强震作用下块状岩体边坡稳定性研究
|
摘要
地震荷载作用下块状结构岩体边坡的稳定性研究是我国西部强地震区大型水利水电工程建设、山区高速公路工程、铁路客运专线以及核电工程建设中需要解决的难点和热点问题。对边坡在地震作用下的动力响应规律、失稳机制、稳定性评价方法等科学问题进行系统深入的研究,不仅能推动地震边坡稳定性理论的发展和创新,而且能够为岩土工程设施的规划、设计和施工提供必要的技术支持,具有重要的理论意义和现实意义。
岩体是由结构面网络及其所围限的岩石块体所组成。结构面对地震波在岩体中的传播过程及规律有着很重要的影响。研究地震波在节理岩体中的传播特征是分析岩体边坡动力响应和动力稳定性的基础。
边坡的地震动力响应包括加速度、速度、位移、动应力和动应变响应等等多方面的内容。广义上,除了上述这些标准参量外,某些抽象的、人为定义的变量,例如动态的稳定系数,也可以视为边坡对地震动力的响应。在所有的这些能够表征边坡动力响应的物理量、信号量中,加速度无疑是居于基础性地位。这主要有如下两个方面的原因：第一,速度和位移可分别由加速度对时间积分和二次积分获得,因此不具有独立性。第二,边坡体内任意微元的动应力状态与其加速度、质量之间的关系符合牛顿第二定律,并且动应力与动应变通过模量建立联系,从这个意义上来说,动应力和动应变对加速度也具有依存关系。事实上,边坡的各种动力响应皆由地震加速度引发。因此,研究加速度的动力响应规律(时间和空间分布)已成为这一领域的基本问题之一,同时对于评价边坡的动力稳定性也有着重要的价值。
在岩体边坡动力稳定性计算中,永久位移分析和动力稳定性系数分析方法是两种主要的动力稳定性评价方法。永久位移标准较稳定性系数标准能够更为准确地反映边坡在地震工况下的动力响应,在理论上永久位移标准比单一的稳定性系数更为合理,但是永久位移法却存在诸多不足,首先从本质上看永久位移法是一个较为粗略的评价方法,在计算边坡地震永久位移时不能考虑边坡材料自身的变形、动力条件下岩体的强度以及变形特性;其次,永久位移法计算的地震永久位移其实是平均位移,不能反映具有复杂节理岩体在地震作用下真实的位移分布情况；另外,永久位移法无法得出地震荷载作用下边坡的稳定性系数,这在实际工程中进行边坡稳定性评价是极为不便的。在此背景下,本文将尝试通过将永久位移法与动力强度折减法相结合,以永久位移作为边坡的动力失稳评价指标,并通过强度折减法来计算得出边坡的稳定性系数。由于强度折减法物理意义明确,计算过程简洁,因此国内外很多学者采用强度折减法对边坡的稳定性系数数进行了分析。目前,主要存在以下两种边坡的动力失稳判据：(1)从关键点永久位移和折减系数的关系曲线来判断。(2)以地震荷载结束后关键点永久位移的时程曲线是否发散来判断。然而就目前国内外的研究进展来看,上述两种失稳判据均有它们的不足之处,本文将在上述动力失稳判据的基础上分别提出新的计算方法。
通常情况下,岩体质量较好、岩体结构完整、倾向坡外的结构面未发育或较少发育的块状岩体边坡整体稳定性较好。但在强震作用下,岩体震裂松动、结构面加剧扩展、结构面抗剪强度显著降低,该类岩体边坡的整体稳定性也大大降低。目前,关于该类岩体边坡地震动力响应以及地震条件下的失稳破坏方式方面的研究尚少。鉴于地震的强大破坏力,正确分析强震作用下块状岩体边坡的动力响应及失稳破坏方式则显得尤为迫切和重要。
本文主要针对块状结构岩体边坡,采用三维离散单元法(3DEC)对其在地震荷载作用下的动力响应规律、稳定性分析以及破坏方式进行了深入研究。目的是揭示地震荷载对块状结构岩体边坡稳定性的影响机制,为更准确地分析块状结构岩体边坡的动力稳定性提供有效的理论依据。论文完成的主要工作包括以下几个方面：
(1)基于三维离散元软件3DEC,建模分析了地震波在含单个节理岩体中的传播特征。首先,建立简谐地震波在均质岩体中传播的数值模型,通过参数研究选取了合理的建模参数和动力分析参数,包括边界条件、网格单元尺寸、动力时间步等,为选取合理的参数应用于动力学问题方面的研究提供了依据。接着建立地震波在单个节理岩体中的传播模型,并分别考虑了地震波垂直入射结构面和地震波倾斜入射结构面时结构面刚度对波传播规律的影响,并结合前人的理论研究成果,探讨数值模拟方法的可行性,结果表明采用离散元软件3DEC来分析节理岩体的动力问题是非常可靠的。
(2)通过密集的数值模拟计算,对地震作用下各结构面因素对岩体边坡动力响应的影响规律进行了研究。岩体边坡地震动力响应分析是一个十分复杂的研究课题。除了地震荷载的复杂性之外,岩石材料的性质、结构面的物理力学特性及其在岩体内的分布和规模等因素,都将对岩体边坡的地震响应产生一定的影响。如果要全面地考虑上述因素的影响,将使得这一问题变得相当复杂以至于难以求解。因此为了突出重点,本文主要研究了结构面物理力学特性以及其在岩体边坡内的分布特征对岩体边坡动力响应的影响。鉴于结构面的刚度对地震波的透射系数和反射系数有着重大的影响,在结构面物理力学特性方面主要考虑结构面刚度对岩体边坡动力响应的影响。此外在结构面分布特征方面,主要从结构面的产状、结构面的起始位置以及结构面的密度这几个角度来分别进行研究。研究结果表明,①、结构面产状的变化会使得结构面对地震波的反射方向和折射方向发生变化,进而影响地震波场能量在坡体中的分布情况,最终体现为边坡PGA放大系数等值线分布的空间变化。对于顺倾结构面边坡,当结构面倾角较小时,结构面对地震波的传播起着一定的衰减作用,而当结构面倾角较大时,则起着相反的作用。边坡的动力稳定性随着结构面倾角的增大而不断变差。逆倾结构面的存在会对地震波在岩质边坡中的传播产生衰减作用,并且随着结构面倾角的增大而不断弱化。相比于顺倾结构面边坡,逆倾结构面边坡的动力稳定性大体上要强于前者。②、结构面的起始位置对于岩体边坡的地震动力响应有着比较明显的影响,其位置越高,岩体边坡的地震动力响应就越强,反之则越弱。③、随着结构面刚度的增大,岩体边坡的地震动力响应的强度呈现出明显的递增趋势。结构面刚度对各反射波和透射波的影响作用主要体现在它们的能量分配关系上,而对于它们在岩体边坡中的传播路径则没有什么影响。当入射波为剪切波时,岩体边坡地震动力响应对结构面剪切刚度的敏感性要明显地高于其法向刚度。④、结构面发育愈密集,边坡岩体的完整性愈差,岩体边坡的地震动力响应就越强烈,其动力稳定性也就越差。
(3)运用正交试验设计法,通过数值计算与数理统计分析评价了岩体边坡PGA放大系数极大值影响因素的敏感性。虽然PGA放大系数极大值并不能全面地反映岩体边坡地震动力响应的整体情况,但其能在一定程度上诠释岩体边坡地震动力响应的强度问题。在分析各种结构面因素单独作用时PGA放大系数极大值的变化规律的基础上,综合考虑各种结构面因素之间的相关性和随机联动性,分别采用极差分析法和方差分析法对岩体边坡PGA放大系数极大值影响因素的敏感性进行了排序。参与分析的5个结构面因素中,敏感性由大到小的顺序依次为：结构面倾角、结构面起始位置、结构面剪切刚度、结构面法向刚度、结构面间距。因此,当岩体边坡中发育有倾角较陡的结构面且结构面发育深度较浅时,其动力响应的强度往往就会越强,在地震荷载的作用下,这类岩体边坡的动力稳定性问题也将显得更为突出。
(4)针对动力强度折减法中第一种失稳判据在实际应用中的局限性,提出了“基于永久位移比的岩体边坡动力稳定性计算方法”。地震荷载作用下,地震永久位移随强度折减系数的增加而增加,且在强度折减系数较小时增幅不明显,当超过某一定值时,地震永久位移的增幅迅速增大,呈明显的指数函数形式变化。关于如何在地震永久位移与折减系数的关系曲线中标定出边坡的动力稳定性系数,目前的解决方法主要是以该曲线“拐点”即永久位移值突变点所对应的折减系数来确定,然而对于“拐点”的位置该如何确定则存在较大的人为主观因素,并且缺乏合理的数学理论公式做支撑,使得该方法在使用上存在着一定的局限性。在此背景下,本文提出永久位移比理论新概念,即当岩体边坡沿滑动面的地震永久位移达到滑动面长度的一定比值时认为该边坡失稳破坏。将此方法运用于汶川地震区块状岩体边坡实例研究中,计算得出该实例边坡在汶川地震荷载作用下的动力稳定性系数为1.04,稳定性计算结果与实际地质调查情况相符,验证了本方法的工程实用性。
(5)针对动力强度折减法中第二种失稳判据的不足之处,提出了“考虑结构面退化的岩体边坡动力稳定性计算方法”。当采用第二种失稳判据来分析岩体边坡的动力稳定性时,通过结构面静态强度参数计算所得的岩体边坡动力稳定性系数与其静力稳定性系数进是相等的,地震荷载的振幅对边坡动力稳定性系数的影响得不到任何体现,在此背景下,基于前人有关结构面摩擦系数随累积位移和相对运动速率不断衰减的研究成果,提出了考虑结构面退化的岩体边坡动力稳定性计算方法,给出了相应的实施流程,并用汶川地震区的工程实例进行了说明,计算结果表明,使用该方法来计算岩体边坡的动力稳定性是可行的。
(6)老虎嘴岩体边坡是汶川地震区典型的受优势结构面控制的块状岩体边坡,5·12汶川大地震使得该边坡内部的结构面贯通,形成楔形体在地震作用下向临空面方向运动,以至产生严重的崩滑现象,并导致岷江堵塞和交通封闭。以老虎嘴块状结构岩体边坡的地质原型为基础,应用三维离散元数值模拟软件3DEC,建立了老虎嘴块状结构岩体边坡的三维离散元数值计算模型,并通过动力计算还原了该边坡在汶川地震荷载作用下变形破坏的演化过程,对其动力失稳机制进行了详细分析,为研究具有相同结构类型的岩体边坡在强震作用下的破坏方式提供了参考依据。
The study on the stability of block rock slope under seismic loading is a hot and hard issue. It affects much on the construction of large-scale hydraulic and hydropower station, mountain high way, railway, nuclear power station. The deep researches into dynamic response rule, failure mechanism, stability evaluation and so on are of great significance. Not only can it push the development and creativity of slope stability theory under earthquake, but also support the planning, designing and constructing of geotechnical facility.
