Parallel 3-D Simulation of a Fault Gouge Using the Lattice Solid Model

Despite the insight gained from 2-D particle models, and given that the dynamics of crustal faults occur in 3-D space, the question remains, how do the 3-D fault gouge dynamics differ from those in 2-D? Traditionally, 2-D modeling has been preferred over 3-D simulations because of the computational cost of solving 3-D problems. However, modern high performance computing architectures, combined with a parallel implementation of the Lattice Solid Model (LSM), provide the opportunity to explore 3-D fault micro-mechanics and to advance understanding of effective constitutive relations of fault gouge layers. In this paper, macroscopic friction values from 2-D and 3-D LSM simulations, performed on an SGI Altix 3700 super-cluster, are compared. Two rectangular elastic blocks of bonded particles, with a rough fault plane and separated by a region of randomly sized non-bonded gouge particles, are sheared in opposite directions by normally-loaded driving plates. The results demonstrate that the gouge particles in the 3-D models undergo significant out-of-plane motion during shear. The 3-D models also exhibit a higher mean macroscopic friction than the 2-D models for varying values of interparticle friction. 2-D LSM gouge models have previously been shown to exhibit accelerating energy release in simulated earthquake cycles, supporting the Critical Point hypothesis. The 3-D models are shown to also display accelerating energy release, and good fits of power law time-to-failure functions to the cumulative energy release are obtained.     

Implementation of Particle-scale Rotation in the 3-D Lattice Solid Model

In this study, 3-D Lattice Solid Model (LSMearth or LSM) was extended by introducing particle-scale rotation. In the new model, for each 3-D particle, we introduce six degrees of freedom: Three for translational motion, and three for orientation. Six kinds of relative motions are permitted between two neighboring particles, and six interactions are transferred, i.e., radial, two shearing forces, twisting and two bending torques. By using quaternion algebra, relative rotation between two particles is decomposed into two sequence-independent rotations such that all interactions due to the relative motions between interactive rigid bodies can be uniquely decided. After incorporating this mechanism and introducing bond breaking under torsion and bending into the LSM, several tests on 2-D and 3-D rock failure under uni-axial compression are carried out. Compared with the simulations without the single particle rotational mechanism, the new simulation results match more closely experimental results of rock fracture and hence, are encouraging. Since more parameters are introduced, an approach for choosing the new parameters is presented.     

Simulation of the Load-Unload Response Ratio and Critical Sensitivity in the Lattice Solid Model

— The Load-Unload Response Ratio (LURR) method is an intermediate-term earthquake prediction approach that has shown considerable promise. It involves calculating the ratio of a specified energy release measure during loading and unloading where loading and unloading periods are determined from the earth tide induced perturbations in the Coulomb Failure Stress on optimally oriented faults. In the lead-up to large earthquakes, high LURR values are frequently observed a few months or years prior to the event. These signals may have a similar origin to the observed accelerating seismic moment release (AMR) prior to many large earthquakes or may be due to critical sensitivity of the crust when a large earthquake is imminent. As a first step towards studying the underlying physical mechanism for the LURR observations, numerical studies are conducted using the particle based lattice solid model (LSM) to determine whether LURR observations can be reproduced. The model is initialized as a heterogeneous 2-D block made up of random-sized particles bonded by elastic-brittle links. The system is subjected to uniaxial compression from rigid driving plates on the upper and lower edges of the model. Experiments are conducted using both strain and stress control to load the plates. A sinusoidal stress perturbation is added to the gradual compressional loading to simulate loading and unloading cycles and LURR is calculated. The results reproduce signals similar to those observed in earthquake prediction practice with a high LURR value followed by a sudden drop prior to macroscopic failure of the sample. The results suggest that LURR provides a good predictor for catastrophic failure in elastic-brittle systems and motivate further research to study the underlying physical mechanisms and statistical properties of high LURR values. The results provide encouragement for earthquake prediction research and the use of advanced simulation models to probe the physics of earthquakes.     

