岩溶地区石灰岩疲劳特性试验研究及工程应用
|
摘要
目前,国内外对不同载荷条件下岩石疲劳力学特性研究相对滞后,尤其缺乏对岩溶石灰岩的疲劳特性和损伤演化规律的系统研究。鉴于岩溶铁路隧道与溶洞(腔)间围岩长期稳定性分析的需要,本文依托国家自然基金项目,以宜昌万州铁路隧道石灰岩为研究对象,采用文献调查、室内试验、理论分析和数值模拟相结合的研究方法,系统的研究了石灰岩在静力学范围内的应变率效应；探索了不同载荷条件下石灰岩疲劳力学特性；建立了考虑多因素影响的石灰岩疲劳寿命预测模型和疲劳损伤演化模型,并将其应用于弹塑性数值计算中。为考虑岩石疲劳损伤的岩溶隧道围岩长期稳定性分析提供了重要的基础资料和可借鉴的研究思路。取得的主要研究成果如下：
(1)在静态加载范围内,石灰岩具有很强的率敏感性。试验表明,石灰岩破坏峰值强度随加载速率的增加有明显提高,峰值强度与应变率的对数呈线性关系。而峰值应变随应变率增加却有小幅减小的趋势。分析石灰岩破裂过程,发现提高加载应变率对岩石裂纹不稳定扩展阶段影响不大,对岩石裂纹稳定扩展阶段却有较大影响。加载应变率越高,岩石进入裂纹扩展阶段(塑性阶段)就越晚,塑性段在全应力应变曲线中所占比例相应减小,弹性阶段比例增加,岩石的弹性特性更为明显。
(2)研究了测试程序对施密特锤回弹测试结果的影响,给出了一种扰动较小且测量准确的施密特锤测试程序。在对比研究了超声、回弹和超声回弹综合法三种无损方法估算单轴压缩强度方法的预测精度的基础上,建立了一套估算标准试样单轴强度的无损方法。由测试数据建立了双参数指数型石灰岩标准试样单轴压缩强度估算模型。
(3)利用宜万铁路石灰岩开展了各种加载条件下的疲劳力学试验。发现：随着上限应力水平的降低,石灰岩疲劳寿命在半对数坐标下呈线性增长的趋势；应力幅值对疲劳寿命起着关键作用,应力幅值越大岩石的疲劳寿命越短;岩石疲劳“门槛值”不仅与岩石类型密切相关,而且随着加载速率的增加而提高；在0.5～3Hz加载范围内,石灰岩疲劳寿命随加载频率的增加而增加,疲劳寿命与加载频率满足双对数坐标下的线性关系。在试验基础上,建立了基于S-N曲线的疲劳寿命估算模型、同时考虑上限应力和应力幅值影响的石灰岩疲劳寿命估算模型以及基于加载频率和上限应力的多因素疲劳寿命估算模型。
(4)石灰岩疲劳变形经历初始变形阶段、稳定发展阶段和加速阶段三个不同阶段。对比疲劳极限变形和静力全曲线控制变形,发现两者之间十分接近；在0.5～3Hz范围内,改变加载频率对石灰岩疲劳破坏时轴向极限变形几乎无影响；说明“岩石疲劳破坏时的极限变形规律”不受加载频率的影响。依据石灰岩疲劳变形发展规律,提出了基于平均应变增量的疲劳寿命计算模型。确定该模型计算参数仅需要开展有限次数的循环压缩试验和单轴压缩试验,从而极大的缩减了试验投入。
(5)探讨了岩石的非线性变形滞后效应并分析了其形成原因。总结了循环加卸载变形曲线中常见的五种回滞环形态,并就各种形态的成因开展了讨论。
(6)利用单轴静态压缩试验、循环动力试验和超声测试三种试验手段,对比研究了石灰岩静态、准动态和动态弹性模量之间的关系。
(7)疲劳试验结果表明,石灰岩动态弹性模量随循环加载呈三阶段衰减规律,由此建立了基于剩余刚度的石灰岩疲劳损伤演化模型。结合石灰岩疲劳寿命多因素估算模型,提出了一套适用于岩石工程的能考虑围岩动力疲劳损伤的计算方法。采用FLAC3D进行二次开发,实现了该计算方法的数值程序化,并将其应用于鲁竹坝二号(Ⅱ线)隧道地震灾变作用下的动态模拟计算中。
It is known that the research on fatigue mechanical characteristics of rock under different loading condition is relatively lagging behind in institute foreign and domestic; a systematic research about the fatigue properties and damage evolution laws of karst limestone is absence in particular. For analyzing the long-term stability of surrounding rock between railway tunnel and karst cave, relying on the project of National Natural Science Foundation, a systematic research which take Yichang Wanzhou railway tunnel limestone as research subject was conducted by using combining methods of literature survey, laboratory testing, theoretical analysis and numerical simulation in this paper. The strain rate effect of limestone within static category was studied systematically; fatigue mechanical properties of limestone in different load conditions was explored; multi-factors fatigue life prediction models and fatigue damage evolution model were established and were applied in elastoplastic numerical calculations in this article. For the analysis of surrounding rock long-time stability when taking rock fatigue damage into account in karst tunnel, important basic information and research ideas for future reference were provided by those research results. The main research conclusions are as follows:
(1) In the range of static loading rate, limestone has strong rate sensitivity. Tests show that the peak strength of limestone increases obviously with the rise of loading rate, and the relationship between peak strength and logarithm of strain rate is linear. However peak strain shows decreasing trend with the increase of strain rate. By analyzing the rupture process of limestone, it is concluded that there is little effect on unstable crack expansion phase while greater impacts on the stable crack expansion when increasing strain rate. The higher the strain rate, the later rock sample reaches the crack propagation stage (plastic phase) which means the proportion of plastic stage in the whole stress-strain curve decrease and that of elastic stage increase correspondingly.
(2) The effect of tests procedure on the tests results of Schmidt hammer was studied, and a tests procedure of Schmidt hammer with smaller tests disturbance and more accurate was proposed. The accuracy for predicting limestone uniaxial compression strength (UCS) by using ultrasonic, Schmidt rebound and ultrasonic-rebound combined methods, three non-destructive estimation tests, was comparatively studied. Basted on the results, a non-destructive method for estimating the strength of standard samples was established. And, according to tests data, a two-parameter exponential model for predicting UCS of limestone was proposed
(3) Fatigue mechanical tests under various loading conditions were carried out by using Yiwan railway limestone. The conclusion is that the fatigue life of limestone was trading to prolong linearly in the semi-logarithmic coordinate with the decrease of upper limit stress; the greater stress amplitude the shorter fatigue life of rock which means stress amplitude play a key role on fatigue life; rock fatigue "threshold value" is not only closely associated with rock types, and increased with the raise of loading rate; in the range of0.5-3Hz, fatigue life of limestone advanced with the growth of loading frequency, and they met a linear relationship in double logarithmic coordinates. According to the tests, the S-N curve based, taking into account the impact of supper limit stress and stress amplitude life estimation models as well as a multi-factors fatigue life estimation model based on loading frequency and supper limit stress were estimated.
(4) The limestone fatigue deformation underwent initial deformation stage and stable development stage as well as acceleration phase three different stages. Contrasting fatigue terminal deformation and control deformation of static whole stress-strain curve, it is found that they were very close. It is hardly affected by changing loading frequency to the fatigue axial terminal deformation of limestone which means'the limit deformation law when approaching to fatigue failure'untouched by the load frequency. An average strain increment based fatigue life calculation model was proposed according to the development rules of limestone fatigue deformation. Only a limited number of cyclic compression tests and uniaxial compression tests were required to determine the model parameters, which greatly reduced the fatigue tests inputs.
(5) Nonlinear deformation lagged effects of rock was explored and its cause was analyzed. Five common hysteresis loop shapes of cyclic loading and unloading deformation curves were summarized and the causes of those various forms were discussed also.
(6) Uniaxial static compression experiment, cyclic dynamic tests and ultrasonic tests were adopted to research the relationship among static, quasi-dynamic and dynamic elastic moduli of limestone.
(7) Fatigue tests results showed that the decay of limestone dynamic elastic modulus went through three different stages with the conduction of cyclic loading. Thus, a fatigue damage development model of limestone was established based on the residual stiffness. And, a set of calculation method which can consider dynamic fatigue damage of surrounding rock and suit for application in rock engineering was proposed by combining with multivariate estimation model of limestone fatigue life. The numerical programming producer of this method was achieved by utilizing a secondary development of FLAC3D software. And, it was applied to a dynamic simulation calculation of Luzhuba2nd tunnel under the action of earthquake disaster.
(1)在静态加载范围内,石灰岩具有很强的率敏感性。试验表明,石灰岩破坏峰值强度随加载速率的增加有明显提高,峰值强度与应变率的对数呈线性关系。而峰值应变随应变率增加却有小幅减小的趋势。分析石灰岩破裂过程,发现提高加载应变率对岩石裂纹不稳定扩展阶段影响不大,对岩石裂纹稳定扩展阶段却有较大影响。加载应变率越高,岩石进入裂纹扩展阶段(塑性阶段)就越晚,塑性段在全应力应变曲线中所占比例相应减小,弹性阶段比例增加,岩石的弹性特性更为明显。
(2)研究了测试程序对施密特锤回弹测试结果的影响,给出了一种扰动较小且测量准确的施密特锤测试程序。在对比研究了超声、回弹和超声回弹综合法三种无损方法估算单轴压缩强度方法的预测精度的基础上,建立了一套估算标准试样单轴强度的无损方法。由测试数据建立了双参数指数型石灰岩标准试样单轴压缩强度估算模型。
(3)利用宜万铁路石灰岩开展了各种加载条件下的疲劳力学试验。发现：随着上限应力水平的降低,石灰岩疲劳寿命在半对数坐标下呈线性增长的趋势；应力幅值对疲劳寿命起着关键作用,应力幅值越大岩石的疲劳寿命越短;岩石疲劳“门槛值”不仅与岩石类型密切相关,而且随着加载速率的增加而提高；在0.5～3Hz加载范围内,石灰岩疲劳寿命随加载频率的增加而增加,疲劳寿命与加载频率满足双对数坐标下的线性关系。在试验基础上,建立了基于S-N曲线的疲劳寿命估算模型、同时考虑上限应力和应力幅值影响的石灰岩疲劳寿命估算模型以及基于加载频率和上限应力的多因素疲劳寿命估算模型。
(4)石灰岩疲劳变形经历初始变形阶段、稳定发展阶段和加速阶段三个不同阶段。对比疲劳极限变形和静力全曲线控制变形,发现两者之间十分接近；在0.5～3Hz范围内,改变加载频率对石灰岩疲劳破坏时轴向极限变形几乎无影响；说明“岩石疲劳破坏时的极限变形规律”不受加载频率的影响。依据石灰岩疲劳变形发展规律,提出了基于平均应变增量的疲劳寿命计算模型。确定该模型计算参数仅需要开展有限次数的循环压缩试验和单轴压缩试验,从而极大的缩减了试验投入。
(5)探讨了岩石的非线性变形滞后效应并分析了其形成原因。总结了循环加卸载变形曲线中常见的五种回滞环形态,并就各种形态的成因开展了讨论。
(6)利用单轴静态压缩试验、循环动力试验和超声测试三种试验手段,对比研究了石灰岩静态、准动态和动态弹性模量之间的关系。
(7)疲劳试验结果表明,石灰岩动态弹性模量随循环加载呈三阶段衰减规律,由此建立了基于剩余刚度的石灰岩疲劳损伤演化模型。结合石灰岩疲劳寿命多因素估算模型,提出了一套适用于岩石工程的能考虑围岩动力疲劳损伤的计算方法。采用FLAC3D进行二次开发,实现了该计算方法的数值程序化,并将其应用于鲁竹坝二号(Ⅱ线)隧道地震灾变作用下的动态模拟计算中。
It is known that the research on fatigue mechanical characteristics of rock under different loading condition is relatively lagging behind in institute foreign and domestic; a systematic research about the fatigue properties and damage evolution laws of karst limestone is absence in particular. For analyzing the long-term stability of surrounding rock between railway tunnel and karst cave, relying on the project of National Natural Science Foundation, a systematic research which take Yichang Wanzhou railway tunnel limestone as research subject was conducted by using combining methods of literature survey, laboratory testing, theoretical analysis and numerical simulation in this paper. The strain rate effect of limestone within static category was studied systematically; fatigue mechanical properties of limestone in different load conditions was explored; multi-factors fatigue life prediction models and fatigue damage evolution model were established and were applied in elastoplastic numerical calculations in this article. For the analysis of surrounding rock long-time stability when taking rock fatigue damage into account in karst tunnel, important basic information and research ideas for future reference were provided by those research results. The main research conclusions are as follows:
(1) In the range of static loading rate, limestone has strong rate sensitivity. Tests show that the peak strength of limestone increases obviously with the rise of loading rate, and the relationship between peak strength and logarithm of strain rate is linear. However peak strain shows decreasing trend with the increase of strain rate. By analyzing the rupture process of limestone, it is concluded that there is little effect on unstable crack expansion phase while greater impacts on the stable crack expansion when increasing strain rate. The higher the strain rate, the later rock sample reaches the crack propagation stage (plastic phase) which means the proportion of plastic stage in the whole stress-strain curve decrease and that of elastic stage increase correspondingly.
