Horizontal Correlation Length Research Articles

CO2 storage in saline aquifers: A simulation on quantifying the impact of permeability heterogeneity

As one promising technology to mitigate CO2 emission, CO2 capture utilization and storage (CCUS) plays a crucial role in achieving carbon neutrality. The deep saline aquifer is a prime candidate for CO2 geological storage. The subsurface flow and effectiveness of CO2 storage in deep saline aquifer are highly related to the permeability heterogeneity of formations, which needs in-depth study. To bridge the gap, this study focused on quantifying the impact of permeability heterogeneity on the CO2 flow patterns, the well injectivity and the storage efficiency, which aims to enhance the understanding of CO2 storage characteristics in deep saline aquifers. The heterogeneous saline aquifer model was built by using the Sequential Gaussian Simulation (SGSIM) method. A novel classification template was proposed with the CO2 flow patterns classified as “Dispersive”, “Sweeping”, “Fingering”, and “Channeling” for CO2 storage in deep saline aquifers according to the geostatistical parameters (including dimensionless correlation lengths, first and second spatial moment, and Dykstra-Parsons coefficient). For the well injectivity, the results showed that high injectivity occurred when both horizontal and vertical correlation lengths were high or at a favourable connectivity of permeability in the horizontal and vertical directions. In addition, CO2 storage efficiency is higher when both dimensionless horizontal and vertical correlation lengths are in the range of 0.1–0.2. This is because frequent changes between high and low permeability regions led to frequent mutual displacement of water and CO2, resulting in higher residual trapping and slow CO2 front. Therefore, the dimensionless correlation lengths and breakthrough time should be considered simultaneously to achieve safer trapping and maximize the CO2 storage capacity. The findings of this work provide insights into the subsurface flow of CO2 storage in deep saline aquifers with permeability heterogeneity.

Analysis of sensitive clay landslide mechanism and impact pipeline bearing characteristics considering spatial variability

Landslides caused by the progressive failure of sensitive clay slopes may cause substantial economic losses and environmental pollution to pipelines. This study utilizes the Karhunen-Loève (K-L) expansion method, the coupled Eulerian-Lagrangian (CEL) method, and the Monte Carlo method to model the large deformation behaviour of slopes with spatial variability. The proposed RCEL-MC framework for joint analysis of extensive deformation-probability statistics of landslide impact on pipelines confirms that the spatial variability clay slope instability failure mechanism, considering the soil softening effect under earthquake action, aligns more closely with real-world scenarios. Furthermore, based on the statistical failure probability of pipelines impacted by landslides, a sensitive clay slope pipeline safety design method is suggested. The research highlights that the random field parameters significantly influence the load-bearing characteristics of pipelines affected by spatially variable slope progressive failure landslides. The uncertainty surrounding the maximum impact force on pipelines notably increases with the rise of the horizontal correlation length and variability coefficient. When accounting for spatial variability, the maximum impact force on landslide pipelines surpasses the deterministic model analysis results by 28-69 %. It is emphasized that the deterministic model analysis, which neglects the spatial variability of soil and the soil softening effect, may seriously underestimate landslide risk. Based on the criteria for pipeline buckling failure and yield failure, it is advised that the safe design parameters for pipelines in practical projects should fall within the intersection of the secure regions defined by the two failure criteria.

Reliability and landslide consequence analysis of long heterogeneous soil infrastructure slopes: A parallel computing investigation

Long infrastructures, like flood defense levees, built upon diverse soils, often face complex landslide failures. Risk assessments for such structures involve evaluating slope stability reliability and potential landslide consequences. Historically, embankment slope reliability and failure assessments focused on shorter sections due to computational limitations. This study, however, delves into a longer 3D soil slope section, 100 times the height, using the random finite element method to analyse the size or length effect. It conducts a parametric study varying the soil strength’s horizontal correlation length to understand slope failure initiation in heterogeneous soils. In contrast to prior work, this paper emphasises several facets: the realised factor of safety (FOS) distribution, quantification of discrete unstable zones and failures, and the size impact on the reliability and landslide consequences of long embankment slopes. Findings indicate the Weibull distribution better fits the realised FOS, aiding in predicting long embankment slope system reliability when combined with the weakest link theory. While multiple failures are possible for very long soil embankment slopes, observations suggest a greater likelihood of a single localised failure despite this potential.

