边坡稳定性分析及滑移面快速确定

针对边坡稳定性分析及滑移面确定这一工程问题,提出一种解析法。首先根据基本假设及边坡的几何关系,建立边坡滑移面确定模型,推导出滑移面控制方程;然后基于极限平衡理论,采用解析的方法推导出与滑移面控制方程相关联的安全系数解析表达式;最后通过求解目标函数（一元函数）在定义域上的最小值,求出边坡最小安全系数及对应的临界滑移面。通过算例验证表明：本文方法的边坡稳定性分析结果与传统极限平衡条分法分析结果基本一致,最小安全系数偏差不超过±5%;本文方法所确定的临界滑移面与基于传统极限平衡条分法所广泛搜索的临界滑移面比较接近。本文方法对于高效、精准地进行边坡稳定性分析及滑移面确定具有借鉴意义。     

基于粒子群优化算法的边坡临界滑动面搜索方法

采用数值计算结果进行极限平衡分析是边坡稳定性分析的重要方法,最危险滑移面位置的确定是边坡稳定性分析的关键。采用粒子群优化理论控制位于滑移面后缘范围的滑入点和前缘剪出区域的滑出点,以均分逼近法控制滑面半径,实现了边坡内潜在滑移面位置的搜索及安全系数的计算,进而确定了边坡的最小安全系数及最危险潜在滑移面位置,搜索出的滑面不依赖于网格节点。以昆明某公路滑坡为例,将搜索出的最危险滑面与现场勘察成果进行对比,结果表明,采用本文方法计算所得的结果与工程实际较为吻合,证明了该方法的有效性。     

Constitutive relations for fault slip and earthquake instabilities

Constitutive relations for fault slip are described and adopted as a basis for analyzing slip motion and its instability in the form of earthquakes on crustal faults. The constitutive relations discussed include simple rate-independent slip-weakening models, in which shear strength degrades with ongoing slip to a residual frictional strength, and also more realistic but as yet less extensively applied slip-rate and surface-state-dependent relations. For the latter the state of the surface is characterized by one or more variables that evolve with ongoing slip, seeking values consistent with the current slip rate. Models of crustal faults range from simple, single-degree-of-freedom spring-slider systems to more complex continuous systems that incorporate nonuniform slip and locked patches on faults of depth-dependent constitutive properties within elastic lithospheric plates that may be coupled to a viscoelastic asthenosphere. Most progress for the rate and state-dependent constitutive relations is at present limited to single-degree-of-freedom systems. Results for stable and unstable slip with the various constitutive models are summarized. Instability conditions are compared for spatially uniform versus nonuniform slip, including the elastic — brittle crack limit of the nonuniform mode. Inferences of constitutive and fracture parameters are discussed, based on earthquake data for large ruptures that begin with slip at depth, concentrating stress on locked regions within a brittle upper crust. Results of nonlinear stability theory, including regimes of complex sustained stress and slip rate oscillations, are outlined for rate and state-dependent constitutive relations, and the manner in which these allow phenomena like time-dependent failure, restrengthening in nearly stationary contact, and weakening in rapidly accelerated slip, is discussed.     

Evolution of Wear and Friction Along Experimental Faults

We investigate the evolution of wear and friction along experimental faults composed of solid rock blocks. This evolution is analyzed through shear experiments along five rock types, and the experiments were conducted in a rotary apparatus at slip velocities of 0.002–0.97 m/s, slip distances from a few millimeters to tens of meters, and normal stress of 0.25–6.9 MPa. The wear and friction measurements and fault surface observations revealed three evolution phases: A) An initial stage (slip distances <50 mm) of wear by failure of isolated asperities associated with roughening of the fault surface; B) a running-in stage of slip distances of 1–3 m with intense wear-rate, failure of many asperities, and simultaneous reduction of the friction coefficient and wear-rate; and C) a steady-state stage that initiates when the fault surface is covered by a gouge layer, and during which both wear-rate and friction coefficient maintain quasi-constant, low levels. While these evolution stages are clearly recognizable for experimental faults made from bare rock blocks, our analysis suggests that natural faults “bypass” the first two stages and slip at gouge-controlled steady-state conditions.     