(2) The effect of tests procedure on the tests results of Schmidt hammer was studied, and a tests procedure of Schmidt hammer with smaller tests disturbance and more accurate was proposed. The accuracy for predicting limestone uniaxial compression strength (UCS) by using ultrasonic, Schmidt rebound and ultrasonic-rebound combined methods, three non-destructive estimation tests, was comparatively studied. Basted on the results, a non-destructive method for estimating the strength of standard samples was established. And, according to tests data, a two-parameter exponential model for predicting UCS of limestone was proposed
(3) Fatigue mechanical tests under various loading conditions were carried out by using Yiwan railway limestone. The conclusion is that the fatigue life of limestone was trading to prolong linearly in the semi-logarithmic coordinate with the decrease of upper limit stress; the greater stress amplitude the shorter fatigue life of rock which means stress amplitude play a key role on fatigue life; rock fatigue "threshold value" is not only closely associated with rock types, and increased with the raise of loading rate; in the range of0.5-3Hz, fatigue life of limestone advanced with the growth of loading frequency, and they met a linear relationship in double logarithmic coordinates. According to the tests, the S-N curve based, taking into account the impact of supper limit stress and stress amplitude life estimation models as well as a multi-factors fatigue life estimation model based on loading frequency and supper limit stress were estimated.
(4) The limestone fatigue deformation underwent initial deformation stage and stable development stage as well as acceleration phase three different stages. Contrasting fatigue terminal deformation and control deformation of static whole stress-strain curve, it is found that they were very close. It is hardly affected by changing loading frequency to the fatigue axial terminal deformation of limestone which means'the limit deformation law when approaching to fatigue failure'untouched by the load frequency. An average strain increment based fatigue life calculation model was proposed according to the development rules of limestone fatigue deformation. Only a limited number of cyclic compression tests and uniaxial compression tests were required to determine the model parameters, which greatly reduced the fatigue tests inputs.
(5) Nonlinear deformation lagged effects of rock was explored and its cause was analyzed. Five common hysteresis loop shapes of cyclic loading and unloading deformation curves were summarized and the causes of those various forms were discussed also.
(6) Uniaxial static compression experiment, cyclic dynamic tests and ultrasonic tests were adopted to research the relationship among static, quasi-dynamic and dynamic elastic moduli of limestone.
(7) Fatigue tests results showed that the decay of limestone dynamic elastic modulus went through three different stages with the conduction of cyclic loading. Thus, a fatigue damage development model of limestone was established based on the residual stiffness. And, a set of calculation method which can consider dynamic fatigue damage of surrounding rock and suit for application in rock engineering was proposed by combining with multivariate estimation model of limestone fatigue life. The numerical programming producer of this method was achieved by utilizing a secondary development of FLAC3D software. And, it was applied to a dynamic simulation calculation of Luzhuba2nd tunnel under the action of earthquake disaster.
引文
[1]E. Hoek, E.T. Brown.岩石地下工程[M].连志生,田良灿等译.北京：冶金工业出版社,1986.
[2]B.H.G.布雷迪,E.T.布朗.地下采矿岩石力学[M].冯树仁,佘诗刚等译.北京：煤炭工业出版社,1986.
[3]中华人民共和国交通部,公路隧道设计规范TJGD70-2004,北京：人民交通出版社,2004.
[4]王梦恕.对岩溶区隧道施工水文地质超前预报的意见[J].铁道勘察,2004(1)：7-9.
[5]于波.深埋隧洞中的岩溶地基工程地质问题及地基处理[J].岩石力学与工程学报,2004,23(1)：403-407.
[6]李彪,梁富清.高速公路隧道施工中的岩溶问题研究[J].工程力学,2000(增刊)764-768.
[7]铁道部第二勘察设计院.岩溶工程地质[M].北京：中国铁道出版社,1984.
[8]吴梦军,许锡宾,赵明阶.岩溶地区公路隧道施工力学响应研究[J].岩石力学与工程学报,2004,23(9)：1525-1529.
[9]傅鹤林.隧道衬砌荷载计算理论及岩溶处治技术[M].长沙：中南大学出版社,2005.
[10]邹成杰.水利水电岩溶工程地质[M].北京：地质出版社,1994.
[11]刘招伟,张民庆,王树仁.岩溶隧道灾变预测与处治技术[M].第二版.北京：科学出版社,2007.
[12]王勇,乔春生,孙彩红,刘开云,岩溶隧道溶洞顶板安全厚度智能预测模型[J],岩土力学,2006,27(6)：1000-1006
[13]宋战平.隐伏溶洞对隧道围岩——支护结构稳定性的影响研究[D].西安：西安理工大学,2006.
[14]郭佳奇.岩溶隧道防突厚度及突水机制研究[D].北京：北京交通大学,2011.
[15]李利平.高风险岩溶隧道突水灾变演化机制及其应用研究[D].济南：山东大学,2009.
[16]赖永标,乔春生,基于SVM隧道与溶洞安全距离预测模型[J],四川大学学报(工程科学版),2007,39(增刊)：72-77
[17]陈传尧.疲劳与断裂[M].武汉：华中科技大学出版社,2001.
[18]蒋宇.周期荷载作用下岩石疲劳破坏及变形发展规律[D硕士学位论文].上海：上海交通大学.2003
[19]张滨生,朱照宏.水泥混凝土路面的疲劳损伤分析[J].土木工程学报.1986(04)：54-60
[20]张滨生,吴科如.水泥混凝土疲劳破坏的损伤力学分析[J].同济大学学报.1989(01)：59-70
[21]B.Zhang,D.V.Phillips and K.Wu Effects of loading frequency and stress reversal on fatigue life of plain concrete[J]. Magazine of Concrete Research,1996,No.177,361-375
[22]过镇海.混凝土的强度和变形：试验基础和本构关系[M].北京：清华大学出版社,1997.
[23]过镇海,张秀琴.混凝土在反复荷载作用下的应力-应变全曲线[J].冶金建筑,1981(9)：14-17
[24]王瑞敏,赵国藩,宋玉普.混凝土的受压疲劳性能研究[J].土木工程学报.1991(04)：38-47
[25]王瑞敏,宋玉普,赵国藩.混凝土疲劳累积损伤准则[J].水利学报.1992(05)：72-76
[26]宋玉普.混凝土结构的疲劳性能及设计原理[M].机械工业出版社,2006
[27]董毓利,谢和平,赵鹏.循环受压砼全过程声发射实验及其本构关系[J].实验力学,1996(2)：216-221
[28]林燕清,欧进萍.混凝土疲劳损伤试验中试件初始极限强度的推测方法[J].哈尔滨建筑大学学报.1997(06)：9-20
[29]欧进萍,林燕清.混凝土疲劳损伤的强度和刚度衰减试验研究[J].哈尔滨建筑大学学报.1998(04)：1-8
[30]林燕清,欧进萍.混凝土多级等幅疲劳的变形发展规律试验研究[J].哈尔滨建筑大学学报.1999(01)：11-17
[31]欧进萍,林燕清.混凝土高周疲劳损伤的性能劣化试验研究[J].土木工程学报.1999(05)：15-22
[32]易成,沈世钊.疲劳裂纹扩展理论及其在混凝土疲劳性能研究中的应用[J].哈尔滨建筑大学学报.2000(05)：20-24
[33]李朝阳,宋玉普,赵国藩.混凝土疲劳残余应变性能研究[J].大连理工大学学报.2001(03)：355-358
[34]李朝阳,宋玉普,车轶.混凝土的单轴抗压疲劳损伤累积性能研究[J].土木工程学报.2002(02)：38-40
[35]吕培印.混凝土单轴、双轴动态强度和变形试验研究[D].大连理工大学2002
[36]赵东拂.混凝土多轴疲劳破坏准则研究[D].大连理工大学2002
[37]朱劲松.混凝土双轴疲劳试验与破坏预测理论研究[D].大连理工大学2003
[38]曹伟,宋玉普.多级加载下混凝土疲劳剩余寿命预测新方法[J].大连理工大学学报.2003(05)：659-662
[39]曹伟.定侧压下混凝土三轴疲劳性能试验与理论研究[D].大连理工大学2004
[40]孟宪宏.混凝土疲劳剩余强度试验及理论研究[D].大连理工大学2006
[41]Burdine NT. Rock failure under dynamic loading conditions. [J]. Soc Petr Eng J 1963(03):1-8.
[42]Haimson BC, Kim CM. Mechanical behaviour of rock under cyclic fatigue. In:Cording EJ, editor. Stability of rock slopes Proceedings of the 13th Synposium on Rock Mechanics, New York:ASCE,1972:845-863.
[43]Attewell PB, Farmer IW. Fatigue behaviour of rock. [J]. Int J Rock Mech Min Sci 1973(10): 1-9.
[44]Singh SK. Fatigue and strain hardening behaviour of Graywacke from the Flagstaff formation, New South Wales. [J]. Engineering Geology 1989(26):171-179.
[45]Zhenyu T, Haihong M. Technical note:an experimental study and analysis of the behaviour of rock under cyclic loading. [J]. Int J Rock Mech Min Sci Geomech Abstr 1990 27(1):51-56.
[46]Ishizuka Y, Abe T, Kodama J. Fatigue behaviour of granite under cyclic loading. In:Brumer R, editor, ISRM international symposium-static and dynamic considerations In rock engineering,Swaziland,1990:139-46.
[47]Tien YM, Lee DH, Juang CH. Strain, pore pressure and fatigue characteristics of sandstone under various load conditions. [J]. Int J Rock Mech Min Sci Geomech Abstr 1990;27(4):283-9.
[48]Yamashita S, Sugimoto F, Imai T, Namsrai D, Yamauchi M.Kamoshida N. The relationshipbetween the failure process of the creepor fatigue test and of the conventional compression test on rock. In:Vouille G, Berest P, editors. ISRM nineth international congress on rock mechanics, Vol.2, Paris/France,1999:699-702.
[49]Lajtai EZ, Scott Duncan EJ, Carter BJ. The effect of strain rate on rock strength. [J]. Rock Mech Rock Eng 1991 (24):99-109.
[50]Ray SK, Sarkar M, Singh TN. Effect of loading and strain rate on the mechanical behaviour of sandstone. [J]. Int J Rock Mech Min Sci 1999(36):543-549.
[51]Bagde MN, Petros V. The effect of machine behaviour and mechanical properties of intact sandstone under static and dynamic uniaxial cyclic loading. [J]. Rock Mech Rock Eng 2005;38(1):59-67.
[52]Bagde MN, Petros V. Fatigue properties of intact sandstone samples subjected to dynamic uniaxial cyclical loading. [J]. Int J Rock Mech Min Sci 2005(42):237-250.
[53]Bagde MN, Petros V. Fatigue and dynamic energy behaviour of rock subjected to cyclical loading. [J]. Int J Rock Mech Min Sci 2009(46):200-206.
[54]葛修润,卢应发.循环荷载作用下岩石疲劳破坏和不可逆变形问题的探讨[J].岩土工程学报,1992(3)：56-60.
[55]葛修润,蒋宇等.周期荷载作用下岩石疲劳变形特性试验研究[J].岩石力学与工程学报,2003,22(10)：1581-1585.
[56]章清叙,葛修润等.周期荷载作用下红砂岩三轴疲劳变形特性试验研究[J].岩石力学与工程学报,2006,25(3)：474-478.
[57]Li N, Chen W, Zhang P, Swoboda G. Technical note:the mechanical properties and a fatigue-damage model for jointed rock masses subjected to dynamic cyclical loading [J].Int J Rock Mech Min Sci 2001;38:1071-1079.
[58]Li N, Zhang P, Chen Y, Swoboda G. Technical note:fatigue properties of a cracked, saturated and frozen sandstone samples under cyclic loading. [J]. Int J Rock Mech Min Sci 2003;40: 145-50.
[59]许江,杨秀贵,王鸿,等.周期性载荷作用下岩石滞回曲线的演化规律[J].西南交通大学学报,2005.40(6)：754-758.
[60]许江,王维忠,杨秀贵,等.细粒砂岩在周期性循环荷载作用下变形实验[J].重庆大学学报(自然科学版),2004,27(12)：60-62.
[61]许江,鲜学福,王鸿,等.循环加、卸载条件下岩石类材料变形特性的实验研究[J].岩石力学与工程学报,2006,25(s.1)：3040-3045.
