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Article(id=1241089937789997689, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241089933696364783, articleNumber=null, orderNo=null, doi=10.3963/j.issn.1001-487X.2023.02.005, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1674662400000, receivedDateStr=2023-01-26, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773828499505, onlineDateStr=2026-03-18, pubDate=1685548800000, pubDateStr=2023-06-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773828499505, onlineIssueDateStr=2026-03-18, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773828499505, creator=13701087609, updateTime=1773828499505, updator=13701087609, issue=Issue{id=1241089933696364783, tenantId=1146029695717560320, journalId=1240670690148397066, year='2023', volume='40', issue='2', pageStart='1', pageEnd='229', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773828498529, creator=13701087609, updateTime=1773828588505, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241090311141782020, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241089933696364783, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241090311141782021, tenantId=1146029695717560320, journalId=1240670690148397066, issueId=1241089933696364783, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=29, endPage=41, ext={EN=ArticleExt(id=1241089938083598977, articleId=1241089937789997689, tenantId=1146029695717560320, journalId=1240670690148397066, language=EN, title=Study on Cyclic Impact Failure Characteristics of Quartz Sandstone under Medium Strain Rate, columnId=1240702071733801442, journalTitle=Blasting, columnName=THEORETICAL AND TECHNOLOGICAL EXPLORATION, runingTitle=null, highlight=null, articleAbstract=

Quartz sandstone samples were tested under cyclic impact loadings by the drop weight impact test equipment to study its mechanical properties and failure process under medium strain rates. Three specimens were selected at each impact height of 0.3~0.6 m, and each specimen was subjected to 8 cycles of impact with medium strain rates of 26.33 s-1, 29.7 s-1, 32.03 s-1 and 35.17 s-1, respectively. Then, the influence of cyclic loading times on the dynamic compressive strength, elastic modulus and energy efficiency of quartz sandstone were discussed. The results show that under different medium strain rates, the dynamic compressive strength of the specimens under the impact loading of the 8th cycle is about 13 MPa, which is lower than that of the first cycle. During the process, the resistance to deformation is weakened, and the elastic modulus is significantly reduced. The dynamic compressive strength of the specimens has a positively correlation with the elastic modulus. From the perspective of energy, the dissipated energy, energy efficiency and unit volume dissipated energy of the specimen are improved after 8 cycles of impact loading. The effect is most obvious when the impact energy is 70.27 J, the dissipated energy of rock is increased by 6 J, the energy efficiency is increased by 8.8%, and the unit volume dissipated energy is increased by 50%. For fracture fractal, the fracture morphology of rock under medium strain rates includes splitting failure, edge collapse failure, block failure and crushing failure. When the strain rate increases from 26.33 s-1 to 35.17 s-1, the characteristic value of the average particle size of the sample fragments decreases from 24.49 mm to 21.15 mm. The fractal dimension increases from 1.07 to 1.75 linearly.

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利用落锤冲击试验设备对石英砂岩进行循环冲击加载，在0.3~0.6 m各冲击高度下均选取3个试样，每个试样进行8次循环冲击，应变率分别选取为26.33 s-1、29.7 s-1、32.03 s-1和35.17 s-1，研究中应变率下石英砂岩受循环冲击加载下的力学性能。通过对试验数据进行分析总结，讨论循环加载次数对石英砂岩动态抗压强度、弹性模量和能量效率的影响以及中应变率下石英砂岩的破坏过程。结果表明：不同中应变率条件下，第8次循环冲击加载作用下试件的动态抗压强度均较第一次循环冲击减小约13 MPa，抵抗变形能力减弱，同时弹性模量明显降低，试件动态抗压强度与弹性模量表现出正向相关关系；从能量角度研究，在8次循环冲击加载后，试样耗散能、能量效率、单位体积耗散能均有提高，其中在冲击能为70.27 J效果最为明显，岩石耗散能提高6 J、能量效率提高8.8%、单位体积耗散能增幅50%；从破碎分形角度进行研究，中应变率下岩石破碎形态有劈裂破坏、边缘崩落破坏、块状破坏和粉碎破坏，当应变率由26.33 s-1增大至35.17 s-1时，试样碎块块度平均粒径特征值由24.49 mm减小到21.15 mm；分形维数由1.07增加至1.75，岩石分形维数呈线性增大趋势。

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王军祥（1985-），男，博士、副教授，主要从事岩石力学与工程方面的教学和科研工作，（E-mail）。

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王军祥（1985-），男，博士、副教授，主要从事岩石力学与工程方面的教学和科研工作，（E-mail）。

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王军祥（1985-），男，博士、副教授，主要从事岩石力学与工程方面的教学和科研工作，（E-mail）。