Rock mass is composed of rock blocks that divided by the discontinuity network. Discontinuity is an important factor that determines the process and rule of the propagation of seismic wave. It is the foundation of research into rock slope dynamic response and dynamic stability to study the propagation characteristics of seismic wave in joint rock mass.
Earthquake dynamic response of slope includes acceleration, velocity, displacement, dynamic stress, strain response, etc. In a broader sense, except for the standard parameters above, some abstract and human defined variables like dynamic factor of safety can also be viewed as the slope dynamic response to seismic. Of all the physical quantities and semaphores that can stand for the slope dynamic response, acceleration is the basic one. Because for one thing, velocity and displacement can be obtained by acceleration integral and double integral for time, respectively. For another, the relationship between dynamic stress and acceleration, dynamic stress and quality of any infinitesimals in the slope are in accordance to Newton's second law. Dynamic stress and strain can be connected by modulus. In this sense, dynamic stress, dynamic strain and acceleration are also connected. Actually, the dynamic responses in slope are all induced by acceleration of seismic. Therefore, the study of dynamic response rules in time and space of acceleration is becoming the basic problem in this field, and it is of great value in evaluate the slope dynamic stability.
In calculation of dynamic stability, permanent displacement analysis and factor analysis of dynamic stability are two main methods in evaluation of dynamic stability. Permanent displacement can reflect more precisely the dynamic response of slope to earthquake compared to factor of stability. Theoretically, the standard of permanent displacement is more reasonable than that of factor of stability. However, much insufficient exists in it. First of all, naturally, permanent displacement analysis is a relatively rough method. In calculation of slope permanent displacement caused by earthquake, slope material deformation, rock strength under dynamic situation and deformation character are not taken into consideration. Second, average displacement can be obtained through the permanent displacement analysis, which can not reflect the real condition. Third, stability factor of slope will not be received through the analysis and it will cause much inconvenience in stability evaluation. So, permanent displacement analysis and dynamic strength reduction method are combined here to get the factor of stability. Permanent displacement is taken as the index of dynamic failure, and strength reduction method is used to calculate the factor of stability. Currently, two criterions can be used to determine dynamic failure. One is the relation curve of permanent displacement and reduction coefficient. The other is whether the permanent curve is divergence at the key point after earthquake. Two criteria are not so perfect and a new calculation method will be put forward here.
Commonly, slopes with rocks of integrity, inclining to the slope and less amount of discontinuities are relatively stable. But under the effect of strong earthquake, the rocks become less composed and more discontinuities appear. Shear strength reduced rapidly, so is the whole slope stability. Now, not so much work has been done on the aspect of earthquake caused dynamic response to that kind of rock slope and failure manners. As long as how strong the destructive can be, it appears to be urgent and important to take research into the study of the problem.
Study in this paper mainly aims at block rock mass slope.3DEC simulation is used to take further study into the dynamic response rule, stability analysis and failure mode. It aims to reveal the earthquake affect on block rock slope and its mechanism. In this way, theoretical criterion can be provided to evaluate more precisely the dynamic stability of rock slope. Main contents of this paper are listed as follows:
(1) Based on3DEC simulation model, the characters of propagation in single joint rock mass is analyzed. First, the numerical model of harmonic seismic wave propagating in homogeneous rock is built. Model and dynamic analysis parameters are chosen according to real parameters, which include boundary conditions, size of grid cells and time step of dynamic calculation and so on. Next, the propagation model of seismic in single joint rock is built and another factor is taken into consideration. The factor is the influence of discontinuity stiffness on propagation rules when seismic wave vertically oblique and incident on structure plans. The feasibility of simulation is taken into consideration and combined much work done by others. It is quite reliable to utilize3DEC simulation to analyze the dynamic problems of joint rock mass.
(2) Through much numerical simulation calculation, the influence rules of discontinuities on rock mass slope dynamic response are studied. The analysis of earthquake dynamic response to rock mass slope is a rather complicated problem. Except for the complication of seismic loading, rock materials, physical and mechanical properties and the distribution of discontinuities, scale and other factors play a role in the response. It is not reasonable to take all the factors above into consideration. In this paper, the physical and mechanical properties and the distribution of discontinuities are taken into account. On the aspect of physical mechanism, structure stiffness is the main factor for its influence on transmission and reflection coefficient of seismic wave. In addition, on the aspect of discontinuity contribution, occurrence, starting position, and density of structures are the studying points. The results indicate:1) Change of structure occurrence will lead to the different directions of reflection and refraction of seismic wave. And then the distribution of field energy of seismic wave will be changed. It finally reflects on the spatial variation of slope amplification factor PFA contours. As for dip layered slope, when dip angle of structure is relatively small, structures have a reduction effect on seismic propagation. When the angle is relatively big, it has the opposite effect. The dynamic stability of slope decreases with the increase of dip angle. The existing of anti-dip layered slope will make the propagation of seismic in rock slope decay. As structure dip angle increases, the strength of discontinuity decreases. The dynamic stability of anti-dip layered structure is better than that of dip layered structure.2) The starting position of structure is a big factor on seismic dynamic response of rock slope. The higher the position is, the stronger the response is.3) With the increasing of structure stiffness, the strength of seismic dynamic response has the tendency increase. The effect of structure stiffness on reflected and transmitted waves is mainly on the relationship of energy distribution, but not impact can be seen at the propagation path of them in rock slope. When the incident wave is shear wave, the seismic dynamic response to structure shear stiffness is more sensitive than that to normal stiffness.4) More intense the discontinuities are, worse the integrity the rock slope is, and stronger the seismic dynamic response is, which means the poorer the dynamic stability of slope is.
(3) Orthogonal experiment design method is applied, and evaluation on the sensibility of the maximum value of PGA amplification factor in rock mass slope through numerical calculation and statistics. Though the maximum value of PGA amplification factor can not reflect the whole condition of dynamic response to rock slope comprehensively, it can to some degree determine the strength of it. The changing rule of maximum PGA amplification factor is analyzed under structure effect. Based on this, taken into consideration the correlations and random linkage in structure factors, range analysis and variance analysis are used to put the sensibility of maximum PGA amplification factors in order. The sensibilities of dip angle starting position, shear stiffness, normal stiffness and distance of discontinuities are in descending orders. Therefore, when there is structure with big dip angle and develops shallowly, the dynamic response will be stronger. Under the effect of seismic loading, this type of dynamic stability problem in rock slope will be more prominent.
(4) On the limitations of the first failure criterion in dynamic strength reduction method in practical, a calculation method of dynamic stability in rock mass slope based on permanent displacement is put forward. Under seismic loading, the permanent displacement of earthquake increase with strength reduction factor. When the factor is relative small, its increase amplitude will not be obvious and when it exceeds a certain value, the increase amplitude of earthquake permanent displacement will increase rapidly and show a change in the form of an exponential function. On how to set the dynamic stability factor on the relation curve of seismic permanent displacement and reduction factor, the current solution is take the corresponding reduction factor of turning point. But many subjective factors exist in determining the turning point, making the method more insufficient in utilizing. A new concept of permanent displacement is proposed. That is when the permanent displacement along rock slope caused by earthquake reaches a certain ratio of the length of slip surface, the slope will be in unstable state. Applied this approach to the study of block rock slope in Wenchuan earthquake area, the dynamic stability factor is1.04under the Wenchuan earthquake load. The result is in consistent with geological survey condition and verifies the practicability of this method.
(5) On the limitations of the second failure criterion in dynamic reduction method, a calculation method of dynamic stability factor in rock slope considering structure degradation. When the second criterion is taken to analyze the dynamic stability in rock mass slope, the dynamic stability factor that obtained through static strength parameters is the same with the static stability factor, which means the effect of amplitude of seismic load on dynamic stability factor can not been seen here. Based on relative research achievement about the friction coefficient decays with the cumulative displacement and relative rates that done by others, a calculation method of dynamic stability factor in rock slope considering structure degradation is proposed and corresponding implementation process is given. Projects in Wenchuan earthquake area is taken for illustration. The results indicate it is feasible to put the method into calculation of dynamic stability in rock mass slope.
(6) The Tiger Mouth rock mass slope is a typical slope that is controlled by dominant joint plan in Wenchuan earthquake area. The5.12Wenchuan earthquake makes the discontinuities in the slope connect with each other, which lead to the formation of wedge and it will slide towards the free face under the effect of seismic. A heavy landslide happened, making the Min River block and traffic close. Based on the block rock mass slope of Tiger Mouth, a numerical model is built in3DEC software. The evolution process of the slope getting deformed under Wenchuan earthquake has been restored, and the dynamic mechanism has been analyzed in detaisl. It brings reference to the study on the failure mode of the same type rock mass slope under heavy earthquake.
