndash66 2014
[12] L F Fan and L N Y Wong ldquoStress wave transmissionacross a filled joint with different loadingunloading behaviorrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 60 pp 227ndash234 2013
[13] R Q Huang and D Huang ldquoEvolution of rock cracks underunloading conditionrdquo Rock Mechanics and Rock Engineeringvol 47 no 2 pp 453ndash466 2014
[14] R Q Huang X N Wang and L S Chan ldquoTriaxial unloadingtest of rocks and its implication for rock burstrdquo Bulletin ofEngineering Geology and the Environment vol 60 no 1 pp 37ndash41 2001
[15] J Li X Chen L Dang Y Dong Z Cheng and J Guo ldquoTriaxialunloading test of sandstone after high temperaturerdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 8 pp1587ndash1595 2011
[16] M Cai ldquoInfluence of stress path on tunnel excavationresponsemdashnumerical tool selection and modeling strategyrdquo
Tunnelling andUnderground Space Technology vol 23 no 6 pp618ndash628 2008
[17] Y-T Guo C-H Yang andH-JMao ldquoMechanical properties ofJintan mine rock salt under complex stress pathsrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 56 pp 54ndash61 2012
[18] Y-T Guo C-H Yang and J-J Fu ldquoExperimental research onmechanical characteristics of salt rock under triaxial unloadingtestrdquo Rock and Soil Mechanics vol 33 no 3 pp 725ndash738 2012
[19] S-L Qiu X-T Feng J-Q Xiao and C-Q Zhang ldquoAn exper-imental study on the pre-peak unloading damage evolution ofmarblerdquoRockMechanics and Rock Engineering vol 47 no 2 pp401ndash419 2014
[20] S-L Qiu X-T Feng and C-Q Zhang ldquoExperimental researchon mechanical properties of deep-buried marble under differ-ent unloading rates of confining pressuresrdquo Chinese Journal ofRock Mechanics and Engineering vol 29 no 9 pp 1807ndash18172010
[21] R Ulusay and J A Hudson The Complete ISRM SuggestedMethods for Rock Characterization Testing and Monitoring1974ndash2006 International Society for Rock Mechanics 2007
[22] P A Vermeer and R de Borst ldquoNon-associated plasticity forsoils concrete and rockrdquo Heron vol 29 3 pp 1ndash64 1984
(1) Using hydrostatic pressure the axial stress 1205901is
increased to the initial lateral stress 1205903 maintaining
120590
1= 120590
3
(2) The axial stress 1205901is increased to 80 of the peak
intensity maintaining a constant 1205903
(3) The axial stress and lateral stress are varied at differentunloading rates until the specimen is destroyed Inthis step there are three schemes Scheme I main-taining a constant for axial pressure while decreas-ing confining pressure Scheme II increasing axialpressure while decreasing confining pressure SchemeIII decreasing axial pressure and confining pressureInitial condition of various specimens is shown inTable 1
5 Test Results
51 Characteristics of Stress Strain Curves Figure 1 showsthe relationship between the stress and strain of specimensunder unloading conditions Observations from Figure 1 canbe summarized as follows
(1) The axial strain increases slowly and the lateral strainincreases rapidly The increment of lateral strain is4sim15 times than that of axial strain during the processof unloading confining pressures in three paths Itshould be noted that the volume strain changedinto negative in Figure 1 which indicates that thedilatancy of specimens occur It shows the lateraltension The dilatancy of specimens in path II is notobvious this is because the deviatoric stress increasedin path II It provides more energy to the specimenswhich accelerated the damage of rock accelerated thecrack extension and accelerated the macro failure ofspecimens In path III the dilatancy of specimens ismost obvious Because the unloading time in path IIIis greater than that in path I and path II
(2) The increment of axial strain decreases with unload-ing rates of confining pressures increases Whenthe unloading rate is 005MPas 01MPas and05MPas in path III the increment of axial strainchanges into negative In addition it can be seenthat the increment of axial strain decreases withinitial confining pressures increases When the ini-tial confining pressures are 20MPa and 30MPathe increment of axial strain reduced approximately20 and 40 compared with 10MPa This indicatesthat the unloading rates of confining pressures andinitial confining pressures increases the brittle failurecharacteristics of specimens is more obvious
52 Deformation Characteristics To describe the deforma-tion characteristics of specimens in the process of unloadingit presents a description variable-variation of strain incre-ment The variation of the strain increment is the ratio of
strain increment at any time point and strain increment inall process of unloading They are defined below
119863ax =(Δ120576ax)119894sumΔ120576ax
119863lat =(Δ120576lat)119894sumΔ120576lat
(1)
where 119863ax and 119863lat are the variation of strain increment ofaxial and lateral respectively 120576ax and 120576lat are the axial andlateral respectively and 119894 is any time point in the process ofunloading
According to the equation mentioned above the respec-tive 119863ax and 119863lat are calculated and then the evolution ofthem is analyzed Figure 2 shows the relationship between thevariation of unloading confining pressure 30MPa incrementand the two variables As shown in Figure 2 the evolution ofvariables may be summarized as follows
(1) Firstly the curve shows the linear steady evolutionstage in which there are linear increases of thevariation of strain increment of axial and lateraluntil the variation of unloading confining pressureis between 05 and 06 in path I Additionally thevariation of strain increment of axial and lateral isabout 20 of the variation of total strain incrementIt indicates that the damage of specimens growsslowly with the variation of unloading confiningpressure increases in this stage suggesting that themicrocracks have initiated and increased steadilywhile no interaction has occurred among the cracksThen the curve shows the nonlinear evolution stageAbout 80of the variation of strain increment of axialand lateral occurs in this stage This indicates thatlots of microcracks are produced and opened rapidlyresulting in fast increases of strain Also it can be seenfrom the Figure 2 the unloading rates have a littleinfluence on the variation of strain increment of axialand lateral in whole unloading process
(2) The variation of strain increment of axial is slightlylarger than that of lateral at same time in path II Andthe difference between them is affected by unload-ing rates When the unloading rate increases from005MPas to 1MPas the difference between themincreases firstly and then decreases Additionallyabout 60sim80 of the variation of strain incrementoccurs with the variation of unloading confiningpressure change from 08 to 10 Also the variationof strain increment increases with unloading ratesincreases
(3) In path III the variation of the strain increment ofaxial decreases firstly and then increases with thevariation of unloading confining pressure increasesAnd the rule decreases firstly and then increases withthe unloading rates increases These results indicatethat the axial strain is rebound with the unloadingof axial in the initial stage When the variation ofunloading confining pressure is larger than 04 or so
