随机裂隙对节理岩体稳定性影响研究及其在海底隧道中的应用
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摘要
对于节理岩体围岩稳定性问题,国内外学者采用离散介质模型和连续介质模型,并结合断裂力学、损伤力学及岩体损伤力学等理论对其开展了众多的研究,但是由于受到随机裂隙三维网络模拟技术的限制,较少涉及到随机裂隙空间分布、密度及其充填情况对节理岩体围岩稳定性的影响问题研究,然而岩体的节理裂隙面形态及其分布方式和受力特征直接制约和控制着岩体的强度、变形和破坏方式,因此研究随机裂隙对节理岩体围岩稳定性的影响对于实际岩体工程有着极其重要的作用。随着Monte-Carlo模拟技术的日趋成熟,通过现场勘探得到的裂隙资料再现节理岩体的三维裂隙网络成为可能,从而研究随机裂隙对节理岩体围岩稳定性的影响也变成现实。本文采用裂隙网络模拟技术(Monte-Carlo模拟技术)、岩体损伤力学及有限元编程思想,通过编制二阶张量损伤有限元程序并结合大型有限差分软件Flac3D研究了随机裂隙的几何特征(倾向、倾角)、裂隙的损伤参数(反映随机节理或者裂隙的密度的参数)及裂隙充填情况等因素对节理岩体围岩稳定性的影响,并结合厦门翔安海底隧道工程,研究了随机裂隙对确定厦门翔安海底隧道ZK9+750剖面的最小岩石覆盖厚度的影响。具体的研究思路及得到的研究结论如下:
(1)利用网络裂隙模拟技术、岩体损伤力学理论及有限元思想,编制二阶张量损伤有限元程序并结合大型有限差分软件来分析随机裂隙对节理岩体区域海底隧道围岩稳定性的影响。通过网络裂隙模拟方法,根据现场勘探得到的裂隙的几何特征,利用数学概率统计的思想,采用Monte-Carlo方法重构岩体的三维裂隙,计算节理岩体的初始损伤张量。采用岩体损伤力学理论和有限元思想编制二阶张量损伤有限元程序,得到基于能量等效原理的全局损伤张量,克服了仅根据所有局部损伤张量叠加的方法来计算整体损伤张量的缺点,更好地反映节理岩体的各向异性力学特性;编制二阶张量损伤有限元程序分析随机裂隙的倾向、倾角、损伤因子及裂隙充填情况等因素对节理岩体的稳定性的影响,并通过实例分析得到裂隙的倾角对隧洞周边的损伤位移影响不同,倾角不大于30°的裂隙对隧道的拱顶和底板的损伤位移影响较大,并与初始无损岩体隧道的拱顶和底板的位移同向;倾角大于30°的裂隙对隧道的拱顶和顶板的损伤位移影响也较大,但是损伤位移随着损伤因子的增加而与初始无损岩体隧道的拱顶和底板的位移反向;隧道周边的损伤位移随着损伤因子的增大而增加;隧道周边的损伤位移受压剪应力传递系数影响比拉剪应力传递系数的影响要大;并根据得到的分析结果,对隧道施工过程中的监测和加固提供依据。
(2)自从二十世纪四十年代日本修建世界上最早的海峡隧道—关门海峡铁路隧道以来,世界发达国家陆续开始海底隧道的建设。由于所处地理条件的限制,日本和挪威是目前世界上修建海底隧道最多的两个国家。随着国家现代化建设的高速发展,我国有多条海峡海底隧道正在规划和建设之中,其中正在建设的厦门翔安海底隧道和青岛胶州湾海底公路隧道均采用钻爆法施工。对于采用钻爆法施工的海底隧道来说,海底隧道的修建存在着不少关键问题,其中一个关键问题的确定对海底隧道的成功修建至关重要—海底隧道最小岩石覆盖厚度确定问题。
最小岩石覆盖厚度作为海底隧道的关键参数之一,对海底隧道的修建非常重要。如果隧道岩石覆盖厚度太小,隧道施工作业面局部性失稳与涌、突水患的险情加大;且因浅部地质较差,在辅助工法(如注浆封堵,各种预支护及加固等)上的投入将急剧增加;隧道岩石覆盖厚度过厚,海底隧道长度加大,作用于衬砌结构上的水头压力增大;而且也会增加隧道的长度,因而提高造价。由此可见,海底隧道覆盖层厚度的选定不仅是一个安全问题,而且也是一个经济问题。不过应该明确的一点是,覆盖层厚度并没有技术上的限制,也就是说不因为最小岩石覆盖层厚度的问题,在技术上使海底隧道无法修建。无非是采用较高的开挖支护技术和投入较高的费用而已,但这样做工程风险之大是显而易见的。
海底隧道最小岩石覆盖厚度目前主要采用工程类比法和数值计算方法来确定,主要思路是先通过工程类比方法得到隧道的初始的岩石覆盖厚度,然后再以该厚度为基准进行数值模拟,来验算该厚度的合理性,并对岩石覆盖厚度进行优化;当前这种确定海底隧道最小岩石覆盖厚度的思路是比较合理的,但其中也存在着不少问题。对工程类比方法来说,工程类比方法是综合世界各个国家修建隧道得到的经验方法,其对海底隧道的工程地质条件和水文条件的依赖性非常大,而每个国家的海底隧道的地质条件和水文条件不尽相同,因此使工程类比方法具有明显的局限性;对数值计算方法来说,主要采用有限元方法进行稳定性计算,对于隧道地质中出现的断层、软弱破碎带及节理、裂隙密集区等较差的地层,数值模拟时对参数根据经验进行弱化,使数值模拟过程中带有明显的主观性,而忽略或减弱了隧道自然地质条件的客观性,从而数值模拟计算的结果的实用性受到一定的局限。
考虑到工程类比法和数值模拟方法在研究节理岩体海底隧道最小岩石覆盖厚度问题上的局限性。本文采用网络裂隙模拟技术、岩体损伤力学理论及有限元思想,编制了二阶张量损伤有限元程序;并结合大型有限差分软件FLac3D研究了厦门翔安海底隧道ZK9+750剖面的最小岩石覆盖厚度,根据研究结果分析了随机裂隙对节理岩体区域海底隧道最小岩石覆盖厚度的影响。分析表明,随机裂隙使隧洞对称关键点的位移不再对称,而且隧洞周边关键点的位移比无损伤时的位移明显增加,特别是在水平方向的位移。对于厦门翔安海底隧道剖面ZK9+750的最小岩石覆盖厚度,从隧道围岩稳定性的角度分析,考虑随机裂隙的作用得到的厚度要比不考虑随机裂隙时的厚度增大约8米。
Associating with fracture mechanics, damage mechanics and damage mechanics of rock mass, many experts studied the stability of jointed rock mass by using discrete medium model and continuum model. But there are a few researches to study the effect of random fracture to the stability of jointed rock mass, because of the limits of the 3D fracture network simulation technique. Because shape and distributing fashion of joints, as well as the mechanics character of joints, restrict and control directly the strength, displacement and destructive mode, it is more important for the rock engineering to study the stability effect of jointed rock mass by random fractures. With the development of Monte-Carlo simulation technique, it is possible to restructure the three dimension fracture network on basis of the fracture data in site. So it is to be true to research the stability effect of rock mass by random fractures. On based of simulation technique of fracture network, damage mechanics of rock mass and idea of the finite element method, this paper studies the stability effect of jointed rock mass by variable factors of random fractures by means of the finite element method with two-order damage tensor and finite difference method-Flac3D. These factors include the geometry character, damage parameter and filling condition of fracture. And this paper analyzes how to choose the minimum rock cover of profile (ZK9+750) of XIANG'AN sub sea tunnel in XIAMEN considering the effect of random fractures. The detailed research idea and result are as following.