Surrogate model for geological CO[formula omitted] storage and its use in hierarchical MCMC history matching

Deep-learning-based surrogate models show great promise for use in geological carbon storage operations. In this work we target an important application — the history matching of storage systems characterized by a high degree of (prior) geological uncertainty. Toward this goal, we extend the recently introduced recurrent R-U-Net surrogate model to treat geomodel realizations drawn from a wide range of geological scenarios. These scenarios are defined by a set of metaparameters, which include the horizontal correlation length, mean and standard deviation of log-permeability, permeability anisotropy ratio, and constants in the porosity-permeability relationship. An infinite number of realizations can be generated for each set of metaparameters, so the range of prior uncertainty is large. The surrogate model is trained with flow simulation results, generated using the open-source simulator GEOS, for 2000 random realizations. The flow problems involve four wells, each injecting 1 Mt CO2/year, for 30 years. The trained surrogate model is shown to provide accurate predictions for new realizations over the full range of geological scenarios, with median relative error of 1.3% in pressure and 4.5% in saturation. The surrogate model is incorporated into a hierarchical Markov chain Monte Carlo history matching workflow, where the goal is to generate history matched geomodel realizations and posterior estimates of the metaparameters. We show that, using observed data from monitoring wells in synthetic ‘true’ models, geological uncertainty is reduced substantially. This leads to posterior 3D pressure and saturation fields that display much closer agreement with the true-model responses than do prior predictions.

Assessing the potential of composite confining systems for secure and long-term CO2 retention in geosequestration

A potential geologic target for CO2 storage should ensure secure containment of injected CO2. Traditionally, this objective has been achieved by targeting reservoirs with overlying seals-regionally extensive, low permeability units that have been proven capable of retaining buoyant fluid accumulations over geologic time. However, considering that the amount of CO2 is limited by a decadal injection period, vertical migration of CO2 can be effectively halted by a composite system of discontinuous shale/silt/mudstone barriers in bedded sedimentary rocks. Here, we studied the impact of depositional architectures in a composite confining system on CO2 migration and confinement at reservoir scale. We stochastically generated lithologically heterogeneous reservoir models containing discontinuous barriers consistent with statistical distributions of net-sand-to-gross-shale ratio (NTG) and horizontal correlation lengths derived from well log data and observations of producing hydrocarbon fields in Southern Louisiana. We then performed an extensive suite of reservoir simulations of CO2 injection and post-injection to evaluate the sensitivity of CO2 plume migration and pressure response of the composite system to a series of geologic and fluid parameters including the lateral continuity of barriers, NTG, permeability anisotropy within the sand body, and capillary pressure contrast between the sand and shale facies. The results indicate that lateral continuity of barriers and NTG are the dominant controls on CO2 plume geometry and pressure build-up in the reservoir, while the impact of NTG is particularly pronounced. The significance of intraformational barriers becomes apparent as they facilitate the local capillary trapping of CO2. Those barriers improve the pore space occupancy by promoting a more dispersed shape of the plume and ultimately retard the buoyancy-driven upward migration of the plume post injection.

Numerical investigations of influence on thermal conductive heating in DNAPL-impacted soils by heterogeneity

The treatment of dense non-aqueous phase liquid (DNAPL) source zones is challenging, particularly in heterogeneous media. Thermal conductive heating (TCH) has the potential to treat DNAPL source zones for its ability to enhance mass transfer. This study uses numerical modeling combined with Monte Carlo simulation to examine the influence of heterogeneity of the permeability field on the DNAPL distribution and TCH remediation. It is found that the longer horizontal correlation length of high-permeable clay lens would contribute to accelerate multiphase convection and then heat conduction in horizontal direction. The presence of DNAPL (both in NAPL phase and dissolved), pressure, and permeability are all contributory factors to phase change. Realizations with shorter horizontal correlation lengths always have a larger vertical spreading of DNAPL. As a shallow vapor extraction well was applied in this study, higher TCE removal rate can be obtained in the realizations with a shorter horizontal correlation length when NAPL phase of TCE is existed in the domain.