Figure 1 Complete stress-strain curves of rock under different paths and unloading rates of confining pressures
Shock and Vibration 5
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 005MPas
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 01MPas
12
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 05MPas 12
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 1MPas
1
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 005MPas1
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 01MPas
1
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 05MPas
1
12
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 1MPas
1
12
08
06
04
02
0
minus02
D
minus01minus01
01 03 05 07 09 11
Δ1205909984003Δ1205903
Path III v1205903 = 005MPas
1
12
08
06
04
02
0
minus02
D
01 03 05 07 09 11
Δ1205909984003Δ1205903
Path III v1205903 = 01MPas
DlatDax
DlatDax
Figure 2 Continued
6 Shock and Vibration
1
12
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
DlatDax
DlatDax
Path III v1205903 = 05MPas
1
12
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path III v1205903 = 1MPas
Figure 2 The evolution of variation of axial strain increment with unloading confining pressures
the variation of strain increment of axial graduallyincreases It indicates that interaction has occurredamong cracks resulting in rapid increases of strainand the dilatancy of specimens has occurred obvi-ously in path III
53 Analysis of Dilation Characteristics In the theory ofrock mechanics the dilatancy angle 120595 is usually used todescribe the dilation characteristics Vermeer and de Borst[22] defined the dilatancy angle as follows
120595 = arcsin(120576
1015840
V
minus2120576
1015840
1+ 120576
1015840
V) (2)
where 12057610158401and 1205761015840V are the strain increment of axial and
volumetric respectivelyFigure 3 shows the evolution of dilatancy angle120595with the
variation of strain increment lateral in process of unloadingconfining pressures
(1) From Figure 3 it can be seen that the initial confiningpressure has an important influence on the dilatancyangle 120595 which decreases with the initial confiningpressure increases This indicates that the initial con-fining pressure hinders the dilatancy angle to extend
(2) The evolution of dilatancy angle first increases slowlyto about 15 times of the initial dilatancy angle thenmaintain approximate the same dilatancy angle untilthe rock failureswith 005MPas of unloading rate Asthe unloading rate adds up to 01MPas the dilatancyangle quickly enhances and reaches a limit value thendecreases a bit and ultimately reaches a fixed valueWhen the unloading rate ranges from 05MPas to1MPas the dilatancy angle reaches a limit valuemorerapidly that is 2sim5 times of the initial dilatancy anglethen reduced to a fixed level until the rock failures
(3) It is particularlyworth noting that the rate of dilatancyangle from initial value to limit value increases withthe unloading rates increases as shown in Figure 3It indicates that when the unloading rate is rapidthe strain energy quickly releases resulting in many
microcracks produced and expanded It leads to anincrease of the lateral strains occur and propagatebut the axial strains have less time to expandedgenerating the process of dilatancy angle increasesfast Then with the unloading the strain energy isconsumed by extending of microcracks the dilatancyangle decreases slowly to a stable state until the rockfailures
(4) Comparedwith the rate of dilatancy angle from initialvalue to limit value in path I and path II the rateof dilatancy angle from initial value to limit value inpath I is greater than that in path II with the sameunloading rates The result indicates that loadingof axial in path II provides more energy to rocksome microcracks expanded rapidly resulting in thedilatancy angle increasing rapidly
6 Conclusions
(1) The axial strain increases slowly and the lateral strainincreases rapidly in the process of unloading the dila-tancy of specimens occurs In path III the dilatancyof specimens is the most obvious The unloadingrates of confining pressures and initial confiningpressures increase the brittle failure characteristics ofspecimens are more obvious
(2) A description variable-variation of strain increment ispresented in this paper According to the relationshipsbetween variation of strain increment and variationof the confining pressure there are linear increases ofthe variation of strain increment of axial and lateraluntil the variation of unloading confining pressure isbetween 05 and 06 in path I The variation of strainincrement of axial is slightly larger than that of lateralat same time in path II The difference between themis affected by unloading rates In path III the variationof strain increment of axial decreases firstly and thenincreases with the variation of unloading confiningpressure increases The rule decreases firstly and thenincreases with the unloading rates increases
Shock and Vibration 7
minus01 01 03 05 07 09 11
80
70
60
50
40
30
Dlat
Path I 1205903 = 005MPas120595
(∘)
30
35
40
45
50
55
60
minus01 01 03 05 07 09
Dlat
11
Path I 1205903 = 01MPas
120595(∘
)30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path I 1205903 = 05MPas
30
40
50
60
70
80
minus01 01 03 05 07 09 11Dlat
120595(∘
)
Path I 1205903 = 1MPas
10
20
30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 005MPas
20
25
30
35
40
45
50
55
60
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 01MPas
0
10
20
30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 05MPas
1015202530354045505560
Dlat
120595(∘
)
minus01 01 03 05 07 09 11
Path II v1205903 = 1MPas
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
Figure 3 The evolution of dilatancy angle with variation of lateral strain increment
(3) According to the analysis of the evolution of dilatancyanglewith the variation of strain increment lateral theinitial confining pressure has an important influenceon the dilatancy angle 120595 which decreases with theinitial confining pressure increases The rate of dila-tancy angle from initial value to limit value increaseswith the unloading rates increases The rate of thedilatancy angle from the initial value to the limit value
in path I is greater than that in path II under the sameunloading rates
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
8 Shock and Vibration
References
[1] W Gang S Jun and W Zhong-ru ldquoDamage mechanicalanalysis of unloading failure of intact rock under complex stressstaterdquo Journal of Hehai University vol 25 no 3 pp 44ndash49 1997
[2] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission source location for cuboid monitoringnetwork without pre-measured wave velocityrdquo Transactions ofNonferrous Metals Society of China vol 25 no 1 pp 293ndash3022015
[3] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission or microseismic source location undercube monitoring networkrdquo Transactions of Nonferrous MetalsSociety of China vol 22 no 12 pp 3087ndash3094 2012
[4] L-J Dong and X-B Li ldquoA microseismicacoustic emissionsource location method using arrival times of PS waves forunknown velocity systemrdquo International Journal of DistributedSensor Networks vol 2013 Article ID 307489 8 pages 2013