(1) This paper analyzes the stability effect of the sub sea tunnels in jointed rock masses by random fractures by means of the finite element method and finite element program considering a two-order damage tensor. It is compiled based on the simulation technique of fracture network, damage mechanics of rock mass and the finite element method. According to the geometry character of fractures in site, the 3D fracture network is restructured by the Monte-Carlo method by using the mathematic model. So the initial damage tensor of rock masses is rewarded by the three-dimensional fracture network. Global damage tensor based on the principle of energy equivalence can be obtained by the program of this paper. The global damage tensor is not the sum of the local damage tensor. So it can describe the anisotropic mechanical property of the rock masses. This program can research the stability of jointed rock masses which are effect by the influenced factors, such as dip direction angle, dip angle and the filling of the fractures and damage parameter. The engineering example is studied and some conclusions are as following:
When the fracture dip angle is not great than 30 degree, the damage displacement of tunnel vaults and motherboard is great than that of the other place of tunnel. And the direction of this displacement is the same as that of the equivalent undamaged rock masses. While the fracture dip angel is great than 30 degree, the damage displacement of tunnel vaults and motherboard is great too. But this displacement direction is opposite to that of the equivalent undamaged rock masses with the increase of the damage parameter. The damage displacement around the tunnel increases with the increase of the damage parameter. The effect to the damage displacement around the tunnel by the parameter C_nis great than that by the parameter C_t. These analytic results can be the data to monitor and to reinforce the tunnel.
(2)Since the first sub-sea tunnel of the world has been constructed in 1940s in Japan, other developed country began to construct the sub-sea tunnel. Because of their topographty, Japan and Norway have the most sub-sea tunnels in the world recently. With the development of the country, lots of sub-sea tunnels are planning to built, others are constructing. XIANG'AN sub-sea tunnel in XIAMEN and JIAOZHOU bay sub-sea tunnel in QINGDAO are constructing now, both of them are built by drill and blast method. There are some crucial problems for sub-sea tunnel constructed by drill and blast method. One of the most important problems is how to choose optimal rock cover of the sub-sea tunnel.
The minimum rock cover is one of the key-parameters in the design of hard rock sub sea tunnels. If the rock cover is too small, more sever stability problems and large water inflow may be the result, and in worst case a total collapse of the tunnel. On the other hand, if the rock cover is too conservative, considerable extra costs due to extra tunnel length will be the result, and the water pressure on the lining structure increased will be the result too. So how to choose the rock cover of the sub sea tunnel is not only to consider safety but also to consider case. But it is obvious to know that the sub sea tunnel can be built no matter how the rock cover is. When the rock cover is too small to excavate the sub sea tunnel, the advanced excavation and support technique and more case will be the result. It is obviously dangerous for sub sea tunnel to be excavated.
At present there are two methods, engineering analogism and numerical simulation, to design the minimum rock cover of sub sea tunnel. The main idea to confirm the minimum rock cover is as following. Firstly, the initial rock cover is chose by means of engineering analogism. Then it is to be reference rock cover, and it is to be checked by numerical simulation to ensure if the rock cover is rational. Final, the rock cover of the sub sea tunnel is optimized. The idea to choose the minimum rock cover is feasible presently but there are some shortcomings. Firstly, engineering analogism is the experience method which is gained by summarizing the sub sea tunneling experience all over the world. This method depends on the engineering geological and hydrological conditions of the sub sea tunnels. Because of the engineering geological and hydrological conditions of the sub sea tunnels are different, so the method has obvious limitations. Secondly, the idea of numerical simulation is to check the rock stability by means of the finite element method. This method has the defect to deal with the faults, weakness zones or joints. When the rock conditions are bad, they are simulated by degrading parameter based on the experience. So the result of the numerical simulation has its limitations.
According to the limitations of the engineering analogism and numerical simulation to research the minimum rock cover of the sub sea tunnels in jointed rock masses. By means of definite differential method-Flac3D, the finite element method considering a two-order damage tensor can be used to discuss the minimum rock cover of profile ZkK9+750 of the sub sea tunnel in XIAMEN under random fractures. According to the results, the effects to minimum rock cover of jointed rock cover by random fractures are analyzed. The analysis shows that the displacement of symmetrical location around the tunnel is unsymmetrical. And the displacement of key points around tunnel under damage conditions is larger obviously than that under undamaged conditions, especially the horizontal displacement. According to the stability of the rock masses, the results rewarded show that the minimum rock cover of profile ZK9+750 of the sub sea tunnel in XIAMEN is about 8-meter thicker on damaged conditions than that on undamaged conditions.
(1)利用网络裂隙模拟技术、岩体损伤力学理论及有限元思想,编制二阶张量损伤有限元程序并结合大型有限差分软件来分析随机裂隙对节理岩体区域海底隧道围岩稳定性的影响。通过网络裂隙模拟方法,根据现场勘探得到的裂隙的几何特征,利用数学概率统计的思想,采用Monte-Carlo方法重构岩体的三维裂隙,计算节理岩体的初始损伤张量。采用岩体损伤力学理论和有限元思想编制二阶张量损伤有限元程序,得到基于能量等效原理的全局损伤张量,克服了仅根据所有局部损伤张量叠加的方法来计算整体损伤张量的缺点,更好地反映节理岩体的各向异性力学特性;编制二阶张量损伤有限元程序分析随机裂隙的倾向、倾角、损伤因子及裂隙充填情况等因素对节理岩体的稳定性的影响,并通过实例分析得到裂隙的倾角对隧洞周边的损伤位移影响不同,倾角不大于30°的裂隙对隧道的拱顶和底板的损伤位移影响较大,并与初始无损岩体隧道的拱顶和底板的位移同向;倾角大于30°的裂隙对隧道的拱顶和顶板的损伤位移影响也较大,但是损伤位移随着损伤因子的增加而与初始无损岩体隧道的拱顶和底板的位移反向;隧道周边的损伤位移随着损伤因子的增大而增加;隧道周边的损伤位移受压剪应力传递系数影响比拉剪应力传递系数的影响要大;并根据得到的分析结果,对隧道施工过程中的监测和加固提供依据。
(2)自从二十世纪四十年代日本修建世界上最早的海峡隧道—关门海峡铁路隧道以来,世界发达国家陆续开始海底隧道的建设。由于所处地理条件的限制,日本和挪威是目前世界上修建海底隧道最多的两个国家。随着国家现代化建设的高速发展,我国有多条海峡海底隧道正在规划和建设之中,其中正在建设的厦门翔安海底隧道和青岛胶州湾海底公路隧道均采用钻爆法施工。对于采用钻爆法施工的海底隧道来说,海底隧道的修建存在着不少关键问题,其中一个关键问题的确定对海底隧道的成功修建至关重要—海底隧道最小岩石覆盖厚度确定问题。
最小岩石覆盖厚度作为海底隧道的关键参数之一,对海底隧道的修建非常重要。如果隧道岩石覆盖厚度太小,隧道施工作业面局部性失稳与涌、突水患的险情加大;且因浅部地质较差,在辅助工法(如注浆封堵,各种预支护及加固等)上的投入将急剧增加;隧道岩石覆盖厚度过厚,海底隧道长度加大,作用于衬砌结构上的水头压力增大;而且也会增加隧道的长度,因而提高造价。由此可见,海底隧道覆盖层厚度的选定不仅是一个安全问题,而且也是一个经济问题。不过应该明确的一点是,覆盖层厚度并没有技术上的限制,也就是说不因为最小岩石覆盖层厚度的问题,在技术上使海底隧道无法修建。无非是采用较高的开挖支护技术和投入较高的费用而已,但这样做工程风险之大是显而易见的。