Numerical modeling of double-ring infiltrometers for determining saturated hydraulic conductivity in heterogeneous and anisotropic soils

Philip’s two-term infiltration equation has been widely used to infer soil saturated hydraulic conductivity (Ks), the accuracy of which is usually influenced by the size of infiltration rings and soil conditions. Previous studies have primarily focused on exploring the ring-size dependence of Ks estimations under specific soil conditions (e.g., soil isotropy and/or uniform initial water content). This study aims to provide a comprehensive analysis by systematically considering eight heterogeneous and anisotropic soils with non-uniform initial water contents. Specifically, we first examined the validity of Philip’s equation as well as the recently proposed two forms (i.e., infiltration- and time-form) of Parlange’s infiltration equations both theoretically and in practical applications of double-ring infiltration. Then the time form of Parlange’s infiltration equation was applied to infer Ks using double-ring infiltrometer measurements with different combinations of six inner ring diameters (di = 10, 20, 40, 80, 120, and 200 cm) and three buffer indices (i.e., defined as the ratio of the difference between inner and outer ring diameters to the outer ring diameter, here b = 0.2, 0.33, and 0.5). For each infiltrometer set, 20 stochastic Ks fields were randomly generated by adopting five standard deviation values (i.e., σlnKs = 0.1, 0.3, 0.5, 0.7, and 0.9). Furthermore, we investigated the influence of the horizontal correlation length (i.e., λx = 30, 60, 150, 300, and 600 cm) on Ks estimations. The results demonstrate that Parlange’s equation, compared to Philip’s equation, is more universal in describing the cumulative infiltration relationship for the test soils; the optimal combination of inner ring diameter and buffer index was 40 cm and 0.2, respectively, which satisfied most of the practical requirements for determining Ks in the Soil Water Infiltration Global (SWIG) database; when the horizontal correlation length exceeds a threshold (i.e., 150 cm in our study), the inner ring diameter is required to increase to 80 cm. Our findings contribute to accurate Ks estimations of different soils using double-ring infiltrometers.

Polar firn properties in Greenland and Antarctica and related effects on microwave brightness temperatures

Abstract. In studying the mass balance of polar ice sheets, fluctuations in firn density near the surface is a major uncertainty. In this paper, we explore these variations at locations on the Greenland Ice Sheet and at the Dome C location in Antarctica. Borehole in situ measurements, snow radar echoes, microwave brightness temperatures, and modeling results from the Community Firn Model (CFM) are used. It is shown that firn density profiles can be represented using three processes: “long-scale” and “short-scale” density variations and “refrozen layers”. Consistency with this description is observed in the dynamic range of airborne 0.5–2 GHz brightness temperatures and snow radar echo peaks in measurements performed in Greenland in 2017. Based on these insights, a new analytical partially coherent model is implemented to explain the microwave brightness temperatures using the three-scale description of the firn. Short- and long-scale firn processes are modeled as a 3D continuous random medium with finite vertical and horizontal correlation lengths as opposed to past 1D randomly layered medium descriptions. Refrozen layers are described as deterministic sheets with planar interfaces, with the number of refrozen-layer interfaces determined by radar observations. Firn density and correlation length parameters used in forward modeling to match measured 0.5–2 GHz brightness temperatures in Greenland show consistency with similar parameters in CFM predictions. Model predictions also are in good agreement with multi-angle 1.4 GHz vertically and horizontally polarized brightness temperature measured by the Soil Moisture and Ocean Salinity (SMOS) satellite at Dome C, Antarctica. This work shows that co-located active and passive microwave measurements can be used to infer polar firn properties that can be compared with predictions of the CFM. In particular, 0.5–2 GHz brightness temperature measurements are shown to be sensitive to long-scale firn density fluctuations with density standard deviations in the range of 0.01–0.06 g cm−3 and vertical correlation lengths of 6–20 cm.

Estimating hydraulic conductivity correlation lengths of an aquitard by inverse geostatistical modelling of a pumping test

Aquitards are common hydrogeological features in the subsurface. Typically, pumping tests are used to parameterize the hydraulic conductivity of heterogeneous aquitards. However, they do not take spatial variability and uncertainty into account. Alternatively, core-scale measurements of hydraulic conductivity are used in geostatistical upscaling methods, for which their correlation lengths are needed, but this information is extremely difficult to obtain. This study investigates whether a pumping test can be used to obtain the correlation lengths needed for geostatistical upscaling and account for the uncertainty about heterogeneous aquitard conductivity. Random realizations are generated from core-scale data with varying correlation lengths and inserted into a groundwater flow model which simulates the outcome of an actual pumping test. The realizations yielded a better fit to the pumping test data than the traditional pumping test result, assuming homogeneous layers are selected. Ranges of horizontal and vertical correlation lengths that fit the pumping-test well are found. However, considerable uncertainty regarding the correlation lengths remains, which should be considered when parameterizing a regional groundwater flow model.