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articleId=1241089937789997689, language=CN, label=图11, caption=平均粒径特征值-应变率, figureFileSmall=Vjk2DqlRhj9n3Uz3FPyfAw==, figureFileBig=omz08F6zMvKjeYMMQ/LTsQ==, tableContent=null), ArticleFig(id=1241089953334088170, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=EN, label=Fig. 12, caption=Rock lg x0-lg[M (x0）/M] fitting curve, figureFileSmall=lbdsAaBIcErPBv+drO6Bnw==, figureFileBig=oAD8leX+EP85WK45BDcDtw==, tableContent=null), ArticleFig(id=1241089954877592051, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=CN, label=图12, caption=岩石lg x0-lg[M（x0）/M]拟合曲线, figureFileSmall=lbdsAaBIcErPBv+drO6Bnw==, figureFileBig=oAD8leX+EP85WK45BDcDtw==, tableContent=null), ArticleFig(id=1241089955032781308, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=EN, label=Fig. 13, caption=Rock fractal dimension-strain rate, figureFileSmall=8syNXvGYkKNSH1dE80C0Pg==, figureFileBig=4WcQ+wnX0wq5as4DEEAFVw==, tableContent=null), ArticleFig(id=1241089955133444610, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=CN, label=图13, caption=岩石分形维数-应变率, figureFileSmall=8syNXvGYkKNSH1dE80C0Pg==, figureFileBig=4WcQ+wnX0wq5as4DEEAFVw==, tableContent=null), ArticleFig(id=1241089955213136393, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=EN, label=Table 1, caption=

Test data of representative samples

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试样编号冲击高度/m循环冲击次数应变率/s-1平均应变率/s-1动态抗压强度/MPa最大应变
SH1-20.3123.3826.3368.390.0034
225.6070.300.0037
326.3370.830.0041
427.6769.170.0041
527.7869.220.0042
625.4568.840.0038
725.4465.950.0037
828.9860.230.0047
SH2-20.4128.0429.7081.960.0037
229.1081.860.0039
329.2980.750.0039
429.4580.040.0043
530.3178.280.0042
630.7879.920.0042
729.2675.750.0039
831.3466.720.0044
SH3-10.5130.3632.0391.380.0036
230.7991.430.0036
331.0591.320.0037
431.1490.720.0040
531.3689.930.0041
633.0790.040.0042
733.5688.050.0043
834.9478.160.0045
SH4-30.6132.2935.17104.720.0035
232.96103.740.0036
333.30103.750.0037
434.40102.960.0037
534.92103.020.0039
636.71103.020.0040
737.2299.660.0042
839.5492.760.0045
), ArticleFig(id=1241089955305411084, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=CN, label=表1, caption=

代表性试样的试验结果数据

, figureFileSmall=null, figureFileBig=null, tableContent=
试样编号冲击高度/m循环冲击次数应变率/s-1平均应变率/s-1动态抗压强度/MPa最大应变
SH1-20.3123.3826.3368.390.0034
225.6070.300.0037
326.3370.830.0041
427.6769.170.0041
527.7869.220.0042
625.4568.840.0038
725.4465.950.0037
828.9860.230.0047
SH2-20.4128.0429.7081.960.0037
229.1081.860.0039
329.2980.750.0039
429.4580.040.0043
530.3178.280.0042
630.7879.920.0042
729.2675.750.0039
831.3466.720.0044
SH3-10.5130.3632.0391.380.0036
230.7991.430.0036
331.0591.320.0037
431.1490.720.0040
531.3689.930.0041
633.0790.040.0042
733.5688.050.0043
834.9478.160.0045
SH4-30.6132.2935.17104.720.0035
232.96103.740.0036
333.30103.750.0037
434.40102.960.0037
534.92103.020.0039
636.71103.020.0040
737.2299.660.0042
839.5492.760.0045
), ArticleFig(id=1241089955401880084, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=EN, label=Table 2, caption=

Statistics of rock dissipated energy

, figureFileSmall=null, figureFileBig=null, tableContent=
试样编号冲击能/J循环冲击次数耗散能/J能量效率/%单位体积耗散能/（J·cm-3）
SH1-270.27111.6416.560.12
211.9717.030.12
312.8618.300.13
412.9018.360.13
513.0018.500.13
614.4520.560.15
716.8323.950.17
817.8225.360.18
SH2-293.69121.3222.760.22
221.7823.250.22
322.4423.950.23
422.7324.260.23
522.8124.350.23
623.0324.580.23
723.5725.160.24
824.2125.840.25
SH3-1117.11123.5520.110.24
224.1220.600.25
324.2720.720.25
424.3120.760.25
524.621.010.25
625.0421.380.26
725.3521.650.26
825.9722.180.26
SH4-3140.53129.1320.730.30
229.2720.830.30
329.2820.840.30
429.7521.170.30
530.3621.600.31
630.4421.660.31
731.7822.610.32
832.9623.450.34
), ArticleFig(id=1241089955494154778, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=CN, label=表2, caption=