岩体是由结构面网络及其所围限的岩石块体所组成。结构面对地震波在岩体中的传播过程及规律有着很重要的影响。研究地震波在节理岩体中的传播特征是分析岩体边坡动力响应和动力稳定性的基础。
边坡的地震动力响应包括加速度、速度、位移、动应力和动应变响应等等多方面的内容。广义上,除了上述这些标准参量外,某些抽象的、人为定义的变量,例如动态的稳定系数,也可以视为边坡对地震动力的响应。在所有的这些能够表征边坡动力响应的物理量、信号量中,加速度无疑是居于基础性地位。这主要有如下两个方面的原因：第一,速度和位移可分别由加速度对时间积分和二次积分获得,因此不具有独立性。第二,边坡体内任意微元的动应力状态与其加速度、质量之间的关系符合牛顿第二定律,并且动应力与动应变通过模量建立联系,从这个意义上来说,动应力和动应变对加速度也具有依存关系。事实上,边坡的各种动力响应皆由地震加速度引发。因此,研究加速度的动力响应规律(时间和空间分布)已成为这一领域的基本问题之一,同时对于评价边坡的动力稳定性也有着重要的价值。
在岩体边坡动力稳定性计算中,永久位移分析和动力稳定性系数分析方法是两种主要的动力稳定性评价方法。永久位移标准较稳定性系数标准能够更为准确地反映边坡在地震工况下的动力响应,在理论上永久位移标准比单一的稳定性系数更为合理,但是永久位移法却存在诸多不足,首先从本质上看永久位移法是一个较为粗略的评价方法,在计算边坡地震永久位移时不能考虑边坡材料自身的变形、动力条件下岩体的强度以及变形特性;其次,永久位移法计算的地震永久位移其实是平均位移,不能反映具有复杂节理岩体在地震作用下真实的位移分布情况；另外,永久位移法无法得出地震荷载作用下边坡的稳定性系数,这在实际工程中进行边坡稳定性评价是极为不便的。在此背景下,本文将尝试通过将永久位移法与动力强度折减法相结合,以永久位移作为边坡的动力失稳评价指标,并通过强度折减法来计算得出边坡的稳定性系数。由于强度折减法物理意义明确,计算过程简洁,因此国内外很多学者采用强度折减法对边坡的稳定性系数数进行了分析。目前,主要存在以下两种边坡的动力失稳判据：(1)从关键点永久位移和折减系数的关系曲线来判断。(2)以地震荷载结束后关键点永久位移的时程曲线是否发散来判断。然而就目前国内外的研究进展来看,上述两种失稳判据均有它们的不足之处,本文将在上述动力失稳判据的基础上分别提出新的计算方法。
通常情况下,岩体质量较好、岩体结构完整、倾向坡外的结构面未发育或较少发育的块状岩体边坡整体稳定性较好。但在强震作用下,岩体震裂松动、结构面加剧扩展、结构面抗剪强度显著降低,该类岩体边坡的整体稳定性也大大降低。目前,关于该类岩体边坡地震动力响应以及地震条件下的失稳破坏方式方面的研究尚少。鉴于地震的强大破坏力,正确分析强震作用下块状岩体边坡的动力响应及失稳破坏方式则显得尤为迫切和重要。
本文主要针对块状结构岩体边坡,采用三维离散单元法(3DEC)对其在地震荷载作用下的动力响应规律、稳定性分析以及破坏方式进行了深入研究。目的是揭示地震荷载对块状结构岩体边坡稳定性的影响机制,为更准确地分析块状结构岩体边坡的动力稳定性提供有效的理论依据。论文完成的主要工作包括以下几个方面：
(1)基于三维离散元软件3DEC,建模分析了地震波在含单个节理岩体中的传播特征。首先,建立简谐地震波在均质岩体中传播的数值模型,通过参数研究选取了合理的建模参数和动力分析参数,包括边界条件、网格单元尺寸、动力时间步等,为选取合理的参数应用于动力学问题方面的研究提供了依据。接着建立地震波在单个节理岩体中的传播模型,并分别考虑了地震波垂直入射结构面和地震波倾斜入射结构面时结构面刚度对波传播规律的影响,并结合前人的理论研究成果,探讨数值模拟方法的可行性,结果表明采用离散元软件3DEC来分析节理岩体的动力问题是非常可靠的。
(2)通过密集的数值模拟计算,对地震作用下各结构面因素对岩体边坡动力响应的影响规律进行了研究。岩体边坡地震动力响应分析是一个十分复杂的研究课题。除了地震荷载的复杂性之外,岩石材料的性质、结构面的物理力学特性及其在岩体内的分布和规模等因素,都将对岩体边坡的地震响应产生一定的影响。如果要全面地考虑上述因素的影响,将使得这一问题变得相当复杂以至于难以求解。因此为了突出重点,本文主要研究了结构面物理力学特性以及其在岩体边坡内的分布特征对岩体边坡动力响应的影响。鉴于结构面的刚度对地震波的透射系数和反射系数有着重大的影响,在结构面物理力学特性方面主要考虑结构面刚度对岩体边坡动力响应的影响。此外在结构面分布特征方面,主要从结构面的产状、结构面的起始位置以及结构面的密度这几个角度来分别进行研究。研究结果表明,①、结构面产状的变化会使得结构面对地震波的反射方向和折射方向发生变化,进而影响地震波场能量在坡体中的分布情况,最终体现为边坡PGA放大系数等值线分布的空间变化。对于顺倾结构面边坡,当结构面倾角较小时,结构面对地震波的传播起着一定的衰减作用,而当结构面倾角较大时,则起着相反的作用。边坡的动力稳定性随着结构面倾角的增大而不断变差。逆倾结构面的存在会对地震波在岩质边坡中的传播产生衰减作用,并且随着结构面倾角的增大而不断弱化。相比于顺倾结构面边坡,逆倾结构面边坡的动力稳定性大体上要强于前者。②、结构面的起始位置对于岩体边坡的地震动力响应有着比较明显的影响,其位置越高,岩体边坡的地震动力响应就越强,反之则越弱。③、随着结构面刚度的增大,岩体边坡的地震动力响应的强度呈现出明显的递增趋势。结构面刚度对各反射波和透射波的影响作用主要体现在它们的能量分配关系上,而对于它们在岩体边坡中的传播路径则没有什么影响。当入射波为剪切波时,岩体边坡地震动力响应对结构面剪切刚度的敏感性要明显地高于其法向刚度。④、结构面发育愈密集,边坡岩体的完整性愈差,岩体边坡的地震动力响应就越强烈,其动力稳定性也就越差。
(3)运用正交试验设计法,通过数值计算与数理统计分析评价了岩体边坡PGA放大系数极大值影响因素的敏感性。虽然PGA放大系数极大值并不能全面地反映岩体边坡地震动力响应的整体情况,但其能在一定程度上诠释岩体边坡地震动力响应的强度问题。在分析各种结构面因素单独作用时PGA放大系数极大值的变化规律的基础上,综合考虑各种结构面因素之间的相关性和随机联动性,分别采用极差分析法和方差分析法对岩体边坡PGA放大系数极大值影响因素的敏感性进行了排序。参与分析的5个结构面因素中,敏感性由大到小的顺序依次为：结构面倾角、结构面起始位置、结构面剪切刚度、结构面法向刚度、结构面间距。因此,当岩体边坡中发育有倾角较陡的结构面且结构面发育深度较浅时,其动力响应的强度往往就会越强,在地震荷载的作用下,这类岩体边坡的动力稳定性问题也将显得更为突出。
(4)针对动力强度折减法中第一种失稳判据在实际应用中的局限性,提出了“基于永久位移比的岩体边坡动力稳定性计算方法”。地震荷载作用下,地震永久位移随强度折减系数的增加而增加,且在强度折减系数较小时增幅不明显,当超过某一定值时,地震永久位移的增幅迅速增大,呈明显的指数函数形式变化。关于如何在地震永久位移与折减系数的关系曲线中标定出边坡的动力稳定性系数,目前的解决方法主要是以该曲线“拐点”即永久位移值突变点所对应的折减系数来确定,然而对于“拐点”的位置该如何确定则存在较大的人为主观因素,并且缺乏合理的数学理论公式做支撑,使得该方法在使用上存在着一定的局限性。在此背景下,本文提出永久位移比理论新概念,即当岩体边坡沿滑动面的地震永久位移达到滑动面长度的一定比值时认为该边坡失稳破坏。将此方法运用于汶川地震区块状岩体边坡实例研究中,计算得出该实例边坡在汶川地震荷载作用下的动力稳定性系数为1.04,稳定性计算结果与实际地质调查情况相符,验证了本方法的工程实用性。
(5)针对动力强度折减法中第二种失稳判据的不足之处,提出了“考虑结构面退化的岩体边坡动力稳定性计算方法”。当采用第二种失稳判据来分析岩体边坡的动力稳定性时,通过结构面静态强度参数计算所得的岩体边坡动力稳定性系数与其静力稳定性系数进是相等的,地震荷载的振幅对边坡动力稳定性系数的影响得不到任何体现,在此背景下,基于前人有关结构面摩擦系数随累积位移和相对运动速率不断衰减的研究成果,提出了考虑结构面退化的岩体边坡动力稳定性计算方法,给出了相应的实施流程,并用汶川地震区的工程实例进行了说明,计算结果表明,使用该方法来计算岩体边坡的动力稳定性是可行的。
(6)老虎嘴岩体边坡是汶川地震区典型的受优势结构面控制的块状岩体边坡,5·12汶川大地震使得该边坡内部的结构面贯通,形成楔形体在地震作用下向临空面方向运动,以至产生严重的崩滑现象,并导致岷江堵塞和交通封闭。以老虎嘴块状结构岩体边坡的地质原型为基础,应用三维离散元数值模拟软件3DEC,建立了老虎嘴块状结构岩体边坡的三维离散元数值计算模型,并通过动力计算还原了该边坡在汶川地震荷载作用下变形破坏的演化过程,对其动力失稳机制进行了详细分析,为研究具有相同结构类型的岩体边坡在强震作用下的破坏方式提供了参考依据。
The study on the stability of block rock slope under seismic loading is a hot and hard issue. It affects much on the construction of large-scale hydraulic and hydropower station, mountain high way, railway, nuclear power station. The deep researches into dynamic response rule, failure mechanism, stability evaluation and so on are of great significance. Not only can it push the development and creativity of slope stability theory under earthquake, but also support the planning, designing and constructing of geotechnical facility.
Rock mass is composed of rock blocks that divided by the discontinuity network. Discontinuity is an important factor that determines the process and rule of the propagation of seismic wave. It is the foundation of research into rock slope dynamic response and dynamic stability to study the propagation characteristics of seismic wave in joint rock mass.
Earthquake dynamic response of slope includes acceleration, velocity, displacement, dynamic stress, strain response, etc. In a broader sense, except for the standard parameters above, some abstract and human defined variables like dynamic factor of safety can also be viewed as the slope dynamic response to seismic. Of all the physical quantities and semaphores that can stand for the slope dynamic response, acceleration is the basic one. Because for one thing, velocity and displacement can be obtained by acceleration integral and double integral for time, respectively. For another, the relationship between dynamic stress and acceleration, dynamic stress and quality of any infinitesimals in the slope are in accordance to Newton's second law. Dynamic stress and strain can be connected by modulus. In this sense, dynamic stress, dynamic strain and acceleration are also connected. Actually, the dynamic responses in slope are all induced by acceleration of seismic. Therefore, the study of dynamic response rules in time and space of acceleration is becoming the basic problem in this field, and it is of great value in evaluate the slope dynamic stability.
In calculation of dynamic stability, permanent displacement analysis and factor analysis of dynamic stability are two main methods in evaluation of dynamic stability. Permanent displacement can reflect more precisely the dynamic response of slope to earthquake compared to factor of stability. Theoretically, the standard of permanent displacement is more reasonable than that of factor of stability. However, much insufficient exists in it. First of all, naturally, permanent displacement analysis is a relatively rough method. In calculation of slope permanent displacement caused by earthquake, slope material deformation, rock strength under dynamic situation and deformation character are not taken into consideration. Second, average displacement can be obtained through the permanent displacement analysis, which can not reflect the real condition. Third, stability factor of slope will not be received through the analysis and it will cause much inconvenience in stability evaluation. So, permanent displacement analysis and dynamic strength reduction method are combined here to get the factor of stability. Permanent displacement is taken as the index of dynamic failure, and strength reduction method is used to calculate the factor of stability. Currently, two criterions can be used to determine dynamic failure. One is the relation curve of permanent displacement and reduction coefficient. The other is whether the permanent curve is divergence at the key point after earthquake. Two criteria are not so perfect and a new calculation method will be put forward here.