海底隧道最小岩石覆盖厚度目前主要采用工程类比法和数值计算方法来确定,主要思路是先通过工程类比方法得到隧道的初始的岩石覆盖厚度,然后再以该厚度为基准进行数值模拟,来验算该厚度的合理性,并对岩石覆盖厚度进行优化;当前这种确定海底隧道最小岩石覆盖厚度的思路是比较合理的,但其中也存在着不少问题。对工程类比方法来说,工程类比方法是综合世界各个国家修建隧道得到的经验方法,其对海底隧道的工程地质条件和水文条件的依赖性非常大,而每个国家的海底隧道的地质条件和水文条件不尽相同,因此使工程类比方法具有明显的局限性;对数值计算方法来说,主要采用有限元方法进行稳定性计算,对于隧道地质中出现的断层、软弱破碎带及节理、裂隙密集区等较差的地层,数值模拟时对参数根据经验进行弱化,使数值模拟过程中带有明显的主观性,而忽略或减弱了隧道自然地质条件的客观性,从而数值模拟计算的结果的实用性受到一定的局限。
考虑到工程类比法和数值模拟方法在研究节理岩体海底隧道最小岩石覆盖厚度问题上的局限性。本文采用网络裂隙模拟技术、岩体损伤力学理论及有限元思想,编制了二阶张量损伤有限元程序;并结合大型有限差分软件FLac3D研究了厦门翔安海底隧道ZK9+750剖面的最小岩石覆盖厚度,根据研究结果分析了随机裂隙对节理岩体区域海底隧道最小岩石覆盖厚度的影响。分析表明,随机裂隙使隧洞对称关键点的位移不再对称,而且隧洞周边关键点的位移比无损伤时的位移明显增加,特别是在水平方向的位移。对于厦门翔安海底隧道剖面ZK9+750的最小岩石覆盖厚度,从隧道围岩稳定性的角度分析,考虑随机裂隙的作用得到的厚度要比不考虑随机裂隙时的厚度增大约8米。
Associating with fracture mechanics, damage mechanics and damage mechanics of rock mass, many experts studied the stability of jointed rock mass by using discrete medium model and continuum model. But there are a few researches to study the effect of random fracture to the stability of jointed rock mass, because of the limits of the 3D fracture network simulation technique. Because shape and distributing fashion of joints, as well as the mechanics character of joints, restrict and control directly the strength, displacement and destructive mode, it is more important for the rock engineering to study the stability effect of jointed rock mass by random fractures. With the development of Monte-Carlo simulation technique, it is possible to restructure the three dimension fracture network on basis of the fracture data in site. So it is to be true to research the stability effect of rock mass by random fractures. On based of simulation technique of fracture network, damage mechanics of rock mass and idea of the finite element method, this paper studies the stability effect of jointed rock mass by variable factors of random fractures by means of the finite element method with two-order damage tensor and finite difference method-Flac3D. These factors include the geometry character, damage parameter and filling condition of fracture. And this paper analyzes how to choose the minimum rock cover of profile (ZK9+750) of XIANG'AN sub sea tunnel in XIAMEN considering the effect of random fractures. The detailed research idea and result are as following.
(1) This paper analyzes the stability effect of the sub sea tunnels in jointed rock masses by random fractures by means of the finite element method and finite element program considering a two-order damage tensor. It is compiled based on the simulation technique of fracture network, damage mechanics of rock mass and the finite element method. According to the geometry character of fractures in site, the 3D fracture network is restructured by the Monte-Carlo method by using the mathematic model. So the initial damage tensor of rock masses is rewarded by the three-dimensional fracture network. Global damage tensor based on the principle of energy equivalence can be obtained by the program of this paper. The global damage tensor is not the sum of the local damage tensor. So it can describe the anisotropic mechanical property of the rock masses. This program can research the stability of jointed rock masses which are effect by the influenced factors, such as dip direction angle, dip angle and the filling of the fractures and damage parameter. The engineering example is studied and some conclusions are as following:
When the fracture dip angle is not great than 30 degree, the damage displacement of tunnel vaults and motherboard is great than that of the other place of tunnel. And the direction of this displacement is the same as that of the equivalent undamaged rock masses. While the fracture dip angel is great than 30 degree, the damage displacement of tunnel vaults and motherboard is great too. But this displacement direction is opposite to that of the equivalent undamaged rock masses with the increase of the damage parameter. The damage displacement around the tunnel increases with the increase of the damage parameter. The effect to the damage displacement around the tunnel by the parameter C_nis great than that by the parameter C_t. These analytic results can be the data to monitor and to reinforce the tunnel.
(2)Since the first sub-sea tunnel of the world has been constructed in 1940s in Japan, other developed country began to construct the sub-sea tunnel. Because of their topographty, Japan and Norway have the most sub-sea tunnels in the world recently. With the development of the country, lots of sub-sea tunnels are planning to built, others are constructing. XIANG'AN sub-sea tunnel in XIAMEN and JIAOZHOU bay sub-sea tunnel in QINGDAO are constructing now, both of them are built by drill and blast method. There are some crucial problems for sub-sea tunnel constructed by drill and blast method. One of the most important problems is how to choose optimal rock cover of the sub-sea tunnel.
The minimum rock cover is one of the key-parameters in the design of hard rock sub sea tunnels. If the rock cover is too small, more sever stability problems and large water inflow may be the result, and in worst case a total collapse of the tunnel. On the other hand, if the rock cover is too conservative, considerable extra costs due to extra tunnel length will be the result, and the water pressure on the lining structure increased will be the result too. So how to choose the rock cover of the sub sea tunnel is not only to consider safety but also to consider case. But it is obvious to know that the sub sea tunnel can be built no matter how the rock cover is. When the rock cover is too small to excavate the sub sea tunnel, the advanced excavation and support technique and more case will be the result. It is obviously dangerous for sub sea tunnel to be excavated.
At present there are two methods, engineering analogism and numerical simulation, to design the minimum rock cover of sub sea tunnel. The main idea to confirm the minimum rock cover is as following. Firstly, the initial rock cover is chose by means of engineering analogism. Then it is to be reference rock cover, and it is to be checked by numerical simulation to ensure if the rock cover is rational. Final, the rock cover of the sub sea tunnel is optimized. The idea to choose the minimum rock cover is feasible presently but there are some shortcomings. Firstly, engineering analogism is the experience method which is gained by summarizing the sub sea tunneling experience all over the world. This method depends on the engineering geological and hydrological conditions of the sub sea tunnels. Because of the engineering geological and hydrological conditions of the sub sea tunnels are different, so the method has obvious limitations. Secondly, the idea of numerical simulation is to check the rock stability by means of the finite element method. This method has the defect to deal with the faults, weakness zones or joints. When the rock conditions are bad, they are simulated by degrading parameter based on the experience. So the result of the numerical simulation has its limitations.
