Seismic wave propagation analysis in vertical arrays at Kashiwazaki–Kariwa nuclear power plant site by using modified normalized input–output minimization (mod‐NIOM) method

A new approach on numerical modeling of wave propagation is introduced and is used to analyze the effect of earthquake magnitudes (ground motion amplitudes) on wave propagation. In this method, the sum of the maximum amplitudes of the first output model at time 0 s and rest of the output models at different times are normalized to unity. Considering this as a constraint, the sum of the weighted‐squared Fourier amplitudes is minimized by using the Lagrange multiplier method. The proposed method can reveal the relationship of actual time histories by showing simple clear peaks. This method is used to analyze the time histories of various earthquake events at different vertical array sites of the Kashiwazaki–Kariwa nuclear power plant of Tokyo electric power company (TEPCO). The wave arrival times obtained from this method and down‐hole measurements are compared. The results show increase in the arrival times at surface layer when the magnitude of earthquake is large. The results reveal that the amplitudes of small magnitude earthquakes at depths are small and are largely amplified at surface, whereas in case of large magnitude earthquakes, the amplitudes are large at depths and are deamplified at surface reflecting the effects of the strain‐dependent soil properties that result in non‐linear site response to strong shaking. The results also show that the reflected peak amplitudes are higher for small magnitude earthquakes than for large magnitude earthquakes. Copyright © 2010 John Wiley & Sons, Ltd.     

Recent Advances in Prediction and Processing of Strong Ground Motions

We present an overview of our recent results on utilizing small earthquakes in the earthquake engineering practice. Site-specific ground motion time-histories of large earthquakes can be successfully simulated using recordings of small earthquakes which are often referred to as 'empirical Green's functions' in seismology. Another important practical problem is whether and how these observations can be used in seismic risk studies which are based on empirical attenuation relations for ground motion parameters. We study a possibility of extrapolating attenuation relations for small earthquakes, to larger magnitudes using the data from the Garner Valley downhole array in Southern California. Finally we introduce efficient ground motion processing techniques in frequency- and time-domains and apply them to site response estimation.     

Tectonic stress,seismicity, and seismic hazard in the southeastern Carpathians

Intermediate-depth earthquakes in the Vrancea region occur in response to stress generation due to descending lithosphere beneath the southeastern Carpathians. In this article, tectonic stress and seismicity are analyzed in the region on the basis of a vast body of observations. We show a correlation between the location of intermediate-depth earthquakes and the predicted localization of maximum shear stress in the lithosphere. A probabilistic seismic hazard assessment (PSHA) for the region is presented in terms of various ground motion parameters on the utilization of Fourier amplitude spectra used in engineering practice and risk assessment (peak ground acceleration, response spectra amplitude, and seismic intensity). We review the PSHA carried out in the region, and present new PSHA results for the eastern and southern parts of Romania. Our seismic hazard assessment is based on the information about the features of earthquake ground motion excitation, seismic wave propagation (attenuation), and site effect in the region. Spectral models and characteristics of site-response on earthquake ground motions are obtained from the regional ground motion data including several hundred records of small and large earthquakes. Results of the probabilistic seismic hazard assessment are consistent with the features of observed earthquake effects in the southeastern Carpathians and show that geological factors play an important part in the distribution of the earthquake ground motion parameters.     

Research on the February 18, 1996 earthquake in the caves of Saint-Paul-de-Fenouillet area, (eastern Pyrenees,France)

Eight caves have been investigated near Saint-Paul-de-Fenouillet after the earthquake of 5.2 magnitude of February 1996 which occurred in the eastern Pyrenees (France) and caused moderate damage at the ground surface. The earthquake has been associated with the movement of an E-W fault. The caves had not been visited since the earthquake. Some damage, mainly collapses of soda straws and small rocks, could be attributed to this earthquake. The most interesting cave in the epicentral area is the Paradet cave which is situated on a recently activated fault plane. In this cave, soda straw falls could be attributed to the earthquake, but other more ancient damage was also observed. Analysis of the azimuth of fallen speleothems, which are natural pendulums, may indicate the directions, and an estimation of their mechanical properties gives the threshold of the seismic ground motion amplitude responsible for their collapse, thus supplying information to calibrate damage due to past earthquakes. A statistical study indicates that the main direction of the collapsed soda straws is E-W. Numerical simulations confirm that soda straws are relatively strong objects that may break under certain conditions during earthquakes.     