Commonly, slopes with rocks of integrity, inclining to the slope and less amount of discontinuities are relatively stable. But under the effect of strong earthquake, the rocks become less composed and more discontinuities appear. Shear strength reduced rapidly, so is the whole slope stability. Now, not so much work has been done on the aspect of earthquake caused dynamic response to that kind of rock slope and failure manners. As long as how strong the destructive can be, it appears to be urgent and important to take research into the study of the problem.
Study in this paper mainly aims at block rock mass slope.3DEC simulation is used to take further study into the dynamic response rule, stability analysis and failure mode. It aims to reveal the earthquake affect on block rock slope and its mechanism. In this way, theoretical criterion can be provided to evaluate more precisely the dynamic stability of rock slope. Main contents of this paper are listed as follows:
(1) Based on3DEC simulation model, the characters of propagation in single joint rock mass is analyzed. First, the numerical model of harmonic seismic wave propagating in homogeneous rock is built. Model and dynamic analysis parameters are chosen according to real parameters, which include boundary conditions, size of grid cells and time step of dynamic calculation and so on. Next, the propagation model of seismic in single joint rock is built and another factor is taken into consideration. The factor is the influence of discontinuity stiffness on propagation rules when seismic wave vertically oblique and incident on structure plans. The feasibility of simulation is taken into consideration and combined much work done by others. It is quite reliable to utilize3DEC simulation to analyze the dynamic problems of joint rock mass.
(2) Through much numerical simulation calculation, the influence rules of discontinuities on rock mass slope dynamic response are studied. The analysis of earthquake dynamic response to rock mass slope is a rather complicated problem. Except for the complication of seismic loading, rock materials, physical and mechanical properties and the distribution of discontinuities, scale and other factors play a role in the response. It is not reasonable to take all the factors above into consideration. In this paper, the physical and mechanical properties and the distribution of discontinuities are taken into account. On the aspect of physical mechanism, structure stiffness is the main factor for its influence on transmission and reflection coefficient of seismic wave. In addition, on the aspect of discontinuity contribution, occurrence, starting position, and density of structures are the studying points. The results indicate:1) Change of structure occurrence will lead to the different directions of reflection and refraction of seismic wave. And then the distribution of field energy of seismic wave will be changed. It finally reflects on the spatial variation of slope amplification factor PFA contours. As for dip layered slope, when dip angle of structure is relatively small, structures have a reduction effect on seismic propagation. When the angle is relatively big, it has the opposite effect. The dynamic stability of slope decreases with the increase of dip angle. The existing of anti-dip layered slope will make the propagation of seismic in rock slope decay. As structure dip angle increases, the strength of discontinuity decreases. The dynamic stability of anti-dip layered structure is better than that of dip layered structure.2) The starting position of structure is a big factor on seismic dynamic response of rock slope. The higher the position is, the stronger the response is.3) With the increasing of structure stiffness, the strength of seismic dynamic response has the tendency increase. The effect of structure stiffness on reflected and transmitted waves is mainly on the relationship of energy distribution, but not impact can be seen at the propagation path of them in rock slope. When the incident wave is shear wave, the seismic dynamic response to structure shear stiffness is more sensitive than that to normal stiffness.4) More intense the discontinuities are, worse the integrity the rock slope is, and stronger the seismic dynamic response is, which means the poorer the dynamic stability of slope is.
(3) Orthogonal experiment design method is applied, and evaluation on the sensibility of the maximum value of PGA amplification factor in rock mass slope through numerical calculation and statistics. Though the maximum value of PGA amplification factor can not reflect the whole condition of dynamic response to rock slope comprehensively, it can to some degree determine the strength of it. The changing rule of maximum PGA amplification factor is analyzed under structure effect. Based on this, taken into consideration the correlations and random linkage in structure factors, range analysis and variance analysis are used to put the sensibility of maximum PGA amplification factors in order. The sensibilities of dip angle starting position, shear stiffness, normal stiffness and distance of discontinuities are in descending orders. Therefore, when there is structure with big dip angle and develops shallowly, the dynamic response will be stronger. Under the effect of seismic loading, this type of dynamic stability problem in rock slope will be more prominent.
(4) On the limitations of the first failure criterion in dynamic strength reduction method in practical, a calculation method of dynamic stability in rock mass slope based on permanent displacement is put forward. Under seismic loading, the permanent displacement of earthquake increase with strength reduction factor. When the factor is relative small, its increase amplitude will not be obvious and when it exceeds a certain value, the increase amplitude of earthquake permanent displacement will increase rapidly and show a change in the form of an exponential function. On how to set the dynamic stability factor on the relation curve of seismic permanent displacement and reduction factor, the current solution is take the corresponding reduction factor of turning point. But many subjective factors exist in determining the turning point, making the method more insufficient in utilizing. A new concept of permanent displacement is proposed. That is when the permanent displacement along rock slope caused by earthquake reaches a certain ratio of the length of slip surface, the slope will be in unstable state. Applied this approach to the study of block rock slope in Wenchuan earthquake area, the dynamic stability factor is1.04under the Wenchuan earthquake load. The result is in consistent with geological survey condition and verifies the practicability of this method.
(5) On the limitations of the second failure criterion in dynamic reduction method, a calculation method of dynamic stability factor in rock slope considering structure degradation. When the second criterion is taken to analyze the dynamic stability in rock mass slope, the dynamic stability factor that obtained through static strength parameters is the same with the static stability factor, which means the effect of amplitude of seismic load on dynamic stability factor can not been seen here. Based on relative research achievement about the friction coefficient decays with the cumulative displacement and relative rates that done by others, a calculation method of dynamic stability factor in rock slope considering structure degradation is proposed and corresponding implementation process is given. Projects in Wenchuan earthquake area is taken for illustration. The results indicate it is feasible to put the method into calculation of dynamic stability in rock mass slope.
(6) The Tiger Mouth rock mass slope is a typical slope that is controlled by dominant joint plan in Wenchuan earthquake area. The5.12Wenchuan earthquake makes the discontinuities in the slope connect with each other, which lead to the formation of wedge and it will slide towards the free face under the effect of seismic. A heavy landslide happened, making the Min River block and traffic close. Based on the block rock mass slope of Tiger Mouth, a numerical model is built in3DEC software. The evolution process of the slope getting deformed under Wenchuan earthquake has been restored, and the dynamic mechanism has been analyzed in detaisl. It brings reference to the study on the failure mode of the same type rock mass slope under heavy earthquake.
引文
[1]唐辉明.工程地质学基础[M].北京：化学工业出版社,2008.
[2]苏凤环,刘洪江,韩用顺.汶川地震山地灾害遥感快速提取及其分布特点分析[J].遥感学报,2008.12(6)：936-962.
[3]祁生文,伍法权,严福章等.岩质边坡动力反应分析[M].北京：科学出版社,2007.
[4]王思敬.岩石边坡动态稳定性的初步探讨[J].地质科学,1977,(4)：372-376.
[5]GazetasG. Seismic response of earth dams[J]. SoilDyn. Earthq. Engrg.,1987,6(1):3-47.
[6]祁生文,伍法权,刘春玲等.地震边坡稳定性的工程地质分析[J].岩石力学与工程学报,2004,23(16)：2792-2796.
[7]廖少波,方正,刘晓.考虑结构面分布特征的岩质边坡地震响应分析[J].人民长江,2013,44(3)：40-43.
[8]邵龙潭,唐洪祥,孔宪京.随机地震作用下土石坝边坡的稳定性分析[J].水利学报,1999,(11)：66-71.
[9]祁生文.单面边坡的两种动力反应形式及其临界高度[J].地球物理学报,2006.49(2)：518-523.
[10]LAWARENCE L DAVIS,LEWIS R WEST. Observed effects of topography on ground motion[J].Bulletin of the Seismological Society of America,1973,63:283-298.
[11]HARTZELL S H, CARVER D L, KING K W. Initial investigation of site and topographic effects at Robinwood ridge California[J].Bulletin of the Seismological Society of America, 1994,84:1336-1349.
[12]ASHFORD S A,SITARN.Topographic amplification in the 1994 Northridge earthquake: Analysis and observation.6th U.S National conference on Earthquake Engineering[C],1997.
[13]ASHFORD S A,SITAR N,LYSMER J.DENG N.Topographic effects on the seismic response of steep[J].Bulletin of the Seismological Society of America,1997,87:701-709.
[14]刘昌森,吕美丽.上海地区地震放大效应的初步探讨[J].上海地质,1998,1：7-13.
[15]刘洪兵,朱晞.地震中地形放大效应的观测和研究进展[J].世界地震工程,1999,15(3)：20-25.
[16]王福海,王运生,孙刚等.地震荷载作用下斜坡响应研究：以四川青川东山—狮子梁剖面为例[J].现代地质,2011,25(1)：142-150.
[17]祁生文,伍法权,孙进忠.边坡动力响应规律研究[J].中国科学E辑技术科学,2003,33(增刊)：28-40.
[18]王环玲,徐卫亚.高烈度区水电工程岩石高边坡三维地震动力响应分析[J].岩石力学与工程学报,2005,24(增2)：5890-5895.
[19]秋仁东,石玉成,付长华.高边坡在水平动荷载作用下的动力响应规律研究[J].世界地震工程,2007,23(2)：131-138.
[20]王义锋,郑文棠,石崇.岩质高边坡的地震时程响应分析[J].三峡大学学报(自然科学版),2008,30(3)：1-5.
[21]Sun Jinzhong, Tian Xiaofu. Numerical analysis of the influence of structure planes on earthquake motion in rock slopes[A]. Geological Engineering Problems in Major Construction Projects[C].Chengdu,2009:451-462.
[22]毕忠伟,张明,金峰等.地震作用下边坡的动态响应规律研究[J].岩土力学,2009,30(增刊)：180-183.
[23]刘和平,郭永刚.岩质边坡在不同地震波入射方向下的动力响应分析[J].水电能源科学,2010,28(1)：76-79.
[24]周剑,张路青,王学良.水平层状岩体边坡动力响应中的结构面效应研究[J].工程地质学报,2011,19(3)：352-358.
[25]王存玉,王思敬.边坡模型振动试验研究.岩体工程地质力学问题(七).北京：科学出版社,1987.
[26]王存玉.地震条件下二滩水库岸坡稳定性研究.岩体工程地质力学问题(八).北京：科学出版社,1987.
[27]李金贝,张鸿儒,李志强.路基动力响应与动力破坏的大型振动台模型试验研究[J].岩石力学与工程学报,201],30(增刊)：3746-3754.