Evaluating Latent-Heat-Nudging Schemes and Radar forward Operator Settings for a Convective Summer Period over Germany Using the ICON-KENDA System

Radar data assimilation has been operational at the Deutscher Wetterdienst for several years and is essential for generating accurate precipitation forecasts. The current work attempts to further enhance the radar data assimilation by improving the latent heat nudging (LHN) scheme and by reducing the observation error (OE) caused by the representation error of the efficient modular volume radar operator (EMVORADO). First of all, a series of hindcasts for a one-month convective period over Germany are performed. Compared with radar reflectivity and satellite observations, it is found that the LHN scheme that implicitly adjusts temperature performs better, and the beam broadening effect and the choice of the scattering schemes in EMVORADO are important. Moreover, the Mie scheme with the new parameterization to reduce the brightband effect not only proves to be the best in hindcasts but also that it results in the smallest standard deviations and the shortest horizontal correlation length scales of the OE in data assimilation experiments.

Study on Sensitivity of Observation Error Statistics of Doppler Radars to the Radar forward Operator in Convective-Scale Data Assimilation

In the present work, we investigate the impacts on the observation error (OE) statistics due to different types of errors in the forward operator (FE) for both radar reflectivity and radial wind data, in the context of convective-scale data assimilation in the summertime. A series of sensitivity experiments were conducted with the Efficient Modular VOlume RADar Operator (EMVORADO), using the operational data assimilation system of the Deutscher Wetterdienst (DWD, German Weather Service). The investigated FEs are versatile, including errors caused by neglecting the terminal fall speed of hydrometeor, the reflectivity weighting, and the beam broadening and attenuation effects, as well as errors caused by different scattering schemes and formulations for melting particles. For reflectivity, it is found that accounting for the beam broadening effect evidently reduces the standard deviations, especially at higher altitudes. However, it does not shorten the horizontal or along-beam correlation length scales. In comparison between the Rayleigh and the Mie schemes (with specific configurations), the former one results in much smaller standard deviations for heights up to 4 km, and aloft, slightly larger standard deviations. Imposing the attenuation to the Mie scheme slightly reduces the standard deviations at lower altitudes; however, it largely increases the standard deviations at higher altitudes and it also leads to longer correlation length scales. For radial wind, positive impacts of considering the beam broadening effect on standard deviations and neutral impacts on correlations are observed. For both reflectivity and radial wind, taking the terminal fall speed of hydrometeor and the reflectivity weighting into account does not make remarkable differences in the estimated OE statistics.

Numerical investigation of the influences of geological controlling factors on heat extraction from hydrothermal reservoirs by CO2 recycling

Injection of CO2 into deep hydrothermal reservoirs is considered as an attractive way for heat extraction, which has been proved in the previous studies. However, how different geological factors govern the heat extraction efficiency by CO2 circulation are not clearly understood. In this study, the mechanisms of geological factors in controlling the heat mining process by CO2 injection are numerically explored. The effects of horizontal correlation length, degree of permeability heterogeneity, permeability anisotropy, and the magnitude of mean permeability on the heat extraction performance are systematically investigated. The simulation results show that heat extraction using CO2 as working fluid can obtain a high heat mining rate, but the CO2 plume in the subsurface exhibits severe segregation effect. Heat extraction by CO2 recycling is more sensitive to the variation of horizontal correlation length in comparison with that by water circulation. The increase of horizontal correlation length and mean permeability can effectively promote the heat mining rate. The increase of permeability heterogeneity and anisotropy can cause a reversed trend of heat mining rate variation. The findings from this study may provide important implications for the selection of feasible hydrothermal reservoirs or deep high water cut oil reservoirs for heat extraction by CO2 recycling.