According to the limitations of the engineering analogism and numerical simulation to research the minimum rock cover of the sub sea tunnels in jointed rock masses. By means of definite differential method-Flac3D, the finite element method considering a two-order damage tensor can be used to discuss the minimum rock cover of profile ZkK9+750 of the sub sea tunnel in XIAMEN under random fractures. According to the results, the effects to minimum rock cover of jointed rock cover by random fractures are analyzed. The analysis shows that the displacement of symmetrical location around the tunnel is unsymmetrical. And the displacement of key points around tunnel under damage conditions is larger obviously than that under undamaged conditions, especially the horizontal displacement. According to the stability of the rock masses, the results rewarded show that the minimum rock cover of profile ZK9+750 of the sub sea tunnel in XIAMEN is about 8-meter thicker on damaged conditions than that on undamaged conditions.
引文
[1]朱维申,李术才,陈卫忠等.节理岩体破坏机理和锚杆效应及工程应用[M].北京:科学出版社,2002.
[2]陈剑平,肖树芳等.随机不连续面三维网络计算机的模拟原理[M].长春:东北师范大学出版社,1995.
[3]Fisher S R.Dispersion on a Sphere.Proc.Roy.Soc.Lond.[A].1953,217:295-305
[4]Shanley R J,Mahtab M A.Delineation and Analysis of Clusters in Oorientation Date[J].Math.Geology,1976,8:9-23
[5]Priest S D,Hudson J A.Estimation of Discontinuity Spacing and Trace Length using Scanline Surveys[J].Inter.J.Rock Mech.Sci.and Geomech.Abstr.,1981,18:183-197
[6]Zaitsev Y V,Wittmann F H.Simulation of Crack Propagation and Failure of Concrete[J].Materiaux eet Constructions,1981,14:357-365
[7]潘别桐,井兰如.岩体结构概率模型模拟和应用[J].岩石力学新进展.1988,5:5-72
[8]Kaulatilake P H S W.Joint Network Modeling with a Validation Exercise in Stripa Mine Swede[J].Int.J.Rock Meh.Sci.and Geomech.Abstr.,1993,1:1-23
[9]陈剑平.岩体随机不连续面三维网络数值模拟技术[J].岩土工程学报,2001,23(4):397-402
[10]汪小刚,贾志欣等.岩石结构面网络模拟原理在节理岩体连通率研究中的应用[J].水利水电技术.1998,29:43-47
[11]杨米加,贺永年.蒙特卡洛模拟的随机性及裂隙岩体渗透张量分析[J].岩土工程学报,1999,21(4):492-494
[12]陈征宙,韦杰等.随机断裂网络的Monte-Carlo模拟研究[J].南京大学学报(自然科学),1999,35(6):683-688
[13]张发明,汪小刚等.3D裂隙网络随机模拟及其工程应用研究[J].现代地质,2002,16(1):100-103
[14]赵红亮,陈剑平.裂隙岩体三维网络流的渗透路径搜索[J].岩石力学与工程学报,2005,24(4):622-627
[15]宋晓晨,徐卫亚.裂隙岩体渗流模拟的三维离散裂隙网络数值模拟(Ⅰ):裂隙 网络的随机生成[J].岩石力学与工程学报,2004,23(12):2015-2020
[16]Korehide Miyaguchi.Maintenance of The Kanmon Railway Tunnels [J].Tunneling and Underground Space Technology,1986,1(3/4):307-314
[17]日本海下隧道[J].隧道译丛,1990,(5):54-56
[18]日本1994年隧道工程状况[J].世界隧道,1996,(1):14-28
[19]吴效良,陆锦荣.英、法海底隧道工程简介[J].煤矿设计,l 998,8:50~52
[20]英法海底隧道结构设计和安全设施[J].地下空间,1997,17(3)
[21]挪威隧道施工法[J].隧道译丛,1993,(7):1-17
[22]隧道设计指南[J].隧道译丛,1990,(10):16-18
[23]挪威隧道及地下工程近况[J].隧道及地下工程,1999,(2):62-63
[24]挪威奥勒松海底深长公路隧道[J].隧道译丛,1990,(12):49-51
[25]近25年来美国隧道掘进技术的进展[J].世界隧道,1995,(4):25-30
[26]冰岛第一座海底隧道-华尔峡湾隧道[J].隧道及地下工程,1998,(1):37-41
[27]康宁.对美国几个城市地铁和水下隧道的观感[J].现代隧道技术,2001,38(4)
[28]波罗的海环状铁路线的隧道工程[J].隧道及地下工程,2000,(2):16-24
[29]法国修建海底隧洞的经验[J].隧道译丛,1988,(8):8-19
[30]青函隧道的技术发展[J].隧道译丛,1988,(8):46-55
[31]挪威海底隧道的设计与施工[J].世界隧道,1996,(3):25-33
[32]挪威对海底隧道工程的研究[J].世界隧道,1995,(3):68-76
[33]挪威的海底隧道工程[J].探矿工程,1996,(2):51-52
[34]世界上最长最深的海底隧道[J].国外公路,1995,15(4):40-42
[35]沙梦麟.世界海底铁路隧道[J].轨道交通,2003,(1):20-21
[36]世界各地的隧道[J].建筑机械,2006,(7):19-24
[37]丁大均.丹麦瑞典间厄勒海峡固定链设计方案[J].国外桥梁,1994,(3):183-185
[38]M.蒂克,J.M.萨利诺.直布罗陀海峡隧道[J].隧道工程与地下空间技术,1991,(6):63-68
[39]楼如岳.悉尼海底隧道工程,工程技术信息[J].地下工程与隧道,1996:46
[40]冰岛隧道建设的过去、现状和未来[J].世界隧道,1996,(2):79-80
[41]冰岛伊萨湾公路隧道[J].世界隧道,1996,(2):81-86
[42]小森博,吉川大三.日本的海底隧道和水下隧道[R].北京海底隧道会议
[43]Akira Kitamura.Technical Development for The Seikan Tunnel[J].Tunneling and Underground Space Technology,1986,1(3/4):341-349
[44]Shogo Matsuo.An Overview of The Seikan Tunnel Project[J].Tunneling and Underground Space Technology,1986,1(3/4):323-331
[45]吕明,Grov E,Nilsen B,Melby K.挪威海底隧道经验[J].岩石力学与工程学报,2005,24(23):4219-4225
[46]王梦恕.蓬勃发展的中国水底隧道[R].北京海底隧道会议
[47]杨亮,苏强,吴波.南京玄武湖隧道关键施工技术[J].施工技术,2003,32(8):1-3
[48]江级辉.琼州海峡兴建海底隧道可行性初探[J].地下空间,1994,14(2):122-129
[49]曾超,张建斌.厦门翔安(海底)隧道土建工程简介[R].北京海底隧道会议
[50]刘保华,孙永福,赵月霞等.海洋地球物理探测技术在青岛海底隧道工程中的应用[R].北京海底隧道会议
[51]王梦恕,皇甫明.海底隧道修建中的关键问题[J].建筑科学与工程学报,2005,22(4):1-4
[52]李术才,李廷春等.厦门东通道暗挖隧道最小安全顶板厚度研究[R].2002,10
[53]李术才,李树忱,丁万涛等.象山港海底隧道钻爆法施工最小安全顶板厚度研究[R].北京海底隧道会议,2005,2
[54]李术才,徐帮树,丁万涛等.青岛胶州湾海底隧道最小岩石覆盖厚度研究[R].2007,2
[55]李术才,李树忱,徐帮树等.海底隧道最小岩石覆盖厚度确定方法研究[J].岩石力学与工程学报,2007,26(11):2289-2295.
