Back analysis of a large landslide in a flysch rock mass

Flysch is a sedimentary rock consisting of a rhythmic alternation of hard (limestone, sandstone, siltstone) and weak (marl, mudstone, claystone) layers. Because of the presence of layers with different physical properties, the mechanical characterization of heterogeneous rock masses such as flysch is a real challenge. Different methods have been proposed in the literature to characterize flysch, combining empirical classification indexes with laboratory tests. Most of these methods, however, were specifically designed for tunneling and underground excavations, and their applicability to slope stability problems is not yet fully investigated. In this study, we analyze a large landslide in a cretaceous flysch rock in order to compare the mobilized strength at failure with those predicted by the modified GSI method (Marinos and Hoek, 2001). The landslide occurred in the Savena River basin (Northern Apennines of Italy) on April 6, 2013, with a volume of about 3 million m³. Soon after the failure, geological, geotechnical, and geophysical investigations were carried out to detect the failure mechanism and define the landslide geometry. Back analyses of the failed slope were performed using both limit equilibrium and finite difference methods to estimate the in situ strength of the flysch. The results show that the mobilized rock mass cohesion is very low (c ^'?≈?20?÷?40 kPa) and that the modified GSI method can predict the in situ strength only assuming a disturbance factor D = 1. Moreover, the analysis shows that the linearization criteria proposed in literature to compute the equivalent Mohr-Coulomb parameters remarkably overestimate the rock mass strength.     

Numerical analysis of effect of baffle configuration on impact force exerted from rock avalanches

In mountainous areas, channelized rock avalanches swarm downslope leading to large impact forces on building structures in residential areas. Arrays of rock avalanche baffles are usually installed in front of rigid barriers to attenuate the flow energy of rock avalanches. However, previous studies have not sufficiently addressed the mechanisms of interaction between the rock avalanches and baffles. In addition, empirical design approaches such as debris flow (Tang et al., Quat Int 250:63–73, 2012), rockfall (Spang and Rautenstrauch, 1237–1243, 1988), snow avalanches (Favier et al., 14:3–15, 2012), and rock avalanches (Manzella and Labiouse, Landslides 10:23–36, 2013), which are applied in natural geo-disasters mitigation cannot met construction requirements. This study presents details of numerical modeling using the discrete element method (DEM) to investigate the effect of the configuration of baffles (number and spacing of baffle columns and rows) on the impact force that rock avalanches exert on baffles. The numerical modeling is firstly conducted to provide insights into the flow interaction between rock avalanches and an array of baffles. Then, a modeling analysis is made to investigate the change pattern of the impact force with respect to baffle configurations. The results demonstrate that three crucial influencing factors (baffle row numbers, baffle column spacing, and baffle row spacing) have close relationship with energy dissipation of baffles. Interestingly, it is found that capacity of energy dissipation of baffles increases with increasing baffle row numbers and baffle row spacing, while it decreases with increasing baffle column spacing. The results obtained from this study are useful for facilitating design of baffles against rock avalanches.     

Experimental Anelastic Strain Recovery Compliance of Three Typical Rocks

The experimental determination of anelastic strain recovery (ASR) compliances for three types of rocks (granite, marble, and sandstone) was performed in the laboratory. Preloading of specimens for uniaxial compression creep tests was at 50 % of the uniaxial compressive strength (UCS) for each rock type. We obtained the shear mode Jas(t) and volumetric mode Jav(t) ASR compliances and calculated the ratio of Jas(t) to Jav(t). The Kelvin model for rock rheology was then applied in numerical simulations and the results were in good agreement with the measured data for Jas(t) and Jav(t). These results showed that both the magnitude and rate of increase of the ASR compliances are strongly dependent on the rock type, and the values of the Jas(t)/Jav(t) ratio for a loading of 50 % of the UCS showed a trend leading to different constants for each of the three rock types. Further experimental and numerical analyses showed approximate power-law relationships between the ASR compliances at 50 % of UCS, and both the UCS and the tangential Young’s modulus at 50 % of UCS (E _t50). These relationships may be useful for the preliminary estimation of ASR compliances.     