地震边坡稳定性分析的拟静力方法适用性探讨

应用极限平衡拟静力方法进行地震边坡稳定性分析时,对粘聚力较小、内摩擦角较大的浅层滑坡而言,随着地震水平设计加速度值的增大,其临界滑动面基本保持不变;然而,对粘聚力较大而摩擦角较小的深层滑坡而言,随着地震水平设计加速度值的增大,临界滑动面越深、越宽,会呈现出发散现象,选取两个典型的均质土坡,设计了由浅及深的多条滑动面,分别采用极限平衡瑞典方法进行了相应安全系数的计算,同时比较了自重、地震力、粘聚力在抗滑力矩以及滑动力矩中所占比重的变动情况。研究发现:对于浅层滑坡,随着滑动面由浅及深的变化,粘聚力产生的抗滑力矩所占百分比下降幅度较大,自重产生的滑动力矩与总体抗滑力矩的比值下降幅度较大;而对于深层滑坡,随着滑动面由浅及深变化,自重产生的抗滑力矩所占百分比增长的幅度较大,地震力产生的滑动力矩与总体抗滑力矩比值增长幅度也较大。     

Monte Carlo Inversion of DInSAR Data for Dislocation Modeling: Application to the 1997 Umbria-Marche Seismic Sequence (Central Italy)

— The study of surface deformation due to seismic activity is often made using dislocations with uniform slip and simple geometries. A better modeling of coseismic and postseismic surface displacements can be obtained by using dislocations with variable slip and nonregular shapes. This is consistent with the asperity model of fault surfaces, assuming a friction distribution on faults made of locked zones with much higher friction than surrounding zones. In this paper we consider the 1997–1998 Colfiorito seismic sequence. The coseismic surface displacements in the Colfiorito zone are used in order to infer the slip distribution on the fault surface at different stages of the sequence. The displacement field has been modeled varying the slip distribution on the fault, and comparing the deformation observed by SAR and GPS techniques with model results. The slip distribution is calculated by Monte Carlo simulations on a normal fault with the dip angle equal to 40°. A good approximation is obtained by using square asperity units of 1.5×1.5 km². In the first stage, we employed a simplified model with uniform slip, in which each asperity unit is allowed to slip a constant amount or not to slip at all, and in the second stage, we evaluate the slip distribution in the dislocation area determined by the Monte Carlo inversion: in this case we allow unit cells to undergo different values of slip in order to refine the initial dislocation model. The results show that the 1997 seismic events of the sequence can be modeled by irregular dislocations, obtaining a good fit to the DInSAR and GPS observations. The model also confirms the results of previous studies by a different methodology, defining the distribution of asperities on the fault plane using the fault geometry, the geodetic data and the seismic moment of the 1997–1998 Colfiorito seismic sequence. Furthermore, the analysis of 1997 aftershocks in the seismogenic region shows a strong correlation between most events and the asperity distribution, which can be considered as an independent test of the validity of the model.     

Factors that contribute to the elongation of drumlins beneath the Green Bay Lobe,Laurentide Ice Sheet

Drumlin shape has been hypothesized to correlate with ice-flow duration and slip speed, but modern-day analogues and the Coulomb nature of till render the basis of these correlations in question. The evolution of flow-parallel subglacial landforms is of importance for ice flow because the form drag they provide may be a dominant factor in regulating glacier slip speeds. Here we examine the relationship between drumlin shape and cumulative slip displacement (i.e. time-integrated slip speed) as a dominant glaciological control on drumlin shape. First, a new method is developed that allows slip speed to be estimated for deformable bedded glaciers along a flow line from an ice surface profile. Then, reconstructed surface profiles for ice margin chronologies of the Green Bay Lobe (GBL) are used to construct and estimate the spatially varying cumulative slip displacement for use in comparison with drumlin elongation ratios. We focus on a sector of the GBL near the central flow line where the geology is simple and glaciological controls are likely to dominate bedform development. Using Bayesian statistical analysis, a positive and statistically robust relationship between cumulative slip displacement and drumlin elongation ratio is found. Our analysis indicates that drumlin shape could be used to infer palaeo glacier slip speeds if time under the ice can be well constrained and geologic influences are minimal. These findings also suggest that drumlin-supplied drag could decrease with increased cumulative slip displacement in the absence of rigid geologic features that fix drumlin positions.     