[62]席道瑛,王春雷,田象燕.滞回曲线对应力振幅和频率的响应[J].物探化探计算技术,2001,23(2)：121·124.
[63]刘云平,席道瑛,张程远等.循环应力作用下大理岩砂岩的动态响应[J].岩石力学与工程学报,2001,20(2)：216-219.
[64]陈运平,席道瑛,薛彦伟.循环载荷下饱和岩石的应力-应变动态响应[J].石油地球物理勘探,2003,38(4)：409-413.
[65]陈运平,席道瑛,薛彦伟.循环荷载下饱和岩石的滞后和衰减[J].地球物理学报,2004,47(4)：672-679.
[66]樊秀峰,简文彬.砂岩疲劳特性的超声波速法试验研究[J].岩石力学与工程学报,2008,27(3)：557-563
[67]Xiao JQ, Ding DX, Xu G, et al. Waveform effect on quasi-dynamic loading condition and the mechanical properties of brittle materials. [J]. Int J Rock Mech Min Sci 2008;45(4):621-626.
[68]杨永杰,宋扬,楚俊.循环荷载作用下煤岩强度及变形特征试验研究[J].岩石力学与工程学报.2007(01)：201-205
[69]朱明礼,朱珍德,李刚,邱玉华,陈哲,李金旺.循环荷载作用下花岗岩动力特性试验研究[J].岩石力学与工程学报.2009(12)：2520-2526
[70]倪骁慧,朱珍德,李晓娟,李志敬,朱明礼.循环荷载下花岗岩细观损伤量化试验研究[J].岩 土力学.2011(07)：1991-1995
[71]Enlong Liu, Siming He. Effects of cyclic dynamic loading on the mechanical properties of intact rock samples under confining pressure conditions[J] Engineering Geology 2012 (125) 81-89
[72]王者超,赵建纲,李术才,薛翊国,张庆松,姜彦彦.循环荷载作用下花岗岩疲劳力学性质及其本构模型[J].岩石力学与工程学报.2012(09)：1888-1900
[73]Jose Fernando Sima, Pere Roca, Climent Molins. Cyclic constitutive model for concrete[J]. Engineering Structures 2008 (30):695-706
[74]Bahn Byong Youl. Hsu Cheng-Tzu Thomas. Stress-strain behavior of concrete under cyclic loading [J] ACI Materiais Journal,1998,95(2)::178-193
[75]Mazars J A description of micro-and macro-scale damage of concrete structures [J]. Engineering Fracture Mechanics,1986,25(5/6):729-737
[76]Enrico Papa, and Alberto Taliercio. Anisotropic damage model for the multi-axial stratic and fatigue behaviour of plain concrete [J] Engineering Fracture Mechanics,1996,55(2):163-179
[77]谢和平,经典损伤定义中的“弹性模量法”探讨[J]力学与实践,1997,19(2)：1-5
[78]齐红宇,温卫东,孙联文.基于刚度下降的疲劳累积损伤模型的研究[J].北京航空航天大学学报.2004(12)：1200-1203
[79]潘华,邱洪兴.基于损伤力学的混凝土疲劳损伤模型[J].东南大学学报(自然科学版).2006(04)：605-608
[80]李树春,许江,陶云奇,等.岩石低周疲劳损伤模型与损伤变量表达方法[J].岩土力学,2009,30(6)：1611-1614
[81]许宏发,王武,方秦,王万波,循环载荷下岩石塑性应变演化模型[J]解放军理工大学学报,2012(13)282-286
[82]吴鸿遥.损伤力学[M].北京：国防工业出版社,1990
[83]Xiao JQ, Ding DX, Xu G, et al. Inverted S-shaped model for nonlinear fatigue damage of rock [J]. Int J Rock Mech Min Sci 2009(46):643-648.
[84]DAFALIAS Y F. On cyclic and anisoisotropic plasticity:(1) A general model including material behavior under stress reversals; (2) Anisotropic hardening for initially orthotropic materials[D]. Berkeley:University of California,1975.
[85]宋玉普,朱劲松.疲劳荷载作用下混凝土的边界面模型研究[J].哈尔滨工业大学学报,2005,37(1)：74-79
[86]Fardis M N, Alibe B, Tassoulas J L. Monotonic and cyclic constitutive law for concrete[J] Journal of Engineering Mechanics, ASCE 1983,109 (2):516-536
[87]Fardis M. N., Chen E. S. A cyclic multiaxial model for concrete[J]. Computational mechanics, 1986,(1):301-315
[88]Yang B. L., Dafalias Y. F., Herrmann L. R. A bounding surface plasticity model for concrete[J]. Journal of Engineering Mechanics, ASCE,1985,111(3):359-380
[89]Aas-Jakobsen K. Fatigue of concrete beams and condumns[J]. Bulletiin No.70-1.NTH insititute of Betonkonstruksjoner, Trondheim,1970
[90]Thomas, hsu. Fatigue of plain concrete[J]. ACI Journal,1981,78(3):292-305
[91]Jan Ove Holmen. Fatigue of concrete by constant and variable amplitude loading[J]. FatigueStrength of Concrete Structures, SP-75, ACI,1982:71-11
[92]赵造东；张立翔；王时越等幅循环荷载下水工混凝土疲劳寿命分析[J]昆明理工大学学报(自然科学版)2001(03)：8-11
[93]赵造东,张立翔,王时越谱荷载下剩余强度衰减的混凝土疲劳寿命可靠性分析[J]；力学与实践；2002(01)：8-11
[94]朱劲松,宋玉普.基于剩余强度衰减的混凝土疲劳寿命估算方法[J].海洋工程.2003(03)：78-82
[95]吕培印,宋玉普.基于人工神经网络的混凝土疲劳寿命估算[J].海洋工程.2001(03)：72-76
[96]李士彬,朱慈勉,汤红卫.由刚度衰减规律预测混凝土梁疲劳寿命的试验研究[J]建筑结构,2006(02)：51-54
[97]刘建坤,肖军华,杨献永,陈立宏.提速条件下粉土铁路路基动态稳定性研究[J].岩土力学.2009(02)：399-406
[1]E. EBERHARDT. Brittle rock fracture and progressive damage in uniaxial compression[D]. Saskatoon:University of Saskatchenwan.1998.
[2]刘佑荣,唐辉明.岩体力学[M].中国地质大学出版社.1999.
[3]Qi C, Wang M, Qian Q. Strain rate effects on the strength and fragmentation size of rocks. [J]. Int J Impact Eng 2009;36(12):1355-64.
[4]Li Z, Wang Q. Experimental research on effect of loading rate for dynamic fracture toughness of rock. [J]. Chin J Geotech Eng 2006;28:2116-20.
[5]S Yang, S Zeng, H Wang. Experimental analysis on mechanical effects of loading rates on limestone. [J]. Chin J Geotech Eng 2005;27:786-8.
[6]R C FRANSSEN, M W. The rheology of synthetic rocksalt in uniaxial compression[J]. Tectonophysics.1994; 223(1/2):1-40.
[7]WG LIANG, YS ZHAO, S G XU, et al. Effect of strain rate on the mechanical properties of salt rock[J]. Int J Rock Mech Min Sci.2011; 48(1):161-167.
[8]姜德义,陈结,任松,王维忠,白月明.盐岩单轴应变率效应与声发射特征试验研究[J].岩石力学与工程学报.2012(02)：326-336
[9]W. F. Brace. Comparison of uniaxial deformation in shock and static loading of the three rock[J] Geo-Phys. Res,1971(76):4913-4921.
[10]Y. Mahmutoglu. The effects of strain rate and saturation on a micro-cracked marble. [J] Eng Geol 2006;82:137-44.
[11]S.H. Cho, Y. Ogata, K. Kaneko. Strain-rate dependency of the dynamic tensile strength of rock. [J] Int J Rock Mech Min Sci 2003;40:763-77.
[12]席道瑛,谢端,张毅,何炬.加载速率对岩石力学性质及声发射率的影响[A].第四届全国岩石动力学学术会议论文选集[C].1994：469-471
[13]洪亮,李夕兵,马春德,尹土兵,叶洲元,廖国燕.岩石动态强度及其应变率灵敏性的尺寸效应研究[J].岩石力学与工程学报.2008(03)：526-533
[14]杨仕教,曾晟,王和龙.加载速率对石灰岩力学效应的试验研究[J].岩土工程学报.2005(07)：786-788
[151杨海清,周小平.灰岩单轴压缩损伤演化试验研究[J].土木工程学报.2010(05)：117-123
[16]黄达,黄润秋,张永兴.粗晶大理岩单轴压缩力学特性的静态加载速率效应及能量机制试验研究[J].岩石力学与工程学报.2012(02)：245-254
[17]肖诗云,张剑.不同应变率下混凝土受压损伤试验研究[J].土木工程学报.2010(03)：40-45
[18]W. Janach. The role of bulking in brittle Failure of rocks under rapid compression[J]. Int J Rock Mech Min Sci & Geo Abs,1976,13(6):177-186.
[19]梁昌玉,李晓,马超锋.中等应变率加载条件下岩石的变形和力学特性研究进展及展望[J].工程地质学报.2012(01)：88-94
[20]王洪亮,范鹏贤,王明洋,李文培,钱岳红.应变率对红砂岩渐进破坏过程和特征应力的影响[J].岩土力学.2011(05)：1340-1346
[21]金丰年,岩石的载荷速度效应[J].岩石力学与工程学报.1998(12)711-717
[22]尤明庆.两种晶粒大理岩的力学性质研究[J].岩土力学,2005,26(1)；91-96.
[23]梁卫国,徐素国,莫江,吴迪,张传达.盐岩力学特性应变率效应的试验研究[J].岩石力学与工程学报.2010(01)：43-50
[24]S.K. Ray, M. Sarkar, T.N. Singh. Effect of cyclic loading and strain rate on the mechanical behaviour of sandstone [J]. Int J Rock Mech Min Sci 1999 (36):543-49
[25]朱泽奇,盛谦,冷先伦,等.三峡花岗岩起裂机制研究[J].岩石力学与工程学报,2007,26(12)：2570-2575
[26]C. D. Martin, N. A. Chardler. The progressive fracture of Lac du Bonnet granite[J]. Int J Rock Mech Min Sci & Geo Abs,1994,31(6):643-659
[27]XB Li, TS Lok, J Zhao. Dynamic characteristics of granite subjected to intermediate loading rate [J. Rock Mech & Rock En.2005; 38(1):21-29.
[1]葛修润,蒋宇,卢允德,任建喜.周期荷载作用下岩石疲劳变形特性试验研究[J].岩石力学与工程学报.2003(10)：1581-1585
[2]葛修润.岩石疲劳破坏的变形控制律、岩土力学试验的实时X射线CT扫描和边坡坝基抗滑稳定分析的新方法[J].岩土工程学报.2008(01)：1-20
[3]林燕清,欧进萍.混凝土疲劳损伤试验中试件初始极限强度的推测方法[J].哈尔滨建筑大学学报.1997(06)：9-20
[4]ISRM Suggested Methods. In:Brown ET, editor. Rock characterization testing and monitoring. Oxford:Pergamon Press,1981.
[5]American Society for Testing and Materials. Standard test method for unconfined compressive strength of intact rock core specimens. Soil and Rock, Building Stones:Annual Book of ASTM Standards 4.08. Philadelphia, Pennsylvania:ASTM,1984.
[6]Cargill, J.S., Shakoor, A. Evaluation of empirical methods for measuring the uniaxial compressive strength of rock [J]. Int J Rock Mech Min Sci & Geomech Abstr.1990;27(6): 495-503.
[7]Kahraman S. Evaluation of simple methods for assessing the uniaxial compressive strength of rock[J] International Journal of Rock Mechanics & Mining Sciences (2001);38:981-994
[8]Sarkar, K., Vishal, V. et al. An empirical correlation of index geomechanical parameters with the compressional wave velocity [J]. Geotech Geol Eng.2012;30:469-479.
[9]Yasar, E., Erdogan, Y. Correlating sound velocity with the density, compressive strength and Young's modulus ofcarbonate rocks [J]. Int J Rock Mech Min Sci.2004; 41:871-875.
[10]Gaviglio, PLongitudinal waves propagation in a limestone:The relationship between velocity and density[J] Rock Mechanics and Rock Engineering,1989; 22(04):299-306.
[11]Kahraman Sair. Yeken Tekin. Determination of physical properties of carbonate rocks from P-wave velocity[J] Bull Eng Geol Environ 2008;67:277-281
[12]Khandelwal M., Singh T.N. Correlating static properties of coal measures rocks with P-wave velocity[J] International Journal of Coal Geology 2009,79:55-60
[13]Entwisle D.C., Hobbs P.R.N., Jones L.D., Gunn D. and Raines M.G.. The relationships between effective porosity, uniaxial compressive strength and sonic velocity of intact Borrowdale Volcanic Group core samples from Sellafield [J] Geotech Geol Eng.2005;23:793-809
[14]Kahraman, S., Soylemez, M. et al. Determination of fracture depth of rock blocks from P-wave velocity [J]. Bull Eng Geol Environ.2008;67:11-16.