Chemo‐thermo‐mechanically coupled seismic analysis of methane hydrate‐bearing sediments during a predicted Nankai Trough Earthquake

In the present study, we have developed a numerical method which can simulate the dynamic behaviour of a seabed ground during gas production from methane hydrate‐bearing sediments. The proposed method can describe the chemo‐thermo‐mechanical‐seismic coupled behaviours, such as phase changes from hydrates to water and gas, temperature changes and ground deformation related to the flow of pore fluids during earthquakes. In the first part of the present study, the governing equations for the proposed method and its discretization are presented. Then, numerical analyses are performed for hydrate‐bearing sediments in order to investigate the dynamic behaviour during gas production. The geological conditions and the material parameters are determined using the data of the seabed ground at Daini‐Atsumi knoll, Eastern Nankai Trough, Japan, where the first offshore production test of methane hydrates was conducted. A predicted earthquake at the site is used in the analyses. Regarding the seismic response to the earthquake which occur during gas production process, the wave profiles of horizontal acceleration and horizontal velocity were not extensively affected by the gas production. Hydrate dissociation behaviour is sensitive to changes in the pore pressure during earthquakes. Methane hydrate dissociation temporarily became active in some areas because of the main motion of the earthquake, then methane hydrate dissociation brought about an increase in the average pressure of the fluids during the earthquake. And, it was this increase in average pore pressure that finally caused the methane hydrate dissociation to cease during the earthquake. Copyright © 2016 John Wiley & Sons, Ltd.     

Long-period ground motion in the epicentral area of major earthquakes

In view of the potential importance of long-period ground motion in the design of large structures, near-field ground displacement is computed by the elastic dislocation theory for several earthquake fault models. The validity of such computations is confirmed by comparing the computed seismogram with the observed long-period seismogram of the 1923 Kanto earthquake. The ground motions are computed for three hypothetical earthquakes, a hypothetical Kanto earthquake, Tokai earthquake and Nemuro-Oki earthquake. The location and the nature of the faulting of these earthquakes are predicted by plate tectonics and precise earthquake mechanism studies. Major conclusions are: Tokyo may suffer, in the hypothetical Kanto earthquake, ground motions about half as large as those experienced in the 1923 Kanto earthquake; Hamamatsu, a large city on the Tokai coast, may experience in the hypothetical Tokai earthquake ground motions which are as large as, or even larger than, those experienced in the epicentral area of the 1923 Kanto earthquake; the hypothetical Nemuro-Oki earthquake may cause ground motions as large as those experienced in the 1968 Tokachi-Oki earthquake on the coastal cities in Hokkaido.     

Research on the February 18, 1996 earthquake in the caves of Saint-Paul-de-Fenouillet area, (eastern Pyrenees,France)

Abstract

Eight caves have been investigated near Saint-Paul- de-Fenouillet after the earthquake of 5.2 magnitude of February 1996 which occurred in the eastern Pyrenees (France) and caused moderate damage at the ground surface. The earthquake has been associated with the movement of an E-W fault. The caves had not been visited since the earthquake. Some damage, mainly collapses of soda straws and small rocks, could be attributed to this earthquake. The most interesting cave in the epicentral area is the Paradet cave which is situated on a recently activated fault plane. In this cave, soda straw falls could be attributed to the earthquake, but other more ancient damage was also observed. Analysis of the azimuth of fallen speleothems, which are natural pendulums, may indicate the directions, and an estimation of their mechanical properties gives the threshold of the seismic ground motion amplitude responsible for their collapse, thus supplying information to calibrate damage due to past earthquakes. A statistical study indicates that the main direction of the collapsed soda straws is E–W. Numerical simulations confirm that soda straws are relatively strong objects that may break under certain conditions during earthquakes. © Elsevier, Paris     

Sensitivity analysis of seismic hazard for the northwestern portion of the state of Gujarat, India