地震作用下深埋隧道围岩形变的数值模拟研究

隧道围岩受地震荷载作用影响产生开裂变形,给交通、安全与经济带来极大影响,为提升隧道安全稳定性能,以某市隧道为对象,研究地震作用下深埋隧道围岩形变的数值模拟。综合考虑地震动作用与地震波扩散特性,利用FLAC软件构建三维动力模型;通过边界设置解决地震波反射问题,基于物理力学参数与地震荷载条件,通过相对变形法研究地震条件下深埋隧道围岩变形特性、能量聚集特性与安全性能。研究结果显示:深埋隧道围岩受地震荷载作用影响,形成挤让、椭圆化的变形走向;变形达到最高值时,应变能量密度高于2350 J/m^3的区域集中在隧道Ⅰ洞左侧围岩边墙和中夹岩柱上;各监测点安全系数呈非对称性,隧道右侧下角区域安全系数低于国家相关标准,计算结果与实际测量结果一致。     

Statistical Tests of Load-Unload Response Ratio Signals by Lattice Solid Model: Implication to Tidal Triggering and Earthquake Prediction

— Statistical tests of Load-Unload Response Ratio (LURR) signals are carried in order to verify statistical robustness of the previous studies using the Lattice Solid Model (Mora et al., 2002b). In each case 24 groups of samples with the same macroscopic parameters (tidal perturbation amplitude A, period T and tectonic loading rate k) but different particle arrangements are employed. Results of uni-axial compression experiments show that before the normalized time of catastrophic failure, the ensemble average LURR value rises significantly, in agreement with the observations of high LURR prior to the large earthquakes. In shearing tests, two parameters are found to control the correlation between earthquake occurrence and tidal stress. One is, A/(k T) controlling the phase shift between the peak seismicity rate and the peak amplitude of the perturbation stress. With an increase of this parameter, the phase shift is found to decrease. Another parameter, A T/k, controls the height of the probability density function (Pdf) of modeled seismicity. As this parameter increases, the Pdf becomes sharper and narrower, indicating a strong triggering. Statistical studies of LURR signals in shearing tests also suggest that except in strong triggering cases, where LURR cannot be calculated due to poor data in unloading cycles, the larger events are more likely to occur in higher LURR periods than the smaller ones, supporting the LURR hypothesis.     

Simulation of the Influence of Rate- and State-dependent Friction on the Macroscopic Behavior of Complex Fault Zones with the Lattice Solid Model

-- In order to understand the earthquake nucleation process, we need to understand the effective frictional behavior of faults with complex geometry and fault gouge zones. One important aspect of this is the interaction between the friction law governing the behavior of the fault on the microscopic level and the resulting macroscopic behavior of the fault zone. Numerical simulations offer a possibility to investigate the behavior of faults on many different scales and thus provide a means to gain insight into fault zone dynamics on scales which are not accessible to laboratory experiments. Numerical experiments have been performed to investigate the influence of the geometric configuration of faults with a rate- and state-dependent friction at the particle contacts on the effective frictional behavior of these faults. The numerical experiments are designed to be similar to laboratory experiments by Dieterich and Kilgore (1994) in which a slide-hold-slide cycle was performed between two blocks of material and the resulting peak friction was plotted vs. holding time. Simulations with a flat fault without a fault gouge have been performed to verify the implementation. These have shown close agreement with comparable laboratory experiments. The simulations performed with a fault containing fault gouge have demonstrated a strong dependence of the critical slip distance D_c on the roughness of the fault surfaces and are in qualitative agreement with laboratory experiments.     

A Damage Mechanics Model for Aftershocks

— All earthquakes are followed by an aftershock sequence. A universal feature of aftershock sequences is that they decay in time according to the modified Omori’s law, a power-law decay. In this paper we consider the applicability of damage mechanics to earthquake aftershocks. The damage variable introduced in damage mechanics quantifies the deviation of a brittle solid from linear elasticity. We draw an analogy between the metastable behavior of a stressed brittle solid and the metastable behavior of a superheated liquid. The nucleation of microcracks is analogous to the nucleation of bubbles in the superheated liquid. In this paper we obtain a solution for the evolution of damage after the instantaneous application of a constant strain to a rod. We show that the subsequent stress relaxation can reproduce the modified Omori’s law. It is argued that the aftershocks themselves cause random fluctuations similar to the thermal fluctuations associated with phase transitions.     