[15]Sharma P.K., Khandelwal M., Singh T.N. A correlation between Schmidt hammer rebound numbers with impact strength index, slake durability index and P-wave velocity. [J] Int J Earth Sci 2011; 100:189-195
[16]Sharma P. K., Singh T. N. A correlation between P-wave velocity, impact strength index, slake durability index and uniaxial compressive strength[J] Bull Eng Geol Environ 2008; 67:17-22
[17]Kahraman S.. The correlations between the saturated and dry P-wave velocity of rocks[J] Ultrasonics 2007;46:341-348
[18]Goktan RM. Theoretical and practical analysis of rock rippability.[D] Istanbul Technical University,1988.
[19]Ibrahim Cobanoglu, Sefer Beran Celik Estimation of uniaxial compressive strength from point load strength, Schmidt hardness and P-wave velocity[J] Bull Eng Geol Environ.2008;67(04): 491-498
[20]Yilmaz I., Sendir H. Correlation of Schmidt hardness with unconfined compressive strength and Young's modulus in gypsum from Sivas (Turkey)[J] Engineering Geology 2002;66: 211-219
[21]Guney A. Altindag R.Yavuz H.& Sarac S. The 19th International Mining Congress and Fair of Turkey, IMCET2005, izmir, Turkey,2005; 07:09-12
[22]Aydin A., Basu A. The Schmidt hammer in rock material characterization[J] Engineering Geology 2005;81:1-14
[23]Buyuksagis I.S., Goktan R.M. The effect of Schmidt hammer type on uniaxial compressive strength prediction of rock International.[J] Int J Rock Mech Min Sci.2007;44:299-307
[24]ISRM. Suggested methods for determining hardness and abrasiveness of rocks.[J] Int J Rock Mech Min Sci Geomech Abstr 1978;15:89-98.
[25]ASTM. Standard test method for determination of rock hardness by rebound hammer method. ASTM Stand.04.09 (D 5873-00).2001.
[26]Poole RW, Farmer IW. Consistency and repeatability of Schmidt hammer rebound data during field testing.[J] Int J Rock Mech Min Sci Geomech Abstr 1980;17:167-71.
[27]Goktan RM, Ayday C. A suggested improvement to the Schmidt rebound hardness ISRM suggested method with particular reference to rock machineability.[J] Int J Rock Mech Min Sci Geomech Abstr 1993;30:321-2.
[28]Hucka V. A rapid method for determining the strength of rocks in situ. [J]Int J Rock Mech Min Sci Geomech Abstr 1965;2:127-134.
[29]Yagiz Saffet. Predicting uniaxial compressive strength, modulus of elasticity and index properties of rocks using the Schmidt hammer [J]. Bull Eng Geol Environ.2009; 68:55-63.
[30]McCarroll D. The Schmidt hammer as a measure of degree of rock surface weathering and terrain age. In:Beck C, editor. Dating in exposed and surface contexts. Mexico:University of New Mexico Press; 1994:29-45.
[31]Kahraman S., Fener M., Gunaydin O. Predicting the Schmidt hammer values of in-situ intact rock from core sample values[J] Int J Rock Mech Min Sci.2002;39:395-399
[32]刘宗平,王润起,吴小林,孙金龙.施密特锤试验数据处理方法及其在预估岩石可钻性中的应用[J].现代地质.1990(04)：113-123
[33]Deere DU, Miller RP. Engineering classifications and index properties of intact rock. Technical report no. AFWL-TR 65-116, University of Illinois:1966; p.300.
[34]Soiltest Inc., Operating instructions-concrete test hammer. Evanston, IL.1976.
[35]Young RP, Fowell RJ. Assesing rock discontinuities. [J]Tunnels Tunnelling. June 1978; 45-48.
[36]Matthews JA, Shakesby RA. The status of the Little Ice Age in southern Norway:relative-age dating of Neoglacial moraines with Schmidt hammer and lichenometry. Boreas 1984;13:333-34
[37]Katz O, Reches Z, Roegiers J. C. Evaluation of mechanical rock properties using a schmidt hammer.[J] Int J Rock Mech Min Sci 2000;37:723-728.
[38]Sumner P, Nel W. The effect of rock moisture on Schmidt hammer rebound:tests on rock samples from Marion Island and South Africa. Earth Surf Process Landforms 2002;27:l 137-42.
[39]Fowell RJ, McFeat Smith I. Factors influencing the cutting performance of a selective tunnelling machine. In:Tunnelling'76, proc int symp IMM, London,1976:301-9.
[40]Poole RW, Farmer IW. Consistency and repeatability of Schmidt hammer rebound data during field testing. [J]Int J Rock Mech Min Sci Geomech Abstr 1980; 17:167-71
[41]Kazi A, Al-Mansour ZR. Empirical relationship between Los Angeles Abrasion and Schmidt hammer strength tests with application to aggregates around Jeddah. Q J Eng Geol London: 1980;13:45-52.
[42]Goktan, R.M., Gunes, N. A comparative study of Schmidt hammer testing procedures with reference to rock cutting machine performance prediction [J]. Int. J. Rock Mech & Minng Sci. 2005;42:466-472.
[43]Singh, R.N., Hassani, F.P., Elkington, P.A.S., The application of strength and deformation index testing to the stability assessment of coal measures excavations. Proc.24th US Symp. On Rock Mech., Texas A&M Univ., AEG. Balkema, Rotterdam,1983; 599-609.
[44]Shorey, P.R., Barat, D., Das, M.N., Mukherjee, K.P., Singh, B., Schmidt hammer rebound data for estimation of large scale in-situ coal strength.[J] Int. J. Rock Mech. Min. Sci. Geomech. Abstr.1984;21:39-4
[45]Haramy, K.Y., DeMarco, M.J., Use of Schmidt hammer for rock and coal testing. Proc.26th US Symp. on Rock Mech.26-28 June, Rapid City. Balkema, Rotterdam,1985; 549-555.
[46]Ghose, A.K., Chakraborti, S., Empirical strength indices of Indian coals-an investigation. Proceedings of 27th US Symp. on Rock Mechanics. Balkema, Rotterdam,1986;59-61.
[47]Sachpazis, C.I., Correlating Schmidt hardness with compressive strength and Young's modulus of carbonate rocks.[J] Bull. Int. Assoc. Eng. Geol.1990;42:75-83.
[48]Xu, S., Grasso, P., Mahtab, A., Use of Schmidt hammer for estimating mechanical properties of weak rock.6th Int. IAEG Congress. Balkema, Rotterdam,1990; 511-519.
[49]Tugrul, A., Zarif, I.H., Correlation of mineralogical and textural characteristics with engineering properties of selected granitic rocks from Turkey. [J] Eng. Geol.1999.51:303-317.
[50]Shalabi F, Cording EJ, Al-Hattamleh OH Estimation of rock engineering properties using hardness tests[J]Eng. Geol.2007:90:138-147
[51]CECS02:2005超声回弹综合法检测混凝土强度技术规程[S].中国工程建设标准化协会标准.
[1]Jenkins H. H., Stephenson J. E., Clayton G. A. et al. The effect of track and vehicle parameters on wheel/rail vertical dynamic forces[J] Railway Engineering Journal,1974;3(1):2-16.
[2]刘建坤,肖军华,杨献永,陈立宏.提速条件下粉土铁路路基动态稳定性研究[J].岩土力学.2009(02)：399405.
[3]黄娟.基于损伤理论的高速铁路隧道结构振动响应分析及疲劳寿命研究[D].中南大学2010.
[4]Mor A. Gerwick B.C. Hester W.T. Fatigue of high strength reinforced concrete[J]. ACI Journal, 1992;89(2):197-207.
[5]Bagde MN, Petros V. Fatigue and dynamic energy behaviour of rock subjected to cyclical loading[J] Int J Rock Mech Min Sci 2009;46:200-206.
[6]莫海鸿.岩石的循环试验及本构关系的研究[J]岩石力学与工程学报,1988；7(3)：215-224.
[7]林卓英,吴玉山.岩石在循环荷载作用下的强度及变形特性[J].岩土力学,1987；8(3)：31-37.
[8]蒋宇.周期载荷作用下岩石疲劳破坏及变形发展规律[D]上海：上海交通大学,2003.
[9]MeCall John T. Probability of fatigue failure of Plain concrete[J]. ACI Journal, Proeeedings, 1958;55(2):233-244.
[10]赵造东,张立翔,王时越.等幅循环荷载下水工混凝土疲劳寿命分析[J].昆明理工大学学报(自然科学版).2001(03)：8-11.
[11]Yamashita S, Sugimoto F, Imai T, Namsrai D, Yamauchi M, Kamoshida N. The relationship between the failure process of the creepor fatigue test and of the conventional compression test on rock. In:Vouille G, Berest P, editors. ISRM nineth international congress on rock mechanics, Vol.2, Paris/France,1999. p.699-702.
[12]葛修润,蒋宇,卢允德,任建喜.周期荷载作用下岩石疲劳变形特性试验研究[J].岩石力学与工程学报.2003(10)：1581-1585.
[13]葛修润,卢应发循环荷载作用下岩石疲劳破坏和不可逆变形问题的探讨[J].岩土工程学报,1992(3)：56-60.
[14]肖建清.循环荷载作用下岩石疲劳特性的理论与实验研究[D].中南大学2009.
[15]陶振宇.岩石力学原理与方法,武汉,中国地质大学出版社,1991.87-89.
[16]Aas-Jakobson K..Fatigue of concrete beams and columns[J]. Bulletin No.70-1. NTH Institute of Betonkonstruksjoner, Trondheim,1970.
[17]Tepfers R., and Kutti T.. Fatigue strength of plain, ordinary and lightweight concrete[J]. ACI Journal,1979,76(5):635-652.
[18]Tepfers R., Gorlin J., and Samuelsson T.. Concrete subjected to pulsating load and pulsating deformation of different pulse wave-form[J]. Nordisk Betong,1973,4:27-36.
[19]Tao Z. Y, Mo H. H.. Technical note:an experimental study and analysis of the behaviour of rock under cyclic loading.[J] Int J Rock Mech Min Sci Geomech Abstr 1990;27(1):51-56.
[20]JianQing Xiao,DeXin Dingb, Gen Xua, FuLiang Jianga. Waveform effect on quasi-dynamic loading condition and the mechanical properties of brittle materials[J] Int J Rock Mech Min Sci 2009;45:621-626.
[21]任建喜,蒋宇,葛修润.单轴压缩岩石疲劳寿命影响因素试验分析[J].岩土工程学报.2005(11)：1282-1285.
[22]Bagde M. N., Petros V. Waveform Effect on Fatigue Properties of Intact Sandstone in Uniaxial Cyclical Loading[J] Rock Mech. Rock Eng.2005; 38 (3):169-196.
[23]Bagde, M. N., Petros, V. Fatigue properties of intact sandstone samples subjected to dynamic uniaxial cyclical loading. [J] Int. J. Rock Mech. Min. Sci.2005; 42(2):237-250.
[24]Graf O., Brenner E.. Experiments for investigating the resistance of concrete under often repeated compression loads.1[J] Bulletin, Deutscher Ausschuss fur Stahlbeton, Berlin, 1934;76:17-25.
[25]Graf O., Brenner E.. Experiments for investigating the resistance of concrete under often repeated compression loads.2[J] Bulletin, Deutscher Ausschuss fur Stahlbeton, Berlin, 1936;83:45-53.
[26]Kesler C. E.. Effects of speed of testing on flextural fatigue strength of plain concrete[J]. Proceedings Highway Research Board,1953:32; 251-258.
[27]Raithby K. D. Galloway J. W. Effects of moisture condition, age, and rate of loading on fatigue of plain concrete[J] Fatigue of concrete, ACI SP-41, Detroit,1974; 15-34.
[28]Gray W. H., Mclaughlin J. F., Antrim J.D. Fatigue properties of lightweight aggregate concrete[J].ACI Journal, Proceedings,1961;58:149-160.
[29]Raithby K. D. Flexural fatigue behavior of plain concrete[J] Fatigue of Engineering Materials and Structures 1979;2:269-278.
[30]Wagaard K. Fatigue of offshore concrete structures-design and experimental investigations[J]. 9th Annual Offshore Technology Conference in Huston 1977; 341-350.
[31]Arthur P. D. Carl J. C. Hodgkiess T. Corrosion fatigue in concrete for marine applictions[J] Fatigue of Concrete Structures ACI SP-75, Detroit,1982; 1-24.
[32]Sparks P. R. Menzies J. B. The effects of rate of loading upon the static and fatigue strengths of plain concrete in compression[J] Magazine of Concrete Research,1973;83:73-80.