加筋土边坡临界滑动场

在分析加筋土边坡稳定性时,将加筋材料的作用视为施加于滑面上的等效力,建立了满足力平衡的加筋土边坡安全系数的计算格式;将边坡临界滑动场数值模拟方法进行推广,提出了基于力平衡的加筋土边坡临界滑动场计算方法,可以得到形状任意的临界滑动面及边坡最小安全系数。通过算例,比较加筋前后临界滑动面和安全系数的变化,并探讨了加筋水平间距、强度、长度对加筋土边坡稳定性的影响。     

Fault rock analysis of the northern part of the Chelungpu Fault and its relation to earthquake faulting of the 1999 Chi-Chi earthquake, Taiwan

Abstract   The 1999 Chi-Chi earthquake in Taiwan ( M _w = 7.6) produced a surface rupture along the north–south-striking Chelungpu thrust fault with pure dip-slip (east side up) and left lateral strike-slip displacements. Near-field strong-motion data for the northern part of the fault illustrate a distinct lack of the high-frequency seismic radiation associated with a large slip (10–15 m) and a rapid slip velocity (2–4 m/s), suggesting a smooth seismic slip associated with low dynamic frictional resistance on the fault. A drillhole was constructed at shallow depths in the possible fault zones of the northern part of the Chelungpu Fault, which may have slipped during the 1999 earthquake. One of the zones consists of a 20-cm-thick, unconsolidated fault breccia with a chaotic texture lacking both discrete slip surfaces (e.g. Riedel shears) and grain crushing. Other possible fault zones are marked by the narrow (less than a few centimeters) gouge zone in which clayey material intrudes into the damaged zone outside of the gouge zone. These characteristic fault rock textures suggest that the slip mechanisms at shallow levels during the earthquake involved either granular flow of initially unconsolidated material or slip localization under elevated pore pressure along the narrow clayey gouge zone. Because both mechanisms lead to low dynamic frictional resistance on the fault, the rapid seismic slip in the deep portions of the fault (i.e. the source region of strong-motion radiation) could have been accommodated by frictionless slip on the shallow portions of the fault. The combination of strong-motion data and fault rock analysis suggests that smooth slip associated with low dynamic friction occurred on both the deep and shallow portions of the fault, resulting in a large slip between the source region and the surface in the northern region.     

Local Tsunamis and Distributed Slip at the Source

—Variations in the local tsunami wave field are examined in relation to heterogeneous slip distributions that are characteristic of many shallow subduction zone earthquakes. Assumptions inherent in calculating the coseismic vertical displacement field that defines the initial condition for tsunami propagation are examined. By comparing the seafloor displacement from uniform slip to that from an ideal static crack, we demonstrate that dip-directed slip variations significantly affect the initial cross-sectional wave profile. Because of the hydrodynamic stability of tsunami wave forms, these effects directly impact estimates of maximum runup from the local tsunami. In most cases, an assumption of uniform slip in the dip direction significantly underestimates the maximum amplitude and leading wave steepness of the local tsunami. Whereas dip-directed slip variations affect the initial wave profile, strike-directed slip variations result in wavefront-parallel changes in amplitude that are largely preserved during propagation from the source region toward shore, owing to the effects of refraction. Tests of discretizing slip distributions indicate that small fault surface elements of dimensions similar to the source depth can acceptably approximate the vertical displacement field in comparison to continuous slip distributions. Crack models for tsunamis generated by shallow subduction zone earthquakes indicate that a rupture intersecting the free surface results in approximately twice the average slip. Therefore, the observation of higher slip associated with tsunami earthquakes relative to typical subduction zone earthquakes of the same magnitude suggests that tsunami earthquakes involve rupture of the seafloor, whereas rupture of deeper subduction zone earthquakes may be imbedded and not reach the seafloor.     