[5] L-J Dong X-B Li and G Xie ldquoAn analytical solution foracoustic emission source location for known P wave velocitysystemrdquoMathematical Problems in Engineering vol 2014 Arti-cle ID 290686 6 pages 2014
[6] X Li W Cao Z Zhou and Y Zou ldquoInfluence of stress path onexcavation unloading responserdquo Tunnelling and UndergroundSpace Technology vol 42 pp 237ndash246 2014
[7] Y Ming-qing and H An-zeng ldquoTri-axial confining depressuretest of rock samplerdquo Chinese Journal of Rock Mechanics andEngineering vol 17 no 1 pp 24ndash29 1998
[8] Q-R Huang and D Huang ldquoExperimental research on affec-tion laws unloading rates on mechanical properties of Jinpingmarble under high geostressrdquoChinese Journal of RockMechanicsand Engineering vol 29 no 1 pp 21ndash33 2010
[9] L-J Dong X-B Li and K Peng ldquoPrediction of rockburstclassification using Random Forestrdquo Transactions of NonferrousMetals Society of China (English Edition) vol 23 no 2 pp 472ndash477 2013
[10] M C Torres-Suarez A Alarcon-Guzman and R Berdugo-DeMoya ldquoEffects of loading-unloading and wetting-drying cycleson geomechanical behaviors of mudrocks in the ColombianAndesrdquo Journal of Rock Mechanics and Geotechnical Engineer-ing vol 6 no 3 pp 257ndash268 2014
[11] H Q Yang Y Y Zeng Y F Lan and X P Zhou ldquoAnalysisof the excavation damaged zone around a tunnel accountingfor geostress and unloadingrdquo International Journal of RockMechanics and Mining Sciences vol 69 pp 59ndash66 2014
[12] L F Fan and L N Y Wong ldquoStress wave transmissionacross a filled joint with different loadingunloading behaviorrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 60 pp 227ndash234 2013
[13] R Q Huang and D Huang ldquoEvolution of rock cracks underunloading conditionrdquo Rock Mechanics and Rock Engineeringvol 47 no 2 pp 453ndash466 2014
[14] R Q Huang X N Wang and L S Chan ldquoTriaxial unloadingtest of rocks and its implication for rock burstrdquo Bulletin ofEngineering Geology and the Environment vol 60 no 1 pp 37ndash41 2001
[15] J Li X Chen L Dang Y Dong Z Cheng and J Guo ldquoTriaxialunloading test of sandstone after high temperaturerdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 8 pp1587ndash1595 2011
[16] M Cai ldquoInfluence of stress path on tunnel excavationresponsemdashnumerical tool selection and modeling strategyrdquo
Tunnelling andUnderground Space Technology vol 23 no 6 pp618ndash628 2008
[17] Y-T Guo C-H Yang andH-JMao ldquoMechanical properties ofJintan mine rock salt under complex stress pathsrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 56 pp 54ndash61 2012
[18] Y-T Guo C-H Yang and J-J Fu ldquoExperimental research onmechanical characteristics of salt rock under triaxial unloadingtestrdquo Rock and Soil Mechanics vol 33 no 3 pp 725ndash738 2012
[19] S-L Qiu X-T Feng J-Q Xiao and C-Q Zhang ldquoAn exper-imental study on the pre-peak unloading damage evolution ofmarblerdquoRockMechanics and Rock Engineering vol 47 no 2 pp401ndash419 2014
[20] S-L Qiu X-T Feng and C-Q Zhang ldquoExperimental researchon mechanical properties of deep-buried marble under differ-ent unloading rates of confining pressuresrdquo Chinese Journal ofRock Mechanics and Engineering vol 29 no 9 pp 1807ndash18172010
[21] R Ulusay and J A Hudson The Complete ISRM SuggestedMethods for Rock Characterization Testing and Monitoring1974ndash2006 International Society for Rock Mechanics 2007
[22] P A Vermeer and R de Borst ldquoNon-associated plasticity forsoils concrete and rockrdquo Heron vol 29 3 pp 1ndash64 1984
Figure 1 Complete stress-strain curves of rock under different paths and unloading rates of confining pressures
Shock and Vibration 5
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 005MPas
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 01MPas
12
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 05MPas 12
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
1
08
06
04
02
0
minus02
D
Path I v1205903 = 1MPas
1
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 005MPas1
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 01MPas
1
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 05MPas
1
12
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path II v1205903 = 1MPas
1
12
08
06
04
02
0
minus02
D
minus01minus01
01 03 05 07 09 11
Δ1205909984003Δ1205903
Path III v1205903 = 005MPas
1
12
08
06
04
02
0
minus02
D
01 03 05 07 09 11
Δ1205909984003Δ1205903
Path III v1205903 = 01MPas
DlatDax
DlatDax
Figure 2 Continued
6 Shock and Vibration
1
12
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
DlatDax
DlatDax
Path III v1205903 = 05MPas
1
12
08
06
04
02
0
minus02
D
minus01 01 03 05 07 09 11
Δ1205909984003Δ1205903
Path III v1205903 = 1MPas
Figure 2 The evolution of variation of axial strain increment with unloading confining pressures
the variation of strain increment of axial graduallyincreases It indicates that interaction has occurredamong cracks resulting in rapid increases of strainand the dilatancy of specimens has occurred obvi-ously in path III
53 Analysis of Dilation Characteristics In the theory ofrock mechanics the dilatancy angle 120595 is usually used todescribe the dilation characteristics Vermeer and de Borst[22] defined the dilatancy angle as follows
120595 = arcsin(120576
1015840
V
minus2120576
1015840
1+ 120576
1015840
V) (2)
where 12057610158401and 1205761015840V are the strain increment of axial and
volumetric respectivelyFigure 3 shows the evolution of dilatancy angle120595with the
variation of strain increment lateral in process of unloadingconfining pressures
(1) From Figure 3 it can be seen that the initial confiningpressure has an important influence on the dilatancyangle 120595 which decreases with the initial confiningpressure increases This indicates that the initial con-fining pressure hinders the dilatancy angle to extend
(2) The evolution of dilatancy angle first increases slowlyto about 15 times of the initial dilatancy angle thenmaintain approximate the same dilatancy angle untilthe rock failureswith 005MPas of unloading rate Asthe unloading rate adds up to 01MPas the dilatancyangle quickly enhances and reaches a limit value thendecreases a bit and ultimately reaches a fixed valueWhen the unloading rate ranges from 05MPas to1MPas the dilatancy angle reaches a limit valuemorerapidly that is 2sim5 times of the initial dilatancy anglethen reduced to a fixed level until the rock failures
(3) It is particularlyworth noting that the rate of dilatancyangle from initial value to limit value increases withthe unloading rates increases as shown in Figure 3It indicates that when the unloading rate is rapidthe strain energy quickly releases resulting in many
microcracks produced and expanded It leads to anincrease of the lateral strains occur and propagatebut the axial strains have less time to expandedgenerating the process of dilatancy angle increasesfast Then with the unloading the strain energy isconsumed by extending of microcracks the dilatancyangle decreases slowly to a stable state until the rockfailures