[33]Sparks P. R. Influence of rate of loading and material variability on the fatigue characteristics of concrete[J] ACI Journal, Special Publication,1982; 216:331-342.
[34]Hatano T. Watanabe H. Fatigue failure of concrete under periodic compressive load[J] Transactions of Japan Society of Civil Engineering (Tokyo),1971;1:106-107.
[35]Turtak K, Ein verfahren zur berechnumg der betonfestigkeit unter schwellenden belastungen[J] Cement and Concrete Research,1984;6:855-865.
[36]Li N, Chen W, Zhang P, Swoboda G. The mechanical properties and a fatigue-damage model for jointed rock masses subjected to dynamic cyclical loading. [J] Int J Rock Mech Min Sci 2001;38(7):1071-1079.
[37]Ray S.K., Sarkar M., Singh T.N. Effect of cyclic loading and strain rate on the mechanical behaviour of sandstone[J] Int J Rock Mech Min Sci 1999;36:543-549.
[38]Attewell P. B. Farmer I. W. Fatigue behaviour of rock[J] Int J Rock Mech Min Sci 1973;10:1-9.
[39]Y.Ishizuka & T.Abe Fatigue behaviour of granite under cyclic loading. Static and Dynamic Considerations in Rock Engineering, Brummer, Balkema, Rotterdam,1990; 139-147.
[40]宋玉普,赵东拂.混凝土强度与疲劳寿命试验样本容量分析[J].大连理工大学学报,2002；42(4)：464-466.
[41]杨仕教,曾晟,王和龙.加载速率对石灰岩力学效应的试验研究[J].岩土工程学报.2005(07)：786-788.
[42]王瑞敏.混凝土结构疲劳性能研究[D].大连：大连理工大学,1989.
[43]姚明初.混凝土在变幅重复应力下疲劳性能的研究.[R].北京：“铁道建筑安全度(可靠性)及设计原理”专题报告,1986,4.
[44]葛修润.周期荷载作用下岩石大型三轴试验的变形和强度特性研究[J]岩土力学.1987；2.
[45]葛修润,任建喜,蒲毅彬等.岩土损伤力学宏细观试验研究[M].北京：科学出版社,2004.
[46]葛修润.周期荷载作用下岩石疲劳破坏及变形发展规律研究[A].第八次全国岩石力学与工程学术大会论文集[C].2004：23-31.
[47]章清叙,葛修润,黄铭,孙红.周期荷载作用下红砂岩三轴疲劳变形特性试验研究[J].岩石力学与工程学报.2006(03)：474-478.
[48]李树春.周期荷载作用下岩石变形与损伤规律及其非线性特征[D].重庆大学,2008.
[49]王鸿,许江,杨秀贵.循环载荷条件下岩石塑性滞回环的演化规律[J].重庆大学学报(自然科学版).2006(04)：80-82.
[50]吕培印.混凝土单轴、双轴动态强度和变形试验研究[D].大连理工大学2002.
[51]林燕清.混凝土疲劳累计损伤与力学性能劣化研究[D].哈尔滨：哈尔滨建筑大学,1998.
[52]李朝阳,宁玉普,赵国藩.混凝土疲劳残余应变性能研究[J].大连理工大学学报,2001,41(3)：355-358.
[53]王鸿,许江,李树春,胡玉红.不同水饱和度下岩石滞回曲线演化的实验研究[J].矿业研究与开发.2007；(03)：18-21.
[54]蒋宇,葛修润,任建喜.岩石疲劳破坏过程中的变形规律及声发射特性[J].岩石力学与工程学报,2004；23(11)：1810-1814.
[55]杨永杰,宋扬,楚俊.循环荷载作用下煤岩强度及变形特征试验研究[J].岩石力学与工程学报.2007(01)：201-205.
[56]Tutuncu A N, Podio A L, Sharma M M. Nonlinear viscoelastic behavior of sedimentary rock, part Ⅰ:effect of frequency and strain amplitude[J]. Geophysics,1998;63(1):184-190.
[57]Tutuncu A N, Podio A L, Sharma M M. Nonlinear viscoelastic behavior of sedimentary rock, part Ⅱ:hysteresis effects and influence of type of fluid on elastic moduli[J]. Geophysics, 1998;63(1):195-203.
[58]席道瑛,陈运平,陶月赞,等.岩石的非线性弹性滞后特征[J].岩石力学与工程学报,2006；25(6)：1086-1093.
[59]陈运平,席道瑛,薛彦伟.循环载荷下饱和岩石的滞后和衰减[J].地球物理学报,2004；7：672-680.
[60]陈运平,席道瑛,薛彦伟.循环载荷下饱和岩石的应力-应变动态响应[J].石油地球物理勘探,2003,38(4)：409-413.
[61]刘建峰,徐进,李青松,李刚林.循环载荷下岩石阻尼参数测试的试验研究[J].岩石力学与工程学报.2010；5：1036-1041.
[62]朱明礼,朱珍德,李刚,等.循环荷载作用下花岗岩动力特性试验研究[J].岩石力学与工程学报,2009,28(12)：2520-2526.
[63]肖建清,冯夏庭,丁德馨,蒋复量.常幅循环载荷作用下岩石的滞后和阻尼效应研究[J].岩石力学与工程学报,2010；8(29)：1677-1684.
[64]尤明庆,苏承东,杨圣奇.岩石动静态参数间关系的研究[J].焦作工学院学报(自然科学版),2002,21(6)：413-419.
[65]林英松,葛洪魁,王顺昌.岩石动静态力学参数的试验研究[J].岩石力学与工程学报,1998,17(2)：216-222.
[66]耿乃光等.岩石动态与静态杨氏模量的对比测量研究.第二届全国岩石力学学术会议,宜 昌：1990：50-54.
[67]Tutuncu A N, Sharma M M. Relating static and ultrasonic laboratory measurement to acoustic log measurement in tight gas sands. SPE24689,1993,299-311.
[68]Yale D P, Jamieson W H. Static and dynamic rock mechanical properties in the Hugo ton and Panoma field, Kansas.SPE27939,1995:209-219.
[69]Fairhurst C E, Hudson J A.单轴压缩试验测定完整岩石应力-应变全程曲线ISRM建议方法草案[J].岩石力学与工程学报,2000,19(6)：802-808.
[70]Naser, A AI-Shayea. Effects of testing methods and conditons on the elastic properties of limestone rock [J]. Engineering Geology.2004. (74):139-56.
[71]朱珍德,孙林柱,王明洋.不同频率循环荷载作用下岩石阻尼比试验与变形破坏机制细观分析[J].岩土力学,2010,31(1)：8-12.
[72]Lajtai E.Z., Scott Duncan E.J. et al. The effect of stain rate on rock strength [J]. Rock Mech and Rock Eng 1991;(24):99-109.
[1]张滨生,吴科如.水泥混凝土疲劳破坏的损伤力学分析[J].同济大学学报,1989,17(1)；59-69.
[2]谢和平,经典损伤定义中的“弹性模量法”探讨[J].力学与实践,1997,19(2)：1-5.
[3]杨永杰,宋扬,楚俊.循环荷载作用下煤岩强度及变形特征试验研究[J].岩石力学与工程学报.2007(01)：201-205.
[4]徐速超,冯夏庭,陈炳瑞.矽卡岩单轴循环加卸载试验及声发射特性研究[J].岩土力学.2009(10)：2929-2934.
[5]许江,李树春,唐晓军,陶云奇,杨红伟.基于声发射的岩石疲劳损伤演化[J].北京科技大学学报.2009(01)：19-24.
[6]姚卫星.结构疲劳寿命分析[M].北京：国防工业出版社.2003.
[7]宋玉普,赵东拂.混凝土强度与疲劳寿命试验样本容量分析[J].大连理工大学学报,2002,42(4)：464-466.
[8]赵造东.水工混凝土受压疲劳性能及累计损伤研究[D].昆明：昆明理工大学.2011.
[9]郭佳奇.岩溶隧道防突厚度及突水机制研究[D].北京：北京交通大学.2011.
[10]乔春生.溶洞、暗河地段隧道的结构型式和施工技术研究阶段成果报告[R].北京：北京交通大学,2008.
[11]曹茜.岩溶隧道与溶洞的安全距离研究.[D].北京：北京交通大学.2010.
[2]B.H.G.布雷迪,E.T.布朗.地下采矿岩石力学[M].冯树仁,佘诗刚等译.北京：煤炭工业出版社,1986.
[3]中华人民共和国交通部,公路隧道设计规范TJGD70-2004,北京：人民交通出版社,2004.
[4]王梦恕.对岩溶区隧道施工水文地质超前预报的意见[J].铁道勘察,2004(1)：7-9.
[5]于波.深埋隧洞中的岩溶地基工程地质问题及地基处理[J].岩石力学与工程学报,2004,23(1)：403-407.
[6]李彪,梁富清.高速公路隧道施工中的岩溶问题研究[J].工程力学,2000(增刊)764-768.
[7]铁道部第二勘察设计院.岩溶工程地质[M].北京：中国铁道出版社,1984.
[8]吴梦军,许锡宾,赵明阶.岩溶地区公路隧道施工力学响应研究[J].岩石力学与工程学报,2004,23(9)：1525-1529.
[9]傅鹤林.隧道衬砌荷载计算理论及岩溶处治技术[M].长沙：中南大学出版社,2005.
[10]邹成杰.水利水电岩溶工程地质[M].北京：地质出版社,1994.
[11]刘招伟,张民庆,王树仁.岩溶隧道灾变预测与处治技术[M].第二版.北京：科学出版社,2007.
[12]王勇,乔春生,孙彩红,刘开云,岩溶隧道溶洞顶板安全厚度智能预测模型[J],岩土力学,2006,27(6)：1000-1006
[13]宋战平.隐伏溶洞对隧道围岩——支护结构稳定性的影响研究[D].西安：西安理工大学,2006.
[14]郭佳奇.岩溶隧道防突厚度及突水机制研究[D].北京：北京交通大学,2011.
[15]李利平.高风险岩溶隧道突水灾变演化机制及其应用研究[D].济南：山东大学,2009.
[16]赖永标,乔春生,基于SVM隧道与溶洞安全距离预测模型[J],四川大学学报(工程科学版),2007,39(增刊)：72-77
[17]陈传尧.疲劳与断裂[M].武汉：华中科技大学出版社,2001.
[18]蒋宇.周期荷载作用下岩石疲劳破坏及变形发展规律[D硕士学位论文].上海：上海交通大学.2003
[19]张滨生,朱照宏.水泥混凝土路面的疲劳损伤分析[J].土木工程学报.1986(04)：54-60
[20]张滨生,吴科如.水泥混凝土疲劳破坏的损伤力学分析[J].同济大学学报.1989(01)：59-70
[21]B.Zhang,D.V.Phillips and K.Wu Effects of loading frequency and stress reversal on fatigue life of plain concrete[J]. Magazine of Concrete Research,1996,No.177,361-375
[22]过镇海.混凝土的强度和变形：试验基础和本构关系[M].北京：清华大学出版社,1997.
[23]过镇海,张秀琴.混凝土在反复荷载作用下的应力-应变全曲线[J].冶金建筑,1981(9)：14-17
[24]王瑞敏,赵国藩,宋玉普.混凝土的受压疲劳性能研究[J].土木工程学报.1991(04)：38-47
[25]王瑞敏,宋玉普,赵国藩.混凝土疲劳累积损伤准则[J].水利学报.1992(05)：72-76
[26]宋玉普.混凝土结构的疲劳性能及设计原理[M].机械工业出版社,2006
[27]董毓利,谢和平,赵鹏.循环受压砼全过程声发射实验及其本构关系[J].实验力学,1996(2)：216-221
[28]林燕清,欧进萍.混凝土疲劳损伤试验中试件初始极限强度的推测方法[J].哈尔滨建筑大学学报.1997(06)：9-20
[29]欧进萍,林燕清.混凝土疲劳损伤的强度和刚度衰减试验研究[J].哈尔滨建筑大学学报.1998(04)：1-8
[30]林燕清,欧进萍.混凝土多级等幅疲劳的变形发展规律试验研究[J].哈尔滨建筑大学学报.1999(01)：11-17
[31]欧进萍,林燕清.混凝土高周疲劳损伤的性能劣化试验研究[J].土木工程学报.1999(05)：15-22
[32]易成,沈世钊.疲劳裂纹扩展理论及其在混凝土疲劳性能研究中的应用[J].哈尔滨建筑大学学报.2000(05)：20-24
[33]李朝阳,宋玉普,赵国藩.混凝土疲劳残余应变性能研究[J].大连理工大学学报.2001(03)：355-358
[34]李朝阳,宋玉普,车轶.混凝土的单轴抗压疲劳损伤累积性能研究[J].土木工程学报.2002(02)：38-40
[35]吕培印.混凝土单轴、双轴动态强度和变形试验研究[D].大连理工大学2002
[36]赵东拂.混凝土多轴疲劳破坏准则研究[D].大连理工大学2002
[37]朱劲松.混凝土双轴疲劳试验与破坏预测理论研究[D].大连理工大学2003
[38]曹伟,宋玉普.多级加载下混凝土疲劳剩余寿命预测新方法[J].大连理工大学学报.2003(05)：659-662
[39]曹伟.定侧压下混凝土三轴疲劳性能试验与理论研究[D].大连理工大学2004
[40]孟宪宏.混凝土疲劳剩余强度试验及理论研究[D].大连理工大学2006
[41]Burdine NT. Rock failure under dynamic loading conditions. [J]. Soc Petr Eng J 1963(03):1-8.