[56]杨家岭,李术才,邱祥波等.海峡海底隧道及其最小岩石覆盖厚度问题[J].岩石力学与工程学报,2003,22(增1):2132-2137.
[57]Arild P.,黄子平.挪威海底隧道经验在厦门海底隧道建设中的应用[J].岩石力学与工程学报,2007,26(11):2236-2246.
[58]Nilsen,B.Empirical Analysis of Minimum Rock Cover for Subsea Rock Tunnels[J].Options for Tunnelling,Elsevier,1993:677-687
[59]Z.D.Eisensteir.Large Undersea Tunnels and The Progress of Tunnelling Technology[J].Tunnelling and Underground Space Technology,1994,9(3):283-292
[60]T.S.Dahlo,B.Nilsen.Stability and Rock Cover of Hard Rock Subsea
Tunnels[J].Tunneling and Underground Space Technology,1994,9(2):151-158
[61]徐帮树,张宪堂,张芹.海底隧道涌水量预测及应用研究[J].武汉理工大学学报,2007,31(4):599-602
[62]刘松.矿山法修建海底隧道最小埋深的探讨[J].隧道建设,2003,23(3):4-6
[63]孙红星.龙口矿区近海厚冲积层下综放采煤防水煤岩柱的留设研究[J].煤炭科学技术,1999,27(6):6-9
[64]国家煤炭工业局.建筑物、水体、铁路及主要井巷煤柱留设与压煤开采规程[M].北京:煤炭工业出版社,2000
[65]李廷春,李术才,白世伟.厦门海底隧道顶板厚度选择及其开挖稳定性分析[J].岩土力学,2005,26(12):2010-2014.
[66]李树忱,张京伟,李术才等.海底隧道最小岩石覆盖厚度的位移收敛法[J].岩土力学,2007,28(7):1443-1447.
[67]李术才,李廷春,陈卫忠等.厦门海底隧道最小顶板厚度三维弹塑性断裂损伤研究[J].岩石力学与工程学报,2004,23(18):3138-3143.
[68]李廷春,李术才,陈卫忠等.厦门海底隧道的流固耦合分析[J].岩土工程学报,2004,26(3):397-401.
[69]张欣,李术才.爆破荷载作用下青岛胶州湾海底隧道覆盖岩层稳定性分析[J].2007,26(11):2348-2355.
[70]丁万涛,李术才,朱维申.某海底隧道岩石覆盖厚度及选线方案优化研究[J].地下空间与工程学报,2007,6:463-469
[71]National Research Council,Rock Fracture and Fluid Flow:Contemporary Understanding and Applications[M].National Academy Press,Washington,D.C.,1996
[72]Oda M.Fabric Tensor for Discontinuous Geological Materials[J].Soils and Foundation,1982,22:96-108
[73]于青春,大西有三岩体三维不连续裂隙网络及其逆建模方法[J].地球科学-中国地质大学学报,2003,28(5):522-526
[74]Warburton P M.A Stereological Interpretation of Joint Trace Data[J].Int J Rock Mech Sci & Geomech Abstra 17,181-190,1980
[75]于青春,薛果夫,陈德基.裂隙岩体一般块体理论[M].北京:中国水力水电出版社,2007
[76]张有天.岩石水力学与工程[M].北京:中国水力水电出版社,2005
[77]陈剑平.窗口不连续面迹长概率估算法[J].工程地质学报,1996,4(1):8-13
[78]卓家寿,章青.不连续介质力学问题的界面元法[M].北京:科学出版社,2000
[79]徐钟济.蒙特卡罗方法[M].上海:上海科学技术出版社,1985
[80]楼志文.损伤力学基础[M].西安:西安交通大学出版社,1991
[81]余寿文,冯西桥.损伤力学[M].北京:清华大学出版社,1997
[82]余天庆,钱济成.损伤理论及其应用[M].北京:国防工业出版社,1993
[83]沈为,彭立华.损伤力学[M].武汉:华中理工大学出版社,1995
[84]Rabotnov Y N.On The Equations of State for Creep[J].Progress in Applied Mechanics,1963,307-315
[85]Janson J,Hult J.Fracture Mechanics and Damage Mechanics-A Combined Approach[J].J.de Mech.Appl.,1996,1(1),59-64
[86]Murakami S.Anisotropic Aspects of Matertal Damage and Application of Continuum Damage Mechanics,Continuum Damage Mechanics-Theory and Applications[M].Krajcinovic D,Lemaitre J Leds.Springer-Verlay Wien-New York,1987,81-134
[87]Shen W,Peng L H,Yue Y G,Shen Z,Tang X D.Elastic Damage and Energy Dissipation in Anisotropic Sold Material Engng[J].Fracture Mech.,1987,33(2)
[88]Chen X F,Lu Y B,Lee H.An Endochronic Plastic Theory with Anisatropic Damage[J].Engng.Fracture Mech.,1989,32(4)
[89]Tzou D Y,Chert E P.Mesocrack Damage Induced by A Macro-crack in Heterogeneous Materials[J].Engng.Fracture Mech.,1991,39(2)
[90]Murakami S.Mechanical Modeling of Material Damage[J].Joural of Applied Mechanics.55(1),988:24-27
[91]Kachanov,L.M.Time of The Rrupture Process under Creep Condition[J].IVZ Akad Nauk,S.S.R.,Otd Tech Nauk,1958,8,26-31
[92]Lemaitre,J.A Course on Damage Mechanics-2~(nd)[M].Springer,Berlin,1990
[93]Davison L.Stevens A.L.Thermomechanical Constitution of Spalling Elastic Bodies[J].Journal of Appl.Phys.,1993,44,667-674
[94]Murakami,S.Ohno,N.A Continuum Theory of Creep and Creep Damage[J].Proceedings of 3~(rd)IUTAM Symp.On Creep in Structures,ed.A.R.S.Ponter and D.R.Hayhust.Springer-Verlag,Berlin,1980,422-443.
[95]Kawamoto,T.,Ichikawa,Y.and Kyoya,T.Deformation and Fracturing Behavior of Discontinuous Rock Mass and Damage Mechanics Theory[J].Int. Journal of Numer.Anal.Meth.Geomech.,1988,12,1-30
[96]Dragon,A.Mroz,Z.A Continuum Model for Plastic-Brittle Behavior of Rock and Concrete[J].Int.Journal of Engng.Sci.1979,17,121-137.
[97]Halm,D.,Dragon,A.A Model of Anisotropic Damage by Mecrocrack Growth Unilateral Effect.[J].Int.J.Dama.Mech.,1996,5,384-402.
[98]Ju,J.W.On Energy Based CoupledElastoplastic Damage Theories:Constitutive Modeling and Computational Aspects[J].Int.Journal of Solids Structure,1989,25,803-833.
[99]Malvern,L.E.Introduction to The Mechanics of a Continuous Medium[M].Prentice-Hall,Englewood Cliffs,NJ,1969.