(4) Comparedwith the rate of dilatancy angle from initialvalue to limit value in path I and path II the rateof dilatancy angle from initial value to limit value inpath I is greater than that in path II with the sameunloading rates The result indicates that loadingof axial in path II provides more energy to rocksome microcracks expanded rapidly resulting in thedilatancy angle increasing rapidly
6 Conclusions
(1) The axial strain increases slowly and the lateral strainincreases rapidly in the process of unloading the dila-tancy of specimens occurs In path III the dilatancyof specimens is the most obvious The unloadingrates of confining pressures and initial confiningpressures increase the brittle failure characteristics ofspecimens are more obvious
(2) A description variable-variation of strain increment ispresented in this paper According to the relationshipsbetween variation of strain increment and variationof the confining pressure there are linear increases ofthe variation of strain increment of axial and lateraluntil the variation of unloading confining pressure isbetween 05 and 06 in path I The variation of strainincrement of axial is slightly larger than that of lateralat same time in path II The difference between themis affected by unloading rates In path III the variationof strain increment of axial decreases firstly and thenincreases with the variation of unloading confiningpressure increases The rule decreases firstly and thenincreases with the unloading rates increases
Shock and Vibration 7
minus01 01 03 05 07 09 11
80
70
60
50
40
30
Dlat
Path I 1205903 = 005MPas120595
(∘)
30
35
40
45
50
55
60
minus01 01 03 05 07 09
Dlat
11
Path I 1205903 = 01MPas
120595(∘
)30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path I 1205903 = 05MPas
30
40
50
60
70
80
minus01 01 03 05 07 09 11Dlat
120595(∘
)
Path I 1205903 = 1MPas
10
20
30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 005MPas
20
25
30
35
40
45
50
55
60
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 01MPas
0
10
20
30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 05MPas
1015202530354045505560
Dlat
120595(∘
)
minus01 01 03 05 07 09 11
Path II v1205903 = 1MPas
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
Figure 3 The evolution of dilatancy angle with variation of lateral strain increment
(3) According to the analysis of the evolution of dilatancyanglewith the variation of strain increment lateral theinitial confining pressure has an important influenceon the dilatancy angle 120595 which decreases with theinitial confining pressure increases The rate of dila-tancy angle from initial value to limit value increaseswith the unloading rates increases The rate of thedilatancy angle from the initial value to the limit value
in path I is greater than that in path II under the sameunloading rates
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
8 Shock and Vibration
References
[1] W Gang S Jun and W Zhong-ru ldquoDamage mechanicalanalysis of unloading failure of intact rock under complex stressstaterdquo Journal of Hehai University vol 25 no 3 pp 44ndash49 1997
[2] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission source location for cuboid monitoringnetwork without pre-measured wave velocityrdquo Transactions ofNonferrous Metals Society of China vol 25 no 1 pp 293ndash3022015
[3] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission or microseismic source location undercube monitoring networkrdquo Transactions of Nonferrous MetalsSociety of China vol 22 no 12 pp 3087ndash3094 2012
[4] L-J Dong and X-B Li ldquoA microseismicacoustic emissionsource location method using arrival times of PS waves forunknown velocity systemrdquo International Journal of DistributedSensor Networks vol 2013 Article ID 307489 8 pages 2013
[5] L-J Dong X-B Li and G Xie ldquoAn analytical solution foracoustic emission source location for known P wave velocitysystemrdquoMathematical Problems in Engineering vol 2014 Arti-cle ID 290686 6 pages 2014
[6] X Li W Cao Z Zhou and Y Zou ldquoInfluence of stress path onexcavation unloading responserdquo Tunnelling and UndergroundSpace Technology vol 42 pp 237ndash246 2014
[7] Y Ming-qing and H An-zeng ldquoTri-axial confining depressuretest of rock samplerdquo Chinese Journal of Rock Mechanics andEngineering vol 17 no 1 pp 24ndash29 1998
[8] Q-R Huang and D Huang ldquoExperimental research on affec-tion laws unloading rates on mechanical properties of Jinpingmarble under high geostressrdquoChinese Journal of RockMechanicsand Engineering vol 29 no 1 pp 21ndash33 2010
[9] L-J Dong X-B Li and K Peng ldquoPrediction of rockburstclassification using Random Forestrdquo Transactions of NonferrousMetals Society of China (English Edition) vol 23 no 2 pp 472ndash477 2013
[10] M C Torres-Suarez A Alarcon-Guzman and R Berdugo-DeMoya ldquoEffects of loading-unloading and wetting-drying cycleson geomechanical behaviors of mudrocks in the ColombianAndesrdquo Journal of Rock Mechanics and Geotechnical Engineer-ing vol 6 no 3 pp 257ndash268 2014
[11] H Q Yang Y Y Zeng Y F Lan and X P Zhou ldquoAnalysisof the excavation damaged zone around a tunnel accountingfor geostress and unloadingrdquo International Journal of RockMechanics and Mining Sciences vol 69 pp 59ndash66 2014
[12] L F Fan and L N Y Wong ldquoStress wave transmissionacross a filled joint with different loadingunloading behaviorrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 60 pp 227ndash234 2013
[13] R Q Huang and D Huang ldquoEvolution of rock cracks underunloading conditionrdquo Rock Mechanics and Rock Engineeringvol 47 no 2 pp 453ndash466 2014
[14] R Q Huang X N Wang and L S Chan ldquoTriaxial unloadingtest of rocks and its implication for rock burstrdquo Bulletin ofEngineering Geology and the Environment vol 60 no 1 pp 37ndash41 2001
[15] J Li X Chen L Dang Y Dong Z Cheng and J Guo ldquoTriaxialunloading test of sandstone after high temperaturerdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 8 pp1587ndash1595 2011
[16] M Cai ldquoInfluence of stress path on tunnel excavationresponsemdashnumerical tool selection and modeling strategyrdquo
Tunnelling andUnderground Space Technology vol 23 no 6 pp618ndash628 2008
[17] Y-T Guo C-H Yang andH-JMao ldquoMechanical properties ofJintan mine rock salt under complex stress pathsrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 56 pp 54ndash61 2012
[18] Y-T Guo C-H Yang and J-J Fu ldquoExperimental research onmechanical characteristics of salt rock under triaxial unloadingtestrdquo Rock and Soil Mechanics vol 33 no 3 pp 725ndash738 2012
[19] S-L Qiu X-T Feng J-Q Xiao and C-Q Zhang ldquoAn exper-imental study on the pre-peak unloading damage evolution ofmarblerdquoRockMechanics and Rock Engineering vol 47 no 2 pp401ndash419 2014
[20] S-L Qiu X-T Feng and C-Q Zhang ldquoExperimental researchon mechanical properties of deep-buried marble under differ-ent unloading rates of confining pressuresrdquo Chinese Journal ofRock Mechanics and Engineering vol 29 no 9 pp 1807ndash18172010
[21] R Ulusay and J A Hudson The Complete ISRM SuggestedMethods for Rock Characterization Testing and Monitoring1974ndash2006 International Society for Rock Mechanics 2007
[22] P A Vermeer and R de Borst ldquoNon-associated plasticity forsoils concrete and rockrdquo Heron vol 29 3 pp 1ndash64 1984
Figure 2 The evolution of variation of axial strain increment with unloading confining pressures