[42]Haimson BC, Kim CM. Mechanical behaviour of rock under cyclic fatigue. In:Cording EJ, editor. Stability of rock slopes Proceedings of the 13th Synposium on Rock Mechanics, New York:ASCE,1972:845-863.
[43]Attewell PB, Farmer IW. Fatigue behaviour of rock. [J]. Int J Rock Mech Min Sci 1973(10): 1-9.
[44]Singh SK. Fatigue and strain hardening behaviour of Graywacke from the Flagstaff formation, New South Wales. [J]. Engineering Geology 1989(26):171-179.
[45]Zhenyu T, Haihong M. Technical note:an experimental study and analysis of the behaviour of rock under cyclic loading. [J]. Int J Rock Mech Min Sci Geomech Abstr 1990 27(1):51-56.
[46]Ishizuka Y, Abe T, Kodama J. Fatigue behaviour of granite under cyclic loading. In:Brumer R, editor, ISRM international symposium-static and dynamic considerations In rock engineering,Swaziland,1990:139-46.
[47]Tien YM, Lee DH, Juang CH. Strain, pore pressure and fatigue characteristics of sandstone under various load conditions. [J]. Int J Rock Mech Min Sci Geomech Abstr 1990;27(4):283-9.
[48]Yamashita S, Sugimoto F, Imai T, Namsrai D, Yamauchi M.Kamoshida N. The relationshipbetween the failure process of the creepor fatigue test and of the conventional compression test on rock. In:Vouille G, Berest P, editors. ISRM nineth international congress on rock mechanics, Vol.2, Paris/France,1999:699-702.
[49]Lajtai EZ, Scott Duncan EJ, Carter BJ. The effect of strain rate on rock strength. [J]. Rock Mech Rock Eng 1991 (24):99-109.
[50]Ray SK, Sarkar M, Singh TN. Effect of loading and strain rate on the mechanical behaviour of sandstone. [J]. Int J Rock Mech Min Sci 1999(36):543-549.
[51]Bagde MN, Petros V. The effect of machine behaviour and mechanical properties of intact sandstone under static and dynamic uniaxial cyclic loading. [J]. Rock Mech Rock Eng 2005;38(1):59-67.
[52]Bagde MN, Petros V. Fatigue properties of intact sandstone samples subjected to dynamic uniaxial cyclical loading. [J]. Int J Rock Mech Min Sci 2005(42):237-250.
[53]Bagde MN, Petros V. Fatigue and dynamic energy behaviour of rock subjected to cyclical loading. [J]. Int J Rock Mech Min Sci 2009(46):200-206.
[54]葛修润,卢应发.循环荷载作用下岩石疲劳破坏和不可逆变形问题的探讨[J].岩土工程学报,1992(3)：56-60.
[55]葛修润,蒋宇等.周期荷载作用下岩石疲劳变形特性试验研究[J].岩石力学与工程学报,2003,22(10)：1581-1585.
[56]章清叙,葛修润等.周期荷载作用下红砂岩三轴疲劳变形特性试验研究[J].岩石力学与工程学报,2006,25(3)：474-478.
[57]Li N, Chen W, Zhang P, Swoboda G. Technical note:the mechanical properties and a fatigue-damage model for jointed rock masses subjected to dynamic cyclical loading [J].Int J Rock Mech Min Sci 2001;38:1071-1079.
[58]Li N, Zhang P, Chen Y, Swoboda G. Technical note:fatigue properties of a cracked, saturated and frozen sandstone samples under cyclic loading. [J]. Int J Rock Mech Min Sci 2003;40: 145-50.
[59]许江,杨秀贵,王鸿,等.周期性载荷作用下岩石滞回曲线的演化规律[J].西南交通大学学报,2005.40(6)：754-758.
[60]许江,王维忠,杨秀贵,等.细粒砂岩在周期性循环荷载作用下变形实验[J].重庆大学学报(自然科学版),2004,27(12)：60-62.
[61]许江,鲜学福,王鸿,等.循环加、卸载条件下岩石类材料变形特性的实验研究[J].岩石力学与工程学报,2006,25(s.1)：3040-3045.
[62]席道瑛,王春雷,田象燕.滞回曲线对应力振幅和频率的响应[J].物探化探计算技术,2001,23(2)：121·124.
[63]刘云平,席道瑛,张程远等.循环应力作用下大理岩砂岩的动态响应[J].岩石力学与工程学报,2001,20(2)：216-219.
[64]陈运平,席道瑛,薛彦伟.循环载荷下饱和岩石的应力-应变动态响应[J].石油地球物理勘探,2003,38(4)：409-413.
[65]陈运平,席道瑛,薛彦伟.循环荷载下饱和岩石的滞后和衰减[J].地球物理学报,2004,47(4)：672-679.
[66]樊秀峰,简文彬.砂岩疲劳特性的超声波速法试验研究[J].岩石力学与工程学报,2008,27(3)：557-563
[67]Xiao JQ, Ding DX, Xu G, et al. Waveform effect on quasi-dynamic loading condition and the mechanical properties of brittle materials. [J]. Int J Rock Mech Min Sci 2008;45(4):621-626.
[68]杨永杰,宋扬,楚俊.循环荷载作用下煤岩强度及变形特征试验研究[J].岩石力学与工程学报.2007(01)：201-205
[69]朱明礼,朱珍德,李刚,邱玉华,陈哲,李金旺.循环荷载作用下花岗岩动力特性试验研究[J].岩石力学与工程学报.2009(12)：2520-2526
[70]倪骁慧,朱珍德,李晓娟,李志敬,朱明礼.循环荷载下花岗岩细观损伤量化试验研究[J].岩 土力学.2011(07)：1991-1995
[71]Enlong Liu, Siming He. Effects of cyclic dynamic loading on the mechanical properties of intact rock samples under confining pressure conditions[J] Engineering Geology 2012 (125) 81-89
[72]王者超,赵建纲,李术才,薛翊国,张庆松,姜彦彦.循环荷载作用下花岗岩疲劳力学性质及其本构模型[J].岩石力学与工程学报.2012(09)：1888-1900
[73]Jose Fernando Sima, Pere Roca, Climent Molins. Cyclic constitutive model for concrete[J]. Engineering Structures 2008 (30):695-706
[74]Bahn Byong Youl. Hsu Cheng-Tzu Thomas. Stress-strain behavior of concrete under cyclic loading [J] ACI Materiais Journal,1998,95(2)::178-193
[75]Mazars J A description of micro-and macro-scale damage of concrete structures [J]. Engineering Fracture Mechanics,1986,25(5/6):729-737
[76]Enrico Papa, and Alberto Taliercio. Anisotropic damage model for the multi-axial stratic and fatigue behaviour of plain concrete [J] Engineering Fracture Mechanics,1996,55(2):163-179
[77]谢和平,经典损伤定义中的“弹性模量法”探讨[J]力学与实践,1997,19(2)：1-5
[78]齐红宇,温卫东,孙联文.基于刚度下降的疲劳累积损伤模型的研究[J].北京航空航天大学学报.2004(12)：1200-1203
[79]潘华,邱洪兴.基于损伤力学的混凝土疲劳损伤模型[J].东南大学学报(自然科学版).2006(04)：605-608
[80]李树春,许江,陶云奇,等.岩石低周疲劳损伤模型与损伤变量表达方法[J].岩土力学,2009,30(6)：1611-1614
[81]许宏发,王武,方秦,王万波,循环载荷下岩石塑性应变演化模型[J]解放军理工大学学报,2012(13)282-286
[82]吴鸿遥.损伤力学[M].北京：国防工业出版社,1990
[83]Xiao JQ, Ding DX, Xu G, et al. Inverted S-shaped model for nonlinear fatigue damage of rock [J]. Int J Rock Mech Min Sci 2009(46):643-648.
[84]DAFALIAS Y F. On cyclic and anisoisotropic plasticity:(1) A general model including material behavior under stress reversals; (2) Anisotropic hardening for initially orthotropic materials[D]. Berkeley:University of California,1975.
[85]宋玉普,朱劲松.疲劳荷载作用下混凝土的边界面模型研究[J].哈尔滨工业大学学报,2005,37(1)：74-79
[86]Fardis M N, Alibe B, Tassoulas J L. Monotonic and cyclic constitutive law for concrete[J] Journal of Engineering Mechanics, ASCE 1983,109 (2):516-536
[87]Fardis M. N., Chen E. S. A cyclic multiaxial model for concrete[J]. Computational mechanics, 1986,(1):301-315
[88]Yang B. L., Dafalias Y. F., Herrmann L. R. A bounding surface plasticity model for concrete[J]. Journal of Engineering Mechanics, ASCE,1985,111(3):359-380
[89]Aas-Jakobsen K. Fatigue of concrete beams and condumns[J]. Bulletiin No.70-1.NTH insititute of Betonkonstruksjoner, Trondheim,1970
[90]Thomas, hsu. Fatigue of plain concrete[J]. ACI Journal,1981,78(3):292-305
[91]Jan Ove Holmen. Fatigue of concrete by constant and variable amplitude loading[J]. FatigueStrength of Concrete Structures, SP-75, ACI,1982:71-11
[92]赵造东；张立翔；王时越等幅循环荷载下水工混凝土疲劳寿命分析[J]昆明理工大学学报(自然科学版)2001(03)：8-11
[93]赵造东,张立翔,王时越谱荷载下剩余强度衰减的混凝土疲劳寿命可靠性分析[J]；力学与实践；2002(01)：8-11
[94]朱劲松,宋玉普.基于剩余强度衰减的混凝土疲劳寿命估算方法[J].海洋工程.2003(03)：78-82
[95]吕培印,宋玉普.基于人工神经网络的混凝土疲劳寿命估算[J].海洋工程.2001(03)：72-76
[96]李士彬,朱慈勉,汤红卫.由刚度衰减规律预测混凝土梁疲劳寿命的试验研究[J]建筑结构,2006(02)：51-54
[97]刘建坤,肖军华,杨献永,陈立宏.提速条件下粉土铁路路基动态稳定性研究[J].岩土力学.2009(02)：399-406
[1]E. EBERHARDT. Brittle rock fracture and progressive damage in uniaxial compression[D]. Saskatoon:University of Saskatchenwan.1998.
[2]刘佑荣,唐辉明.岩体力学[M].中国地质大学出版社.1999.
[3]Qi C, Wang M, Qian Q. Strain rate effects on the strength and fragmentation size of rocks. [J]. Int J Impact Eng 2009;36(12):1355-64.
[4]Li Z, Wang Q. Experimental research on effect of loading rate for dynamic fracture toughness of rock. [J]. Chin J Geotech Eng 2006;28:2116-20.
[5]S Yang, S Zeng, H Wang. Experimental analysis on mechanical effects of loading rates on limestone. [J]. Chin J Geotech Eng 2005;27:786-8.
[6]R C FRANSSEN, M W. The rheology of synthetic rocksalt in uniaxial compression[J]. Tectonophysics.1994; 223(1/2):1-40.
[7]WG LIANG, YS ZHAO, S G XU, et al. Effect of strain rate on the mechanical properties of salt rock[J]. Int J Rock Mech Min Sci.2011; 48(1):161-167.
[8]姜德义,陈结,任松,王维忠,白月明.盐岩单轴应变率效应与声发射特征试验研究[J].岩石力学与工程学报.2012(02)：326-336
[9]W. F. Brace. Comparison of uniaxial deformation in shock and static loading of the three rock[J] Geo-Phys. Res,1971(76):4913-4921.
[10]Y. Mahmutoglu. The effects of strain rate and saturation on a micro-cracked marble. [J] Eng Geol 2006;82:137-44.
[11]S.H. Cho, Y. Ogata, K. Kaneko. Strain-rate dependency of the dynamic tensile strength of rock. [J] Int J Rock Mech Min Sci 2003;40:763-77.