[28]杨国香,伍法权,董金玉等.地震作用下岩质边坡动力响应特性及变形破坏机制研究[J].岩石力学与工程学报,2012,31(4)：696-702.
[29]刘汉香,许强,范宣梅.地震动参数对斜坡加速度动力响应规律的影响[J].地震工程与工程振动,2012,32(2)：41-47.
[30]王思敬,张菊明.岩体结构稳定性的块体力学分析[J].地质科学,1980,(1)：19-33.
[31]王思敬,张菊明.边坡岩体滑动稳定的动力学分析[J].地质科学,1982,2：162-170.
[32]王思敬,薛守义.岩体边坡楔形体动力学分析[J].地质科学,1992,2：177-182.
[33]张菊明,王思敬.层状边坡岩体滑动稳定的三维动力学分析[J].工程地质学报,1994,2(3)：1-12.
[34]张咸恭,王思敬,张倬元等著.中国工程地质学[J].北京：科学出版社,2000.
[35]Wang S.J, Xue S.Y, Maugeri M, et,al. Dynamic stability of the left abutment in the Xiaolangdi Project On the Yellow River. Proc. Int. Symp. On Assessment and Prevention of Failure Phenomena in Rock Engrg. Ankara. April,5-7,1993.
[36]Wang S.J, Zhang J.M. On the dynamic stability of block sliding on rock slopes. Proc.of the Int. Cont. on Recent Advances in Geotechnical Earthquake Engineering and Soil dynamics, St. Louis,431-434.
[37]薛守义.岩体边坡动力性研究[D].中国科学技术大学博士学位论文,1989.
[38]张平,吴德伦.动荷载下边坡滑动的试验研究[D].重庆建筑大学学报,1997,19(2)：80-86.
[39]Kumsar H, Aydan O, Ulusay R. Dynamic and static stability assessment of rock slopes against wedge failures.Rock mechanics and rock engrg,2000, 33(1):31-51.2002,13(1):94-97.
[40]Terzaghi K. Mechanisms of landslides[C].//Geological Society of America Berkey Volume.1950:83-123.
[41]Seed H B. Considerations in the earthquake-resistant design of earth and rockfill dams[J].Geotechnique.1979,29(3):215-263.
[42]Mononobe A H. Seismic stability of the earth dam[C].//Proc.2nd Congress on large dams.Washinton DC:IV:1936.
[43]Seed H B, Martin R G. The seismic coefficient in earth dam design[J]. Journal of Soilmechanics and Foundation Division.1996,104(SM3):59-83.
[44]Newmark N M. Effect of earthquakes on dams and embankments[J]. Geotechnique.1965, 15(2):139-160.
[45]Lin J S, Whitman R V. Earthquake induced displacements of sliding blocks[J]. J GeotechEngng Div.1986,112(1):44-59.
[46]Makdisi F I, Seed H B. Simplified procedure for estimating dam and embankment earthquakeinduced deformations[J]. J Geotech Engng.1978,104(No.GT7):569-587.
[47]Martin R G, Finn W D L, Seed H B. Fundamentals of liquefaction under cyclic loading[J]. J Geotech Engrg Div asce.1975,101 (GT5):423-438.
[48]Sarma S K. Seismic stability of earth dams and embankments[J]. Geotech Engng Div. 1975,105, GT4:449-464.
[49]Sarma S K. Seismic displacement analysis of earth dams[J]. J Geotech Engng Div 107. 1981,GT12:1735-1739.
[50]Wang S J, Xue S Y, Maugeri M. Dynamic stability of the left abutment in the XiaolangdiProject On the Yellow River[C].//Proc Int Symp on Asessment and Prevention of Failur Phenomena in Rock Engrg. Istanbul(Turkey):A. a. Balma, Rotterdam,1993: 619-625.
[51]Yegian M K, Harb J N. Slip displacements of geosynthetic systems underdynamic excitation[M]. Design and performance of solid waste landfills, No.54, Yegian M K, Finn W,San Diego, California, ASCE,:Geotechnical Special Publication,1995,212-236.
[52]Yegian M K, Lahlfa A M. Dynamic interface shear strength properties of geomembrabes and geotexiles[J]. J Geotech Engrg ASCE.1992,118(5):760-779.
[53]刘立平,雷尊宇,周富春.地震边坡稳定分析方法综述[J].重庆交通学院学报,2001,20(3)：83-88.
[54]林宗元.岩土工程勘察设计手册[M].北京：中国建筑工业出版社,1996.
[55]Leshchinsky D, San K.Ching. Pseudo-static seismic stability of slopes. Design charts.J.of Geotech.Engrg.,1994,120(9):1514-1532.
[56]Baker R, Garber M. Theoretical analysis of the stability of slopes. Geotechnique,1978, 28(4):395-411.
[57]Taylor D.W. Stability of earth slopes.J.Boston Society of Civ. Engrgs,1937,24(3):197-246.
[58]Seed H.B. Stability of earth and rockfill dams during earthquakes.in Embankment-Dam Engrg. Casagrande,Vol.(Eds Hirschfeld and Poulos),John Wiley,1973.
[59]Kramer S, Smith D. Modified newmark model for seismic displacement of compliant slopes[J]. Journal of geotechnical and geoenvironmental engineering, ASCE,1997,123(7): 635-644.
[60]Ling H I. Recent applications of sliding block theory to geotechnical design[J]. Soil dynamics and earthquake engineering,2001,21(3):189-197
[61]王思敬.岩石边坡动态稳定性的初步探讨[J].地质科学,1977,(]0)：372-376.
[62]薄景山,徐国栋,景立平.土边坡地震反应及其动力稳定性分析[J].地震工程与工程振动,2001(02)：116-120.
[63]陈玲玲,陈敏中,钱胜国.岩质陡高边坡地震动力稳定分析[J].长江科学院院报,,2004(01)：33-35.
[64]Ford S A A S, Sitar N, Lysmer J, et al. Topographic effects on the seismic response of steep slopes[J]. Bulletin of the Seismological Society of America.1997,87(3):701-709.
[65]刘春玲.祁生文,童立强等.利用FLAC-(3D)分析某边坡地震稳定性[J].岩石力学与工程学报,2004(16)：2730-2733.
[66]许瑾,郑书英.边界元法分析边坡动态稳定性[J].西北建筑工程学院学报(自然科学版),2000(04).
[67]张云.露天矿边坡岩体裂隙含水介质渗流场边界元分析[J].南京大学学报数学半年刊,1992(01)：119-125.
[68]李建平,熊传治.岩石边坡安全系数的边界元解[J].岩石力学与工程学报,1990(3)：238-243.
[69]樊文熙.有限元边界元法在岩体力学与工程中的应用[J].中州煤炭.1985(04)：2-3.
[70]Chunhan Z, Pekau O A, Feng J, et al. Application of disticnct element method in dynamic analysis of high rock slopes and blocky structures[J].Soil Dynamics and Earthquake Engineering.1997,16(6):385-394.
[71]张建海,范景伟,何江达.用刚体弹簧元法求解边坡、坝基动力安全系数[J].岩石力学与工程学报,1999(04)：19-23.
[72]邓学晶,孔宪京,刘君.城市垃圾填埋场的地震响应及稳定性分析[J].岩土力学,2007,22(10)：2095-2100.
[73]卓家涛,章青.不连续介质力学问题的界面元法[M].北京：科学出版社,2004.
[74]裴觉民.数值流形方法与非连续变形分析[J].岩石力学与工程学报,1997(03)：80-93.
[75]刘汉龙,费康,高玉峰.边坡地震稳定性时程分析方法[J].岩土力学,2003,24(4)：553-560.
[76]吴兆营,薄景山,刘红帅,等.岩体边坡地震稳定性动安全系数分析方法[J].防灾减灾工程学报,2004,24(3)：228-241.
[77]陈云敏,柯瀚,凌道盛.城市垃圾填埋体的动力特性及地震响应[J].土木工程学报,2002,35(3)：66-72.
[78]刘君,孔宪京.卫生填埋场复合边坡地震稳定性和永久变形分析[J].岩土力学,2004,25(5)：778-782.
[79]Cundall P A. A computer model for simulating progressive large scale movements in blocky system. In:Muller Led. Proceedings of Symosium of the International Society of Rock Mechanics. Rotterdam:A.A. Balkema,1971(1):8-12.
[80]Cundall P A. The measurement and analysis of acceleration in rock slopes. Ph.D.Dissertation, University of London, Imperial college of Science and Technology, 1971.
[81]Strack O D L, Cundall P A. The distinct element method as a tool for research in granular media. Part I. Report to the National Science Foundation, Minnesota:University of Minnseota,1978.
[82]Cundall P A, Strack O D L. The distinct element method as a tool for research in granular media. Part Ⅱ. Report to the National Science Foundation, Minnesota:University of Minnseota,1979.
[83]Cundall P A, Strack O D L. A discrete numerical method for granular assemblies. Geotechnique,1979,29(1):47-65.
[84]Zhu H P, Zhou Z Y, Yang R Y, Yu A B. Discrete particle simulation of particulate systems: Theoretical developments. Chemical Eengineering Science,2007,62:3378-3396.
[85]Maini T, Cundall P A. Computer modeling of jointed rock mass,(AD-A061658),1978.
[86]Cundall P A. UDEC-A Generalized distinct element progrom for modeling joined rock. Report PCAR-1-80 Perter Cundall Associates,European Research Office,U.S.Army,March 1980.
[87]Cundall P A. BALL-A program to model granular media using the distinct element method.Technical Note, Advanced Technology Group, Dames&Moore, London.1978.
[88]Cambell C S, Brennen C E. Computer simulation of granular shear flows. Journal of Fluid Mechanics.1985,151:167-188.
[89]Cambell C S, Brennen C E. Chute flows of granular materials:some computer simulations. Journal of Applied Mechanics,1985,(52):172-178.
[90]Kishino Y. Disc model analysis of the granular media. In:Micromechanics of granular materials. Satake M, Jenkins JT(Eds):1988,143-153.
[91]Kishino Y. Computer analysis of dissipation mechanism in granular media. In:Powders and Grain. Biarez&Gourves(Eds) 1984:323-330.
[92]Itasca Consulting Group, Inc. UDEC(Universal Distinct Element Code),Version 3.1. Minneapolis:ICG,2000.
[93]Itasca Consulting Group, Inc.3DEC(3-Dimensional Distinct Element Code), Version 2.0. Minneapolis:ICG,1998.
[94]Itasca Consulting Group, Inc. PFC2D(Particle Flow Code in 2 Dimensions),Version 3.0. Minneapolis:ICG,2002.
[95]Itasca Consulting Group, Inc. PFC3D(Particle Flow Code in 3 Dimensions),Version 2.0. Minneapolis:ICG,1999.