We test the sensitivity of seismic hazard to three fault source models for the northwestern portion of Gujarat, India. The models incorporate different characteristic earthquake magnitudes on three faults with individual recurrence intervals of either 800 or 1600 years. These recurrence intervals imply that large earthquakes occur on one of these faults every 266–533 years, similar to the rate of historic large earthquakes in this region during the past two centuries and for earthquakes in intraplate environments like the New Madrid region in the central United States. If one assumes a recurrence interval of 800 years for large earthquakes on each of three local faults, the peak ground accelerations (PGA; horizontal) and 1-Hz spectral acceleration ground motions (5% damping) are greater than 1 g over a broad region for a 2% probability of exceedance in 50 years' hazard level. These probabilistic PGAs at this hazard level are similar to median deterministic ground motions. The PGAs for 10% in 50 years' hazard level are considerably lower, generally ranging between 0.2 g and 0.7 g across northwestern Gujarat. Ground motions calculated from our models that consider fault interevent times of 800 years are considerably higher than other published models even though they imply similar recurrence intervals. These higher ground motions are mainly caused by the application of intraplate attenuation relations, which account for less severe attenuation of seismic waves when compared to the crustal interplate relations used in these previous studies. For sites in Bhuj and Ahmedabad, magnitude (M) 7 3/4 earthquakes contribute most to the PGA and the 0.2- and 1-s spectral acceleration ground motion maps at the two considered hazard levels.     

区域非稳定动力学环境下的岩体松动效应

区域非稳定动力学环境下,长期的构造变形、重力卸荷以及地震动力作用的共同影响,可以导致岩体发生大范围变形、松动。松动岩体内发育大量的软弱结构面,且表现出整体破碎、松弛严重、透水强烈,张性节理裂隙发育、地表裂缝较发育、岩体地震动力破坏信息反映明显等特征。岩体的变形松动可以分为卸荷变形松动、倾倒变形松动、顺层滑移松动、断层控制松动、节理裂隙控制松动等5种模式。岩体的物理振动试验结果表明,地震动力是造成岩体松动的主因。数值模拟结果表明,在单纯自重应力影响作用下,松动岩体不会出现大面积的失稳破坏现象,但在地震动力作用下,松动岩体会发生大面积屈服破坏。     

含消落带劣化岩体的危岩边坡动力累积损伤机制研究

对消落带劣化岩体及水库诱发地震共同影响下三峡库区某典型危岩边坡的稳定性进行了研究,设计并开展了几何相似比为1:100的振动台模型试验,探讨了含消落带劣化岩体的危岩边坡动力累积损伤—失稳破坏演化全过程及其动力响应规律。研究表明：含消落带劣化岩体的危岩边坡动力累积损伤—失稳破坏全过程可归结为坡体内部损伤累积—裂隙发育—次级节理与深大裂隙贯通—失稳倾倒,同时伴随消落带岩体表层松动—掉落—破坏及内部出现渗流网—形成渗流通道—形成“凹腔”的复合破坏模式;随着地震动的持续,危岩体内部动力响应规律具有典型的“趋高”及“趋表”效应,危岩边坡表面累积位移不断增加,消落带处孔隙水压力整体增加,危岩边坡内部水平向及竖直向土压力在全阶段中整体均呈先增大后减小的规律;危岩边坡自振频率及阻尼比在全阶段整体呈减小和增加的趋势;在小震结束前阶段及强震阶段,危岩边坡损伤度曲线分别呈“S”型分布和指数型分布。     

Source model for the Mw 6.1, 31 March 2006, Chalan‐Chulan Earthquake (Iran) from InSAR

We use InSAR to measure deformation and kinematics of the Mw = 4.9 Borujerd (2005/05/03) and Mw = 6.1 Chalan‐Chulan (2006/03/31) earthquakes that occurred in the Zagros fold‐and‐thrust belt. The focal mechanism of the 2006 event is consistent with right lateral strike‐slip motion and the event ruptured the Dorud‐Borujerd segment of the Main Recent Fault. An Envisat interferogram spanning the 2006 event shows peak ground deformation of 9 cm in the satellite line‐of‐sight along a 10 km long fault portion. The interferogram spanning the 2005 earthquake is rather related to atmospheric artefact than to ground deformation. Dislocation models of the 2006 Chalan‐Chulan event indicate dextral slip amounting to a maximum of 90 cm at a depth of 4 km. The predicted vertical displacements are in good agreement with differential levelling data. The 2006 event filled only a small part of the seismic gap located between large M = 7 events that occurred in 1909 and 1957.     