岩石耗散能统计表

, figureFileSmall=null, figureFileBig=null, tableContent=
试样编号冲击能/J循环冲击次数耗散能/J能量效率/%单位体积耗散能/（J·cm-3）
SH1-270.27111.6416.560.12
211.9717.030.12
312.8618.300.13
412.9018.360.13
513.0018.500.13
614.4520.560.15
716.8323.950.17
817.8225.360.18
SH2-293.69121.3222.760.22
221.7823.250.22
322.4423.950.23
422.7324.260.23
522.8124.350.23
623.0324.580.23
723.5725.160.24
824.2125.840.25
SH3-1117.11123.5520.110.24
224.1220.600.25
324.2720.720.25
424.3120.760.25
524.621.010.25
625.0421.380.26
725.3521.650.26
825.9722.180.26
SH4-3140.53129.1320.730.30
229.2720.830.30
329.2820.840.30
429.7521.170.30
530.3621.600.31
630.4421.660.31
731.7822.610.32
832.9623.450.34
), ArticleFig(id=1241089955603206692, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=EN, label=Table 3, caption=

Mass statistics of fragments of each aperture (unit: g)

, figureFileSmall=null, figureFileBig=null, tableContent=
试样编号20 mm10 mm5 mm2 mm0 mm总计
SH1-1239.127.661.240.450.32248.79
SH1-2236.579.960.830.190.29247.84
SH1-3246.610000246.61
SH2-1219.4514.672.133.780.69240.72
SH2-2223.4915.474.781.871.19246.80
SH2-3225.7810.776.222.860.22245.85
SH3-1219.1711.539.254.982.82247.75
SH3-2210.4515.767.679.324.97248.17
SH3-3220.5613.777.946.252.00250.52
SH4-1173.8034.9814.799.577.86241.00
SH4-2183.6929.6515.036.985.44240.79
SH4-3177.2233.6114.248.586.08239.73
), ArticleFig(id=1241089955716452906, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=CN, label=表3, caption=

各孔径碎块质量统计表（单位：g）

, figureFileSmall=null, figureFileBig=null, tableContent=
试样编号20 mm10 mm5 mm2 mm0 mm总计
SH1-1239.127.661.240.450.32248.79
SH1-2236.579.960.830.190.29247.84
SH1-3246.610000246.61
SH2-1219.4514.672.133.780.69240.72
SH2-2223.4915.474.781.871.19246.80
SH2-3225.7810.776.222.860.22245.85
SH3-1219.1711.539.254.982.82247.75
SH3-2210.4515.767.679.324.97248.17
SH3-3220.5613.777.946.252.00250.52
SH4-1173.8034.9814.799.577.86241.00
SH4-2183.6929.6515.036.985.44240.79
SH4-3177.2233.6114.248.586.08239.73
), ArticleFig(id=1241089955825504817, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=EN, label=Table 4, caption=

Fragment quality score statistics table/%

, figureFileSmall=null, figureFileBig=null, tableContent=
试样编号应变率20 mm10 mm5 mm2 mm0 mm
SH1-126.33 s-196.113.080.500.180.001
SH1-295.454.020.330.080.001
SH1-3100.000.000.000.000.000
SH2-129.7 s-191.166.090.881.570.003
SH2-290.566.271.940.760.005
SH2-391.844.382.531.160.001
SH3-132.03 s-188.464.653.732.010.011
SH3-284.806.353.093.760.020
SH3-388.045.503.172.490.008
SH4-135.17 s-172.1214.516.143.970.033
SH4-276.2912.316.242.900.023
SH4-373.9214.025.943.580.025
), ArticleFig(id=1241089955896807989, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=CN, label=表4, caption=

碎块质量分数统计表/%

, figureFileSmall=null, figureFileBig=null, tableContent=
试样编号应变率20 mm10 mm5 mm2 mm0 mm
SH1-126.33 s-196.113.080.500.180.001
SH1-295.454.020.330.080.001
SH1-3100.000.000.000.000.000
SH2-129.7 s-191.166.090.881.570.003
SH2-290.566.271.940.760.005
SH2-391.844.382.531.160.001
SH3-132.03 s-188.464.653.732.010.011
SH3-284.806.353.093.760.020
SH3-388.045.503.172.490.008
SH4-135.17 s-172.1214.516.143.970.033
SH4-276.2912.316.242.900.023
SH4-373.9214.025.943.580.025
), ArticleFig(id=1241089956018442811, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=EN, label=Table 5, caption=