A Simple Model for Earthquake Instability

Based on the heterogeneity of fault plane strength,the macro rupture process of a fault plane can be treated as the rupture accumulation process of local micro-elements in the fault surface.Assuming that the strength of the local micro-elements follows the Weibull probability distribution,the macro-fault constitutive relationship of the complete load-deformation process is derived from a statistical mechanics viewpoint.Applying a one-dimensional earthquake mechanics model and using far-field displacement a as the control variable,the problem of earthquake instability is investigated by employing the stability theory.The results show that the system stiffness ratio(stiffness ratio of fault to surroun-ding rock) β is the important parameter that affects the occurrence of earthquakes.Earthquake instability occurs only when β < 1,and the sudden stress jump appears at the displacement turning point of the equilibrium path curve.The expression of three important parameters for earthquakes(fault half-dislocation distance after earthquake,earthquake stress drop and elastic energy release) is also given.When β≥1,the earthquake does not occur and the fault only slips slowly without an earthquake.     

Stress Correlation Function Evolution in Lattice Solid Elasto-dynamic Models of Shear and Fracture Zones and Earthquake Prediction

--It has been argued that power-law time-to-failure fits for cumulative Benioff strain and an evolution in size-frequency statistics in the lead-up to large earthquakes are evidence that the crust behaves as a Critical Point (CP) system. If so, intermediate-term earthquake prediction is possible. However, this hypothesis has not been proven. If the crust does behave as a CP system, stress correlation lengths should grow in the lead-up to large events through the action of small to moderate ruptures and drop sharply once a large event occurs. However this evolution in stress correlation lengths cannot be observed directly. Here we show, using the lattice solid model to describe discontinuous elasto-dynamic systems subjected to shear and compression, that it is for possible correlation lengths to exhibit CP-type evolution. In the case of a granular system subjected to shear, this evolution occurs in the lead-up to the largest event and is accompanied by an increasing rate of moderate-sized events and power-law acceleration of Benioff strain release. In the case of an intact sample system subjected to compression, the evolution occurs only after a mature fracture system has developed. The results support the existence of a physical mechanism for intermediate-term earthquake forecasting and suggest this mechanism is fault-system dependent. This offers an explanation of why accelerating Benioff strain release is not observed prior to all large earthquakes. The results prove the existence of an underlying evolution in discontinuous elasto-dynamic systems which is capable of providing a basis for forecasting catastrophic failure and earthquakes.     

地震不稳定性的一个简单模型

基于断层面强度的非均匀性,将断层面的宏观破裂过程看作是断面局部微元的破裂累积过程,假设断层局部微元强度遵循Weibull概率分布,从统计力学角度推导出了宏观的断层载荷.变形的全过程本构关系.采用一维地震力学模型,以远场位移a为控制变量,用稳定性理论研究了地震不稳定性问题.研究表明,系统刚度比(围岩刚度与断层刚度之比)β是影响地震发生的重要参数,只有当β<1时才会出现地震失稳,且应力突跳发生在平衡路径曲线的位移转向点,并给出了地震过程的3个重要参数(地震后断层半错距、地震应力降和释放的弹性能)的表达式.当β≥1时,不会发生地震,仅是缓慢的断层滑动,属于无震滑动.     

城市避震救灾最优体系模型仿真

传统GIS空间分析模型进行城市避震救灾疏散方案规划时,未考虑疏散路径的当量长度,获取的避震救灾模型疏散效率较低。采用通行难度系数、次生灾害干扰系数、桥梁阻碍系数获取避震救灾疏散路径当量长度;通过目标函数获取避震救灾疏散路径当量长度的最小值,同时考虑避难场所的容纳量要求、清空避难场所固有人员、疏散距离小于避难场所的服务半径3个约束条件,设计新的城市避震救灾疏散最优模型。实验结果表明,新的城市避震救灾疏散最优模型能够给出精确的疏散路径与方案,高效率地完成城市避震救灾疏散任务。     

考虑时间约束的地震救灾数学模型设计与实现

在地震救灾方面,针对信息实时更新的地震救灾数学模型,为了满足不同受灾点的物资需求,增加了出救点数量以及配送时间,以此来保证地震救援物资需求的满足度,提高了应急响应水平。结合地震救灾特点,设计了一种考虑时间约束的地震救灾数学模型。该模型在地震救灾物资需求预测部分,分析影响地震救灾物资需求量的主要因素,构建地震救灾物资需求量计算模型,对影响地震救灾物资需求量的主要因素构建隶属度函数,给出基于模糊综合评判的地震救灾物资需求分级模型。其次,考虑时间约束以及需求不确定等方面,构建考虑时间约束的地震救灾多目标优化数学模型,并给出求解模型。实验结果表明,该模型减少了救灾物资到达受灾点的延迟时间,可在满足时间约束的条件下提高物资需求满足率。     