[100]Bazant,Z.R.Comment on orthotropic models for concrete and geomaterials[J].Journal of Engng.Mech.ASCE,1983,109,849-865.
[101]Cowin,S.C.The Relationship Between The Elasticity Tensor and The Fabric Tensor[J].Mech.Mater,1985,4,137-147.
[102]G.Swoboda,X.P.Shen,L.Rosas.Damage Model of Jointed Rock Mass and Its Application to Tunnell[J].Computers and Georechnics,1998,22(3/4):183-203
[103]杨更社,张长庆.岩体损伤及检测[M].西安:陕西科学技术出版社,1998
[104]吴 澎,周维垣.节理岩体的损伤模型及非线性有限元分析[J].岩石力学与工程学报,1988,7(3):193-202
[105]周维垣.节理岩体损伤力学模型[J].岩石力学新进展,1989
[106]孙卫军,周维垣.裂隙岩体弹塑性损伤本构模型[J].岩石力学与工程学报,1990,9(2):108-119
[107]周维垣,杨延毅.节理岩体损伤断裂模型及验证[J].岩石力学与工程学报,1991,10(1):43-54
[108]陶振宇,曾亚武,赵震英.节理岩体损伤模型及验证[J].水利学报,1991,6:52-58
[109]王勖成,邵敏.有限元法基本原理和数值方法[M].北京:清华大学出版社,1997
[110]曾攀.有限元分析及应用[M].北京:清华大学出版社,2004.
[111]刘新波,盛建龙.节理岩体损伤模型的有限元分析[J].武汉冶金科技大学学报,1997,20(4):393-396
[112]常来山,王家臣,李慧如等.节理岩体边坡损伤力学与Flac3D耦合分析[J]. 金属矿山,2004,9:16-18
[113]王家臣,常来山,陈亚军.节理岩体边坡概率损伤演化规律研究[J].岩石力学与工程学报,2006,25(7):1396-1401
[114]彭国伦.Fortran 95程序设计[M].北京:中国电力出版社,2002
[115]徐士良.Fortran常用算法程序集[M].北京:清华大学出版社,1995
[116]Kyoya T et al.A Damage Mechanics Theory for Discontinuous Rock Mass[J].5~(th)Int.Conf.Numer.In Geomech.,1985,85-90.
[117]Kyoya T et al.A Damage Mechanics Analysis for Underground Excavation in Jointed Rock Mass[J].Proc.Int.Symp.On Engng.In Complex Rock Formations.,Beijing:1985,506-513.
[118]Kawamoto T et al.Deformation and Fracturing of Discontinuous Rock Mass and Damage Mechanics Theory[J].Int.J.Numer.Anal.Methods Gaomech.,1988,12:1-30.
[119]Zhang W H,Valliappan S.Analysis of Random Anisotropic Damage[J].Mechanics Problems of Rock Mass,Part Ⅰ- Probabilistic Simulation,Part Ⅱ-Statistical Estimation Rock Mass.Rock Engng.,1990,23:241-259.
[120]杨延毅.节理裂隙岩体损伤-断裂力学模型及其在岩体工程中的应用[P].北京:清华大学博士学位论文,1990.
[121]李新平,朱维申.多裂隙岩体的等效弹性损伤模型及其有限元分析[J].第四届全国岩土力学数值分析与解析方法讨论会论文集,武汉:武汉测绘科技大学出版社,1997,1-7.
[122]Cai M,Horii H.A Constitutive Model and FEM Analysis of Joint Rock Masses[J].Int.J.Rock.Min.Sci.& Geomech.Abstr,1993,30(4).
[123]徐靖南.压剪应力作用下多裂隙岩体的力学特性-理论分析与模型试验[P].武汉:中国科学院武汉岩土力学研究所博士学位论文,1993.
[124]徐靖南,朱维申,白世伟.压剪应力作用下多裂隙岩体的力学特性-本构模型[J].岩土力学,1993,14(4):
[125]Swoboda G,Yang Q.Damage Propagation Model and Its Application to Rock Engineering Problems[J].Int.Congress On Rock Mechanics Proceeding,Tokyo,Japan,1995,159-163.
[126]厦门东通道初步设计阶段工程地质报告[R].2002
[127]厦门东通道水文资料报告[R].长江水利科学委员会,2002,
[2]陈剑平,肖树芳等.随机不连续面三维网络计算机的模拟原理[M].长春:东北师范大学出版社,1995.
[3]Fisher S R.Dispersion on a Sphere.Proc.Roy.Soc.Lond.[A].1953,217:295-305
[4]Shanley R J,Mahtab M A.Delineation and Analysis of Clusters in Oorientation Date[J].Math.Geology,1976,8:9-23
[5]Priest S D,Hudson J A.Estimation of Discontinuity Spacing and Trace Length using Scanline Surveys[J].Inter.J.Rock Mech.Sci.and Geomech.Abstr.,1981,18:183-197
[6]Zaitsev Y V,Wittmann F H.Simulation of Crack Propagation and Failure of Concrete[J].Materiaux eet Constructions,1981,14:357-365
[7]潘别桐,井兰如.岩体结构概率模型模拟和应用[J].岩石力学新进展.1988,5:5-72
[8]Kaulatilake P H S W.Joint Network Modeling with a Validation Exercise in Stripa Mine Swede[J].Int.J.Rock Meh.Sci.and Geomech.Abstr.,1993,1:1-23
[9]陈剑平.岩体随机不连续面三维网络数值模拟技术[J].岩土工程学报,2001,23(4):397-402
[10]汪小刚,贾志欣等.岩石结构面网络模拟原理在节理岩体连通率研究中的应用[J].水利水电技术.1998,29:43-47
[11]杨米加,贺永年.蒙特卡洛模拟的随机性及裂隙岩体渗透张量分析[J].岩土工程学报,1999,21(4):492-494
[12]陈征宙,韦杰等.随机断裂网络的Monte-Carlo模拟研究[J].南京大学学报(自然科学),1999,35(6):683-688