Logarithm table of fractal parameter calculation results

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特征尺寸x0/mm25157.53.51
lg x01.41.180.880.540
lg[M（x0）/M]26.33 s-1-0.02-1.40-2.48-3.12-2.93
29.70 s-1-0.04-1.20-1.71-2.12-2.32
32.03 s-1-0.05-1.33-1.43-1.70-1.94
35.17 s-1-0.13-0.85-1.23-1.45-1.60
), ArticleFig(id=1241089956127494723, tenantId=1146029695717560320, journalId=1240670690148397066, articleId=1241089937789997689, language=CN, label=表5, caption=

分形参数计算结果对数表

, figureFileSmall=null, figureFileBig=null, tableContent=
特征尺寸x0/mm25157.53.51
lg x01.41.180.880.540
lg[M（x0）/M]26.33 s-1-0.02-1.40-2.48-3.12-2.93
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中应变率下石英砂岩循环冲击破坏特性研究
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王军祥 1 , 马宝龙 1 , 李树昊 1 , 李林 2 , 寇海军 2 , 孙港 1
爆破 | 理论与技术探索 2023,40(2): 29-41
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爆破 | 理论与技术探索 2023, 40(2): 29-41
中应变率下石英砂岩循环冲击破坏特性研究
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王军祥1 , 马宝龙1, 李树昊1, 李林2, 寇海军2, 孙港1
作者信息
  • 1.沈阳工业大学 建筑与土木工程学院，沈阳 110870
  • 2.中铁十九局集团 第五工程有限公司，大连 116100

    • 王军祥（1985-），男，博士、副教授，主要从事岩石力学与工程方面的教学和科研工作，（E-mail）。

Study on Cyclic Impact Failure Characteristics of Quartz Sandstone under Medium Strain Rate
Jun-xiang WANG1 , Bao-long MA1, Shu-hao LI1, Lin LI2, Hai-jun KOU2, Gang SUN1
Affiliations
  • 1.School of Architecture and Civil Engineering, Shenyang University of Technology, Shenyang 110870, China
  • 2.China Railway 19th Bureau Group Fifth Engineering Co., Ltd., Dalian 116100, China
出版时间: 2023-06-01 doi: 10.3963/j.issn.1001-487X.2023.02.005
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摘要
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利用落锤冲击试验设备对石英砂岩进行循环冲击加载，在0.3~0.6 m各冲击高度下均选取3个试样，每个试样进行8次循环冲击，应变率分别选取为26.33 s-1、29.7 s-1、32.03 s-1和35.17 s-1，研究中应变率下石英砂岩受循环冲击加载下的力学性能。通过对试验数据进行分析总结，讨论循环加载次数对石英砂岩动态抗压强度、弹性模量和能量效率的影响以及中应变率下石英砂岩的破坏过程。结果表明：不同中应变率条件下，第8次循环冲击加载作用下试件的动态抗压强度均较第一次循环冲击减小约13 MPa，抵抗变形能力减弱，同时弹性模量明显降低，试件动态抗压强度与弹性模量表现出正向相关关系；从能量角度研究，在8次循环冲击加载后，试样耗散能、能量效率、单位体积耗散能均有提高，其中在冲击能为70.27 J效果最为明显，岩石耗散能提高6 J、能量效率提高8.8%、单位体积耗散能增幅50%；从破碎分形角度进行研究，中应变率下岩石破碎形态有劈裂破坏、边缘崩落破坏、块状破坏和粉碎破坏，当应变率由26.33 s-1增大至35.17 s-1时，试样碎块块度平均粒径特征值由24.49 mm减小到21.15 mm；分形维数由1.07增加至1.75，岩石分形维数呈线性增大趋势。

中应变率  /  循环冲击  /  破坏特性

Quartz sandstone samples were tested under cyclic impact loadings by the drop weight impact test equipment to study its mechanical properties and failure process under medium strain rates. Three specimens were selected at each impact height of 0.3~0.6 m, and each specimen was subjected to 8 cycles of impact with medium strain rates of 26.33 s-1, 29.7 s-1, 32.03 s-1 and 35.17 s-1, respectively. Then, the influence of cyclic loading times on the dynamic compressive strength, elastic modulus and energy efficiency of quartz sandstone were discussed. The results show that under different medium strain rates, the dynamic compressive strength of the specimens under the impact loading of the 8th cycle is about 13 MPa, which is lower than that of the first cycle. During the process, the resistance to deformation is weakened, and the elastic modulus is significantly reduced. The dynamic compressive strength of the specimens has a positively correlation with the elastic modulus. From the perspective of energy, the dissipated energy, energy efficiency and unit volume dissipated energy of the specimen are improved after 8 cycles of impact loading. The effect is most obvious when the impact energy is 70.27 J, the dissipated energy of rock is increased by 6 J, the energy efficiency is increased by 8.8%, and the unit volume dissipated energy is increased by 50%. For fracture fractal, the fracture morphology of rock under medium strain rates includes splitting failure, edge collapse failure, block failure and crushing failure. When the strain rate increases from 26.33 s-1 to 35.17 s-1, the characteristic value of the average particle size of the sample fragments decreases from 24.49 mm to 21.15 mm. The fractal dimension increases from 1.07 to 1.75 linearly.