Comparison of Squeezing Prediction Methods: A Case Study on Nowsoud Tunnel

According to the International Society of Rock Mechanics, squeezing is a time dependent large deformation occurring during tunnel construction around the tunnel associated with creep caused by exceeding a limiting shear stress (Barla in ISRM News J 2:44–49, 1995). This research is conducted using a case study on the Nowsoud Tunnel, Iran. Being 14 km in length and 4.5 m in diameter, the tunnel is located in the western part of Iran near the Iraq border. Nowsoud tunnel, which was excavated using a double shield TBM, exhibited severe squeezing (with 8919 m) in its critical zone which resulted in excavation termination. In this research, the best approach for predicting squeezing among the recommended methods for reducing the damages caused by squeezing on TBM was determined. In this regard, approaches commonly used to predict squeezing are empirical, semi-empirical, and theoretical–analytical methods. Besides, these methods, numerical modeling is used to estimate convergence generated along the tunnel pathways, which is ultimately used to categorize squeezing. This paper compares squeezing prediction methods in 68 section of Nowsoud Tunnel. These 68 sections indicate that the empirical methods propose a general estimation/overview of squeezing. Among the semi-analytical approaches, the one proposed by Hoek and Marinos (Rock engineering in difficult rock conditions—soft rocks and karst, Taylor & Francis Group, London, pp 49–60, 2000) are compatible with the occurrence of squeezing in the critical zone. However, the degree of predicted squeezing is less than the real degree of squeezing in this zone. Based on the result of Aydan approach, 75 % of the tunnel sections are under squeezing condition. Theoretical–analytical approaches underestimate the possibility of squeezing in the critical zone. Barla?s approach (1995) demonstrated the possibility of squeezing in the critical zone with low intensity. The numerical computations in this paper were performed using Plaxis (version 8.5), a two-dimensional numerical program based on the finite element method. Plaxis results, classified by Hoek and Marinos (2000) method, show that 8800 m of the tunnel length is under the non-squeezing condition. According to all prediction methods, the squeezing zones depend on faulted zones, argillaceous limestone and shale formations such as J₁Kh, J₄Kh, J₅Kh, and Kgr. These formations were identified with a high quantity of shale and argillaceous limestone. Bedding of these geological formations is thin and their geotechnical properties are weaker than those of limestone formations. On the other hand, non-squeezing zones depend on limestone formations such as J₂Kh, J₃Kh, J₆Kh, K^abg, and Kbg. Moreover, all approaches predicted squeezing potential for the critical zone where TBM is jammed.     

Miocene echinoids from the Sadat area,south Gebel Ataqa,NW Gulf of Suez,Egypt: systematics,palaeobiogeography

The echinoid fauna from the Miocene sedimentary succession cropping out south Wadi Tweirig, and Wadi Hommath, south Gebel Ataqa, NW Gulf of Suez, has been examined with the aim to known their stratigraphic and paleogeographic distribution. The Miocene succession includes two formations: Sadat Formation, unconformably overlying the middle/upper Eocene rocks at the base and Hommath Formation at the top. Twenty-eight echinoid species (8 regular and 20 irregular) belonging to 18 genera, 13 families, and 7 orders have been identified, systematically described, and illustrated in this work. Eleven species are recorded for the first time from Egypt: ten of these came from the Hommath Formation (Schizechinus cf. serresii Desor (1856), Schizechinus pentagonus Kier 1972, Clypeaster cf. martini des Moulins 1837, Scutella checchiae occidentalis Desio 1934, Scutella melitensis Airaghi 1902, Echinodiscus desori Duncan and Sladen 1883, Echinolampas cf. zeitensis Fourtau 1920, Schizaster lovisatoi Cotteau 1895, Agassizia (Agassizia) powersi Kier 1972, and Hemipatagus ocellatus Defrance (1827)), and one from the Sadat Formation (Clypeaster campanulatus Schlotheim (1820)). The identified fauna shows a strong affinity with the Mediterranean bio-province.     