Impact of Assimilating High‐Resolution Atmospheric Motion Vectors on Convective Scale Short‐Term Forecasts: 1. Observing System Simulation Experiment (OSSE)

AbstractThis research investigates to what extent the high‐spatiotemporal‐resolution Atmospheric Motion Vector (AMV) product derived from the new‐generation Geostationary Operational Environmental Satellites‐Series R can benefit convective‐scale data assimilation (DA) and forecasts of potential high impact weather events. In the first part of this two‐part study, the impact of AMV DA on convective‐scale numerical weather prediction (NWP) is evaluated with an idealized supercell storm. The simulated AMV observations are synthesized from the idealized supercell storm generated by the Weather Research and Forecasting model and then the data are assimilated with a three‐dimensional variational analysis and forecast system. A baseline DA experiment demonstrates that the wind errors within and around the storms are remarkably reduced by assimilating the AMV data, consequently enhancing the storm top‐level divergence and low‐level convergence signatures associated with two strong splitting supercells. Three sets of sensitivity experiments are then performed to test the impact of observation resolution, DA cycling frequency and horizontal correlation length scale respectively. Generally, assimilating higher‐spatial‐resolution AMVs at higher cycling frequency is able to produce reasonable divergence analysis as well as the subsequent 90 min forecasts. However, too frequent DA cycling tends to produce a warm bias and overestimate nonprecipitating hydrometeor and storm‐relative helicity features, resulting in more spurious cells in the short‐term forecasts. It is also found that the correlation length scale of 20 km produces the best results when assimilating the AMV data.

Field simulation of settlement analysis for shallow foundation using cone penetration data

This paper deals with the settlement analysis of a vertically loaded strip footing by the use of two-dimensional random field finite element method. Total settlement and rotation of the footing have been calculated by elasto-plastic solution in finite element model. Deformation modulus of soil Ed was assigned conforming to 2D Gaussian random field using Karhunen–Loéve series expansion. Spatial variability of Ed was represented by the horizontal and vertical correlation lengths (θvE and θhE). CPTu database from Adapazari, Turkey has been employed to estimate the correlation lengths. Soil profile was modelled with 4 layers in accordance with random field from in-situ test results, and correlation lengths were assigned to each different layer. Random field realizations were produced by MATLAB code, and probability density functions (PDF) of maximum total settlement and rotation of the footing were constructed using Monte Carlo Simulations by iterative solutions of each realization with finite element analysis. Probabilities of failure (Pf) by settlement and rotation were calculated from PDFs. Initially, the analysis was carried out using average values of each horizontal and vertical correlation lengths that were assigned to every soil layer. Subsequently, analyses were iterated with maximum and minimum values of the correlation lengths in order that both the effect of horizontal and vertical spatial variability can be considered. 1000 calculations were performed for the 5 analysis models, with 200 random field realizations for each model. The effect of varying θvE and θhE on total settlement and rotation of the footing has also been investigated.

How to Find Aquifer Statistics Utilizing Pumping Tests? Two Field Studies Using welltestpy.

We present a workflow to estimate geostatistical aquifer parameters from pumping test data using the Python package welltestpy. The procedure of pumping test analysis is exemplified for two data sets from the Horkheimer Insel site and from the Lauswiesen site, Germany. The analysis is based on a semi-analytical drawdown solution from the upscaling approach Radial Coarse Graining, which enables to infer log-transmissivity variance and horizontal correlation length, beside mean transmissivity, and storativity, from pumping test data. We estimate these parameters of aquifer heterogeneity from type-curve analysis and determine their sensitivity. This procedure, implemented in welltestpy, is a template for analyzing any pumping test. It goes beyond the possibilities of standard methods, for example, based on Theis' equation, which are limited to mean transmissivity and storativity. A sensitivity study showed the impact of observation well positions on the parameter estimation quality. The insights of this study help to optimize future test setups for geostatistical aquifer analysis and provides guidance for investigating pumping tests with regard to aquifer statistics using the open-source software package welltestpy.

Transformations of spatial correlation lengths in random fields

The paper describes the theoretical relationship between spatial correlation lengths in lognormal and hyperbolic tangent (“tanh”) random fields, and the underlying Gaussian random fields from which they are derived following transformation. The inevitable change in the spatial correlation length following transformation has been noted in several studies, but has not, to the authors’ knowledge, been rigorously investigated before. The paper presents derivations that show the dependencies for normal/log-normal and normal/tanh transformations together with three different correlation functions. The one-dimensional derivations are extrapolated to two- and three-dimensional models, with particular emphasis on vertical and horizontal correlation lengths. The paper concludes with an example probabilistic bearing capacity analysis using the Random Finite Element Method (RFEM). For the example considered, the untransformed solutions were slightly unconservative, but the differences were generally quite modest.