medium strain rate  /  cyclic shock  /  failure behavior
王军祥, 马宝龙, 李树昊, 李林, 寇海军, 孙港. 中应变率下石英砂岩循环冲击破坏特性研究. 爆破, 2023 , 40 (2) : 29 -41 . DOI: 10.3963/j.issn.1001-487X.2023.02.005
Jun-xiang WANG, Bao-long MA, Shu-hao LI, Lin LI, Hai-jun KOU, Gang SUN. Study on Cyclic Impact Failure Characteristics of Quartz Sandstone under Medium Strain Rate[J]. Blasting, 2023 , 40 (2) : 29 -41 . DOI: 10.3963/j.issn.1001-487X.2023.02.005
正文
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岩石属于天然脆性材料，其动态力学性质的变化规律通常与应变率有很强的关系，动态抗压强度、峰值应变、耗散能与分形维数等重要的参数均会同岩石应变率的变化而发生改变[1-3]。
近年来，许多学者对岩石力学特性进行了广泛的研究，周永强等总结描述了岩石材料强度和模量在不同应变率下的动态增强因子模型的基本类型[4]。苏宏明等对中低应变率加载下弱胶结软岩的动力学特性进行了研究[5]，认为在低应变率加载下，水对红砂岩的动态强度起强化作用。李增等对中低应变率下砂岩的动力特性进行了试验研究[6]，认为中低应变率下岩石的吸收总能量和弹性应变能随变形演化规律基本一致。LI等利用改进的SHPB试验装置对绿色砂岩进行反复冲击压缩试验[7]，研究了材料的声学特性、耗散能、变形特性和微观结构演变。BRAUNAGEL M J等利用SHPB试验装置对花岗岩在循环加载过程中的动态抗压强度以及破坏机理进行研究[8]，认为花岗岩的强度随加载速度的增加而增加，在极快的加载速度下花岗岩的破坏由简单断裂转变为破碎状态。余永强等结合SHPB试验装置分析了冲击荷载下煤系砂岩的应变率效应及能量耗散特征[9]。闫广斌研究了不同应变率对花岗岩峰值应力、峰值应变以及破坏规律的影响[10]。于洋等利用改进的SHPB试验装置对砂岩试样进行循环冲击试验[11]，分析了循环冲击次数对岩石动态强度的影响。采用落锤冲击试验机对岩石进行试验，针对石英砂岩在中应变率下的破坏特性进行研究，进一步分析中应变率条件下，循环冲击荷载对石英砂岩动态抗压强度、弹性模量、能量以及破坏特性的影响。
1 循环冲击试验方案
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1.1 落锤冲击试验机及技术原理
本试验采用XJL-98型落锤冲击试验机，其主要由冲击试验平台、电器柜和控制仪表等组成，如图1所示。落锤锤头重量为23.9 kg，锤头为圆柱体且与试样接触方式为面接触，锤体可以增加砝码，落锤锤头上装配有力传感器。
1.2 试样制备及基本力学参数
试样取自辽宁省阜新市某隧道工程现场，以石英砂岩作为本次试验的研究对象，采用线切割的方式将岩块加工成圆柱体试样共计49个，如图2所示，加工后试样尺寸为直径50 mm，高50 mm。试样两端及侧面用砂纸仔细打磨，直到试样外表面光滑无突起，表面和圆周面的不平整度小于0.02 mm。
1.3 循环冲击试验加载过程
落锤循环冲击高度设定为0.3 m、0.4 m、0.5 m和0.6 m，每种循环冲击高度3个试样，分别进行8次循环冲击。试验时在控制系统中输入冲击高度和锤体重量，电机控制锤体升至冲击高度使其沿竖直导轨近似自由落体运动冲击试样，试样应变的数据信号由粘贴在试样轴向方向的应变片采集，传感器受到冲击力反馈后记录冲击力的数据信号，并通过动态信号分析仪采集及处理，最后传输到系统界面。
2 岩石动态力学特性分析
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通过对冲击试验中得到的数据进行处理，将代表性试样的试验结果统计见表1所示，代表性试样是指在每组试验3个试样中，经过8次冲击后动态抗压强度值最接近平均值的试样。
2.1 岩石应力-应变曲线特征分析