地震巨灾模型中的随机地震事件集模拟

地震巨灾保险是降低地震灾害风险的有效手段之一,而地震危险性分析是地震巨灾模型的主要分析模块之一。传统的概率地震危险性分析主要是基于潜在震源模型、地震活动性模型和地震动衰减模型等并采用概率方法得到场点的地震危险性值,该危险性表示的是未来所有地震对场点的综合影响。然而,在使用地震巨灾模型进行地震风险分析时需要用到单个地震事件对场点的影响,这就需要根据潜在震源区生成一系列单个地震事件,并计算每个事件对场点的影响。本研究采用蒙特卡洛方法,基于第五代中国地震动参数区划图中所采用的地震活动性模型(潜在震源区及其地震活动性参数),模拟符合我国地震活动时间、空间和强度分布特征的地震事件集。模拟时遵从的基本理论为:地震发生在时间上符合泊松分布,震级分布可用古登堡-里克特定律来描述,空间分布特征则用潜在震源区及其地震发生率来描述。模拟得到的地震事件包含以下参数:时间(年、月、日)、地点(经度、纬度)、深度、震级、断层走向以及衰减特征等。该模拟地震事件集可满足地震巨灾模型中地震风险分析的需求,已应用于我国地震巨灾模型中。     

地震力学成因及前兆机理研究——再“读”唐山地震有感

简述弹性回跳学说、板块构造模型及岩浆活动型地震等地震力学成因的现有观点,并对其进行了讨论。通过分析唐山震区的壳幔深部结构、前兆异常时空演化等资料,进一步论证了唐山地震力学成因为岩浆活动的观点。在此基础上对唐山地震前兆机理进行了研究,指出岩浆活动既是该地震发生的成因,也是各类前兆异常的成因,它们是岩浆活动这枚硬币的两面。最后指出只有正确认识地震和前兆的成因,才有可能用前兆资料对地震三要素做出较好的预报。     

岩石水压致裂和诱发地震的实验研究

用7种岩石各制备了几类不同预裂纹的系列试件，并在不同围压下进行水压致裂强度实验。结合典型的水库诱发地震的实际资料和现今构造应力场的实验结果，以及应用岩石强度理论和岩石断裂力学的一些原理、方法，进行岩石孔隙水压诱发地震的探讨。初步结果为：(1)若岩体内构造应力很小，一定大小的孔隙水压力σp，可直接使岩体内的薄弱面致裂并发生小地震。(2)若构造应力较大，存在两类诱发地震的可能：①对岩体浅部一些走向与构造应力的主压应力σ1方向相近的薄弱面，σp可促使其发生张性破裂并诱发小地震。②当构造应力接近于断裂的抗剪强度时，因σp，降低了断裂面上的正应力σn，使原处于稳定状态的断裂失稳，发生滑移破裂并诱发出地震。σp导致断裂的破裂深度增大，使诱发地震的震级大于原潜在的地震震级。(3)各种岩体均存在着一个极限深度，此深度后不再有诱发地震。     

地震预测的加卸载响应比岩石实验模拟

我们在中科院力学所非线性连续介质力放实验室材料试验机上做了岩石压缩破坏的加卸载实验,得到了以应变为尖的加卸载响应比。     

地震孕育过程的非线性动力学模型

本文提出了依据观测数据反演地震孕育过程的非线性动力学模型的方法，给出了可预报时间尺度的确定方法及系统稳定性判别准则，对唐山地震的分析表明，非线性动力学分析方法是行之有效的。     

岩石损伤软化的修正本构模型

利用服从Weibull分布的岩石微元强度表示方法,基于Drucker-Prager破坏准则,通过引入损伤变量的修正系数,利用应力-应变关系曲线峰值点处的应力、应变确定Weibull分布参数的关系式,建立不同围压下的损伤软化本构模型。该模型参数较少且易于确定,其参数的确定方法揭示了模型参数的物理意义。与前人的研究成果进行对比分析,结果表明该模型比未修正前有着明显的优越性,且与实测结果吻合较好,分析结果显示出该模型的合理性。     

遥感图像震害特征组合增强模型及其算法实现

本文在多个震例图像增强方法研究的基础上,建立了一种通过单项方法的组合实现图像增强优化的组合模型,定义了基本模型单元和模型组合型态。基于增强模型库,通过C＋＋编程实现了该算法。同时,使用1976年唐山地震后航空遥感图像对该方法进行了试验,结果表明组合模型提高了震害提取能力。