[13]张发明,汪小刚等.3D裂隙网络随机模拟及其工程应用研究[J].现代地质,2002,16(1):100-103
[14]赵红亮,陈剑平.裂隙岩体三维网络流的渗透路径搜索[J].岩石力学与工程学报,2005,24(4):622-627
[15]宋晓晨,徐卫亚.裂隙岩体渗流模拟的三维离散裂隙网络数值模拟(Ⅰ):裂隙 网络的随机生成[J].岩石力学与工程学报,2004,23(12):2015-2020
[16]Korehide Miyaguchi.Maintenance of The Kanmon Railway Tunnels [J].Tunneling and Underground Space Technology,1986,1(3/4):307-314
[17]日本海下隧道[J].隧道译丛,1990,(5):54-56
[18]日本1994年隧道工程状况[J].世界隧道,1996,(1):14-28
[19]吴效良,陆锦荣.英、法海底隧道工程简介[J].煤矿设计,l 998,8:50~52
[20]英法海底隧道结构设计和安全设施[J].地下空间,1997,17(3)
[21]挪威隧道施工法[J].隧道译丛,1993,(7):1-17
[22]隧道设计指南[J].隧道译丛,1990,(10):16-18
[23]挪威隧道及地下工程近况[J].隧道及地下工程,1999,(2):62-63
[24]挪威奥勒松海底深长公路隧道[J].隧道译丛,1990,(12):49-51
[25]近25年来美国隧道掘进技术的进展[J].世界隧道,1995,(4):25-30
[26]冰岛第一座海底隧道-华尔峡湾隧道[J].隧道及地下工程,1998,(1):37-41
[27]康宁.对美国几个城市地铁和水下隧道的观感[J].现代隧道技术,2001,38(4)
[28]波罗的海环状铁路线的隧道工程[J].隧道及地下工程,2000,(2):16-24
[29]法国修建海底隧洞的经验[J].隧道译丛,1988,(8):8-19
[30]青函隧道的技术发展[J].隧道译丛,1988,(8):46-55
[31]挪威海底隧道的设计与施工[J].世界隧道,1996,(3):25-33
[32]挪威对海底隧道工程的研究[J].世界隧道,1995,(3):68-76
[33]挪威的海底隧道工程[J].探矿工程,1996,(2):51-52
[34]世界上最长最深的海底隧道[J].国外公路,1995,15(4):40-42
[35]沙梦麟.世界海底铁路隧道[J].轨道交通,2003,(1):20-21
[36]世界各地的隧道[J].建筑机械,2006,(7):19-24
[37]丁大均.丹麦瑞典间厄勒海峡固定链设计方案[J].国外桥梁,1994,(3):183-185
[38]M.蒂克,J.M.萨利诺.直布罗陀海峡隧道[J].隧道工程与地下空间技术,1991,(6):63-68
[39]楼如岳.悉尼海底隧道工程,工程技术信息[J].地下工程与隧道,1996:46
[40]冰岛隧道建设的过去、现状和未来[J].世界隧道,1996,(2):79-80
[41]冰岛伊萨湾公路隧道[J].世界隧道,1996,(2):81-86
[42]小森博,吉川大三.日本的海底隧道和水下隧道[R].北京海底隧道会议
[43]Akira Kitamura.Technical Development for The Seikan Tunnel[J].Tunneling and Underground Space Technology,1986,1(3/4):341-349
[44]Shogo Matsuo.An Overview of The Seikan Tunnel Project[J].Tunneling and Underground Space Technology,1986,1(3/4):323-331
[45]吕明,Grov E,Nilsen B,Melby K.挪威海底隧道经验[J].岩石力学与工程学报,2005,24(23):4219-4225
[46]王梦恕.蓬勃发展的中国水底隧道[R].北京海底隧道会议
[47]杨亮,苏强,吴波.南京玄武湖隧道关键施工技术[J].施工技术,2003,32(8):1-3
[48]江级辉.琼州海峡兴建海底隧道可行性初探[J].地下空间,1994,14(2):122-129
[49]曾超,张建斌.厦门翔安(海底)隧道土建工程简介[R].北京海底隧道会议
[50]刘保华,孙永福,赵月霞等.海洋地球物理探测技术在青岛海底隧道工程中的应用[R].北京海底隧道会议
[51]王梦恕,皇甫明.海底隧道修建中的关键问题[J].建筑科学与工程学报,2005,22(4):1-4
[52]李术才,李廷春等.厦门东通道暗挖隧道最小安全顶板厚度研究[R].2002,10
[53]李术才,李树忱,丁万涛等.象山港海底隧道钻爆法施工最小安全顶板厚度研究[R].北京海底隧道会议,2005,2
[54]李术才,徐帮树,丁万涛等.青岛胶州湾海底隧道最小岩石覆盖厚度研究[R].2007,2
[55]李术才,李树忱,徐帮树等.海底隧道最小岩石覆盖厚度确定方法研究[J].岩石力学与工程学报,2007,26(11):2289-2295.
[56]杨家岭,李术才,邱祥波等.海峡海底隧道及其最小岩石覆盖厚度问题[J].岩石力学与工程学报,2003,22(增1):2132-2137.
[57]Arild P.,黄子平.挪威海底隧道经验在厦门海底隧道建设中的应用[J].岩石力学与工程学报,2007,26(11):2236-2246.
[58]Nilsen,B.Empirical Analysis of Minimum Rock Cover for Subsea Rock Tunnels[J].Options for Tunnelling,Elsevier,1993:677-687
[59]Z.D.Eisensteir.Large Undersea Tunnels and The Progress of Tunnelling Technology[J].Tunnelling and Underground Space Technology,1994,9(3):283-292
[60]T.S.Dahlo,B.Nilsen.Stability and Rock Cover of Hard Rock Subsea
Tunnels[J].Tunneling and Underground Space Technology,1994,9(2):151-158
[61]徐帮树,张宪堂,张芹.海底隧道涌水量预测及应用研究[J].武汉理工大学学报,2007,31(4):599-602
[62]刘松.矿山法修建海底隧道最小埋深的探讨[J].隧道建设,2003,23(3):4-6
[63]孙红星.龙口矿区近海厚冲积层下综放采煤防水煤岩柱的留设研究[J].煤炭科学技术,1999,27(6):6-9
[64]国家煤炭工业局.建筑物、水体、铁路及主要井巷煤柱留设与压煤开采规程[M].北京:煤炭工业出版社,2000
[65]李廷春,李术才,白世伟.厦门海底隧道顶板厚度选择及其开挖稳定性分析[J].岩土力学,2005,26(12):2010-2014.
[66]李树忱,张京伟,李术才等.海底隧道最小岩石覆盖厚度的位移收敛法[J].岩土力学,2007,28(7):1443-1447.
[67]李术才,李廷春,陈卫忠等.厦门海底隧道最小顶板厚度三维弹塑性断裂损伤研究[J].岩石力学与工程学报,2004,23(18):3138-3143.
[68]李廷春,李术才,陈卫忠等.厦门海底隧道的流固耦合分析[J].岩土工程学报,2004,26(3):397-401.
[69]张欣,李术才.爆破荷载作用下青岛胶州湾海底隧道覆盖岩层稳定性分析[J].2007,26(11):2348-2355.