[96]Hunt S P, Meyers A G, Louchnikov V. Modeling the Kaiser effect and deformation rate analysis in sandstone using the discrete element method. Computers and Geotechnics, 2003,30:611-621.
[97]Djordjevic N. Discrete element modeling of the influence of lifters on power draw of trumbling mills. Minerals Engineering,2003,16:331-336.
[98]Fakhimi A, Carvalho F, Ishida T, Labuz J F. Simulation of failure aroud a circular opening in rock. International Journal of Rock Mechanics and Mining Sciences,2002,39:507-515.
[99]Wang C, Tannant D D, Lilly P A. Numerical analysis of the stability of heavily jointed rock slopes using PFC2D. International Journal of Rock Mechanics and Mining Sciences,2003, 40:415-424.
[100]Fleissner F, Gaugele T, Eberhard P. Applications of the discrete element method in mechanical engineering. Multibody System Dynamics.2007,18(1):81-94.
[101]王泳嘉.离散元法——一种适用于节离岩石力学分析的数值方法.第一届全国岩石力学数值计算及模型试验讨论论文集,1986：32-37.
[102]剑万禧.离散元法的基本原理及其在岩体工程中的应用.第一届全国岩石力学数值计算及模型试验讨论论文集,1986：43-46.
[103]汪远年,李世海.断续节理岩体随机模型三维离散元数值模拟[J].岩石力学与工程学报,2004,23(21)：3652-3658.
[104]汪远年,李世海.三维离散元计算参数选取方法研究[J].岩石力学与工程学报,2004,23(21)：3658-3664.
[105]王涛,陈晓玲,杨建.基于3DGIS和3DEC的地下洞室围岩稳定性研究[J].岩石力学与工程学报,2005,24(19)：3476-3481.
[106]周家文,徐卫亚,石崇.基于3DEC的节理岩体边坡地震影响下的楔体稳定性分析[J].岩石力学与工程学报,2007,26(增刊)：3402-3409.
[107]白永健,黄润秋,巨能攀等.高陡岩质边坡稳定性三维离散元分析[J].工程地质学报,2008,16(5)：592-597.
[108]尹祥础,尹灿.非线性系统失稳前兆与地震预测中国科学(B),1993,No.1：21-27.
[109]姜彤,马莎,许兵等.边坡在地震作用下的加卸载响应规律研究[J].岩石力学与工程学报,2004,23(22)：3803-3807.
[110]姜彤,马莎,许兵.基于加卸载响应比理论的边坡动力稳定分析方法[J].岩石力学与工程学报,2007,26(3)：626-635
[111]HALATCHEV ROSSEN A. Probabilistic Stability Analysis of Structure Considering Tensile Failure.12WCEE,2000
[112]张倬元,王士天,王兰生.工程地质分析原理[M].北京：地质出版社,1993.
[113]胡广韬.滑坡动力学[M].北京：地质出版社,1995.
[114]毛彦龙,胡广韬,毛新虎等.地震滑坡启程剧动的机理研究及离散元模拟[J].工程地质学 报,2001,9(1)：74-80.
[115]许强,陈建君,冯文凯等.斜坡地震响应的物理模拟试验研究[J].四川大学学报(工程科学版),2009,41(3).
[116]言志信,张刘平,曹小红等.地震作用下顺层岩质边坡动力响应规律及变形机制研究[J].岩土工程学报,2011,33(增刊)：54-58.
[117]叶海林,郑颖人,杜修力等.边坡动力破坏特征的振动台模型试验与数值分析[J].土木工程学报,2012,45(9)：128-135.
[118]刘佑荣,唐辉明.岩体力学[M].北京：化学工业出版社,2008.
[119]Goodman R. E, Taylor R. L, Brekke T. A. A mode of the mechanics of jointed rock[J]. J. Soil Mech. Div., ASCE,1968,94:637-659.
[120]Schwer L. E, Lindberg H. E. Application brief:a finite element slide line approach for calculating tunnel response in jointed rock[J]. Int J Num Anal Methods Geomech,1992, 16:529-540.
[121]Beer G. Implementation of combined boundary element-finite element analysis with applicationsin geomechanics [A]. Applied Science,1986,191-226.
[122]Crotty J M, Wardle L J. Boundary integral analysis of piecewise homogeneous media with structural dis-continuities[J]. Int. J. Rock Mech. Min. Sci. Geomech. Abstr.,1985, 22:419-427.
[123]Itasca Consulting Group, Inc.3 Dimensional Distinct Element Code:Theory and Background [R]. Minneapolis:Itasca Consulting Group, Inc,2003.
[124]刘波,韩彦辉.FLAC原理、实例与应用指南[M].北京：人民交通出版社,2005.
[125]陈育民,徐鼎平.FLAC/FLAC3D基础与工程实例[M].北京：中国水利水电出版社,2008.
[126]J. Lysmer and R. L. Kulemeyer. Finite Dynamic Model for Infinite Media. Journal of Engineering Mechanics Division, ASCE.1969,95(4):759-877.
[127]Kunar, R. R., P. J. Beresford and P. A. Cundall. "A Tested Soil-Structure Model for SurfaceStructures," in Proceedings of the Symposium on Soil-Structure Interaction (Roorkee University,India, January,1977), Vol.1, pp.137-144. Meerut, India:Sarita Prakashan,1977.
[128]Kuhlmeyer, R. L., and J. Lysmer. "Finite Element Method Accuracy for Wave Propagation Problems," J. Soil Mech.& Foundations Div., ASCE,99(SM5),421-427 (May,1973).
[129]王礼立.地震波基础[M].北京：国防工业出版社,2005.
[130]王有学.地震波理论基础[M].北京：地质出版社,2011.
[131]MYER L R,PYRAK-NOLTE L J,COOK N G W. Effects of singlefractures on seismic wave propagation[C]//Proceedings of ISRM Symposium on Rock Joints. Rotterdam:A. A. Balkema,1990:467-473.
[132]Pyrak-Nolte L J, Myer L R, Cook N G W. Transmission of seismic waves across single natural fractures[J]. Journal of Geophysical Research,1990,95(6):8617-8638.
[133]Itasca Consulting Group, Inc.3 Dimensional Distinct Element Code:Optional Features[R]. Minneapolis:Itasca Consulting Group, Inc,2003.
[134]徐光兴,姚令侃,李朝红,等.边坡地震动力响应规律及地震动参数影响研究[J].岩土工程学报,2008,30(6)：918-923.
[135]Goodman R E, Seed H B. Earthquake-induced displacements in sand embankment [J].J Soil Mech Fdn Engng Div,92(SM2):125-146.
[136]刘杰,李建林,张玉灯等.基于拟静力法的大岗山坝肩边坡地震工况稳定性分析[J].岩石力学与工程学报,2009,28(8)：1562-1570.
[137]Clough R W, Chopra A K. Earthquakes stress analysis in earth dams [J].J Engrg Mech, 1966,92(EM2):197-211.
[138]张伯艳,陈厚群,杜修力.拱坝坝肩抗震稳定分析[J].水利学报,2000(11)：55—59.
[139]李育枢,高广运,李天斌.偏压隧道洞口边坡地震动力反应及稳定性分析[J].地下空间与工程学报,2006,2(5)：738—743.
[140]汪茜.地震作用下顺层岩质边坡变形破坏机理研究[D].长春：吉林大学,2009.
[141]郑颖人,叶海林,黄润秋,等.边坡地震稳定性分析探讨[J].地震工程与工程振动,2010(002)：173-180.
[142]胡聿贤.地震工程学[M].北京：地震出版社,1988：71-72.
[143]Hoek E, Bray J. Rock slope engineering[M].3rd ed. London:Institution of Mining and Metallurgy,1981.
[144]戴妙林,李同春.基于降强法数值计算的复杂岩体边坡动力稳定性安全评价分析[J].岩石力学与工程学报,2007,26(增刊1)：2049
[145]李海波,肖克强,刘亚群.地震荷载作用下顺层岩质边坡安全系数分析[J].岩石力学与工程学报,2007,26(12)：2385-2394.
[146]HUTSON R W, DOWDING C H. Joint asperity degradation during cyclic shear[J]. Int J Rock Mech Min Sci & Geomech Abstr,1990,27(2):109-119.
[147]LEE H S, PARK Y J, CHO T F, YOU K H. Influence of asperity degradation on the mechanical behavior of rough rock joints under cyclic shear loading[J]. Int J Rock Mech Min Sci,2001,38:967-980.
[148]倪卫达,唐辉明,刘晓等.考虑结构面震动劣化的岩质边坡动力稳定分析[J].岩石力学与工程学报,2013,32(3)：492-500.
[149]孙玉科,牟会宠,姚宝魁.边坡岩体稳定性分析[M].北京：科学出版社,1988.
[2]苏凤环,刘洪江,韩用顺.汶川地震山地灾害遥感快速提取及其分布特点分析[J].遥感学报,2008.12(6)：936-962.
[3]祁生文,伍法权,严福章等.岩质边坡动力反应分析[M].北京：科学出版社,2007.
[4]王思敬.岩石边坡动态稳定性的初步探讨[J].地质科学,1977,(4)：372-376.
[5]GazetasG. Seismic response of earth dams[J]. SoilDyn. Earthq. Engrg.,1987,6(1):3-47.
[6]祁生文,伍法权,刘春玲等.地震边坡稳定性的工程地质分析[J].岩石力学与工程学报,2004,23(16)：2792-2796.
[7]廖少波,方正,刘晓.考虑结构面分布特征的岩质边坡地震响应分析[J].人民长江,2013,44(3)：40-43.
[8]邵龙潭,唐洪祥,孔宪京.随机地震作用下土石坝边坡的稳定性分析[J].水利学报,1999,(11)：66-71.
[9]祁生文.单面边坡的两种动力反应形式及其临界高度[J].地球物理学报,2006.49(2)：518-523.
[10]LAWARENCE L DAVIS,LEWIS R WEST. Observed effects of topography on ground motion[J].Bulletin of the Seismological Society of America,1973,63:283-298.
[11]HARTZELL S H, CARVER D L, KING K W. Initial investigation of site and topographic effects at Robinwood ridge California[J].Bulletin of the Seismological Society of America, 1994,84:1336-1349.
[12]ASHFORD S A,SITARN.Topographic amplification in the 1994 Northridge earthquake: Analysis and observation.6th U.S National conference on Earthquake Engineering[C],1997.
[13]ASHFORD S A,SITAR N,LYSMER J.DENG N.Topographic effects on the seismic response of steep[J].Bulletin of the Seismological Society of America,1997,87:701-709.
[14]刘昌森,吕美丽.上海地区地震放大效应的初步探讨[J].上海地质,1998,1：7-13.