Distribution of postseismic slip on the Calaveras fault,California, following the 1984 M6.2 Morgan Hill earthquake

Repeating earthquakes (REs) are sequences of events that have virtually identical waveforms and are interpreted to represent fault asperities driven to failure by loading from aseismic creep on the surrounding fault surface at depth. To investigate the postseismic deformation after the 1984 M6.2 Morgan Hill earthquake, we identify RE sequences occurring on the central Calaveras fault between 1984 and 2005 using a combination of cross-correlation and spectral coherence techniques. Both the accelerated slip transients due to the earthquake as well as the return to interseismic background creep rates can be imaged from our dataset. A comparison between the regions of the fault that ruptured coseismically and the locations of the REs show that REs preferentially occur in areas adjacent to the coseismic rupture. Using calculated RE-derived subsurface slip distributions at 6 months and 18 months after the mainshock, we predict surface electronic distance meter (EDM) line length changes between stations near the Morgan Hill rupture area. The RE-derived slip model underpredicts a subset of the observed line-length changes. Inclusion of transient aseismic slip below the seismogenic zone is needed to better match the measured surface deformation.     

Fault slip and identification of the second fault plane in the Varzeghan earthquake doublet

An intraplate earthquake doublet, with 11-min delay between the events, devastated the city of Varzeghan in northwestern Iran on August 11, 2012. The first Mw 6.5 strike-slip earthquake, which occurred after more than 200 years of low seismicity, was followed by an Mw 6.4 oblique thrust event at an epicentral separation of about 6 km. While the first event can be associated with a distinct surface rupture, the absence of a surface fault trace and no clear aftershock signature makes it challenging to identify the fault plane of the second event. We use teleseismic body wave inversion to deduce the slip distribution in the first event. Using both P and SH waves stabilize the inversion and we further constrain the result with the surface rupture extent and the aftershock distribution. The obtained slip pattern shows two distinct slip patches with dissimilar slip directions where aftershocks avoid high-slip areas. Using the estimated slip for the first event, we calculate the induced Coulomb stress change on the nodal planes of the second event and find a preference for higher Coulomb stress on the N-S nodal plane. Assuming a simple slip model for the second event, we estimate the combined Coulomb stress changes from the two events on the focal planes of the largest aftershocks. We find that 90% of the aftershocks show increased Coulomb stress on one of their nodal planes when the N-S plane of the second event is assumed to be the correct fault plane.     

Mechanisms of slip nucleation during earthquakes

Slip nucleation during earthquakes is apparently analogous to rupture nucleation within an intact rock sample subjected to triaxial loading. The observations indicate that both these nucleation processes initiate within a relatively small volume and in both the slip propagates unstably along a quasi-planar surface. In both processes a single, pre-existing, shear fracture cannot nucleate the large-scale slip, and in both a ‘process zone' that includes several interacting fractures in a small volume are required to initiate the unstable slip. Both processes require rupture of intact rocks, generate complex fracture geometry, and are associated with intense energy-release rate during slip. Recent observations and analyses are used to correlate rupture nucleation in laboratory tests with nucleation events of large earthquakes. It is proposed that earthquake nucleation occurs by the interaction among multiple fractures within a small volume that develops into unstable yielding of the healed fault zone.     