the variation of strain increment of axial graduallyincreases It indicates that interaction has occurredamong cracks resulting in rapid increases of strainand the dilatancy of specimens has occurred obvi-ously in path III
53 Analysis of Dilation Characteristics In the theory ofrock mechanics the dilatancy angle 120595 is usually used todescribe the dilation characteristics Vermeer and de Borst[22] defined the dilatancy angle as follows
120595 = arcsin(120576
1015840
V
minus2120576
1015840
1+ 120576
1015840
V) (2)
where 12057610158401and 1205761015840V are the strain increment of axial and
volumetric respectivelyFigure 3 shows the evolution of dilatancy angle120595with the
variation of strain increment lateral in process of unloadingconfining pressures
(1) From Figure 3 it can be seen that the initial confiningpressure has an important influence on the dilatancyangle 120595 which decreases with the initial confiningpressure increases This indicates that the initial con-fining pressure hinders the dilatancy angle to extend
(2) The evolution of dilatancy angle first increases slowlyto about 15 times of the initial dilatancy angle thenmaintain approximate the same dilatancy angle untilthe rock failureswith 005MPas of unloading rate Asthe unloading rate adds up to 01MPas the dilatancyangle quickly enhances and reaches a limit value thendecreases a bit and ultimately reaches a fixed valueWhen the unloading rate ranges from 05MPas to1MPas the dilatancy angle reaches a limit valuemorerapidly that is 2sim5 times of the initial dilatancy anglethen reduced to a fixed level until the rock failures
(3) It is particularlyworth noting that the rate of dilatancyangle from initial value to limit value increases withthe unloading rates increases as shown in Figure 3It indicates that when the unloading rate is rapidthe strain energy quickly releases resulting in many
microcracks produced and expanded It leads to anincrease of the lateral strains occur and propagatebut the axial strains have less time to expandedgenerating the process of dilatancy angle increasesfast Then with the unloading the strain energy isconsumed by extending of microcracks the dilatancyangle decreases slowly to a stable state until the rockfailures
(4) Comparedwith the rate of dilatancy angle from initialvalue to limit value in path I and path II the rateof dilatancy angle from initial value to limit value inpath I is greater than that in path II with the sameunloading rates The result indicates that loadingof axial in path II provides more energy to rocksome microcracks expanded rapidly resulting in thedilatancy angle increasing rapidly
6 Conclusions
(1) The axial strain increases slowly and the lateral strainincreases rapidly in the process of unloading the dila-tancy of specimens occurs In path III the dilatancyof specimens is the most obvious The unloadingrates of confining pressures and initial confiningpressures increase the brittle failure characteristics ofspecimens are more obvious
(2) A description variable-variation of strain increment ispresented in this paper According to the relationshipsbetween variation of strain increment and variationof the confining pressure there are linear increases ofthe variation of strain increment of axial and lateraluntil the variation of unloading confining pressure isbetween 05 and 06 in path I The variation of strainincrement of axial is slightly larger than that of lateralat same time in path II The difference between themis affected by unloading rates In path III the variationof strain increment of axial decreases firstly and thenincreases with the variation of unloading confiningpressure increases The rule decreases firstly and thenincreases with the unloading rates increases
Shock and Vibration 7
minus01 01 03 05 07 09 11
80
70
60
50
40
30
Dlat
Path I 1205903 = 005MPas120595
(∘)
30
35
40
45
50
55
60
minus01 01 03 05 07 09
Dlat
11
Path I 1205903 = 01MPas
120595(∘
)30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path I 1205903 = 05MPas
30
40
50
60
70
80
minus01 01 03 05 07 09 11Dlat
120595(∘
)
Path I 1205903 = 1MPas
10
20
30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 005MPas
20
25
30
35
40
45
50
55
60
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 01MPas
0
10
20
30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 05MPas
1015202530354045505560
Dlat
120595(∘
)
minus01 01 03 05 07 09 11
Path II v1205903 = 1MPas
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
Figure 3 The evolution of dilatancy angle with variation of lateral strain increment
(3) According to the analysis of the evolution of dilatancyanglewith the variation of strain increment lateral theinitial confining pressure has an important influenceon the dilatancy angle 120595 which decreases with theinitial confining pressure increases The rate of dila-tancy angle from initial value to limit value increaseswith the unloading rates increases The rate of thedilatancy angle from the initial value to the limit value
in path I is greater than that in path II under the sameunloading rates
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
8 Shock and Vibration
References
[1] W Gang S Jun and W Zhong-ru ldquoDamage mechanicalanalysis of unloading failure of intact rock under complex stressstaterdquo Journal of Hehai University vol 25 no 3 pp 44ndash49 1997
[2] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission source location for cuboid monitoringnetwork without pre-measured wave velocityrdquo Transactions ofNonferrous Metals Society of China vol 25 no 1 pp 293ndash3022015
[3] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission or microseismic source location undercube monitoring networkrdquo Transactions of Nonferrous MetalsSociety of China vol 22 no 12 pp 3087ndash3094 2012
[4] L-J Dong and X-B Li ldquoA microseismicacoustic emissionsource location method using arrival times of PS waves forunknown velocity systemrdquo International Journal of DistributedSensor Networks vol 2013 Article ID 307489 8 pages 2013
[5] L-J Dong X-B Li and G Xie ldquoAn analytical solution foracoustic emission source location for known P wave velocitysystemrdquoMathematical Problems in Engineering vol 2014 Arti-cle ID 290686 6 pages 2014
[6] X Li W Cao Z Zhou and Y Zou ldquoInfluence of stress path onexcavation unloading responserdquo Tunnelling and UndergroundSpace Technology vol 42 pp 237ndash246 2014
[7] Y Ming-qing and H An-zeng ldquoTri-axial confining depressuretest of rock samplerdquo Chinese Journal of Rock Mechanics andEngineering vol 17 no 1 pp 24ndash29 1998
[8] Q-R Huang and D Huang ldquoExperimental research on affec-tion laws unloading rates on mechanical properties of Jinpingmarble under high geostressrdquoChinese Journal of RockMechanicsand Engineering vol 29 no 1 pp 21ndash33 2010
[9] L-J Dong X-B Li and K Peng ldquoPrediction of rockburstclassification using Random Forestrdquo Transactions of NonferrousMetals Society of China (English Edition) vol 23 no 2 pp 472ndash477 2013
[10] M C Torres-Suarez A Alarcon-Guzman and R Berdugo-DeMoya ldquoEffects of loading-unloading and wetting-drying cycleson geomechanical behaviors of mudrocks in the ColombianAndesrdquo Journal of Rock Mechanics and Geotechnical Engineer-ing vol 6 no 3 pp 257ndash268 2014