由表1看出试样在每次循环冲击下应变率相差较小，因此取8次循环冲击下应变率的均值作为试样应变率，在0.3~0.6 m冲击高度下试样应变率分别为26.33 s-1、29.7 s-1、32.03 s-1和35.17 s-1，其值均小于50 s-1属于中应变率。由图3可见，在曲线上只能直观表现出三个阶段，即弹性变形阶段，应力-应变曲线基本上呈线性关系；裂隙发展阶段，试样内部裂隙不断延伸扩展，出现宏观裂隙；破坏阶段，试样卸载产生明显破碎，应力-应变曲线出现了回弹现象。
2.2 岩石动态抗压强度、弹性模量与循环冲击次数关系
在中应变率下石英砂岩试样的动态抗压强度、弹性模量与循环冲击次数的关系如图4所示。在26.33~35.17 s-1应变率下，随着循环冲击次数的增多，试样的动态抗压强度呈下降趋势。32.03 s-1与35.17 s-1应变率下，试样最后一次冲击后动态抗压强度比第一次冲击时动态抗压强度降低了约13 MPa。说明试样动态抗压强度对应变率变化十分敏感，表现出很强的应变率效应，试样应变率越大，试样越容易破坏，同时增加循环冲击次数也会使试样变得更脆弱。试样弹性模量在26.33 s-1与29.70 s-1应变率下无明显规律性变化，当应变率增大后，随循环冲击次数增多，试样弹性模量逐渐减小，抵抗变形能力减弱，试样动态抗压强度越低，弹性模量就越小，弹性模量与动态抗压强度表现出正相关关系。
2.3 岩石冲击力时程与循环冲击次数的关系
图5为石英砂岩试样冲击力时程与循环冲击次数曲线。从图中可以看出，冲击荷载作用在试样上的时间均在2.0 ms以上，随着应变率的增加，冲击荷载作用在试样上的时间逐渐减少；当应变率为32.03 s-1与35.17 s-1时，冲击荷载作用在试样上的时间基本相同。在8次循环冲击荷载作用下，可明显看出前7次冲击时试样所受的冲击力大致相同，均在小范围内浮动，此时试样虽然已经开裂，但并未完全破坏，还可继续承载；进行第8次冲击时试样所受冲击力急剧减小，此时试样有明显碎块脱落直至完全破坏。
2.4 岩石应变时程与循环冲击次数的关系
图6给出了石英砂岩试样在不同应变率下的应变时程曲线，从图中可以直观看出不同应变率下试样的应变时程曲线走势大致相同。在26.33~35.17 s-1应变率下，试样在最后一次冲击时的最大应变均大于第一次冲击时的应变，增幅最大达38%。以能量角度分析，在此过程中试样持续吸收冲击能量，并将所吸收的能量用于裂隙扩展，从而导致试样应变增大。在32.03 s-1与35.17 s-1的应变率下，随着冲击次数增加，试样应变增大得更为明显，说明在较高的应变率下试样的闭合性随冲击次数的增加逐渐增强。
3 岩石能量特性分析
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3.1 能量转化关系与计算方法
落锤冲击试验中，冲击能来自落锤的重力势能，随着锤体的下落，重力对锤体做功并将其重力势能转化为锤体的动能；在锤体与试样接触前，锤体的重力势能全部转化为动能，然后通过冲击试样对其做功。在锤体与试样冲击过程中，总能量分为两部分，一部分能量被锤体、垫片和力传感器所吸收，另一部分能量转化为冲击力对试样做功。冲击力对试块所做的功可由冲击力-位移曲线积分得到。计算岩石的冲击能、耗散能、能量效率以及单位体积耗散能的方法如下
式中：m为落锤质量；g为重力加速度；h为冲击高度；P（t）为岩石冲击力-位移的函数积分；V为岩石试样体积。
将试验所得数据进行计算与统计，结果见表2所示。
3.2 岩石耗散能、能量效率与循环冲击次数的关系
图7所示为中应变率下石英砂岩试样耗散能、能量效率随循环冲击次数变化规律。由图可知，随着循环冲击次数的增加，试样耗散能呈增大的变化趋势，但锤体下落所携带的冲击能并不能完全被试样吸收。同时试样的耗散能在冲击能中的比例并不是固定不变的，这与试样内部裂隙在每次受冲击后均有不同程度扩展有关，裂隙扩展速度越快，试样耗散能就越大。在试样所受不同冲击能条件下，试样承受的冲击力与变形的差异较大，但耗散能与循环冲击次数之间的变化规律还是相同的。
由表2可知，在冲击能为70.27 J、93.69 J、117.11 J和140.53 J的循环冲击下，试样能量效率分别为16.56%~25.36%、22.76%~25.84%、20.11%~22.18%和20.73%~23.45%，随着循环冲击次数的增加，试样能量效率呈增大趋势，较多的冲击次数有利于能量效率的提高。试样受多次冲击后，内部损伤活动加剧，冲击过程中试样发生较大变形，导致耗散能增大，能量效率升高。故循环冲击次数是影响试样耗散能和能量效率的重要因素。
3.3 岩石单位体积耗散能、动态抗压强度与循环冲击次数的关系