近场位移数据约束的2013年芦山地震破裂模型及其构造意义

以往的研究显示了2013年芦山MS7.0级地震发震断层的隐伏逆冲断层基本特征,但是破裂深部细节差异较大.本文以近场密集的同震形变数据约束芦山地震破裂面几何形状及滑动分布,结果显示芦山地震破裂面具有铲状结构,上部16km为43°~50°高角度断层,深部16~25km为小于27°的低角度断层,破裂深度与重定位的余震分布深度一致.破裂分布模型清楚显示上下两个断层上各有一个滑动幅度大于0.5m的峰值破裂区,最大滑动量1.5m位于13km深处.重定位的余震分布基本都落在最大滑动量等值线外部库仑应力增加的区域.芦山地震破裂面几何形状和滑动分布特征与2008年汶川MS8.0级地震映秀—北川破裂相似,支持龙门山冲断带发育大规模的近水平滑脱层,是青藏高原东缘地壳缩短增厚、龙门山挤压隆升的重要证据.     

土坡抗震稳定性分析的有限元-滑动面法

提出了一种土坡抗震稳定性分析的新方法，即将有限元法和传统的滑动面法相结合。首先根据有限元法通过求解动力方程，计算出某一时刻土坡内的有效应力，然后根据有效应力计算该时刻的最危险滑动面及对应的安全系数。该方法不仅能够考虑土的应力应变性质，而且能够在任意时刻确定最危险滑动面的位置及安全系数。给出了该方法的详细算法。     

Constant slip rate during the late Quaternary along the Sulu He segment of the Altyn Tagh Fault near Changma,Gansu, China

The question of whether millennial‐scale geological slip rates are consistent with decade‐scale geodetic slip rates is of great importance in evaluating the nature of continental deformation within the Tibetan Plateau. We determined the time‐averaged slip rate of the Sulu He segment of the Altyn Tagh Fault, near Changma in Gansu Province, China, based on geomorphic analysis, remote sensing data, and cosmogenic ¹⁰Be surface‐exposure age dating. Quaternary alluvial fan deposits in the study area (Qf1, Qf2, Qf3) are displaced by left‐lateral movement along the Altyn Tagh Fault. Because of the large accumulated displacement of these fans, some of them have become disconnected from the fan apexes that are directly linked to the debris‐source areas in the piedmont of the Qilian Shan to the south. The total minimum offsets are estimated to be about 429 ± 41 m for Qf1, about 130 ± 10 m for Qf2, and 32 ± 1 m for Qf3. The ¹⁰Be surface‐exposure ages obtained for Qf1 and Qf2 are 100–112 ka and 31–43 ka, respectively. Accordingly, the slip rate since the period of Qf1 and Qf2 depositions is calculated to have been about 3.7 mm/yr.     

Effects of fault geometry and slip style on near-fault static displacements caused by the 1999 Chi-Chi,Taiwan earthquake

We investigated the fault geometry effects and the corresponding coseismic slip distribution using various proposed earthquake fault models for the Chi-Chi earthquake of 21 September 1999. The types of fault geometries are threefold: a simple planar fault plane, a two segmented planar fault plane and a three dimensional (3D) curved fault surface rupture propagation model. We derived the estimated spatial slip distribution from an inversion analysis of GPS coseismic displacement data and show that the 3D fault model is the preferred solution. The simple and segmented fault models lead to significant artificial slip distributions associated with the pre-defined fault geometry and the spatial distribution of GPS stations. The spatial distribution of coseismic slip deduced from the 3D fault model has three observable features: (1) the overall slip is concentrated at depth of less than 12 km, which may well correspond to a shallow-dipping detachment; (2) the maximum slip of about 10 m is located 45 km to the north of the epicenter; and (3) the slip vector is dominated by the dip-slip component. In addition, the results from the inversion of GPS data are consistent with those from the inversion analysis of teleseismic broadband data. A resolution analysis, further, demonstrates that the results are highly correlated with field GPS data studies when we used synthetic test data. The inversion of spatially distributed GPS data is highly sensitive to fault geometry. We conclude that the use of the 3D fault model is not only necessary but also certainly competent enough to well explain the inferred slip style and the observed static coseismic displacements.     

