Multi‐slicing strategy for the three‐dimensional discontinuity layout optimization (3D DLO)

Discontinuity layout optimization (DLO) is a recently presented topology optimization method for determining the critical layout of discontinuities and the associated upper bound limit load for plane two‐dimensional and three‐dimensional (3D) problems. The modelling process (pre‐processing) for DLO includes defining the discontinuities inside a specified domain and building the target function and the global constraint matrix for the optimization solver, which has great influence on the the efficiency of the computation processes and the reliability of the final results. This paper focuses on efficient and reliable pre‐processing of the discontinuities within the 3D DLO and presents a multi‐slicing strategy, which naturally avoids the overlapping and crossing of different discontinuities. Furthermore, the formulation of the 3D discontinuity considering a shape of an arbitrary convex polygon is introduced, permitting the efficient assembly of the global constraint matrix. The proposed method eliminates unnecessary discontinuities in 3D DLO, making it possible to apply 3D DLO for solving large‐scale engineering problems such as those involving landslides. Numerical examples including a footing test, a 3D landslide and a punch indentation are considered, illustrating the effectiveness of the presented method. © 2016 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.     

2008年汶川MS8.0地震对周边断层地震活动的影响

为分析2008年5月12日四川汶川M_S8.0级地震对周边断层地震活动的影响,本文首先基于Burgers体黏滞松弛模型计算汶川M_S8.0级地震引起的库仑应力动态演化,分析认为2008年汶川M_S8.0级地震在周边断层上引起的库仑应力显著增加的主要有四个断层段,分别为鲜水河断裂道孚-康定段、东昆仑断裂东段玛曲段、青川断裂和龙门山断裂南段.而且震后4年内黏滞松弛引起的库仑应力变化量可能与同震变化相当,相当于再发生一次汶川地震所造成的影响,因此震后效应在分析强震影响时不应忽略.本文基于强震引起的库仑应力变化动态演化,结合背景地震发生率、由Dieterich(1994)模型给出地震发生概率,结合相关构造地质、历史地震、余震活动等方面资料的综合分析认为,上述4个断裂段地震危险性由高到低依次为鲜水河断裂道孚-康定段、龙门山断裂南段、东昆仑断裂东段玛曲段和青川断裂.     

库水载荷对水库触发地震的机制研究

利用有限元方法,研究库水载荷产生的应力场及其在断层面上引起的静态库仑破裂应力变化。通过计算发现,库水载荷的加载位置对地震的触发作用有重要的影响:当库水加载于断层正上方或断层上盘时,对正断层型的地震有促进作用,对逆断层型的地震有抑制作用。但是,当库水载荷作用于断层的下盘时,对于倾角较大的正断层与逆断层地震,库水都起抑制作用;而对倾角很小的断层起促进作用,但不会产生很强的水库地震。     

以2008年汶川8.0级地震为例分析地震触发的静态库仑应力计算的不确定性

人们常用地震产生的静态库仑应力变化解释地震的空间迁移和余震的空间分布规律,但是,在计算静态库仑应力场时,室内试验数据和观测资料往往无法对计算所涉及的参数进行足够的约束,而参数取值的不确定性会直接影响到静态库仑应力的计算结果。不同研究组得到的汶川地震产生的静态库仑应力变化结果并不一样,为研究不同计算模型和参数的选取对静态库仑应力计算的影响,我们通过建立模型并依次改变参数,分析比较了各个参数对计算结果的影响。结果表明:重力、接收断层位置和走向等的影响较小,其他参数均会对静态库仑应力变化量值和符号造成不同程度的影响,其影响在地震破裂面周边尤其明显,计算时参数敏感性分析不可忽略。     

汶川8.0级地震的余震触发作用和对断层的应力加卸载作用

采用可变滑动震源模型,计算和研究了汶川M_S 8.0地震产生的应力变化及对后续6次强余震的应力触发作用,并定量分析了汶川地震对附近活动断裂带的库仑应力加卸载作用。结果显示:汶川地震产生的库仑破裂应力变化分布图案复杂性强,主要由发震断裂复杂的空间展布形态以及震源断层活动具有逆冲兼右旋走滑两种性质决定。汶川地震产生的库仑破裂应力变化对多数强余震存在一定的触发作用。汶川地震的发生对附近的断裂带有不同程度的影响,其中青川断裂中段和北段、岷江断裂南段和灌县-江油断裂南段,主要是以强烈的库仑破裂应力加载作用占主导地位,有利于强余震序列的孕育、加速以至于发生;东昆仑断裂带和鲜水河断裂带受到了轻微的应力加载作用;龙泉山断裂带、华莹山断裂带和西秦岭北缘断裂带主要受到了轻微的卸载作用。     