图8为中应变率下石英砂岩试样单位体积耗散能、动态抗压强度与循环冲击次数的关系图。由图可知，落锤冲击能量相同条件下，随着循环冲击次数的增加，石英砂岩试样的动态抗压强度与单位体积耗散能呈负相关，单位体积耗散能越大，岩石动态抗压强度越小。在试验过程中，每次冲击时岩石的内部结构损伤都会加重，而每次冲击时的冲击能都相同，用于裂隙扩展的耗散能增多，而岩石单位体积耗散能同耗散能的变化规律一致，导致岩石单位体积耗散能增大，动态抗压强度逐渐减低。在冲击能为70.27 J时，岩石单位体积耗散能随冲击次数变化幅度较大，由0.12 J/cm-3增大至0.18 J/cm-3，增幅为50%；其它三种冲击能量下，岩石单位体积耗散能变化幅度较小，较于稳定。说明在冲击能较小且冲击次数少时，岩石裂隙扩展速度较慢，具有一定的抵抗变形能力，随着冲击次数增加，这种抵抗变形的能力突然下降，岩石破坏程度加剧，导致岩石耗散能增大，从而引起单位体积耗散能增多。
4 岩石破碎分形分析
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4.1 岩石宏观破碎形态分析
图9为石英砂岩试样在中应变率下循环冲击破碎形态，每个应变率下使用3个试样，破碎形态对比如图所示。当应变率为26.33 s-1与29.7 s-1时，试样破碎碎块的尺寸较大，碎块数量较少。当应变率为32.03 s-1时，试样破碎更严重，大尺寸碎块数量逐渐减小，碎块逐渐成粉碎状。最后应变率为35.17 s-1时，试样已经破碎成非常小的碎片，同时伴随部分碎片崩出，破碎程度明显高于前三种应变率。说明应变率越大，试样破碎过程中吸收的冲击荷载就越大，试样内部形成的破裂面越多，因此试样的破碎碎块尺寸逐渐减小。从破碎特征方面分析，当应变率为26.33 s-1时试样表现为劈裂破坏，随着应变率逐渐增大至35.17 s-1，试样依次呈现劈裂破坏、块状破碎、粉碎破坏形态。
4.2 岩石破碎分形维数分析
岩石破碎的模拟方式可采用分形几何模型进行分析，主要包括Koch曲线、Cantor集合和Menger海绵[12]，这些模型是由学者构造的，具有严格自相似性，随后Steacy将Menger海绵进一步推广，提出了颗粒破碎的分形模型。通过颗粒破碎的分形几何模型，可以看出岩石的破碎过程在理论上具有自相似性，但是实际上岩石机械破碎过程中每次破碎结果是随机的，在试验前破碎概率和相似比是未知的，需要通过分形的方法深入了解岩石破碎演化的内在规律。
在冲击试验中，岩石被冲击破碎后会产生大量碎块，针对碎块块度分布的研究，众多学者提出多种计算方法[13,14]，其中罗仁-拉姆勒（Rosin-Rammler）分布函数成为应用最多的计算方法，其计算公式为
式中：x为粒度，mm；x0为粒度模数（特征尺寸），由颗粒级配分配曲线筛下累计质量为岩石碎块总质量一半时的“筛孔尺寸”求得，mm；b为分布参数。同时，，式中M（x）为直径小于粒度x的碎块累积质量，M为碎块总质量，将上述两式结合得到
则由式（6）和（7）计算破碎块度分形维数D为
另一种计算破碎块度分形维数的方法为
N为质量大于等于M的碎块数，M为碎块质量，Mmax为最大碎块质量，N0为最大质量是Mmax的碎块数，a为质量-粒度分布指数。
则根据式（9）所计算的分形维数D为
计算碎块块度分布需要利用不同孔径筛对试样破坏后的碎块进行筛分，试验采用标准筛把碎块分为0~2 mm、2~5 mm、5~10 mm、10~20 mm和>20 mm五种粒级。并使用电子秤称量每种孔径下的碎块质量，统计结果见表3。
为进一步分析试样在中应变率下破碎块度分布规律，用各孔径筛分质量除以总质量等于质量分数来表示各粒级筛分下破碎块度分布情况，统计结果见表4。采用为2~20 mm的标准筛对碎块进行筛分，将代表性石英砂岩试样各筛孔径上剩余碎块的质量转换成各筛孔径下碎块的筛下累计百分含量，得到试样在不同应变率下的碎块块度分布曲线，如图10所示。在中应变率下石英砂岩试样受冲击破碎后，碎块粒径大于20 mm占比均在70%以上，随着应变率由26.33 s-1增大至35.17 s-1时，碎块粒径大于20 mm的占比由95.45%下降至73.92%，碎块粒径在5 mm及以下的块度分布几乎没有变化。为了进一步分析试样破坏后块度分布情况，采用平均破碎块度特征值来表示冲击试验中试样破碎程度。
计算式如下
式中：ds为试样破碎平均粒径特征值；di为不同筛径下试样粒径；xi为粒径为di时，对应粒径质量分数。