GPS和InSAR同震形变约束的尼泊尔M_W7.9和M_W7.3地震破裂滑动分布

2015年4月25日尼泊尔爆发MW7.9地震,继而引发5月12日MW7.3级余震,GPS、InSAR监测到震源区及周边大范围同震形变.本文以国内外的GPS和InSAR同震形变为约束,考虑喜马拉雅断裂带岩石圈垂向分层和横向差异的影响,反演主喜马拉雅逆冲断裂在这次主震和余震中破裂面形状和滑动分布.结果显示,主震从USGS确定的震中位置向东偏南延伸100km以上,破裂地面迹线与主前缘逆冲断裂迹线基本一致.破裂面倾角约7°~11°,大部分破裂集中在深度8~20km,同余震分布深度一致.主震最大滑动量约6.0~6.6m,位于14km深处.余震破裂集中在震中附近30km范围内,填补了主震东部破裂空区,最大滑动约3.6~4.6 m,位于13km深.深度20km以下基本没有破裂.地壳介质不均匀性对破裂滑动分布的影响较大,介质不均匀模型的观测值不符值比各向同性弹性半空间模型降低10%以上.本文地震破裂模型特征与地震反射剖面、以及根据震间期大地测量数据反演的喜马拉雅深部蠕滑剖面极其相似.跨喜马拉雅断裂剖面的震间形变量与地震破裂滑移量直接相关.以此推算,尼泊尔中部大震原地复发周期在300年以上.     

Improvement in the Fault Boundary Conditions for a Staggered Grid Finite-difference Method

The staggered grid finite-difference method is a powerful tool in seismology and is commonly used to study earthquake source dynamics. In the staggered grid finite-difference method stress and particle velocity components are calculated at different grid points, and a faulting problem is a mixed boundary problem, therefore different implementations of fault boundary conditions have been proposed. Viriuex and Madariaga (1982) chose the shear stress grid as the fault surface, however, this method has several problems: (1) Fault slip leakage outside the fault, and (2) the stress bump beyond the crack tip caused by S waves is not well resolved. Madariaga et al. (1998) solved the latter problem via thick fault implementation, but the former problem remains and causes a new issue; displacement discontinuity across the slip is not well modeled because of the artificial thickness of the fault. In the present study we improve the implementation of the fault boundary conditions in the staggered grid finite-difference method by using a fictitious surface to satisfy the fault boundary conditions. In our implementation, velocity (or displacement) grids are set on the fault plane, stress grids are shifted half grid spacing from the fault and stress on the fictitious surface in the rupture zone is given such that the interpolated stress on the fault is equal to the frictional stress. Within the area which does not rupture, stress on the fictitious surface is given a condition of no discontinuity of the velocity (or displacement). Fault normal displacement (or velocity) is given such that the normal stress on the fault is continuous across the fault. Artificial viscous damping is introduced on the fault to avoid vibration caused by onset of the slip. Our implementation has five advantages over previous versions: (1) No leakage of the slip prior to rupture and (2) a zero thickness fault, (3) stress on the fault is reliably calculated, (4) our implementation is suitable for the study of fault constitutive laws, as slip is defined as the difference between displacement on the plane of z = + 0 and that of z = − 0, and (5) cessation of slip is achieved correctly.     

黄土边坡“三维最危险滑裂面”的高效搜索和稳定性评价

本文介绍了作者所开发的一套实用型黄土坡体“三维最危险滑裂面”搜索和稳定性评价软件系统的核心思想,即采用Monte Carlo随机搜索法与遗传算法相结合的优化方法,高效生成一系列接近（或包含）“最危险滑裂面”的三维滑裂面,并以Hungr法所确定的稳定性系数最小为筛选依据,搜索确定任意形态黄土坡体的“三维最危险滑裂面”,进而基于已知的“三维最危险滑裂面”,进一步考虑各种可能的参数变化,进行严密的稳定性分析和评价。