[12]席道瑛,谢端,张毅,何炬.加载速率对岩石力学性质及声发射率的影响[A].第四届全国岩石动力学学术会议论文选集[C].1994：469-471
[13]洪亮,李夕兵,马春德,尹土兵,叶洲元,廖国燕.岩石动态强度及其应变率灵敏性的尺寸效应研究[J].岩石力学与工程学报.2008(03)：526-533
[14]杨仕教,曾晟,王和龙.加载速率对石灰岩力学效应的试验研究[J].岩土工程学报.2005(07)：786-788
[151杨海清,周小平.灰岩单轴压缩损伤演化试验研究[J].土木工程学报.2010(05)：117-123
[16]黄达,黄润秋,张永兴.粗晶大理岩单轴压缩力学特性的静态加载速率效应及能量机制试验研究[J].岩石力学与工程学报.2012(02)：245-254
[17]肖诗云,张剑.不同应变率下混凝土受压损伤试验研究[J].土木工程学报.2010(03)：40-45
[18]W. Janach. The role of bulking in brittle Failure of rocks under rapid compression[J]. Int J Rock Mech Min Sci & Geo Abs,1976,13(6):177-186.
[19]梁昌玉,李晓,马超锋.中等应变率加载条件下岩石的变形和力学特性研究进展及展望[J].工程地质学报.2012(01)：88-94
[20]王洪亮,范鹏贤,王明洋,李文培,钱岳红.应变率对红砂岩渐进破坏过程和特征应力的影响[J].岩土力学.2011(05)：1340-1346
[21]金丰年,岩石的载荷速度效应[J].岩石力学与工程学报.1998(12)711-717
[22]尤明庆.两种晶粒大理岩的力学性质研究[J].岩土力学,2005,26(1)；91-96.
[23]梁卫国,徐素国,莫江,吴迪,张传达.盐岩力学特性应变率效应的试验研究[J].岩石力学与工程学报.2010(01)：43-50
[24]S.K. Ray, M. Sarkar, T.N. Singh. Effect of cyclic loading and strain rate on the mechanical behaviour of sandstone [J]. Int J Rock Mech Min Sci 1999 (36):543-49
[25]朱泽奇,盛谦,冷先伦,等.三峡花岗岩起裂机制研究[J].岩石力学与工程学报,2007,26(12)：2570-2575
[26]C. D. Martin, N. A. Chardler. The progressive fracture of Lac du Bonnet granite[J]. Int J Rock Mech Min Sci & Geo Abs,1994,31(6):643-659
[27]XB Li, TS Lok, J Zhao. Dynamic characteristics of granite subjected to intermediate loading rate [J. Rock Mech & Rock En.2005; 38(1):21-29.
[1]葛修润,蒋宇,卢允德,任建喜.周期荷载作用下岩石疲劳变形特性试验研究[J].岩石力学与工程学报.2003(10)：1581-1585
[2]葛修润.岩石疲劳破坏的变形控制律、岩土力学试验的实时X射线CT扫描和边坡坝基抗滑稳定分析的新方法[J].岩土工程学报.2008(01)：1-20
[3]林燕清,欧进萍.混凝土疲劳损伤试验中试件初始极限强度的推测方法[J].哈尔滨建筑大学学报.1997(06)：9-20
[4]ISRM Suggested Methods. In:Brown ET, editor. Rock characterization testing and monitoring. Oxford:Pergamon Press,1981.
[5]American Society for Testing and Materials. Standard test method for unconfined compressive strength of intact rock core specimens. Soil and Rock, Building Stones:Annual Book of ASTM Standards 4.08. Philadelphia, Pennsylvania:ASTM,1984.
[6]Cargill, J.S., Shakoor, A. Evaluation of empirical methods for measuring the uniaxial compressive strength of rock [J]. Int J Rock Mech Min Sci & Geomech Abstr.1990;27(6): 495-503.
[7]Kahraman S. Evaluation of simple methods for assessing the uniaxial compressive strength of rock[J] International Journal of Rock Mechanics & Mining Sciences (2001);38:981-994
[8]Sarkar, K., Vishal, V. et al. An empirical correlation of index geomechanical parameters with the compressional wave velocity [J]. Geotech Geol Eng.2012;30:469-479.
[9]Yasar, E., Erdogan, Y. Correlating sound velocity with the density, compressive strength and Young's modulus ofcarbonate rocks [J]. Int J Rock Mech Min Sci.2004; 41:871-875.
[10]Gaviglio, PLongitudinal waves propagation in a limestone:The relationship between velocity and density[J] Rock Mechanics and Rock Engineering,1989; 22(04):299-306.
[11]Kahraman Sair. Yeken Tekin. Determination of physical properties of carbonate rocks from P-wave velocity[J] Bull Eng Geol Environ 2008;67:277-281
[12]Khandelwal M., Singh T.N. Correlating static properties of coal measures rocks with P-wave velocity[J] International Journal of Coal Geology 2009,79:55-60
[13]Entwisle D.C., Hobbs P.R.N., Jones L.D., Gunn D. and Raines M.G.. The relationships between effective porosity, uniaxial compressive strength and sonic velocity of intact Borrowdale Volcanic Group core samples from Sellafield [J] Geotech Geol Eng.2005;23:793-809
[14]Kahraman, S., Soylemez, M. et al. Determination of fracture depth of rock blocks from P-wave velocity [J]. Bull Eng Geol Environ.2008;67:11-16.
[15]Sharma P.K., Khandelwal M., Singh T.N. A correlation between Schmidt hammer rebound numbers with impact strength index, slake durability index and P-wave velocity. [J] Int J Earth Sci 2011; 100:189-195
[16]Sharma P. K., Singh T. N. A correlation between P-wave velocity, impact strength index, slake durability index and uniaxial compressive strength[J] Bull Eng Geol Environ 2008; 67:17-22
[17]Kahraman S.. The correlations between the saturated and dry P-wave velocity of rocks[J] Ultrasonics 2007;46:341-348
[18]Goktan RM. Theoretical and practical analysis of rock rippability.[D] Istanbul Technical University,1988.
[19]Ibrahim Cobanoglu, Sefer Beran Celik Estimation of uniaxial compressive strength from point load strength, Schmidt hardness and P-wave velocity[J] Bull Eng Geol Environ.2008;67(04): 491-498
[20]Yilmaz I., Sendir H. Correlation of Schmidt hardness with unconfined compressive strength and Young's modulus in gypsum from Sivas (Turkey)[J] Engineering Geology 2002;66: 211-219
[21]Guney A. Altindag R.Yavuz H.& Sarac S. The 19th International Mining Congress and Fair of Turkey, IMCET2005, izmir, Turkey,2005; 07:09-12
[22]Aydin A., Basu A. The Schmidt hammer in rock material characterization[J] Engineering Geology 2005;81:1-14
[23]Buyuksagis I.S., Goktan R.M. The effect of Schmidt hammer type on uniaxial compressive strength prediction of rock International.[J] Int J Rock Mech Min Sci.2007;44:299-307
[24]ISRM. Suggested methods for determining hardness and abrasiveness of rocks.[J] Int J Rock Mech Min Sci Geomech Abstr 1978;15:89-98.
[25]ASTM. Standard test method for determination of rock hardness by rebound hammer method. ASTM Stand.04.09 (D 5873-00).2001.
[26]Poole RW, Farmer IW. Consistency and repeatability of Schmidt hammer rebound data during field testing.[J] Int J Rock Mech Min Sci Geomech Abstr 1980;17:167-71.
[27]Goktan RM, Ayday C. A suggested improvement to the Schmidt rebound hardness ISRM suggested method with particular reference to rock machineability.[J] Int J Rock Mech Min Sci Geomech Abstr 1993;30:321-2.
[28]Hucka V. A rapid method for determining the strength of rocks in situ. [J]Int J Rock Mech Min Sci Geomech Abstr 1965;2:127-134.
[29]Yagiz Saffet. Predicting uniaxial compressive strength, modulus of elasticity and index properties of rocks using the Schmidt hammer [J]. Bull Eng Geol Environ.2009; 68:55-63.
[30]McCarroll D. The Schmidt hammer as a measure of degree of rock surface weathering and terrain age. In:Beck C, editor. Dating in exposed and surface contexts. Mexico:University of New Mexico Press; 1994:29-45.
[31]Kahraman S., Fener M., Gunaydin O. Predicting the Schmidt hammer values of in-situ intact rock from core sample values[J] Int J Rock Mech Min Sci.2002;39:395-399
[32]刘宗平,王润起,吴小林,孙金龙.施密特锤试验数据处理方法及其在预估岩石可钻性中的应用[J].现代地质.1990(04)：113-123
[33]Deere DU, Miller RP. Engineering classifications and index properties of intact rock. Technical report no. AFWL-TR 65-116, University of Illinois:1966; p.300.
[34]Soiltest Inc., Operating instructions-concrete test hammer. Evanston, IL.1976.
[35]Young RP, Fowell RJ. Assesing rock discontinuities. [J]Tunnels Tunnelling. June 1978; 45-48.
[36]Matthews JA, Shakesby RA. The status of the Little Ice Age in southern Norway:relative-age dating of Neoglacial moraines with Schmidt hammer and lichenometry. Boreas 1984;13:333-34
[37]Katz O, Reches Z, Roegiers J. C. Evaluation of mechanical rock properties using a schmidt hammer.[J] Int J Rock Mech Min Sci 2000;37:723-728.
[38]Sumner P, Nel W. The effect of rock moisture on Schmidt hammer rebound:tests on rock samples from Marion Island and South Africa. Earth Surf Process Landforms 2002;27:l 137-42.
[39]Fowell RJ, McFeat Smith I. Factors influencing the cutting performance of a selective tunnelling machine. In:Tunnelling'76, proc int symp IMM, London,1976:301-9.
[40]Poole RW, Farmer IW. Consistency and repeatability of Schmidt hammer rebound data during field testing. [J]Int J Rock Mech Min Sci Geomech Abstr 1980; 17:167-71
[41]Kazi A, Al-Mansour ZR. Empirical relationship between Los Angeles Abrasion and Schmidt hammer strength tests with application to aggregates around Jeddah. Q J Eng Geol London: 1980;13:45-52.
[42]Goktan, R.M., Gunes, N. A comparative study of Schmidt hammer testing procedures with reference to rock cutting machine performance prediction [J]. Int. J. Rock Mech & Minng Sci. 2005;42:466-472.
[43]Singh, R.N., Hassani, F.P., Elkington, P.A.S., The application of strength and deformation index testing to the stability assessment of coal measures excavations. Proc.24th US Symp. On Rock Mech., Texas A&M Univ., AEG. Balkema, Rotterdam,1983; 599-609.
[44]Shorey, P.R., Barat, D., Das, M.N., Mukherjee, K.P., Singh, B., Schmidt hammer rebound data for estimation of large scale in-situ coal strength.[J] Int. J. Rock Mech. Min. Sci. Geomech. Abstr.1984;21:39-4
[45]Haramy, K.Y., DeMarco, M.J., Use of Schmidt hammer for rock and coal testing. Proc.26th US Symp. on Rock Mech.26-28 June, Rapid City. Balkema, Rotterdam,1985; 549-555.
[46]Ghose, A.K., Chakraborti, S., Empirical strength indices of Indian coals-an investigation. Proceedings of 27th US Symp. on Rock Mechanics. Balkema, Rotterdam,1986;59-61.
[47]Sachpazis, C.I., Correlating Schmidt hardness with compressive strength and Young's modulus of carbonate rocks.[J] Bull. Int. Assoc. Eng. Geol.1990;42:75-83.
[48]Xu, S., Grasso, P., Mahtab, A., Use of Schmidt hammer for estimating mechanical properties of weak rock.6th Int. IAEG Congress. Balkema, Rotterdam,1990; 511-519.
[49]Tugrul, A., Zarif, I.H., Correlation of mineralogical and textural characteristics with engineering properties of selected granitic rocks from Turkey. [J] Eng. Geol.1999.51:303-317.
[50]Shalabi F, Cording EJ, Al-Hattamleh OH Estimation of rock engineering properties using hardness tests[J]Eng. Geol.2007:90:138-147
[51]CECS02:2005超声回弹综合法检测混凝土强度技术规程[S].中国工程建设标准化协会标准.
[1]Jenkins H. H., Stephenson J. E., Clayton G. A. et al. The effect of track and vehicle parameters on wheel/rail vertical dynamic forces[J] Railway Engineering Journal,1974;3(1):2-16.
[2]刘建坤,肖军华,杨献永,陈立宏.提速条件下粉土铁路路基动态稳定性研究[J].岩土力学.2009(02)：399405.
[3]黄娟.基于损伤理论的高速铁路隧道结构振动响应分析及疲劳寿命研究[D].中南大学2010.
[4]Mor A. Gerwick B.C. Hester W.T. Fatigue of high strength reinforced concrete[J]. ACI Journal, 1992;89(2):197-207.
[5]Bagde MN, Petros V. Fatigue and dynamic energy behaviour of rock subjected to cyclical loading[J] Int J Rock Mech Min Sci 2009;46:200-206.
[6]莫海鸿.岩石的循环试验及本构关系的研究[J]岩石力学与工程学报,1988；7(3)：215-224.