Assimilation of Radial Velocity from Coastal NEXRAD into HWRF for Improved Forecasts of Landfalling Hurricanes

AbstractThe benefits of assimilating Next Generation Weather Radar (NEXRAD) radial velocity data for convective systems have been demonstrated in previous studies. However, impacts of assimilation of such high spatial and temporal resolution observations on hurricane forecasts have not been demonstrated with the National Centers for Environmental Prediction (NCEP) Hurricane Weather and Research Forecasting (HWRF) system. This study investigates impacts of NEXRAD radial velocity data on forecasts of the evolution of landfalling hurricanes with different configurations of data assimilation. The sensitivity of data assimilation results to influencing parameters within the data assimilation system, such as the maximum range of the radar data, superobservations, horizontal and vertical localization correlation length scale, and weight of background error covariances, are examined. Two hurricane cases, Florence and Michael, which occurred in the summer of 2018 are chosen to conduct a series of experiments. Results show that hurricane intensity, asymmetric structure of inland wind and precipitation, and quantitative precipitation forecasting are improved. Suggestions for implementation of operational configurations are provided.

Simultaneous Retrieval of Surface Roughness Parameters for Bare Soils From Combined Active–Passive Microwave SMAP Observations

An active–passive microwave retrieval algorithm for simultaneous determination of soil surface roughness parameters [vertical root-mean-square (RMS) height ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${s}$ </tex-math></inline-formula> ) and horizontal correlation length ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${l}$ </tex-math></inline-formula> )] is presented for bare soils. The algorithm is based on active–passive microwave covariation, including the improved Integral Equation Method (I <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> EM), and is tested with global soil moisture active passive (SMAP) observations. The estimated retrieval results for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${s}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${l}$ </tex-math></inline-formula> are overall consistent with values in the literature, indicating the validity of the proposed algorithm. Sensitivity analyses showed that the developed roughness retrieval algorithm is independent of permittivity for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\varepsilon }_{s} &gt; 10$ </tex-math></inline-formula> [-]. Furthermore, the physical model basis of this approach (I <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> EM) allows the application of different autocorrelation functions (ACF), such as Gaussian and exponential ACFs. Global roughness retrieval results confirm bare areas in deserts such as Sahara or Gobi. However, the type of ACF used within roughness parameter estimation is important. Retrieval results for the Gaussian ACF describe a rougher surface than retrieval results for the exponential ACF. No correlations were found between roughness results and the amount of precipitation or the soil texture, which could be due to the coarse spatial resolution of the SMAP data. The extension of this approach to vegetated soils is planned as an add-on study.

Investigation of impact of submarine landslide on pipelines with large deformation analysis considering spatially varied soil

In-situ soil properties exhibit natural spatial variability. In this study, the Karhunen-Loève (K-L) expansion method and the Coupled Eulerian-Lagrangian (CEL) method are integrated to simulate large deformation behavior of slopes with spatially varied shear strengths. The impact on pipelines induced by spatially varied landslides is investigated. The mean value of the maximum impact force is significantly larger than the deterministic value obtained for a homogeneous slope. The proportion of the maximum impact force from stochastic analysis that exceeds the deterministic value is much greater than 50%. This result shows that the deterministic study can significantly underestimate the damage of pipeline by a landslide if the spatial variability is not considered. The uncertainty of the impact force increases with the coefficient of variation (COV) of the undrained shear strength and decreases with the reduction of horizontal correlation length. By considering buckling failure and plastic yielding failure of pipelines, the failure probabilities are assessed and a pipeline design based on stochastic analysis for spatially varied slope is presented.

Numerical Study of Density-Driven Convection in Laminated Heterogeneous Porous Media

ABSTRACTIn the present study, we use direct numerical simulation to investigate the density-driven convection in a two-dimensional anisotropic heterogeneous porous media associated with significant laminated formation. At first, the heterogeneous porous media are randomly generated to represent laminated structure, in which the horizontal correlation length of permeability field is much longer than the vertical counterpart. Then, a highly accurate pseudo-spectral method and compact finite difference scheme with higher order of accuracy are employed to numerically reproduce the convection flow in the laminated porous media. The results show that the laminated structures restrict interactions among the downward plumes of heavier fluid. The plumes tend to descend more straightly in a laminated porous medium associated with a slower growth rate. As a result, the laminated distribution of permeability is considered having an inhibiting effect on the convection flow.