A logistic regression classifier for long-term probabilistic prediction of rock burst hazard

Rock burst is a complex dynamic process can lead to casualties, to failure and deformation of the supporting structures, and to damage of the equipment on site; hence, its prediction is of great importance in underground construction. We present a novel empirical method to predict rock burst based on the theory of logistic regression classifiers. An extensive database collected from the literature, which includes observations about rock burst occurrence (or not) in underground excavations in projects from all over the world, is used to train and validate the model. The proposed approach allows us to compute new class separation lines (or planes) to estimate the probability of rock burst, using different combinations of five possible input parameters—tunnel depth, H; maximum tangential stress, MTS; elastic energy index, W _et; uniaxial compressive strength of rock, UCS; uniaxial tensile strength of rock, UTS—among which it was found that the preferable model could be developed in H–W _et–UCS space. The proposed model is validated with goodness-of-fit tests and nine-fold cross-validation; results show that its predictive capability compares well with previously proposed empirical methods and confirm that, as expected, the probability of rock burst increases with excavation depth, and that both W _et and UCS have a similarly significant influence on rock burst occurrence. Finally, expressions are proposed for identification of conditions associated with several reference values of rock burst probability, which can be employed in preliminary risk analyses.     

Prediction of strength parameters of sedimentary rocks using artificial neural networks and regression analysis

Accurate laboratory measurement of geo-engineering properties of intact rock including uniaxial compressive strength (UCS) and modulus of elasticity (E) involves high costs and a substantial amount of time. For this reason, it is of great necessity to develop some relationships and models for estimating these parameters in rock engineering. The present study was conducted to forecast UCS and E in the sedimentary rocks using artificial neural networks (ANNs) and multivariable regression analysis (MLR). For this purpose, a total of 196 rock samples from four rock types (i.e., sandstone, conglomerate, limestone, and marl) were cored and subjected to comprehensive laboratory tests. To develop the predictive models, physical properties of studied rocks such as P wave velocity (V_p), dry density (γ_d), porosity, and water absorption (A_b) were considered as model inputs, while UCS and E were the output parameters. We evaluated the performance of MLR and ANN models by calculating correlation coefficient (R), mean absolute error (MAE), and root-mean-square error (RMSE) indices. The comparison of the obtained results revealed that ANN outperforms MLR when predicting the UCS and E.     

Hybrid discretization of multi-phase flow in porous media in the presence of viscous,gravitational, and capillary forces

Multi-phase flow in porous media in the presence of viscous, gravitational, and capillary forces is described by advection diffusion equations with nonlinear parameters of relative permeability and capillary pressures. The conventional numerical method employs a fully implicit finite volume formulation. The phase-potential-based upwind direction is commonly used in computing the transport terms between two adjacent cells. The numerical method, however, often experiences non-convergence in a nonlinear iterative solution due to the discontinuity of transmissibilities, especially in transition between co-current and counter-current flows. Recently, Lee et al. (Adv. Wat. Res. 82, 27–38, 2015) proposed a hybrid upwinding method for the two-phase transport equation that comprises viscous and gravitational fluxes. The viscous part is a co-current flow with a one-point upwinding based on the total velocity and the buoyancy part is modeled by a counter-current flow with zero total velocity. The hybrid scheme yields C¹-continuous discretization for the transport equation and improves numerical convergence in the Newton nonlinear solver. Lee and Efendiev (Adv. Wat. Res. 96, 209–224, 2016) extended the hybrid upwind method to three-phase flow in the presence of gravity. In this paper, we present the hybrid-upwind formula in a generalized form that describes two- and three-phase flows with viscous, gravity, and capillary forces. In the derivation of the hybrid scheme for capillarity, we note that there is a strong similarity in mathematical formulation between gravity and capillarity. We thus greatly utilize the previous derivation of the hybrid upwind scheme for gravitational force in deriving that for capillary force. Furthermore, we also discuss some mathematical issues related to heterogeneous capillary domains and propose a simple discretization model by adapting multi-valued capillary pressures at the end points of capillary pressure curves. We demonstrate this new model always admits a consistent solution that is within the discretization error. This new generalized hybrid scheme yields a discretization method that improves numerical stability in reservoir simulation.     

SWAT hydrological model as a DaaS cloud service

Earth Science community depends on the exploration, analysis and reprocessing of high volumes of data as well as the modeling and simulation of complex coupled systems on multiple scales. The main aim of this article is to introduce a new hydrological modeling service based on the Soil and Water Assessment Tool (SWAT) (Arnold et al. J American Water Resour Assoc 34(1), 73–89, 1998 ; Arnold and Fohrer Hydrol Process 19(3), 563–572, 2005) model using high efficiency, resource sharing and low cost cloud computing resources (Astsatryan et al. International Journal of Scientific & Engineering Research 1(1), 1130–1133, 2014). Such a Desktop as a Service (DaaS) approach allowing users to work from anywhere, and gives centralized desktop management and great performance. Within the Spatial Data Infrastructure (SDI) and cloud platform, the DaaS service gives secure access to the model and a centralized data storage to get a SWAT model input. The article illustrates the analyses of the implementation of the SWAT model for the Sotk watershed of Lake Sevan in Armenia (Sargsyan 2007).     