RELIABILITY BASED ANALYSIS ON RESERVOIR INDUCED EARTHQUAKES

Reservoir induced earthquakes (RIE) are caused by impoundment of reservoir,with the characteristics of small magnitude and shallow focal depth,but they can also lead to not only economic loss,but also many serious secondary disasters,such as dam destruction,landslide,producing greater damages far more than the damages directly produced by earthquakes.So study on RIE is quite significant in the field of dam construction,thus more attentions should be paid to RIE.There are many factors to induce reservoir earthquakes,such as geological condition,rock mass mechanical index,state of crustal stress,pore pressure distribution,all of which are extremely difficult to measure due to the presence of many randomness;even if applying most advanced methods to measure them,the values fluctuate in great range,without a certain value in time and space.The great variety of these parameters gives rise to troubles to analyze RIE by deterministic approaches.How to handle the randomness of these factors has become vital problem in the field of RIE research.In this study,based on probability theory,and taking the main influence factors as stochastic variables,a new method to analyze probability of RIE was proposed by applying reliability theory.Firstly,the factors inducing reservoir earthquakes were analyzed,of which pore pressure in fault caused by water impounding of reservoir plays a vital role in triggering earthquakes.Then,taking these factors,including attitude,friction coefficient,cohesion of fault plane,stress state of fault plane and pore pressure in fault,as stochastic variables,performance function of triggering earthquakes was established by applying Coulomb stress on the fault plane,and reliability theory was used to analyze probability of earthquake induced by main factors.A special case analysis showed that:(1) The probability of induced earthquakes dramatically increases as pore pressure in fault increases;under the condition of equal pore pressure at triggering earthquakes area,probability of induced earthquakes obviously rises with enlarging of variation of pore pressure;(2) those faults with strike approximately parallel to horizontal maximum principal stress direction or with steep dip angle about more than 60° are prone to inducing earthquake;(3) as horizontal minimum principal stress increases,which has greater effect on induced earthquakes than horizontal maximum principal stress,probability of induced earthquakes becomes lower and fault keeps in more stable condition;(4) probability of induced earthquakes gradually decreases with the increase of friction coefficient and cohesion of fault plane;However,the effect of friction coefficient on induced earthquakes is much greater than the cohesion of fault plane.     

京西盆岭构造区积累库仑破裂应力变化对强震的影响

Since 231 B. C.,a total of 15 M6.0 - 7.5 earthquakes have been recorded in the west Beijing basin-range tectonic region( 38.3°- 41.5° E,112°- 116.2° N),a region mainly under the action of tensional normal faulting. In this paper,we calculate the Coulomb stress change of each earthquake and the cumulative Coulomb stress change,and on this basis we analyze the stress triggering of strong earthquakes. The research shows that there are 10 of 14 earthquakes that occurred in the trigger zones,in which the Coulomb stress change is positive,and the trigger rate is 71%. The positive areas of cumulative Coulomb stress change caused by these 15 earthquakes are: middle of northern Liulengshan fault,Northern Huaizhuo basin fault,Xinbaoan-Shacheng fault,Sangganhe fault and Southern Yuxian basin fault. This necessarily increases the seismic risk of these faults and can be used as a reference for future seismic risk analysis in this area.     

京西盆岭构造区积累库仑破裂应力变化对强震的影响

以拉张正断层作用为主的京西盆岭活动构造区(112°～116.2°N, 38.3°～41.5°E)自BC231年以来共记载和记录15次M6～7.5地震。 本研究计算每一次强震产生的以及逐次积累的库仑破裂静应力变化, 并分析强震之间的应力触发关系。 结果显示在14次后发的强震中, 有10次发生在先发强震产生的积累库仑破裂静应力变化为正的触发区, 触发率为71%。 所有15次历史强震作用共同引起研究区积累库仑破裂静应力变化的正值区, 主要分布于六棱山北麓断裂中段、 怀涿盆地北缘断裂、 新保安沙城断裂、 桑干河断裂以及蔚县盆地南缘断裂, 并使得这些断裂(段)的强震危险性有所增加, 这可为分析研究区的未来强震危险性提供参考。     

1966年邢台地震静态库仑应力触发分析

通过分析1966年邢台5次地震的静态库仑应力触发情况发现,前2次地震对后面的地震有较好的触发,而MS7.2以后地震的触发不理想。从而认为,随着地震的发生和震源深度的增加,岩浆活动对地壳介质的影响越来越大,地壳介质弹性性能越来越弱,即该区域浅部可以用均匀弹性半空间来近似,而深部在岩浆等因素的影响下,用均匀弹性半空间来近似存在较大的误差,不适合用弹性位错理论计算地震的触发关系。这从侧面反映了该地区岩浆活动的剧烈性和超壳断层存在的客观性。     

应力演变方法及其在华北地区河北省的应用

本文研究了库仑应力变化与自1484年以来中国河北省内发生的强震的关系。华北板块在过去的一个世纪里有许多历史地震和一些破坏性的地震发生,其中包括1976年的唐山大地震(M = 7.8)。我们的研究包含了河北省及其邻近区域的最活跃的地震断裂带和频繁遭受过强烈地震的区域。华北板块,包括鄂尔多斯高原和华北平原,是中国太古宙克拉通的一部分,而且是世界上地震最活跃的地区之一。这些地震活动主要发生在东西向的走滑断裂带上。研究区域内的断裂活动导致了复杂的应力场。通过计算库仑破裂函数(ACFF)的变化来得出这个地区的地震灾害评估,这库仑破裂函数的变化是由强震(MS≥6.5)产生的同震滑动和主要区域性大断裂的连续构造载荷产生的应力引起的。在应力演化模型计算的每一步都对下一次可能触发的强震进行了估计,模型最终提出了易于发生即将到来的强烈活动断层段的理由。从而提供了未来地震危险性评价研究依据。在本文中,以张家口断裂,夏垫断裂,廊坊断裂的结果为例,说明通过计算得出的ACFF结果,对未来地震危险性提供依据是可行的。