根据式（11）计算中应变率下石英砂岩试样碎块的平均粒径特征值，为了直观地分析应变率对石英砂岩试样破坏程度的影响规律，图11给出试样碎块块度平均粒径特征值ds随应变率的变化关系。
由图11可以看出，应变率由26.33 s-1增大至35.17 s-1时，试样碎块块度平均粒径特征值随应变率的增大而减小，由24.49 mm减小到21.15 mm，降幅为13.64%。平均粒径特征值与应变率拟合曲线拟合度较高且呈线性关系，表现出明显的应变率效应。若碎块块度平均粒径特征值越小，则说明试样破碎程度越高，碎块越粉碎。
4.3 岩石分形维数与应变率的关系
为了更具体表达石英砂岩试样在中应变率下碎块破碎块度分形变化规律，通过计算得到石英砂岩试样筛分粒径对应的质量统计，得到M（x0）/M的值，然后再与特征尺寸x0共同取对数，计算结果如表5所示。根据表5绘制石英砂岩试样的lg x0-lg[M（x0）/M]双对数曲线，再进行拟合，结果如图12所示。
从图12中可知，石英砂岩试样的lg x0-lg[M（x0）/M]拟合曲线具有一定规律，并且其碎块筛下累计质量的百分含量与筛孔尺寸在双对数坐标系中具有良好的拟合关系，拟合度R2均在0.85以上，拟合度较高。同时结合式（11）~（12）计算试样分形维数并将分形维数与应变率关系绘制如图13。
由图13可知，在应变率为26.33~35.17 s-1时，石英砂岩试样的分形维数在1.07~1.75之间。试样分形维数与应变率之间存在高度线性拟合关系，拟合度R2=0.98235，岩石的分形维数随应变率的增大而增加，由1.07增加至1.75，增幅为64%。由于分形维数可以表征试样的破碎程度，若破碎后大尺寸碎块占比高，则分形维数会较大些，同时也说明试样破碎程度较低，由此可知试样在较高的应变率下分形维数会增大，小尺寸碎块占比会增加，试样破碎形态越会呈粉碎状。
5 结论
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采用落锤冲击试验机对石英砂岩进行中应变率冲击试验，分别从动力特性、能量耗散和破碎分形角度进行分析，主要结论如下：
（1）应变率一定时，随循环冲击次数增加，岩石动态抗压强度降低，应变整体呈增大趋势。随着应变率的增加，冲击力作用在岩石上的时间逐渐减少，岩石发生破坏的速度加快。
（2）在对石英砂岩进行循环冲击加载试验过程中，在冲击能较小且冲击次数少时，岩石裂隙扩展速度较慢，具有一定的抵抗变形能力，随着循环冲击次数的增加，岩石耗散能、能量效率均增大，裂隙扩展速度加快，岩石破碎程度加剧；但动态抗压强度降低，岩石抵抗冲击变形的能力减弱。
（3）岩石碎块块度平均粒径特征值随着应变率的增大减小，相反，分形维数则增大且拟合曲线呈一次函数关系，同时岩石内部形成较多破裂面，破碎形态由劈裂破坏逐渐转变为粉碎状破坏形态，证明分形维数可反映岩石破坏程度。
基金
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  • 国家自然科学基金(51974187)
  • 辽宁省自然科学基金(2019-MS-242)
  • 辽宁省教育厅重点攻关项目(LZGD2020004)
文献
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2023年第40卷第2期
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doi: 10.3963/j.issn.1001-487X.2023.02.005
  • 接收时间：2023-01-26
  • 首发时间：2026-03-18
  • 出版时间：2023-06-01
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  • 收稿日期：2023-01-26
基金
国家自然科学基金(51974187)
辽宁省自然科学基金(2019-MS-242)
辽宁省教育厅重点攻关项目(LZGD2020004)
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    1.沈阳工业大学 建筑与土木工程学院，沈阳 110870
    2.中铁十九局集团 第五工程有限公司，大连 116100
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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