Relations of Rock Structure and Composition to Petrophysical and Geomechanical Rock Properties: Examples from Permocarboniferous Red-Beds

Summary. This study relates textural properties to physical and mechanical properties of coarse grained sedimentary rocks of Permocarboniferous age. As an equivalent to rock texture the principle of geomechanical order is applied. The geomechanical order describes a rock as a function of its structural and compositional order which are derived from petrological analyses. Our results indicate that rock properties like density and porosity are stronger dependent on the structural order, while strength properties additionally depend on the compositional order. The ultrasonic wave velocity responds to both structural and compositional properties. These evidences imply that the geomechanical order is not an independent parameter but a variable function of structural or compositional features, which needs specification for correlation purposes to distinct physical and mechanical rock properties.     

Shock trains on a planar beach: quasi-analytical and fully numerical solutions

This study, part of the Special Issue dedicated to the 70th anniversary of Professor Efim Pelinovsky, focuses on a topic that has been central in Professor Pelinovsky’s research, i.e. the analytical and numerical modelling of shallow water waves. We specifically focus on the evolution of trains of shock waves on a planar beach. Antuono (J Fluid Mech 658:166–187, 2011) has, for the first time, proposed a quasi-analytical solution for a train of shock waves forced by a constant Riemann invariant. The present contribution clarifies the validity of such solution and its value for benchmarking nonlinear shallow water equation solvers. Hence, the same tests of Antuono (J Fluid Mech 658:166–187, 2011) have been run by means of the solver of Brocchini et al. (Coast Eng 43(2):105–129, 2001) revealing surprisingly and reassuring good agreements. This provides significant support to the mentioned analytical solution and allows to critically analyse the eventual discrepancies, due to the practicalities of running numerical shallow water solutions (e.g. influence of the boundary conditions, of the numerical resolution, etc.).     

Multiscale model reduction for shale gas transport in fractured media

In this paper, we develop a multiscale model reduction technique that describes shale gas transport in fractured media. Due to the pore-scale heterogeneities and processes, we use upscaled models to describe the matrix. We follow our previous work (Akkutlu et al. Transp. Porous Media 107(1), 235–260, 2015), where we derived an upscaled model in the form of generalized nonlinear diffusion model to describe the effects of kerogen. To model the interaction between the matrix and the fractures, we use Generalized Multiscale Finite Element Method (Efendiev et al. J. Comput. Phys. 251, 116–135, 2013, 2015). In this approach, the matrix and the fracture interaction is modeled via local multiscale basis functions. In Efendiev et al. (2015), we developed the GMsFEM and applied for linear flows with horizontal or vertical fracture orientations aligned with a Cartesian fine grid. The approach in Efendiev et al. (2015) does not allow handling arbitrary fracture distributions. In this paper, we (1) consider arbitrary fracture distributions on an unstructured grid; (2) develop GMsFEM for nonlinear flows; and (3) develop online basis function strategies to adaptively improve the convergence. The number of multiscale basis functions in each coarse region represents the degrees of freedom needed to achieve a certain error threshold. Our approach is adaptive in a sense that the multiscale basis functions can be added in the regions of interest. Numerical results for two-dimensional problem are presented to demonstrate the efficiency of proposed approach.     

Anchorage behaviour of reinforced specimens containing a single fissure under uniaxial loading: a particle mechanics approach