Earthquake loss estimation of residential buildings in Pakistan

Pakistan is an earthquake-prone region due to its tectonic setting resulting in high hazard with moderate-to-strong ground motions and vulnerability of structures and infrastructures, leading to the loss of lives and livelihood, property damage and economic losses. Earthquake-related disaster in Pakistan is a regular and serious threat to the community; however, the country lack tools for earthquake risk reduction through early warning (pre-earthquake planning), rapid response (prompt response at locations of high risk) and pre-financing earthquake risk (property insurance against disaster). This paper presents models for physical damageability assessment and socioeconomic loss estimation of structures in Pakistan for earthquake-induced ground motions, derived using state-of-the-art earthquake loss estimation methodologies. The methodologies are being calibrated with the site-specific materials and structures response, whereas the derived models are tested and validated against recent observed earthquakes in the region. The models can be used to develop damage scenario for earthquakes (assess damaged and collapsed structures, casualties and homeless) and estimate economic losses, i.e., cost of repair and reconstruction (for a single earthquake event as well as all possible earthquakes). The models can provide help on policy- and decision-making toward earthquake risk mitigation and disaster risk reduction in Pakistan.     

Probabilistic seismic hazard analysis for Sumatra, Indonesia and across the Southern Malaysian Peninsula

The ground motion hazard for Sumatra and the Malaysian peninsula is calculated in a probabilistic framework, using procedures developed for the US National Seismic Hazard Maps. We constructed regional earthquake source models and used standard published and modified attenuation equations to calculate peak ground acceleration at 2% and 10% probability of exceedance in 50 years for rock site conditions. We developed or modified earthquake catalogs and declustered these catalogs to include only independent earthquakes. The resulting catalogs were used to define four source zones that characterize earthquakes in four tectonic environments: subduction zone interface earthquakes, subduction zone deep intraslab earthquakes, strike-slip transform earthquakes, and intraplate earthquakes. The recurrence rates and sizes of historical earthquakes on known faults and across zones were also determined from this modified catalog. In addition to the source zones, our seismic source model considers two major faults that are known historically to generate large earthquakes: the Sumatran subduction zone and the Sumatran transform fault. Several published studies were used to describe earthquakes along these faults during historical and pre-historical time, as well as to identify segmentation models of faults. Peak horizontal ground accelerations were calculated using ground motion prediction relations that were developed from seismic data obtained from the crustal interplate environment, crustal intraplate environment, along the subduction zone interface, and from deep intraslab earthquakes. Most of these relations, however, have not been developed for large distances that are needed for calculating the hazard across the Malaysian peninsula, and none were developed for earthquake ground motions generated in an interplate tectonic environment that are propagated into an intraplate tectonic environment. For the interplate and intraplate crustal earthquakes, we have applied ground-motion prediction relations that are consistent with California (interplate) and India (intraplate) strong motion data that we collected for distances beyond 200 km. For the subduction zone equations, we recognized that the published relationships at large distances were not consistent with global earthquake data that we collected and modified the relations to be compatible with the global subduction zone ground motions. In this analysis, we have used alternative source and attenuation models and weighted them to account for our uncertainty in which model is most appropriate for Sumatra or for the Malaysian peninsula. The resulting peak horizontal ground accelerations for 2% probability of exceedance in 50 years range from over 100% g to about 10% g across Sumatra and generally less than 20% g across most of the Malaysian peninsula. The ground motions at 10% probability of exceedance in 50 years are typically about 60% of the ground motions derived for a hazard level at 2% probability of exceedance in 50 years. The largest contributors to hazard are from the Sumatran faults.     

Local Site Effect Due to Past Earthquakes in Kolkata

Kolkata, capital of West Bengal, India, presently congested with moderate to high rise buildings, has undergone low to moderate damages due to past earthquakes. The city is situated on the world’s largest delta island with soft thick alluvial soil layer. In this study, an attempt has been made to study ground response due to a number of past earthquakes, 1897 Shillong earthquake, 1964 Calcutta earthquake and 2011 Sikkim earthquake, for the purpose of preliminary microzonation of the Kolkata city. For this, synthetic ground motions have been generated at bedrock level by stochastic method. By using 1D wave propagation technique, the synthetic ground motion has been computed at surface level for 144 borehole locations in the city. Contours of PGA, PGV and PGD parameters in the city have been drawn for these three earthquakes. Response spectra for these three earthquakes have also been computed and an optimum response spectrum has been determined. A good correlation has been obtained with predicted ground motion at surface level of the city with the reported intensity and damages occurred in buildings of Kolkata during past earthquakes. The scenario of simulated ground motion for the past three earthquakes depicts that Kolkata city is very much prone to damages even due to moderate far and near source earthquakes.     