[70]丁万涛,李术才,朱维申.某海底隧道岩石覆盖厚度及选线方案优化研究[J].地下空间与工程学报,2007,6:463-469
[71]National Research Council,Rock Fracture and Fluid Flow:Contemporary Understanding and Applications[M].National Academy Press,Washington,D.C.,1996
[72]Oda M.Fabric Tensor for Discontinuous Geological Materials[J].Soils and Foundation,1982,22:96-108
[73]于青春,大西有三岩体三维不连续裂隙网络及其逆建模方法[J].地球科学-中国地质大学学报,2003,28(5):522-526
[74]Warburton P M.A Stereological Interpretation of Joint Trace Data[J].Int J Rock Mech Sci & Geomech Abstra 17,181-190,1980
[75]于青春,薛果夫,陈德基.裂隙岩体一般块体理论[M].北京:中国水力水电出版社,2007
[76]张有天.岩石水力学与工程[M].北京:中国水力水电出版社,2005
[77]陈剑平.窗口不连续面迹长概率估算法[J].工程地质学报,1996,4(1):8-13
[78]卓家寿,章青.不连续介质力学问题的界面元法[M].北京:科学出版社,2000
[79]徐钟济.蒙特卡罗方法[M].上海:上海科学技术出版社,1985
[80]楼志文.损伤力学基础[M].西安:西安交通大学出版社,1991
[81]余寿文,冯西桥.损伤力学[M].北京:清华大学出版社,1997
[82]余天庆,钱济成.损伤理论及其应用[M].北京:国防工业出版社,1993
[83]沈为,彭立华.损伤力学[M].武汉:华中理工大学出版社,1995
[84]Rabotnov Y N.On The Equations of State for Creep[J].Progress in Applied Mechanics,1963,307-315
[85]Janson J,Hult J.Fracture Mechanics and Damage Mechanics-A Combined Approach[J].J.de Mech.Appl.,1996,1(1),59-64
[86]Murakami S.Anisotropic Aspects of Matertal Damage and Application of Continuum Damage Mechanics,Continuum Damage Mechanics-Theory and Applications[M].Krajcinovic D,Lemaitre J Leds.Springer-Verlay Wien-New York,1987,81-134
[87]Shen W,Peng L H,Yue Y G,Shen Z,Tang X D.Elastic Damage and Energy Dissipation in Anisotropic Sold Material Engng[J].Fracture Mech.,1987,33(2)
[88]Chen X F,Lu Y B,Lee H.An Endochronic Plastic Theory with Anisatropic Damage[J].Engng.Fracture Mech.,1989,32(4)
[89]Tzou D Y,Chert E P.Mesocrack Damage Induced by A Macro-crack in Heterogeneous Materials[J].Engng.Fracture Mech.,1991,39(2)
[90]Murakami S.Mechanical Modeling of Material Damage[J].Joural of Applied Mechanics.55(1),988:24-27
[91]Kachanov,L.M.Time of The Rrupture Process under Creep Condition[J].IVZ Akad Nauk,S.S.R.,Otd Tech Nauk,1958,8,26-31
[92]Lemaitre,J.A Course on Damage Mechanics-2~(nd)[M].Springer,Berlin,1990
[93]Davison L.Stevens A.L.Thermomechanical Constitution of Spalling Elastic Bodies[J].Journal of Appl.Phys.,1993,44,667-674
[94]Murakami,S.Ohno,N.A Continuum Theory of Creep and Creep Damage[J].Proceedings of 3~(rd)IUTAM Symp.On Creep in Structures,ed.A.R.S.Ponter and D.R.Hayhust.Springer-Verlag,Berlin,1980,422-443.
[95]Kawamoto,T.,Ichikawa,Y.and Kyoya,T.Deformation and Fracturing Behavior of Discontinuous Rock Mass and Damage Mechanics Theory[J].Int. Journal of Numer.Anal.Meth.Geomech.,1988,12,1-30
[96]Dragon,A.Mroz,Z.A Continuum Model for Plastic-Brittle Behavior of Rock and Concrete[J].Int.Journal of Engng.Sci.1979,17,121-137.
[97]Halm,D.,Dragon,A.A Model of Anisotropic Damage by Mecrocrack Growth Unilateral Effect.[J].Int.J.Dama.Mech.,1996,5,384-402.
[98]Ju,J.W.On Energy Based CoupledElastoplastic Damage Theories:Constitutive Modeling and Computational Aspects[J].Int.Journal of Solids Structure,1989,25,803-833.
[99]Malvern,L.E.Introduction to The Mechanics of a Continuous Medium[M].Prentice-Hall,Englewood Cliffs,NJ,1969.
[100]Bazant,Z.R.Comment on orthotropic models for concrete and geomaterials[J].Journal of Engng.Mech.ASCE,1983,109,849-865.
[101]Cowin,S.C.The Relationship Between The Elasticity Tensor and The Fabric Tensor[J].Mech.Mater,1985,4,137-147.
[102]G.Swoboda,X.P.Shen,L.Rosas.Damage Model of Jointed Rock Mass and Its Application to Tunnell[J].Computers and Georechnics,1998,22(3/4):183-203
[103]杨更社,张长庆.岩体损伤及检测[M].西安:陕西科学技术出版社,1998
[104]吴 澎,周维垣.节理岩体的损伤模型及非线性有限元分析[J].岩石力学与工程学报,1988,7(3):193-202
[105]周维垣.节理岩体损伤力学模型[J].岩石力学新进展,1989
[106]孙卫军,周维垣.裂隙岩体弹塑性损伤本构模型[J].岩石力学与工程学报,1990,9(2):108-119
[107]周维垣,杨延毅.节理岩体损伤断裂模型及验证[J].岩石力学与工程学报,1991,10(1):43-54
[108]陶振宇,曾亚武,赵震英.节理岩体损伤模型及验证[J].水利学报,1991,6:52-58
[109]王勖成,邵敏.有限元法基本原理和数值方法[M].北京:清华大学出版社,1997
[110]曾攀.有限元分析及应用[M].北京:清华大学出版社,2004.
[111]刘新波,盛建龙.节理岩体损伤模型的有限元分析[J].武汉冶金科技大学学报,1997,20(4):393-396
[112]常来山,王家臣,李慧如等.节理岩体边坡损伤力学与Flac3D耦合分析[J]. 金属矿山,2004,9:16-18
[113]王家臣,常来山,陈亚军.节理岩体边坡概率损伤演化规律研究[J].岩石力学与工程学报,2006,25(7):1396-1401
[114]彭国伦.Fortran 95程序设计[M].北京:中国电力出版社,2002
[115]徐士良.Fortran常用算法程序集[M].北京:清华大学出版社,1995
[116]Kyoya T et al.A Damage Mechanics Theory for Discontinuous Rock Mass[J].5~(th)Int.Conf.Numer.In Geomech.,1985,85-90.
[117]Kyoya T et al.A Damage Mechanics Analysis for Underground Excavation in Jointed Rock Mass[J].Proc.Int.Symp.On Engng.In Complex Rock Formations.,Beijing:1985,506-513.
[118]Kawamoto T et al.Deformation and Fracturing of Discontinuous Rock Mass and Damage Mechanics Theory[J].Int.J.Numer.Anal.Methods Gaomech.,1988,12:1-30.
[119]Zhang W H,Valliappan S.Analysis of Random Anisotropic Damage[J].Mechanics Problems of Rock Mass,Part Ⅰ- Probabilistic Simulation,Part Ⅱ-Statistical Estimation Rock Mass.Rock Engng.,1990,23:241-259.
[120]杨延毅.节理裂隙岩体损伤-断裂力学模型及其在岩体工程中的应用[P].北京:清华大学博士学位论文,1990.
[121]李新平,朱维申.多裂隙岩体的等效弹性损伤模型及其有限元分析[J].第四届全国岩土力学数值分析与解析方法讨论会论文集,武汉:武汉测绘科技大学出版社,1997,1-7.
[122]Cai M,Horii H.A Constitutive Model and FEM Analysis of Joint Rock Masses[J].Int.J.Rock.Min.Sci.& Geomech.Abstr,1993,30(4).
[123]徐靖南.压剪应力作用下多裂隙岩体的力学特性-理论分析与模型试验[P].武汉:中国科学院武汉岩土力学研究所博士学位论文,1993.
[124]徐靖南,朱维申,白世伟.压剪应力作用下多裂隙岩体的力学特性-本构模型[J].岩土力学,1993,14(4):
[125]Swoboda G,Yang Q.Damage Propagation Model and Its Application to Rock Engineering Problems[J].Int.Congress On Rock Mechanics Proceeding,Tokyo,Japan,1995,159-163.
[126]厦门东通道初步设计阶段工程地质报告[R].2002
[127]厦门东通道水文资料报告[R].长江水利科学委员会,2002,
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