Particle flow code (PFC^2D) software was adopted to investigate the anchorage behaviour and the characteristics of crack initiation, propagation and coalescence of reinforced specimens containing a single fissure (RSCSF). The microscopic parameters of the specimens in the numerical simulation were first validated by experimental outcomes of intact specimens, while the microscopic parameters of the rock bolts were validated based on the results of the RSCSF tests. Then, the mechanical parameters as well as the failure modes in the physical experiments were compared with those derived by the numerical simulation; the results showed good agreement between the simulated macroscopic mechanical properties and failure modes and those obtained in the laboratory experiments. The peak strength, number of cracks and the failure mode varied considerably as the anchorage angle α and fissure angle β increased. Three types of stress–strain curves, types I to III, were obtained from the RSCSF. Shear cracks were observed for all three categories of curves, but the tensile cracks were dominant. The number of cracks and the rate of bond failures decreased as the curve changed from type II to type I to type III. RSCSF failure can be classified into three failure modes: (1) tip crack propagation mode, (2) midpoint crack propagation mode and (3) rock bolt crack propagation mode. These failure modes are primarily differentiated by relations between α and β, and the ratio UCS_S/UCS_I between the uniaxial compressive strength (UCS, σ _max) of the RSCSF (UCS_S) and the uniaxial compressive strength of the intact specimen (UCS_I).     

A particle mechanics approach for the dynamic strength model of the jointed rock mass considering the joint orientation

In nature, there exist several forms of anisotropy in rock masses due to the presence of bedding planes, joints, and weak layers. It is well understood that the anisotropic properties of jointed rock masses significantly affect the stability of surface and underground excavations. However, these critical anisotropic characteristics are often ignored in existing uniaxial dynamic failure criteria. This study investigates the effect of a pre-existing persistent joint on the rate-dependent mechanical behaviours of a rock mass using a particle mechanics approach, namely, bonded particle model (BPM), to realistically replicate the mechanical response of the rock mass. Firstly, in order to capture the rate-dependent response of the jointed rock mass, the BPM model is validated using published experimental data. Then, a dynamic strength model is proposed based on the Jaeger criterion and simulation results. To further investigate the dynamic behaviours, the dynamic uniaxial compressive strength (UCS) for anisotropic rock masses with various joint orientations is investigated by subjecting the BPM models to uniaxial compression numerical tests with various strain rate. The proposed dynamic strength model is validated based on numerical simulation results. Finally, the fragmentation characteristics of the jointed rock masses are analysed, which demonstrate that the failure mode affects the dynamic UCS. This is further confirmed by the analysis of the orientations of microscopic cracks generated by the compression loading.     

Estimation of uniaxial compressive strength of North Algeria sedimentary rocks using density,porosity, and Schmidt hardness

This study aims to establish new correlations to assess uniaxial compressive strength (UCS) of northern Algeria sedimentary rocks. This estimation is based on the measurements of density, porosity, and Schmidt hammer hardness. To achieve this goal, a geological and geotechnical characterization campaign was conducted on 19 types of sandstone and carbonate rocks which have been collected from different geological areas of the Maghrebides chain. Petrographic analyses were conducted to identify the geological characteristics of each kind of rock. Subsequently, physico-mechanical tests (i.e., density, porosity, hardness, and uniaxial compressive strength) were carried out for all the sampled rocks. The results were then used to develop correlations between UCS values and the other parameter values determined. Finally, the UCS predictive equations which have the best predictive powers (coefficient of determination R ² of 0.75 to 0.94) were discussed taking into account the geological specificities of the rocks, and then compared to similar studies developed by other authors in different areas of the world.     

Numerical Homogenization of the Rigidity Tensor in Hooke''s Law Using the Node-Based Finite Element Method

Combining a geological model with a geomechanical model, it generally turns out that the geomechanical model is built from units that are at least a 100 times larger in volume than the units of the geological model. To counter this mismatch in scales, the geological data model's heterogeneous fine-scale Young's moduli and Poisson's ratios have to be upscaled to one equivalent homogeneous coarse-scale rigidity. This coarse-scale rigidity relates the volume-averaged displacement, strain, stress, and energy to each other, in such a way that the equilibrium equation, Hooke's law, and the energy equation preserve their fine-scale form on the coarse scale. Under the simplifying assumption of spatial periodicity of the heterogeneous fine-scale rigidity, homogenization theory can be applied. However, even then the spatial variability is generally so complex that exact solutions cannot be found. Therefore, numerical approximation methods have to be applied. Here the node-based finite element method for the displacement as primary variable has been used. Three numerical examples showing the upper bound character of this finite element method are presented.     