[11] H Q Yang Y Y Zeng Y F Lan and X P Zhou ldquoAnalysisof the excavation damaged zone around a tunnel accountingfor geostress and unloadingrdquo International Journal of RockMechanics and Mining Sciences vol 69 pp 59ndash66 2014
[12] L F Fan and L N Y Wong ldquoStress wave transmissionacross a filled joint with different loadingunloading behaviorrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 60 pp 227ndash234 2013
[13] R Q Huang and D Huang ldquoEvolution of rock cracks underunloading conditionrdquo Rock Mechanics and Rock Engineeringvol 47 no 2 pp 453ndash466 2014
[14] R Q Huang X N Wang and L S Chan ldquoTriaxial unloadingtest of rocks and its implication for rock burstrdquo Bulletin ofEngineering Geology and the Environment vol 60 no 1 pp 37ndash41 2001
[15] J Li X Chen L Dang Y Dong Z Cheng and J Guo ldquoTriaxialunloading test of sandstone after high temperaturerdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 8 pp1587ndash1595 2011
[16] M Cai ldquoInfluence of stress path on tunnel excavationresponsemdashnumerical tool selection and modeling strategyrdquo
Tunnelling andUnderground Space Technology vol 23 no 6 pp618ndash628 2008
[17] Y-T Guo C-H Yang andH-JMao ldquoMechanical properties ofJintan mine rock salt under complex stress pathsrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 56 pp 54ndash61 2012
[18] Y-T Guo C-H Yang and J-J Fu ldquoExperimental research onmechanical characteristics of salt rock under triaxial unloadingtestrdquo Rock and Soil Mechanics vol 33 no 3 pp 725ndash738 2012
[19] S-L Qiu X-T Feng J-Q Xiao and C-Q Zhang ldquoAn exper-imental study on the pre-peak unloading damage evolution ofmarblerdquoRockMechanics and Rock Engineering vol 47 no 2 pp401ndash419 2014
[20] S-L Qiu X-T Feng and C-Q Zhang ldquoExperimental researchon mechanical properties of deep-buried marble under differ-ent unloading rates of confining pressuresrdquo Chinese Journal ofRock Mechanics and Engineering vol 29 no 9 pp 1807ndash18172010
[21] R Ulusay and J A Hudson The Complete ISRM SuggestedMethods for Rock Characterization Testing and Monitoring1974ndash2006 International Society for Rock Mechanics 2007
[22] P A Vermeer and R de Borst ldquoNon-associated plasticity forsoils concrete and rockrdquo Heron vol 29 3 pp 1ndash64 1984
Figure 2 The evolution of variation of axial strain increment with unloading confining pressures
the variation of strain increment of axial graduallyincreases It indicates that interaction has occurredamong cracks resulting in rapid increases of strainand the dilatancy of specimens has occurred obvi-ously in path III
53 Analysis of Dilation Characteristics In the theory ofrock mechanics the dilatancy angle 120595 is usually used todescribe the dilation characteristics Vermeer and de Borst[22] defined the dilatancy angle as follows
120595 = arcsin(120576
1015840
V
minus2120576
1015840
1+ 120576
1015840
V) (2)
where 12057610158401and 1205761015840V are the strain increment of axial and
volumetric respectivelyFigure 3 shows the evolution of dilatancy angle120595with the
variation of strain increment lateral in process of unloadingconfining pressures
(1) From Figure 3 it can be seen that the initial confiningpressure has an important influence on the dilatancyangle 120595 which decreases with the initial confiningpressure increases This indicates that the initial con-fining pressure hinders the dilatancy angle to extend
(2) The evolution of dilatancy angle first increases slowlyto about 15 times of the initial dilatancy angle thenmaintain approximate the same dilatancy angle untilthe rock failureswith 005MPas of unloading rate Asthe unloading rate adds up to 01MPas the dilatancyangle quickly enhances and reaches a limit value thendecreases a bit and ultimately reaches a fixed valueWhen the unloading rate ranges from 05MPas to1MPas the dilatancy angle reaches a limit valuemorerapidly that is 2sim5 times of the initial dilatancy anglethen reduced to a fixed level until the rock failures
(3) It is particularlyworth noting that the rate of dilatancyangle from initial value to limit value increases withthe unloading rates increases as shown in Figure 3It indicates that when the unloading rate is rapidthe strain energy quickly releases resulting in many
microcracks produced and expanded It leads to anincrease of the lateral strains occur and propagatebut the axial strains have less time to expandedgenerating the process of dilatancy angle increasesfast Then with the unloading the strain energy isconsumed by extending of microcracks the dilatancyangle decreases slowly to a stable state until the rockfailures
(4) Comparedwith the rate of dilatancy angle from initialvalue to limit value in path I and path II the rateof dilatancy angle from initial value to limit value inpath I is greater than that in path II with the sameunloading rates The result indicates that loadingof axial in path II provides more energy to rocksome microcracks expanded rapidly resulting in thedilatancy angle increasing rapidly
6 Conclusions
(1) The axial strain increases slowly and the lateral strainincreases rapidly in the process of unloading the dila-tancy of specimens occurs In path III the dilatancyof specimens is the most obvious The unloadingrates of confining pressures and initial confiningpressures increase the brittle failure characteristics ofspecimens are more obvious
(2) A description variable-variation of strain increment ispresented in this paper According to the relationshipsbetween variation of strain increment and variationof the confining pressure there are linear increases ofthe variation of strain increment of axial and lateraluntil the variation of unloading confining pressure isbetween 05 and 06 in path I The variation of strainincrement of axial is slightly larger than that of lateralat same time in path II The difference between themis affected by unloading rates In path III the variationof strain increment of axial decreases firstly and thenincreases with the variation of unloading confiningpressure increases The rule decreases firstly and thenincreases with the unloading rates increases
Shock and Vibration 7
minus01 01 03 05 07 09 11
80
70
60
50
40
30
Dlat
Path I 1205903 = 005MPas120595
(∘)
30
35
40
45
50
55
60
minus01 01 03 05 07 09
Dlat
11
Path I 1205903 = 01MPas
120595(∘
)30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path I 1205903 = 05MPas
30
40
50
60
70
80
minus01 01 03 05 07 09 11Dlat
120595(∘
)
Path I 1205903 = 1MPas
10
20
30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 005MPas
20
25
30
35
40
45
50
55
60
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 01MPas
0
10
20
30
40
50
60
70
80
minus01 01 03 05 07 09 11
Dlat
120595(∘
)
Path II 1205903 = 05MPas
1015202530354045505560
Dlat
120595(∘
)
minus01 01 03 05 07 09 11
Path II v1205903 = 1MPas
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
Figure 3 The evolution of dilatancy angle with variation of lateral strain increment
(3) According to the analysis of the evolution of dilatancyanglewith the variation of strain increment lateral theinitial confining pressure has an important influenceon the dilatancy angle 120595 which decreases with theinitial confining pressure increases The rate of dila-tancy angle from initial value to limit value increaseswith the unloading rates increases The rate of thedilatancy angle from the initial value to the limit value