从昭通地震破坏实例看山区地震地面破坏特点

1974年5月11日3时25分,东经104度,北纬28.2度我国云南省昭通境内发生M=7.1地震。宏观震中为大关县以北,木杆公社钟(杜)家坪附近。震中烈度为IX度。震区为拔海2000米的滇东北高原地区,地面经受强烈切刻,山高坡陡,尤其震区西部,地形尤显陡峻。地形的坡度一般均在30°以上,主要河流的坡降平均为2.53%。该区地质情况比较复杂。地层分布主要为二迭纪阳新统灰岩,峨眉山玄武岩,三迭纪飞仙关砂页岩等等。     

High‐resolution seismic reflection profiling of neotectonic faults in Lake Timiskaming,Timiskaming Graben,Ontario‐Quebec,Canada

The Timiskaming Graben is a 400 km long, 50 km wide north‐west trending morphotectonic depression within the Canadian Shield of eastern North America and experiences frequent intraplate earthquakes. The graben extends along the border of Ontario and Quebec, connecting southward with the Nipissing and Ottawa‐Bonnechere grabens and the St. Lawrence Rift System which includes a similar structure underlying the Hudson Valley of the eastern USA. Together they form a complex failed rift system related to regional extension of North American crust during the breakup of Rodinia and, later, Pangea. The Timiskaming Graben lies within a belt of heightened seismic activity (Western Quebec Seismic Zone) with frequent moderate magnitude (greater than magnitude 5) earthquakes including a magnitude 6.2 in 1935. These events threaten aging urban infrastructure built on soft glacial sediments; post‐glacial landslides along the Ottawa Valley suggest earthquakes as large as magnitude 7. The inner part of the Timiskaming Graben is filled by Lake Timiskaming, a large 110 km long post‐glacial successor to glacial Lake Barlow that was ponded by the Laurentide Ice Sheet 9500 years ago. The effects of frequent ground shaking on lake floor sediments was assessed by collecting more than 1000 line kilometres of high‐resolution ‘chirp’ seismic profiles. Late glacial Lake Barlow glaciolacustrine and overlying post‐glacial sediments are extensively deformed by extensional faults that define prominent horsts and grabens; multibeam bathymetry data suggest that faults influence the morphology of the modern lake floor, despite high sedimentation rates, and indicate recent neotectonic deformation. The Lake Timiskaming area provides evidence of post‐glacial intracratonic faulting related to recurring earthquake activity along a weak spot within the North American plate.     

A study of the seismic response of the city of Benevento (Southern Italy) through a combined analysis of seismological and geological data

A previous analysis [Improta, L., G. Di Giulio, and A. Rovelli (2005). Variations of local seismic response in Benevento (Southern Italy) using earthquakes and ambient noise recordings, J. Seism. 9, 191–210.] of small magnitude earthquakes recorded at 12 sites within the city of Benevento has stressed the significant role played by near-surface geology in causing variability of the ground motion. In this paper, we extend the study of the seismic response from 12 sites to the entire urban area. Based on inferences from the comparison at the 12 sites between earthquake and ambient vibration results, we have collected ambient noise at about 100 sites within the city, intensifying measurements across the main shallow geological variations. We use borehole data to interpret ambient noise H/V spectral ratios in terms of near-surface geology comparing H/V curves to theoretical transfer functions of 1D models along five well-constrained profiles.

On the basis of geological, geotechnical, and seismic data, we identify three main typologies of seismic response in the city. Each type of response is associated to zones sharing common soil conditions and similar soil classes according to building codes for seismic design. Moreover, we find that the spatial variation of the seismic response in the ancient town area is consistent with the damage pattern produced by a very destructive, well-documented historical earthquake that struck the city in 1688, causing MCS intensity of IX–X in Benevento.