An Empirical Correlation of Index Geomechanical Parameters with the Compressional Wave Velocity

The geomechanical strength of rockmass plays a key role in planning and design of mining and civil construction projects. Determination of geomechanical properties in the field as well as laboratory is time consuming, tedious and a costly affair. In this study, density, slake durability index, uniaxial compressive strength (UCS) and P-wave velocity tests were conducted on four igneous, six sedimentary and three metamorphic rock varieties. These properties are crucial and used extensively in geotechnical engineering to understand the stability of the structures. The main aim of this study is to determine the various mechanical properties of 13 different rock types in the laboratory and establish a possible and acceptable correlation with P-wave velocity which can be determined in the field as well as laboratory with ease and accuracy. Empirical equations were developed to calculate the density, slake durability index and UCS from P-wave velocities. Strong correlations among P-wave velocity with the physical properties of different rock were established. The relations mainly follow a linear trend. Student’s ‘t’ test and ‘F’ test were performed to ensure proper analysis and validation of the proposed correlations. These correlations can save time and reduce cost during design and planning process as they represent a reliable engineering tool.     

Garnet–orthopyroxene (GOPX) geothermometer: a comparative study

The garnet–orthopyroxene pairs are commonly found in the assemblages of basic granulites/charnockite and hence are suitable for estimating equilibrium temperature of these metamorphic rocks. At present, there are many calibrations of garnet–orthopyroxene thermometer that may confuse geologists in choosing a reliable thermometer. To test the accuracy of the garnet–orthopyroxene thermometers, we have applied 14 models formulated by a number of workers since 1980 to date. We have collated 51 samples from the literature all over the world, which has been processed through the “Gt-Opx.EXE” software. Based on the present study, we have identified a set of the best among all the 14 models which were considered under this comparative study. We have concluded that the five garnet–orthopyroxene (Gt-Opx) thermometers are the most valid and reliable of this kind of thermometer: Aranovich and Berman (Am Mineral 82:345–353, 1997), Raith et al. (Earth Sci 73:211–244, 1983), Harley (Contrib Mineral Petrol 86:359–373, 1984), Nimis and Grütter (Contrib Mineral Petrol 159:411–427, 2010), and Sen and Bhattacharya (Contrib Mineral Petrol 88:64–71, 1984).     

Rockfall trajectory modeling combined with heuristic analysis for assessing the rockfall hazard along the Maratea SS18 coastal road (Basilicata,Southern Italy)

In this paper, a study aimed to assess the rockfall hazard along a portion of the SS18 coastal road, located in the coastal area of Maratea (Basilicata Region, Southern Italy), is presented. The relevance of this study derives from the location of the study area, because the SS18 is a strategic roads in a touristic area, and, since the hazard assessment was performed in 2004 within a project financed by the Viability Regional Department of Autonomous National Company of Roads (ANAS), from the possibility to validate the results by using real rockfall events occurred after 2004. The procedure for assessing the rockfall hazard was composed of four sequential analyses: (i) geomechanical and kinematic characterization of rock mass, (ii) implementation of Romana’s (1985) Slope Mass Rating (SMR) method for identifying the potential boulder release areas (rockfall initiation areas), (iii) determination of rockfall trajectories by using a 3D numerical model (ROTOMAP), (iv) calculation and mapping of the hazard index by combining three factors, i.e., (a) lithological features of outcropping materials on rock faces, (b) kinematic compatibility defined by simulating the rockfall trajectories, and (c) spatial distribution of occurred rockfall events. Finally, the proposed methodology was validated by combining the distribution of the hazard levels along the road with the location on the SS18 of the rockfall events occurred from 2004 to 2014.     

The vulnerability of the European air traffic network to spatial hazards

The 2010 eruption of the Eyjafjallajökull volcano had a devastating effect on the European air traffic network, preventing air travel throughout most of Europe for 6 days (Oroian in ProEnvironment 3:5–8, 2010). The severity of the disruption was surprising as previous research suggests that this type of network should be tolerant to random hazard (Albert et al. in Nature 406(6794):378–382, 2000; Strogatz in Nature 410(6825):268–276, 2001). The source of this hazard tolerance lies in the degree distribution of the network which, for many real-world networks, has been shown to follow a power law (Albert et al. in Nature 401(6749):130–131, 1999; Albert et al. in Nature 406(6794):378–382, 2000). In this paper, we demonstrate that the ash cloud was unexpectedly disruptive because it was spatially coherent rather than uniformly random. We analyse the spatial dependence in air traffic networks and demonstrate how the combination of their geographical distribution and their network architectures jeopardises their inherent hazard tolerance.