in path I is greater than that in path II under the sameunloading rates
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
8 Shock and Vibration
References
[1] W Gang S Jun and W Zhong-ru ldquoDamage mechanicalanalysis of unloading failure of intact rock under complex stressstaterdquo Journal of Hehai University vol 25 no 3 pp 44ndash49 1997
[2] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission source location for cuboid monitoringnetwork without pre-measured wave velocityrdquo Transactions ofNonferrous Metals Society of China vol 25 no 1 pp 293ndash3022015
[3] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission or microseismic source location undercube monitoring networkrdquo Transactions of Nonferrous MetalsSociety of China vol 22 no 12 pp 3087ndash3094 2012
[4] L-J Dong and X-B Li ldquoA microseismicacoustic emissionsource location method using arrival times of PS waves forunknown velocity systemrdquo International Journal of DistributedSensor Networks vol 2013 Article ID 307489 8 pages 2013
[5] L-J Dong X-B Li and G Xie ldquoAn analytical solution foracoustic emission source location for known P wave velocitysystemrdquoMathematical Problems in Engineering vol 2014 Arti-cle ID 290686 6 pages 2014
[6] X Li W Cao Z Zhou and Y Zou ldquoInfluence of stress path onexcavation unloading responserdquo Tunnelling and UndergroundSpace Technology vol 42 pp 237ndash246 2014
[7] Y Ming-qing and H An-zeng ldquoTri-axial confining depressuretest of rock samplerdquo Chinese Journal of Rock Mechanics andEngineering vol 17 no 1 pp 24ndash29 1998
[8] Q-R Huang and D Huang ldquoExperimental research on affec-tion laws unloading rates on mechanical properties of Jinpingmarble under high geostressrdquoChinese Journal of RockMechanicsand Engineering vol 29 no 1 pp 21ndash33 2010
[9] L-J Dong X-B Li and K Peng ldquoPrediction of rockburstclassification using Random Forestrdquo Transactions of NonferrousMetals Society of China (English Edition) vol 23 no 2 pp 472ndash477 2013
[10] M C Torres-Suarez A Alarcon-Guzman and R Berdugo-DeMoya ldquoEffects of loading-unloading and wetting-drying cycleson geomechanical behaviors of mudrocks in the ColombianAndesrdquo Journal of Rock Mechanics and Geotechnical Engineer-ing vol 6 no 3 pp 257ndash268 2014
[11] H Q Yang Y Y Zeng Y F Lan and X P Zhou ldquoAnalysisof the excavation damaged zone around a tunnel accountingfor geostress and unloadingrdquo International Journal of RockMechanics and Mining Sciences vol 69 pp 59ndash66 2014
[12] L F Fan and L N Y Wong ldquoStress wave transmissionacross a filled joint with different loadingunloading behaviorrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 60 pp 227ndash234 2013
[13] R Q Huang and D Huang ldquoEvolution of rock cracks underunloading conditionrdquo Rock Mechanics and Rock Engineeringvol 47 no 2 pp 453ndash466 2014
[14] R Q Huang X N Wang and L S Chan ldquoTriaxial unloadingtest of rocks and its implication for rock burstrdquo Bulletin ofEngineering Geology and the Environment vol 60 no 1 pp 37ndash41 2001
[15] J Li X Chen L Dang Y Dong Z Cheng and J Guo ldquoTriaxialunloading test of sandstone after high temperaturerdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 8 pp1587ndash1595 2011
[16] M Cai ldquoInfluence of stress path on tunnel excavationresponsemdashnumerical tool selection and modeling strategyrdquo
Tunnelling andUnderground Space Technology vol 23 no 6 pp618ndash628 2008
[17] Y-T Guo C-H Yang andH-JMao ldquoMechanical properties ofJintan mine rock salt under complex stress pathsrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 56 pp 54ndash61 2012
[18] Y-T Guo C-H Yang and J-J Fu ldquoExperimental research onmechanical characteristics of salt rock under triaxial unloadingtestrdquo Rock and Soil Mechanics vol 33 no 3 pp 725ndash738 2012
[19] S-L Qiu X-T Feng J-Q Xiao and C-Q Zhang ldquoAn exper-imental study on the pre-peak unloading damage evolution ofmarblerdquoRockMechanics and Rock Engineering vol 47 no 2 pp401ndash419 2014
[20] S-L Qiu X-T Feng and C-Q Zhang ldquoExperimental researchon mechanical properties of deep-buried marble under differ-ent unloading rates of confining pressuresrdquo Chinese Journal ofRock Mechanics and Engineering vol 29 no 9 pp 1807ndash18172010
[21] R Ulusay and J A Hudson The Complete ISRM SuggestedMethods for Rock Characterization Testing and Monitoring1974ndash2006 International Society for Rock Mechanics 2007
[22] P A Vermeer and R de Borst ldquoNon-associated plasticity forsoils concrete and rockrdquo Heron vol 29 3 pp 1ndash64 1984
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
The initial confining pressure is 10MPaThe initial confining pressure is 20MPaThe initial confining pressure is 30MPa
Figure 3 The evolution of dilatancy angle with variation of lateral strain increment
(3) According to the analysis of the evolution of dilatancyanglewith the variation of strain increment lateral theinitial confining pressure has an important influenceon the dilatancy angle 120595 which decreases with theinitial confining pressure increases The rate of dila-tancy angle from initial value to limit value increaseswith the unloading rates increases The rate of thedilatancy angle from the initial value to the limit value
in path I is greater than that in path II under the sameunloading rates
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
8 Shock and Vibration
References
[1] W Gang S Jun and W Zhong-ru ldquoDamage mechanicalanalysis of unloading failure of intact rock under complex stressstaterdquo Journal of Hehai University vol 25 no 3 pp 44ndash49 1997
[2] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission source location for cuboid monitoringnetwork without pre-measured wave velocityrdquo Transactions ofNonferrous Metals Society of China vol 25 no 1 pp 293ndash3022015
[3] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission or microseismic source location undercube monitoring networkrdquo Transactions of Nonferrous MetalsSociety of China vol 22 no 12 pp 3087ndash3094 2012
[4] L-J Dong and X-B Li ldquoA microseismicacoustic emissionsource location method using arrival times of PS waves forunknown velocity systemrdquo International Journal of DistributedSensor Networks vol 2013 Article ID 307489 8 pages 2013
[5] L-J Dong X-B Li and G Xie ldquoAn analytical solution foracoustic emission source location for known P wave velocitysystemrdquoMathematical Problems in Engineering vol 2014 Arti-cle ID 290686 6 pages 2014
[6] X Li W Cao Z Zhou and Y Zou ldquoInfluence of stress path onexcavation unloading responserdquo Tunnelling and UndergroundSpace Technology vol 42 pp 237ndash246 2014
[7] Y Ming-qing and H An-zeng ldquoTri-axial confining depressuretest of rock samplerdquo Chinese Journal of Rock Mechanics andEngineering vol 17 no 1 pp 24ndash29 1998
[8] Q-R Huang and D Huang ldquoExperimental research on affec-tion laws unloading rates on mechanical properties of Jinpingmarble under high geostressrdquoChinese Journal of RockMechanicsand Engineering vol 29 no 1 pp 21ndash33 2010