[7]林卓英,吴玉山.岩石在循环荷载作用下的强度及变形特性[J].岩土力学,1987；8(3)：31-37.
[8]蒋宇.周期载荷作用下岩石疲劳破坏及变形发展规律[D]上海：上海交通大学,2003.
[9]MeCall John T. Probability of fatigue failure of Plain concrete[J]. ACI Journal, Proeeedings, 1958;55(2):233-244.
[10]赵造东,张立翔,王时越.等幅循环荷载下水工混凝土疲劳寿命分析[J].昆明理工大学学报(自然科学版).2001(03)：8-11.
[11]Yamashita S, Sugimoto F, Imai T, Namsrai D, Yamauchi M, Kamoshida N. The relationship between the failure process of the creepor fatigue test and of the conventional compression test on rock. In:Vouille G, Berest P, editors. ISRM nineth international congress on rock mechanics, Vol.2, Paris/France,1999. p.699-702.
[12]葛修润,蒋宇,卢允德,任建喜.周期荷载作用下岩石疲劳变形特性试验研究[J].岩石力学与工程学报.2003(10)：1581-1585.
[13]葛修润,卢应发循环荷载作用下岩石疲劳破坏和不可逆变形问题的探讨[J].岩土工程学报,1992(3)：56-60.
[14]肖建清.循环荷载作用下岩石疲劳特性的理论与实验研究[D].中南大学2009.
[15]陶振宇.岩石力学原理与方法,武汉,中国地质大学出版社,1991.87-89.
[16]Aas-Jakobson K..Fatigue of concrete beams and columns[J]. Bulletin No.70-1. NTH Institute of Betonkonstruksjoner, Trondheim,1970.
[17]Tepfers R., and Kutti T.. Fatigue strength of plain, ordinary and lightweight concrete[J]. ACI Journal,1979,76(5):635-652.
[18]Tepfers R., Gorlin J., and Samuelsson T.. Concrete subjected to pulsating load and pulsating deformation of different pulse wave-form[J]. Nordisk Betong,1973,4:27-36.
[19]Tao Z. Y, Mo H. H.. Technical note:an experimental study and analysis of the behaviour of rock under cyclic loading.[J] Int J Rock Mech Min Sci Geomech Abstr 1990;27(1):51-56.
[20]JianQing Xiao,DeXin Dingb, Gen Xua, FuLiang Jianga. Waveform effect on quasi-dynamic loading condition and the mechanical properties of brittle materials[J] Int J Rock Mech Min Sci 2009;45:621-626.
[21]任建喜,蒋宇,葛修润.单轴压缩岩石疲劳寿命影响因素试验分析[J].岩土工程学报.2005(11)：1282-1285.
[22]Bagde M. N., Petros V. Waveform Effect on Fatigue Properties of Intact Sandstone in Uniaxial Cyclical Loading[J] Rock Mech. Rock Eng.2005; 38 (3):169-196.
[23]Bagde, M. N., Petros, V. Fatigue properties of intact sandstone samples subjected to dynamic uniaxial cyclical loading. [J] Int. J. Rock Mech. Min. Sci.2005; 42(2):237-250.
[24]Graf O., Brenner E.. Experiments for investigating the resistance of concrete under often repeated compression loads.1[J] Bulletin, Deutscher Ausschuss fur Stahlbeton, Berlin, 1934;76:17-25.
[25]Graf O., Brenner E.. Experiments for investigating the resistance of concrete under often repeated compression loads.2[J] Bulletin, Deutscher Ausschuss fur Stahlbeton, Berlin, 1936;83:45-53.
[26]Kesler C. E.. Effects of speed of testing on flextural fatigue strength of plain concrete[J]. Proceedings Highway Research Board,1953:32; 251-258.
[27]Raithby K. D. Galloway J. W. Effects of moisture condition, age, and rate of loading on fatigue of plain concrete[J] Fatigue of concrete, ACI SP-41, Detroit,1974; 15-34.
[28]Gray W. H., Mclaughlin J. F., Antrim J.D. Fatigue properties of lightweight aggregate concrete[J].ACI Journal, Proceedings,1961;58:149-160.
[29]Raithby K. D. Flexural fatigue behavior of plain concrete[J] Fatigue of Engineering Materials and Structures 1979;2:269-278.
[30]Wagaard K. Fatigue of offshore concrete structures-design and experimental investigations[J]. 9th Annual Offshore Technology Conference in Huston 1977; 341-350.
[31]Arthur P. D. Carl J. C. Hodgkiess T. Corrosion fatigue in concrete for marine applictions[J] Fatigue of Concrete Structures ACI SP-75, Detroit,1982; 1-24.
[32]Sparks P. R. Menzies J. B. The effects of rate of loading upon the static and fatigue strengths of plain concrete in compression[J] Magazine of Concrete Research,1973;83:73-80.
[33]Sparks P. R. Influence of rate of loading and material variability on the fatigue characteristics of concrete[J] ACI Journal, Special Publication,1982; 216:331-342.
[34]Hatano T. Watanabe H. Fatigue failure of concrete under periodic compressive load[J] Transactions of Japan Society of Civil Engineering (Tokyo),1971;1:106-107.
[35]Turtak K, Ein verfahren zur berechnumg der betonfestigkeit unter schwellenden belastungen[J] Cement and Concrete Research,1984;6:855-865.
[36]Li N, Chen W, Zhang P, Swoboda G. The mechanical properties and a fatigue-damage model for jointed rock masses subjected to dynamic cyclical loading. [J] Int J Rock Mech Min Sci 2001;38(7):1071-1079.
[37]Ray S.K., Sarkar M., Singh T.N. Effect of cyclic loading and strain rate on the mechanical behaviour of sandstone[J] Int J Rock Mech Min Sci 1999;36:543-549.
[38]Attewell P. B. Farmer I. W. Fatigue behaviour of rock[J] Int J Rock Mech Min Sci 1973;10:1-9.
[39]Y.Ishizuka & T.Abe Fatigue behaviour of granite under cyclic loading. Static and Dynamic Considerations in Rock Engineering, Brummer, Balkema, Rotterdam,1990; 139-147.
[40]宋玉普,赵东拂.混凝土强度与疲劳寿命试验样本容量分析[J].大连理工大学学报,2002；42(4)：464-466.
[41]杨仕教,曾晟,王和龙.加载速率对石灰岩力学效应的试验研究[J].岩土工程学报.2005(07)：786-788.
[42]王瑞敏.混凝土结构疲劳性能研究[D].大连：大连理工大学,1989.
[43]姚明初.混凝土在变幅重复应力下疲劳性能的研究.[R].北京：“铁道建筑安全度(可靠性)及设计原理”专题报告,1986,4.
[44]葛修润.周期荷载作用下岩石大型三轴试验的变形和强度特性研究[J]岩土力学.1987；2.
[45]葛修润,任建喜,蒲毅彬等.岩土损伤力学宏细观试验研究[M].北京：科学出版社,2004.
[46]葛修润.周期荷载作用下岩石疲劳破坏及变形发展规律研究[A].第八次全国岩石力学与工程学术大会论文集[C].2004：23-31.
[47]章清叙,葛修润,黄铭,孙红.周期荷载作用下红砂岩三轴疲劳变形特性试验研究[J].岩石力学与工程学报.2006(03)：474-478.
[48]李树春.周期荷载作用下岩石变形与损伤规律及其非线性特征[D].重庆大学,2008.
[49]王鸿,许江,杨秀贵.循环载荷条件下岩石塑性滞回环的演化规律[J].重庆大学学报(自然科学版).2006(04)：80-82.
[50]吕培印.混凝土单轴、双轴动态强度和变形试验研究[D].大连理工大学2002.
[51]林燕清.混凝土疲劳累计损伤与力学性能劣化研究[D].哈尔滨：哈尔滨建筑大学,1998.
[52]李朝阳,宁玉普,赵国藩.混凝土疲劳残余应变性能研究[J].大连理工大学学报,2001,41(3)：355-358.
[53]王鸿,许江,李树春,胡玉红.不同水饱和度下岩石滞回曲线演化的实验研究[J].矿业研究与开发.2007；(03)：18-21.
[54]蒋宇,葛修润,任建喜.岩石疲劳破坏过程中的变形规律及声发射特性[J].岩石力学与工程学报,2004；23(11)：1810-1814.
[55]杨永杰,宋扬,楚俊.循环荷载作用下煤岩强度及变形特征试验研究[J].岩石力学与工程学报.2007(01)：201-205.
[56]Tutuncu A N, Podio A L, Sharma M M. Nonlinear viscoelastic behavior of sedimentary rock, part Ⅰ:effect of frequency and strain amplitude[J]. Geophysics,1998;63(1):184-190.
[57]Tutuncu A N, Podio A L, Sharma M M. Nonlinear viscoelastic behavior of sedimentary rock, part Ⅱ:hysteresis effects and influence of type of fluid on elastic moduli[J]. Geophysics, 1998;63(1):195-203.
[58]席道瑛,陈运平,陶月赞,等.岩石的非线性弹性滞后特征[J].岩石力学与工程学报,2006；25(6)：1086-1093.
[59]陈运平,席道瑛,薛彦伟.循环载荷下饱和岩石的滞后和衰减[J].地球物理学报,2004；7：672-680.
[60]陈运平,席道瑛,薛彦伟.循环载荷下饱和岩石的应力-应变动态响应[J].石油地球物理勘探,2003,38(4)：409-413.
[61]刘建峰,徐进,李青松,李刚林.循环载荷下岩石阻尼参数测试的试验研究[J].岩石力学与工程学报.2010；5：1036-1041.
[62]朱明礼,朱珍德,李刚,等.循环荷载作用下花岗岩动力特性试验研究[J].岩石力学与工程学报,2009,28(12)：2520-2526.
[63]肖建清,冯夏庭,丁德馨,蒋复量.常幅循环载荷作用下岩石的滞后和阻尼效应研究[J].岩石力学与工程学报,2010；8(29)：1677-1684.
[64]尤明庆,苏承东,杨圣奇.岩石动静态参数间关系的研究[J].焦作工学院学报(自然科学版),2002,21(6)：413-419.
[65]林英松,葛洪魁,王顺昌.岩石动静态力学参数的试验研究[J].岩石力学与工程学报,1998,17(2)：216-222.
[66]耿乃光等.岩石动态与静态杨氏模量的对比测量研究.第二届全国岩石力学学术会议,宜 昌：1990：50-54.
[67]Tutuncu A N, Sharma M M. Relating static and ultrasonic laboratory measurement to acoustic log measurement in tight gas sands. SPE24689,1993,299-311.
[68]Yale D P, Jamieson W H. Static and dynamic rock mechanical properties in the Hugo ton and Panoma field, Kansas.SPE27939,1995:209-219.
[69]Fairhurst C E, Hudson J A.单轴压缩试验测定完整岩石应力-应变全程曲线ISRM建议方法草案[J].岩石力学与工程学报,2000,19(6)：802-808.
[70]Naser, A AI-Shayea. Effects of testing methods and conditons on the elastic properties of limestone rock [J]. Engineering Geology.2004. (74):139-56.
[71]朱珍德,孙林柱,王明洋.不同频率循环荷载作用下岩石阻尼比试验与变形破坏机制细观分析[J].岩土力学,2010,31(1)：8-12.
[72]Lajtai E.Z., Scott Duncan E.J. et al. The effect of stain rate on rock strength [J]. Rock Mech and Rock Eng 1991;(24):99-109.
[1]张滨生,吴科如.水泥混凝土疲劳破坏的损伤力学分析[J].同济大学学报,1989,17(1)；59-69.
[2]谢和平,经典损伤定义中的“弹性模量法”探讨[J].力学与实践,1997,19(2)：1-5.
[3]杨永杰,宋扬,楚俊.循环荷载作用下煤岩强度及变形特征试验研究[J].岩石力学与工程学报.2007(01)：201-205.
[4]徐速超,冯夏庭,陈炳瑞.矽卡岩单轴循环加卸载试验及声发射特性研究[J].岩土力学.2009(10)：2929-2934.
[5]许江,李树春,唐晓军,陶云奇,杨红伟.基于声发射的岩石疲劳损伤演化[J].北京科技大学学报.2009(01)：19-24.
[6]姚卫星.结构疲劳寿命分析[M].北京：国防工业出版社.2003.
[7]宋玉普,赵东拂.混凝土强度与疲劳寿命试验样本容量分析[J].大连理工大学学报,2002,42(4)：464-466.
[8]赵造东.水工混凝土受压疲劳性能及累计损伤研究[D].昆明：昆明理工大学.2011.
[9]郭佳奇.岩溶隧道防突厚度及突水机制研究[D].北京：北京交通大学.2011.
[10]乔春生.溶洞、暗河地段隧道的结构型式和施工技术研究阶段成果报告[R].北京：北京交通大学,2008.
[11]曹茜.岩溶隧道与溶洞的安全距离研究.[D].北京：北京交通大学.2010.