Finally, we use ground motions recorded during the experiment by Improta et al. [Improta, L., G. Di Giulio, and A. Rovelli (2005). Variations of local seismic response in Benevento (Southern Italy) using earthquakes and ambient noise recordings, J. Seism. 9, 191–210.] to generate synthetic seismograms of moderate to strong (Mw 5.7, Molise 2002 and Ms 6.9, 1980 Irpinia) earthquakes. We calibrate the random summation technique by Ordaz et al. [Ordaz, M., J. Arboleda, and S.K. Singh (1995). A scheme of random summation of an Empirical Green's Function to estimate ground motions for future large earthquakes, Bull. Seism. Soc. Am. 85, 1635–1647.] using recordings of these earthquakes available in Benevento. After a satisfactory fit between observed and synthetic seismograms, we compute response spectra at different sites and speculate on effects of the geology class at large level of shaking, including soil nonlinearity. We find that large discrepancies from design spectra prescribed by seismic codes can occur for a wide sector of Benevento, especially for periods < 0.5 s.     

Shear‐wave splitting and earthquake forecasting

Seismic shear‐wave splitting (SWS) monitors the low‐level deformation of fluid‐saturated microcracked rock. We report evidence of systematic SWS changes, recorded above small earthquakes, monitoring the accumulation of stress before earthquakes that allows the time and magnitude of impending large earthquakes to be stress‐forecast. The effects have been seen with hindsight before some 15 earthquakes ranging in magnitude from an M1.7 seismic swarm event in Iceland to the Ms7.7 Chi‐Chi Earthquake in Taiwan, including a successfully stress‐forecast of a M5.0 earthquake in SW Iceland. Characteristic increases in SWS time‐delays are observed before large earthquakes, which abruptly change to deceases shortly before the earthquake occurs. There is a linear relationship between magnitudes and logarithms of durations of both increases and decreases in SWS time‐delays before large impending earthquakes. However, suitably persistent swarms of small earthquakes are too scarce for routine stress‐forecasting. Reliable forecasting requires controlled‐source cross‐hole seismics between neighbouring boreholes in stress‐monitoring sites (SMS). It would be possible to stress‐forecast damaging earthquakes worldwide by a global network of SMS in real time.     

Can electromagnetic disturbances related to the recent great earthquakes be detected by satellite magnetometers?

On December 26, 2004 the world's fourth largest earthquake since 1900 and the largest since the 1964 Prince William Sound, Alaska earthquake, occurred off the west coast of northern Sumatra with a magnitude of 9.3. On March 28, 2005 another event of magnitude 8.7 took place in the same region. The December 26, 2004 earthquake has prompted scientists to investigate possible electromagnetic signatures of this event, using ground magnetic observations. Iyemori et al. [Iyemori, T. et al., 2005. Geomagnetic pulsations caused by the Sumatra earthquake on December 26, 2004. Geophys. Res. Lett., 32, L20807, doi:10.1029/2005GL024083.] have suggested that a 3.6 min long geomagnetic pulsation, observed shortly after this event, was generated by the earthquake. They have speculated that a 30 s magnetic pulsation was also caused by the earthquake. Here for the first time, CHAMP satellite magnetic and electron density data are examined to find out if electromagnetic signatures which are possibly related to these recent megathrust earthquakes are observed in satellite magnetic data. We have shown that some specific features are observed after the two earthquakes, with periods of about 16 and 30 s. Our results favor an external source origin for the 30 s pulsation. Moreover, after more than 1 h, CHAMP magnetic data indicate the existence of a feature characterized by the same parameters (duration, amplitude, and frequency content), which could be associated with each earthquake, respectively. Further investigations are required in order to answer the question of whether these signals can be associated with earthquakes and to assign their possible usefulness with respect to earthquake development.     

Controls on Block Toppling Using a Three-Dimensional Distinct Element Approach

Analysis methods for block toppling are most commonly undertaken in two dimensions. This paper investigates the influence of discontinuity orientations on three-dimensional block toppling mechanisms using a three-dimensional distinct element code. The three-dimensional models allow one to kinematically appraise if toppling conditions derived for two-dimensional geometries can be extended into three dimensions. Two conceptual model geometries were considered in order to represent a road cut or open-pit bench. The first geometry examined a slope with fixed vertical lateral boundaries, while the second geometry assumed an unrestrained lateral slope as a model boundary condition. This “along-strike slope profile” of the models was found to play an important role in the failure mechanism and displacement direction. The dip direction and dip angle of the toppling, basal and lateral release discontinuities were varied one at the time using angular ranges of up to 30° from an assumed mutual orthogonal relationship. This made it possible for the influence and importance of each discontinuity set to be independently evaluated. The results are presented in a stereographic format with preliminary zones outlining discontinuity aspect combinations that potentially result in block toppling failures.