[9] L-J Dong X-B Li and K Peng ldquoPrediction of rockburstclassification using Random Forestrdquo Transactions of NonferrousMetals Society of China (English Edition) vol 23 no 2 pp 472ndash477 2013
[10] M C Torres-Suarez A Alarcon-Guzman and R Berdugo-DeMoya ldquoEffects of loading-unloading and wetting-drying cycleson geomechanical behaviors of mudrocks in the ColombianAndesrdquo Journal of Rock Mechanics and Geotechnical Engineer-ing vol 6 no 3 pp 257ndash268 2014
[11] H Q Yang Y Y Zeng Y F Lan and X P Zhou ldquoAnalysisof the excavation damaged zone around a tunnel accountingfor geostress and unloadingrdquo International Journal of RockMechanics and Mining Sciences vol 69 pp 59ndash66 2014
[12] L F Fan and L N Y Wong ldquoStress wave transmissionacross a filled joint with different loadingunloading behaviorrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 60 pp 227ndash234 2013
[13] R Q Huang and D Huang ldquoEvolution of rock cracks underunloading conditionrdquo Rock Mechanics and Rock Engineeringvol 47 no 2 pp 453ndash466 2014
[14] R Q Huang X N Wang and L S Chan ldquoTriaxial unloadingtest of rocks and its implication for rock burstrdquo Bulletin ofEngineering Geology and the Environment vol 60 no 1 pp 37ndash41 2001
[15] J Li X Chen L Dang Y Dong Z Cheng and J Guo ldquoTriaxialunloading test of sandstone after high temperaturerdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 8 pp1587ndash1595 2011
[16] M Cai ldquoInfluence of stress path on tunnel excavationresponsemdashnumerical tool selection and modeling strategyrdquo
Tunnelling andUnderground Space Technology vol 23 no 6 pp618ndash628 2008
[17] Y-T Guo C-H Yang andH-JMao ldquoMechanical properties ofJintan mine rock salt under complex stress pathsrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 56 pp 54ndash61 2012
[18] Y-T Guo C-H Yang and J-J Fu ldquoExperimental research onmechanical characteristics of salt rock under triaxial unloadingtestrdquo Rock and Soil Mechanics vol 33 no 3 pp 725ndash738 2012
[19] S-L Qiu X-T Feng J-Q Xiao and C-Q Zhang ldquoAn exper-imental study on the pre-peak unloading damage evolution ofmarblerdquoRockMechanics and Rock Engineering vol 47 no 2 pp401ndash419 2014
[20] S-L Qiu X-T Feng and C-Q Zhang ldquoExperimental researchon mechanical properties of deep-buried marble under differ-ent unloading rates of confining pressuresrdquo Chinese Journal ofRock Mechanics and Engineering vol 29 no 9 pp 1807ndash18172010
[21] R Ulusay and J A Hudson The Complete ISRM SuggestedMethods for Rock Characterization Testing and Monitoring1974ndash2006 International Society for Rock Mechanics 2007
[22] P A Vermeer and R de Borst ldquoNon-associated plasticity forsoils concrete and rockrdquo Heron vol 29 3 pp 1ndash64 1984
[1] W Gang S Jun and W Zhong-ru ldquoDamage mechanicalanalysis of unloading failure of intact rock under complex stressstaterdquo Journal of Hehai University vol 25 no 3 pp 44ndash49 1997
[2] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission source location for cuboid monitoringnetwork without pre-measured wave velocityrdquo Transactions ofNonferrous Metals Society of China vol 25 no 1 pp 293ndash3022015
[3] L-J Dong and X-B Li ldquoThree-dimensional analytical solutionof acoustic emission or microseismic source location undercube monitoring networkrdquo Transactions of Nonferrous MetalsSociety of China vol 22 no 12 pp 3087ndash3094 2012
[4] L-J Dong and X-B Li ldquoA microseismicacoustic emissionsource location method using arrival times of PS waves forunknown velocity systemrdquo International Journal of DistributedSensor Networks vol 2013 Article ID 307489 8 pages 2013
[5] L-J Dong X-B Li and G Xie ldquoAn analytical solution foracoustic emission source location for known P wave velocitysystemrdquoMathematical Problems in Engineering vol 2014 Arti-cle ID 290686 6 pages 2014
[6] X Li W Cao Z Zhou and Y Zou ldquoInfluence of stress path onexcavation unloading responserdquo Tunnelling and UndergroundSpace Technology vol 42 pp 237ndash246 2014
[7] Y Ming-qing and H An-zeng ldquoTri-axial confining depressuretest of rock samplerdquo Chinese Journal of Rock Mechanics andEngineering vol 17 no 1 pp 24ndash29 1998
[8] Q-R Huang and D Huang ldquoExperimental research on affec-tion laws unloading rates on mechanical properties of Jinpingmarble under high geostressrdquoChinese Journal of RockMechanicsand Engineering vol 29 no 1 pp 21ndash33 2010
[9] L-J Dong X-B Li and K Peng ldquoPrediction of rockburstclassification using Random Forestrdquo Transactions of NonferrousMetals Society of China (English Edition) vol 23 no 2 pp 472ndash477 2013
[10] M C Torres-Suarez A Alarcon-Guzman and R Berdugo-DeMoya ldquoEffects of loading-unloading and wetting-drying cycleson geomechanical behaviors of mudrocks in the ColombianAndesrdquo Journal of Rock Mechanics and Geotechnical Engineer-ing vol 6 no 3 pp 257ndash268 2014
[11] H Q Yang Y Y Zeng Y F Lan and X P Zhou ldquoAnalysisof the excavation damaged zone around a tunnel accountingfor geostress and unloadingrdquo International Journal of RockMechanics and Mining Sciences vol 69 pp 59ndash66 2014
[12] L F Fan and L N Y Wong ldquoStress wave transmissionacross a filled joint with different loadingunloading behaviorrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 60 pp 227ndash234 2013
[13] R Q Huang and D Huang ldquoEvolution of rock cracks underunloading conditionrdquo Rock Mechanics and Rock Engineeringvol 47 no 2 pp 453ndash466 2014
[14] R Q Huang X N Wang and L S Chan ldquoTriaxial unloadingtest of rocks and its implication for rock burstrdquo Bulletin ofEngineering Geology and the Environment vol 60 no 1 pp 37ndash41 2001
[15] J Li X Chen L Dang Y Dong Z Cheng and J Guo ldquoTriaxialunloading test of sandstone after high temperaturerdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 8 pp1587ndash1595 2011
[16] M Cai ldquoInfluence of stress path on tunnel excavationresponsemdashnumerical tool selection and modeling strategyrdquo
Tunnelling andUnderground Space Technology vol 23 no 6 pp618ndash628 2008
[17] Y-T Guo C-H Yang andH-JMao ldquoMechanical properties ofJintan mine rock salt under complex stress pathsrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 56 pp 54ndash61 2012
[18] Y-T Guo C-H Yang and J-J Fu ldquoExperimental research onmechanical characteristics of salt rock under triaxial unloadingtestrdquo Rock and Soil Mechanics vol 33 no 3 pp 725ndash738 2012
[19] S-L Qiu X-T Feng J-Q Xiao and C-Q Zhang ldquoAn exper-imental study on the pre-peak unloading damage evolution ofmarblerdquoRockMechanics and Rock Engineering vol 47 no 2 pp401ndash419 2014
[20] S-L Qiu X-T Feng and C-Q Zhang ldquoExperimental researchon mechanical properties of deep-buried marble under differ-ent unloading rates of confining pressuresrdquo Chinese Journal ofRock Mechanics and Engineering vol 29 no 9 pp 1807ndash18172010
[21] R Ulusay and J A Hudson The Complete ISRM SuggestedMethods for Rock Characterization Testing and Monitoring1974ndash2006 International Society for Rock Mechanics 2007
[22] P A Vermeer and R de Borst ldquoNon-associated plasticity forsoils concrete and rockrdquo Heron vol 29 3 pp 1ndash64 1984