[15]刘洪兵,朱晞.地震中地形放大效应的观测和研究进展[J].世界地震工程,1999,15(3)：20-25.
[16]王福海,王运生,孙刚等.地震荷载作用下斜坡响应研究：以四川青川东山—狮子梁剖面为例[J].现代地质,2011,25(1)：142-150.
[17]祁生文,伍法权,孙进忠.边坡动力响应规律研究[J].中国科学E辑技术科学,2003,33(增刊)：28-40.
[18]王环玲,徐卫亚.高烈度区水电工程岩石高边坡三维地震动力响应分析[J].岩石力学与工程学报,2005,24(增2)：5890-5895.
[19]秋仁东,石玉成,付长华.高边坡在水平动荷载作用下的动力响应规律研究[J].世界地震工程,2007,23(2)：131-138.
[20]王义锋,郑文棠,石崇.岩质高边坡的地震时程响应分析[J].三峡大学学报(自然科学版),2008,30(3)：1-5.
[21]Sun Jinzhong, Tian Xiaofu. Numerical analysis of the influence of structure planes on earthquake motion in rock slopes[A]. Geological Engineering Problems in Major Construction Projects[C].Chengdu,2009:451-462.
[22]毕忠伟,张明,金峰等.地震作用下边坡的动态响应规律研究[J].岩土力学,2009,30(增刊)：180-183.
[23]刘和平,郭永刚.岩质边坡在不同地震波入射方向下的动力响应分析[J].水电能源科学,2010,28(1)：76-79.
[24]周剑,张路青,王学良.水平层状岩体边坡动力响应中的结构面效应研究[J].工程地质学报,2011,19(3)：352-358.
[25]王存玉,王思敬.边坡模型振动试验研究.岩体工程地质力学问题(七).北京：科学出版社,1987.
[26]王存玉.地震条件下二滩水库岸坡稳定性研究.岩体工程地质力学问题(八).北京：科学出版社,1987.
[27]李金贝,张鸿儒,李志强.路基动力响应与动力破坏的大型振动台模型试验研究[J].岩石力学与工程学报,201],30(增刊)：3746-3754.
[28]杨国香,伍法权,董金玉等.地震作用下岩质边坡动力响应特性及变形破坏机制研究[J].岩石力学与工程学报,2012,31(4)：696-702.
[29]刘汉香,许强,范宣梅.地震动参数对斜坡加速度动力响应规律的影响[J].地震工程与工程振动,2012,32(2)：41-47.
[30]王思敬,张菊明.岩体结构稳定性的块体力学分析[J].地质科学,1980,(1)：19-33.
[31]王思敬,张菊明.边坡岩体滑动稳定的动力学分析[J].地质科学,1982,2：162-170.
[32]王思敬,薛守义.岩体边坡楔形体动力学分析[J].地质科学,1992,2：177-182.
[33]张菊明,王思敬.层状边坡岩体滑动稳定的三维动力学分析[J].工程地质学报,1994,2(3)：1-12.
[34]张咸恭,王思敬,张倬元等著.中国工程地质学[J].北京：科学出版社,2000.
[35]Wang S.J, Xue S.Y, Maugeri M, et,al. Dynamic stability of the left abutment in the Xiaolangdi Project On the Yellow River. Proc. Int. Symp. On Assessment and Prevention of Failure Phenomena in Rock Engrg. Ankara. April,5-7,1993.
[36]Wang S.J, Zhang J.M. On the dynamic stability of block sliding on rock slopes. Proc.of the Int. Cont. on Recent Advances in Geotechnical Earthquake Engineering and Soil dynamics, St. Louis,431-434.
[37]薛守义.岩体边坡动力性研究[D].中国科学技术大学博士学位论文,1989.
[38]张平,吴德伦.动荷载下边坡滑动的试验研究[D].重庆建筑大学学报,1997,19(2)：80-86.
[39]Kumsar H, Aydan O, Ulusay R. Dynamic and static stability assessment of rock slopes against wedge failures.Rock mechanics and rock engrg,2000, 33(1):31-51.2002,13(1):94-97.
[40]Terzaghi K. Mechanisms of landslides[C].//Geological Society of America Berkey Volume.1950:83-123.
[41]Seed H B. Considerations in the earthquake-resistant design of earth and rockfill dams[J].Geotechnique.1979,29(3):215-263.
[42]Mononobe A H. Seismic stability of the earth dam[C].//Proc.2nd Congress on large dams.Washinton DC:IV:1936.
[43]Seed H B, Martin R G. The seismic coefficient in earth dam design[J]. Journal of Soilmechanics and Foundation Division.1996,104(SM3):59-83.
[44]Newmark N M. Effect of earthquakes on dams and embankments[J]. Geotechnique.1965, 15(2):139-160.
[45]Lin J S, Whitman R V. Earthquake induced displacements of sliding blocks[J]. J GeotechEngng Div.1986,112(1):44-59.
[46]Makdisi F I, Seed H B. Simplified procedure for estimating dam and embankment earthquakeinduced deformations[J]. J Geotech Engng.1978,104(No.GT7):569-587.
[47]Martin R G, Finn W D L, Seed H B. Fundamentals of liquefaction under cyclic loading[J]. J Geotech Engrg Div asce.1975,101 (GT5):423-438.
[48]Sarma S K. Seismic stability of earth dams and embankments[J]. Geotech Engng Div. 1975,105, GT4:449-464.
[49]Sarma S K. Seismic displacement analysis of earth dams[J]. J Geotech Engng Div 107. 1981,GT12:1735-1739.
[50]Wang S J, Xue S Y, Maugeri M. Dynamic stability of the left abutment in the XiaolangdiProject On the Yellow River[C].//Proc Int Symp on Asessment and Prevention of Failur Phenomena in Rock Engrg. Istanbul(Turkey):A. a. Balma, Rotterdam,1993: 619-625.
[51]Yegian M K, Harb J N. Slip displacements of geosynthetic systems underdynamic excitation[M]. Design and performance of solid waste landfills, No.54, Yegian M K, Finn W,San Diego, California, ASCE,:Geotechnical Special Publication,1995,212-236.
[52]Yegian M K, Lahlfa A M. Dynamic interface shear strength properties of geomembrabes and geotexiles[J]. J Geotech Engrg ASCE.1992,118(5):760-779.
[53]刘立平,雷尊宇,周富春.地震边坡稳定分析方法综述[J].重庆交通学院学报,2001,20(3)：83-88.
[54]林宗元.岩土工程勘察设计手册[M].北京：中国建筑工业出版社,1996.
[55]Leshchinsky D, San K.Ching. Pseudo-static seismic stability of slopes. Design charts.J.of Geotech.Engrg.,1994,120(9):1514-1532.
[56]Baker R, Garber M. Theoretical analysis of the stability of slopes. Geotechnique,1978, 28(4):395-411.
[57]Taylor D.W. Stability of earth slopes.J.Boston Society of Civ. Engrgs,1937,24(3):197-246.
[58]Seed H.B. Stability of earth and rockfill dams during earthquakes.in Embankment-Dam Engrg. Casagrande,Vol.(Eds Hirschfeld and Poulos),John Wiley,1973.
[59]Kramer S, Smith D. Modified newmark model for seismic displacement of compliant slopes[J]. Journal of geotechnical and geoenvironmental engineering, ASCE,1997,123(7): 635-644.
[60]Ling H I. Recent applications of sliding block theory to geotechnical design[J]. Soil dynamics and earthquake engineering,2001,21(3):189-197
[61]王思敬.岩石边坡动态稳定性的初步探讨[J].地质科学,1977,(]0)：372-376.
[62]薄景山,徐国栋,景立平.土边坡地震反应及其动力稳定性分析[J].地震工程与工程振动,2001(02)：116-120.
[63]陈玲玲,陈敏中,钱胜国.岩质陡高边坡地震动力稳定分析[J].长江科学院院报,,2004(01)：33-35.
[64]Ford S A A S, Sitar N, Lysmer J, et al. Topographic effects on the seismic response of steep slopes[J]. Bulletin of the Seismological Society of America.1997,87(3):701-709.
[65]刘春玲.祁生文,童立强等.利用FLAC-(3D)分析某边坡地震稳定性[J].岩石力学与工程学报,2004(16)：2730-2733.
[66]许瑾,郑书英.边界元法分析边坡动态稳定性[J].西北建筑工程学院学报(自然科学版),2000(04).
[67]张云.露天矿边坡岩体裂隙含水介质渗流场边界元分析[J].南京大学学报数学半年刊,1992(01)：119-125.
[68]李建平,熊传治.岩石边坡安全系数的边界元解[J].岩石力学与工程学报,1990(3)：238-243.
[69]樊文熙.有限元边界元法在岩体力学与工程中的应用[J].中州煤炭.1985(04)：2-3.
[70]Chunhan Z, Pekau O A, Feng J, et al. Application of disticnct element method in dynamic analysis of high rock slopes and blocky structures[J].Soil Dynamics and Earthquake Engineering.1997,16(6):385-394.
[71]张建海,范景伟,何江达.用刚体弹簧元法求解边坡、坝基动力安全系数[J].岩石力学与工程学报,1999(04)：19-23.
[72]邓学晶,孔宪京,刘君.城市垃圾填埋场的地震响应及稳定性分析[J].岩土力学,2007,22(10)：2095-2100.
[73]卓家涛,章青.不连续介质力学问题的界面元法[M].北京：科学出版社,2004.
[74]裴觉民.数值流形方法与非连续变形分析[J].岩石力学与工程学报,1997(03)：80-93.
[75]刘汉龙,费康,高玉峰.边坡地震稳定性时程分析方法[J].岩土力学,2003,24(4)：553-560.
[76]吴兆营,薄景山,刘红帅,等.岩体边坡地震稳定性动安全系数分析方法[J].防灾减灾工程学报,2004,24(3)：228-241.
[77]陈云敏,柯瀚,凌道盛.城市垃圾填埋体的动力特性及地震响应[J].土木工程学报,2002,35(3)：66-72.
[78]刘君,孔宪京.卫生填埋场复合边坡地震稳定性和永久变形分析[J].岩土力学,2004,25(5)：778-782.
[79]Cundall P A. A computer model for simulating progressive large scale movements in blocky system. In:Muller Led. Proceedings of Symosium of the International Society of Rock Mechanics. Rotterdam:A.A. Balkema,1971(1):8-12.
[80]Cundall P A. The measurement and analysis of acceleration in rock slopes. Ph.D.Dissertation, University of London, Imperial college of Science and Technology, 1971.
[81]Strack O D L, Cundall P A. The distinct element method as a tool for research in granular media. Part I. Report to the National Science Foundation, Minnesota:University of Minnseota,1978.
[82]Cundall P A, Strack O D L. The distinct element method as a tool for research in granular media. Part Ⅱ. Report to the National Science Foundation, Minnesota:University of Minnseota,1979.
[83]Cundall P A, Strack O D L. A discrete numerical method for granular assemblies. Geotechnique,1979,29(1):47-65.
[84]Zhu H P, Zhou Z Y, Yang R Y, Yu A B. Discrete particle simulation of particulate systems: Theoretical developments. Chemical Eengineering Science,2007,62:3378-3396.
[85]Maini T, Cundall P A. Computer modeling of jointed rock mass,(AD-A061658),1978.
[86]Cundall P A. UDEC-A Generalized distinct element progrom for modeling joined rock. Report PCAR-1-80 Perter Cundall Associates,European Research Office,U.S.Army,March 1980.
[87]Cundall P A. BALL-A program to model granular media using the distinct element method.Technical Note, Advanced Technology Group, Dames&Moore, London.1978.
[88]Cambell C S, Brennen C E. Computer simulation of granular shear flows. Journal of Fluid Mechanics.1985,151:167-188.
[89]Cambell C S, Brennen C E. Chute flows of granular materials:some computer simulations. Journal of Applied Mechanics,1985,(52):172-178.
[90]Kishino Y. Disc model analysis of the granular media. In:Micromechanics of granular materials. Satake M, Jenkins JT(Eds):1988,143-153.
[91]Kishino Y. Computer analysis of dissipation mechanism in granular media. In:Powders and Grain. Biarez&Gourves(Eds) 1984:323-330.
[92]Itasca Consulting Group, Inc. UDEC(Universal Distinct Element Code),Version 3.1. Minneapolis:ICG,2000.
[93]Itasca Consulting Group, Inc.3DEC(3-Dimensional Distinct Element Code), Version 2.0. Minneapolis:ICG,1998.
[94]Itasca Consulting Group, Inc. PFC2D(Particle Flow Code in 2 Dimensions),Version 3.0. Minneapolis:ICG,2002.
[95]Itasca Consulting Group, Inc. PFC3D(Particle Flow Code in 3 Dimensions),Version 2.0. Minneapolis:ICG,1999.
[96]Hunt S P, Meyers A G, Louchnikov V. Modeling the Kaiser effect and deformation rate analysis in sandstone using the discrete element method. Computers and Geotechnics, 2003,30:611-621.
[97]Djordjevic N. Discrete element modeling of the influence of lifters on power draw of trumbling mills. Minerals Engineering,2003,16:331-336.
[98]Fakhimi A, Carvalho F, Ishida T, Labuz J F. Simulation of failure aroud a circular opening in rock. International Journal of Rock Mechanics and Mining Sciences,2002,39:507-515.
[99]Wang C, Tannant D D, Lilly P A. Numerical analysis of the stability of heavily jointed rock slopes using PFC2D. International Journal of Rock Mechanics and Mining Sciences,2003, 40:415-424.
[100]Fleissner F, Gaugele T, Eberhard P. Applications of the discrete element method in mechanical engineering. Multibody System Dynamics.2007,18(1):81-94.
[101]王泳嘉.离散元法——一种适用于节离岩石力学分析的数值方法.第一届全国岩石力学数值计算及模型试验讨论论文集,1986：32-37.
[102]剑万禧.离散元法的基本原理及其在岩体工程中的应用.第一届全国岩石力学数值计算及模型试验讨论论文集,1986：43-46.
[103]汪远年,李世海.断续节理岩体随机模型三维离散元数值模拟[J].岩石力学与工程学报,2004,23(21)：3652-3658.
[104]汪远年,李世海.三维离散元计算参数选取方法研究[J].岩石力学与工程学报,2004,23(21)：3658-3664.
[105]王涛,陈晓玲,杨建.基于3DGIS和3DEC的地下洞室围岩稳定性研究[J].岩石力学与工程学报,2005,24(19)：3476-3481.
[106]周家文,徐卫亚,石崇.基于3DEC的节理岩体边坡地震影响下的楔体稳定性分析[J].岩石力学与工程学报,2007,26(增刊)：3402-3409.
[107]白永健,黄润秋,巨能攀等.高陡岩质边坡稳定性三维离散元分析[J].工程地质学报,2008,16(5)：592-597.
[108]尹祥础,尹灿.非线性系统失稳前兆与地震预测中国科学(B),1993,No.1：21-27.
[109]姜彤,马莎,许兵等.边坡在地震作用下的加卸载响应规律研究[J].岩石力学与工程学报,2004,23(22)：3803-3807.
[110]姜彤,马莎,许兵.基于加卸载响应比理论的边坡动力稳定分析方法[J].岩石力学与工程学报,2007,26(3)：626-635
[111]HALATCHEV ROSSEN A. Probabilistic Stability Analysis of Structure Considering Tensile Failure.12WCEE,2000
[112]张倬元,王士天,王兰生.工程地质分析原理[M].北京：地质出版社,1993.
[113]胡广韬.滑坡动力学[M].北京：地质出版社,1995.
[114]毛彦龙,胡广韬,毛新虎等.地震滑坡启程剧动的机理研究及离散元模拟[J].工程地质学 报,2001,9(1)：74-80.
[115]许强,陈建君,冯文凯等.斜坡地震响应的物理模拟试验研究[J].四川大学学报(工程科学版),2009,41(3).
[116]言志信,张刘平,曹小红等.地震作用下顺层岩质边坡动力响应规律及变形机制研究[J].岩土工程学报,2011,33(增刊)：54-58.
[117]叶海林,郑颖人,杜修力等.边坡动力破坏特征的振动台模型试验与数值分析[J].土木工程学报,2012,45(9)：128-135.
[118]刘佑荣,唐辉明.岩体力学[M].北京：化学工业出版社,2008.
[119]Goodman R. E, Taylor R. L, Brekke T. A. A mode of the mechanics of jointed rock[J]. J. Soil Mech. Div., ASCE,1968,94:637-659.
[120]Schwer L. E, Lindberg H. E. Application brief:a finite element slide line approach for calculating tunnel response in jointed rock[J]. Int J Num Anal Methods Geomech,1992, 16:529-540.
[121]Beer G. Implementation of combined boundary element-finite element analysis with applicationsin geomechanics [A]. Applied Science,1986,191-226.
[122]Crotty J M, Wardle L J. Boundary integral analysis of piecewise homogeneous media with structural dis-continuities[J]. Int. J. Rock Mech. Min. Sci. Geomech. Abstr.,1985, 22:419-427.
[123]Itasca Consulting Group, Inc.3 Dimensional Distinct Element Code:Theory and Background [R]. Minneapolis:Itasca Consulting Group, Inc,2003.
[124]刘波,韩彦辉.FLAC原理、实例与应用指南[M].北京：人民交通出版社,2005.
[125]陈育民,徐鼎平.FLAC/FLAC3D基础与工程实例[M].北京：中国水利水电出版社,2008.
[126]J. Lysmer and R. L. Kulemeyer. Finite Dynamic Model for Infinite Media. Journal of Engineering Mechanics Division, ASCE.1969,95(4):759-877.
[127]Kunar, R. R., P. J. Beresford and P. A. Cundall. "A Tested Soil-Structure Model for SurfaceStructures," in Proceedings of the Symposium on Soil-Structure Interaction (Roorkee University,India, January,1977), Vol.1, pp.137-144. Meerut, India:Sarita Prakashan,1977.
[128]Kuhlmeyer, R. L., and J. Lysmer. "Finite Element Method Accuracy for Wave Propagation Problems," J. Soil Mech.& Foundations Div., ASCE,99(SM5),421-427 (May,1973).
[129]王礼立.地震波基础[M].北京：国防工业出版社,2005.
[130]王有学.地震波理论基础[M].北京：地质出版社,2011.
[131]MYER L R,PYRAK-NOLTE L J,COOK N G W. Effects of singlefractures on seismic wave propagation[C]//Proceedings of ISRM Symposium on Rock Joints. Rotterdam:A. A. Balkema,1990:467-473.
[132]Pyrak-Nolte L J, Myer L R, Cook N G W. Transmission of seismic waves across single natural fractures[J]. Journal of Geophysical Research,1990,95(6):8617-8638.
[133]Itasca Consulting Group, Inc.3 Dimensional Distinct Element Code:Optional Features[R]. Minneapolis:Itasca Consulting Group, Inc,2003.
[134]徐光兴,姚令侃,李朝红,等.边坡地震动力响应规律及地震动参数影响研究[J].岩土工程学报,2008,30(6)：918-923.
[135]Goodman R E, Seed H B. Earthquake-induced displacements in sand embankment [J].J Soil Mech Fdn Engng Div,92(SM2):125-146.
[136]刘杰,李建林,张玉灯等.基于拟静力法的大岗山坝肩边坡地震工况稳定性分析[J].岩石力学与工程学报,2009,28(8)：1562-1570.
[137]Clough R W, Chopra A K. Earthquakes stress analysis in earth dams [J].J Engrg Mech, 1966,92(EM2):197-211.
[138]张伯艳,陈厚群,杜修力.拱坝坝肩抗震稳定分析[J].水利学报,2000(11)：55—59.
[139]李育枢,高广运,李天斌.偏压隧道洞口边坡地震动力反应及稳定性分析[J].地下空间与工程学报,2006,2(5)：738—743.
[140]汪茜.地震作用下顺层岩质边坡变形破坏机理研究[D].长春：吉林大学,2009.
[141]郑颖人,叶海林,黄润秋,等.边坡地震稳定性分析探讨[J].地震工程与工程振动,2010(002)：173-180.
[142]胡聿贤.地震工程学[M].北京：地震出版社,1988：71-72.
[143]Hoek E, Bray J. Rock slope engineering[M].3rd ed. London:Institution of Mining and Metallurgy,1981.
[144]戴妙林,李同春.基于降强法数值计算的复杂岩体边坡动力稳定性安全评价分析[J].岩石力学与工程学报,2007,26(增刊1)：2049
[145]李海波,肖克强,刘亚群.地震荷载作用下顺层岩质边坡安全系数分析[J].岩石力学与工程学报,2007,26(12)：2385-2394.
[146]HUTSON R W, DOWDING C H. Joint asperity degradation during cyclic shear[J]. Int J Rock Mech Min Sci & Geomech Abstr,1990,27(2):109-119.
[147]LEE H S, PARK Y J, CHO T F, YOU K H. Influence of asperity degradation on the mechanical behavior of rough rock joints under cyclic shear loading[J]. Int J Rock Mech Min Sci,2001,38:967-980.
[148]倪卫达,唐辉明,刘晓等.考虑结构面震动劣化的岩质边坡动力稳定分析[J].岩石力学与工程学报,2013,32(3)：492-500.
[149]孙玉科,牟会宠,姚宝魁.边坡岩体稳定性分析[M].北京：科学出版社,1988.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |