The inclusive and simplified forms of Bayesian interpolation for general and monotonic models using Gaussian and Generalized Beta distributions with application to Monte Carlo simulations

A recently developed Bayesian interpolation method (BI) and its application to safety assessment of a flood defense structure are described in this paper. We use a one-dimensional Bayesian Monte Carlo method (BMC) that has been proposed in (Rajabalinejad 2009) to develop a weighted logical dependence between neighboring points. The concept of global uncertainty is adequately explained and different uncertainty association models (UAMs) are presented for linking the local and global uncertainty. Based on the global uncertainty, a simplified approach is introduced. By applying the global uncertainty, we apply the Guassian error estimation to general models and the Generalized Beta (GB) distribution to monotonic models. Our main objective in this research is to simplify the newly developed BMC method and demonstrate that it can dramatically improve the simulation efficiency by using prior information from outcomes of the preceding simulations. We provide theory and numerical algorithms for the BI method geared to multi-dimensional problems, integrate it with a probabilistic finite element model, and apply the coupled models to the reliability assessment of a flood defense for the 17th Street Flood Wall system in New Orleans.     

Determination of failure probabilities of flood defence systems with improved dynamic bounds method

In this paper, we describe the computational framework of a novel method for solving the challenging problem of probabilistic finite elements. The method is called Improved Dynamic Bounds (IDB) and was developed recently to improve the efficiency of the dynamic bounds. The IDB is used in finite element numerical models to calculate time-dependent failure analyses of structures. In applications, the IDB can speed up the overall simulation process by several orders of magnitude. In applications controlled by two influential variables (e.g, two-dimensional problem), the computational efficiency is improved by a factor of 769 according to Rajabalinejad (2009). Applications of IDB indicate the method is most efficient for problems where the number of influential variables are limited. This is often the case for geotechnical and coastal flood defence systems. The IDB method is applied in this paper to the 17th Street Flood Wall, a component of the flood defence system (levee infra-structure) that failed during the Hurricane Katrina, to calculate the failure probability of an I-wall.     

A new probabilistic seismic hazard study of Spain

In this paper, we present a probabilistic seismic hazard analysis (PSHA) for mainland Spain that takes into account recent new results in seismicity, seismic zoning, and strong ground attenuation not considered in the latest PSHA of the Spanish Building Code. Those new input data have been obtained as a three-step project carried out in order to improve the existing hazard map for mainland Spain. We have produced a new earthquake catalogue for the area, in which the earthquakes are given in moment magnitude through specific deduced relationships for our territory based on intensity data (Mezcua et al. in Seismol Res Lett 75:75–81, 2004). In addition, we included a new seismogenetic zoning based on the recent partial zoning studies performed by different authors. Finally, as we have developed a new strong ground motion model for the area García Blanco (2009), it was considered in the hazard calculation together with other attenuations gathered from different authors using data compatible with our region. With this new data, a logic tree process is defined to quantify the epistemic uncertainty related to those parts of the process. A sensitivity test has been included in order to analyze the different models of ground motion and seismotectonic zonation used in this work. Finally, after applying a weighting scheme, a mean hazard map for PGA, based on rock type condition for 10% exceedance probability in 50 years, is presented, including 15th and 85th percentile hazard maps. The main differences with the present official building code hazard map are analyzed.     

Towards realistic simulations of lava dome growth using the level set method

The level set method has been implemented in a computational volcanology context. New techniques are presented to solve the advection equation and the reinitialisation equation. These techniques are based upon an algorithm developed in the finite difference context, but are modified to take advantage of the robustness of the finite element method. The resulting algorithm is tested on a well documented Rayleigh–Taylor instability benchmark [19], and on an axisymmetric problem where the analytical solution is known. Finally, the algorithm is applied to a basic study of lava dome growth.     

Using global node-based velocity in random walk particle tracking in variably saturated porous media: application to contaminant leaching from road constructions

Precise and efficient numerical simulation of transport processes in subsurface systems is a prerequisite for many site investigation or remediation studies. Random walk particle tracking (RWPT) methods have been introduced in the past to overcome numerical difficulties when simulating propagation processes in porous media such as advection-dominated mass transport. Crucial for the precision of RWPT methods is the accuracy of the numerically calculated ground water velocity field. In this paper, a global node-based method for velocity calculation is used, which was originally proposed by Yeh (Water Resour Res 7:1216–1225, 1981). This method is improved in three ways: (1) extension to unstructured grids, (2) significant enhancement of computational efficiency, and (3) extension to saturated (groundwater) as well as unsaturated systems (soil water). The novel RWPT method is tested with numerical benchmark examples from the literature and used in two field scale applications of contaminant transport in saturated and unsaturated ground water. To evaluate advective transport of the model, the accuracy of the velocity field is demonstrated by comparing several published results of particle pathlines or streamlines. Given the chosen test problem, the global node-based velocity estimation is found to be as accurate as the CK method (Cordes and Kinzelbach in Water Resour Res 28(11):2903–2911, 1992) but less accurate than the mixed or mixed-hybrid finite element methods for flow in highly heterogeneous media. To evaluate advective–diffusive transport, a transport problem studied by Hassan and Mohamed (J Hydrol 275(3–4):242–260, 2003) is investigated here and evaluated using different numbers of particles. The results indicate that the number of particles required for the given problem is decreased using the proposed method by about two orders of magnitude without losing accuracy of the concentration contours as compared to the published numbers.     

Application of the dynamic bounds method in the safety assessment of flood defences,a case study: 17th Street flood wall,New Orleans

In this paper we provide a computational framework for evaluation of reliability and safety assessment of infrastructures. It is based on the combined application of the dynamic bounds (DB) method and a probabilistic finite element model (FEM). The DB improves the computational efficiency of the FEM when calculating time-dependent failure analyses of coastal and offshore structures, and can speed up the simulation process by several orders of magnitude.

Our approach is demonstrated here for an example problem, and shown to be the most efficient method in applications with a limited number of influential variables, which is true for geotechnical and coastal flood defence systems. It is applied to the 17th Street flood wall, a failing component of the flood defence system in New Orleans during Hurricane Katrina. The variation in soil parameters is a critical input in the reliability estimation of this structure, and the calculated probability of failure depends on these assumed values.     

Enhanced velocity mixed finite element methods for modeling coupled flow and transport on non-matching multiblock grids

The enhanced velocity mixed finite element method, due to Wheeler et al. (Comput Geosci 6(3–4):315–332, 2002), is analyzed and extended to the problem of modeling slightly compressible flow coupled to the transport of chemical species through porous media, on non-matching multiblock grids. Applications include modeling bio-remediation of heavy oil spills and many other subsurface hazardous wastes, angiogenesis in transition of tumors from dormant to malignant states, transport of contaminants in ground water flow, and acid injection from well bores to increase permeability of surrounding rock. The analysis and numerical examples presented here demonstrate convergence and computational efficiency of this method.     

An integrative approach to robust design and probabilistic risk assessment for CO<Subscript>2</Subscript> storage in geological formations

CO₂ storage in geological formations is currently being discussed intensively as a technology with a high potential for mitigating CO₂ emissions. However, any large-scale application requires a thorough analysis of the potential risks. Current numerical simulation models are too expensive for probabilistic risk analysis or stochastic approaches based on a brute-force approach of repeated simulation. Even single deterministic simulations may require parallel high-performance computing. The multiphase flow processes involved are too non-linear for quasi-linear error propagation and other simplified stochastic tools. As an alternative approach, we propose a massive stochastic model reduction based on the probabilistic collocation method. The model response is projected onto a higher-order orthogonal basis of polynomials to approximate dependence on uncertain parameters (porosity, permeability, etc.) and design parameters (injection rate, depth, etc.). This allows for a non-linear propagation of model uncertainty affecting the predicted risk, ensures fast computation, and provides a powerful tool for combining design variables and uncertain variables into one approach based on an integrative response surface. Thus, the design task of finding optimal injection regimes explicitly includes uncertainty, which leads to robust designs with a minimum failure probability. We validate our proposed stochastic approach by Monte Carlo simulation using a common 3D benchmark problem (Class et al., Comput Geosci 13:451–467, 2009). A reasonable compromise between computational efforts and precision was reached already with second-order polynomials. In our case study, the proposed approach yields a significant computational speed-up by a factor of 100 compared with the Monte Carlo evaluation. We demonstrate that, due to the non-linearity of the flow and transport processes during CO₂ injection, including uncertainty in the analysis leads to a systematic and significant shift of the predicted leakage rates toward higher values compared with deterministic simulations, affecting both risk estimates and the design of injection scenarios.     

The Analysis of Three Dimensional FEM for Interaction of the Gravity-arch Dam and Complex Ground at Geheyan,Qingjiang River

This paper introduces the analysis of three dimensional finite element method for the gravity-arch dam building on the complex ground. The foundation rock of dip and strain-slip, three faults, two weak intercalations and etc. arc considered in this calculation model. Water static pressure, gravity of dam, uplift, temperature stress and so on are computed, including three dimensional osmotic and temperature fields in the foundation. The range of calculation model is about 1400×900×600m2 . There are 1845 elements of all kinds, 3280 nodes in the network of finite element. The superlax iterative method is used to solve, and three dimensional perspective and software of after treatment are applied in analyses. The dimension of this computation is large, various results of treating complex problems are reasonable. The important basis has applied to designing unit. The computation is important practical significance for Geheyan Dam which is being built.     

清江隔河岩重力拱坝坝体与复杂地基相互作用的三维有限元分析

本文介绍了建在复杂地基上的清江隔河岩重力拱坝的三维有限元分析。计算模型考虑了坝基岩体岩层的倾斜错位,三条大断层与二个沿层面方向的软弱夹层等复杂的地质因素。计算了静水压力、坝自重、扬压力及温度应力等荷载,其中包括地基三维渗流场和温度变化场的计算。坝体结构复杂且呈左右不对称状。计算模型所涉范围约 1400X900X600m~3。有限元网格包括各类单元1845个,节点总数达3280个。采用超松弛迭代法求解。分析中应用了三线透视图象和后处理软件系统。此项计算规模巨大、处理问题复杂的三维有限元的各项计算分析结果均为合理。为设计单位提供了重要依据,对于正在建设中的隔河岩大坝具有重要的实用意义。     

Oxygen isotope heterogeneity of the mantle beneath the Canary Islands: a discussion of the paper of Gurenko et al.

Gurenko et al. (Contrib Mineral Petrol 162:349–363, 2011) report laser-assisted fluorination (LF) and secondary ionization mass spectrometry (SIMS) ¹⁸O/¹⁶O datasets for olivine grains from the Canary Islands of Gran Canaria, Tenerife, La Gomera, La Palma and El Hierro. As with prior studies of oxygen isotopes in Canary Island lavas (e.g. Thirlwall et al. Chem Geol 135:233–262, 1997; Day et al. Geology 37:555–558, 2009, Geochim Cosmochim Acta 74:6565–6589, 2010), these authors find variations in δ¹⁸O_ol (~4.6–6.0 ‰) beyond that measured for mantle peridotite olivine (Mattey et al. Earth Planet Sci Lett 128:231–241, 1994) and interpret this variation to reflect contributions from pyroxenite-peridotite mantle sources. Furthermore, Gurenko et al. (Contrib Mineral Petrol 162:349–363, 2011) speculate that δ¹⁸O_ol values for La Palma olivine grains measured by LF (Day et al. Geology 37:555–558, 2009, Geochim Cosmochim Acta 74:6565–6589, 2010) may be biased to low values due to the presence of altered silicate, possibly serpentine. The range in δ¹⁸O_ol values for Canary Island lavas are of importance for constraining their origin. Gurenko et al. (Contrib Mineral Petrol 162:349–363, 2011) took a subset (39 SIMS analyses from 13 grains from a single El Hierro lava; EH4) of a more extensive dataset (321 SIMS analyses from 110 grains from 16 Canary Island lavas) to suggest that δ¹⁸O_ol is weakly correlated (R ² = 0.291) with the parameter used by Gurenko et al. (Earth Planet Sci Lett 277:514–524, 2009) to describe the estimated weight fraction of pyroxenite-derived melt (Xpx). With this relationship, end-member δ¹⁸O values for HIMU-peridotite (δ¹⁸O = 5.3 ± 0.3 ‰) and depleted pyroxenite (δ¹⁸O = 5.9 ± 0.3 ‰) were defined. Although the model proposed by Gurenko et al. (Contrib Mineral Petrol 162:349–363, 2011) implicates similar pyroxenite-peridotite mantle sources to those proposed by Day et al. (Geology 37:555–558, 2009, Geochim Cosmochim Acta 74:6565–6589, 2010) and Day and Hilton (Earth Planet Sci Lett 305:226–234, 2011), there are significant differences in the predicted δ¹⁸O values of end member components in the two models. In particular, Day et al. (Geochim Cosmochim Acta 74:6565–6589, 2010) proposed a mantle source for La Palma lavas with low-δ¹⁸O (<5 ‰), rather than higher-δ¹⁸O (c.f. the HIMU-peridotite composition of Gurenko et al. in Contrib Mineral Petrol 162:349–363, 2011). Here we question the approach of using weakly correlated variations in δ¹⁸O_ol and the Xpx parameter to define mantle source oxygen isotope compositions, and provide examples of why this approach appears flawed. We also provide reasons why the LF datasets previously published for Canary Island lavas remain robust and discuss why LF and SIMS data may provide complementary information on oxygen isotope variations in ocean island basalts (OIB), despite unresolved small-scale uncertainties associated with both techniques.     

On the theory of consolidation with double porosity—III A finite element formulation

We employ a finite element method to consider the numerical solution of Aifantis' equations of double porosity.^1–5 The physical and mathematical foundations of the theory of double porosity were considered in two previous papers, ^6,7 where analytical solutions of the relevant equations are also given. For practical purposes and for the completeness of the presentation, we re-derive the basic equations without resorting to the more rigorous scheme of multiporosity theory.^1–6 Instead, we follow the more familiar approach of Biot^8,9 which we now extend from the case of single porosity to the case of double porosity. Then a general finite element formulation of the relevant eqations is thoroughly discussed and explicitly described for the two-dimensional case where four-node rectangular non-conforming isoparametric elements are employed. Three numerical examples are presented in detail to illustrate the method and assess the differences between single and double porosity models in consolidation.     

Reliability updating in geotechnical engineering including spatial variability of soil

At geotechnical sites, deformation measurements are routinely performed during the construction process. In this paper, it is shown how information from such measurements can be utilized to update the reliability estimate of the geotechnical site at future construction stages. A recently proposed method for Bayesian updating of the reliability is successfully applied in conjunction with a stochastic nonlinear geotechnical finite element model. Therein, uncertainty in the soil material properties is modelled by non-Gaussian random fields. The structural reliability evaluations required for the Bayesian updating are carried out by means of subset simulation, an efficient adaptive Monte Carlo method. The approach is demonstrated through an application to a sheet pile wall at a deformation-sensitive geotechnical construction site.     

基于水平集法的非均质岩石建模及水力压裂传播特性研究

基于水平集法的基本思想,讨论了含有不同类型包裹体分布的岩石的二维和三维有限元建模方法。对于二维有限元模型的建立,考虑了以椭圆形为例的规则包裹体的周期分布、位置及包裹体大小均随机变化的多种情况。建议了包裹体和基岩之间界面的材料特性过渡处理方法。同时给出了含有非规则形状包裹体的建模方法。对于三维有限元模型的建立,则考虑了以任意大小椭球体为例的包裹体分布情况。该种建模方法的优点是对于不同的含有任意分布的包裹体的岩石试件,均可以采用相同的有限元网格,即,材料特性的变化不受有限元网格的制约。该法缺点是增加了计算资源。最后结合基于弥散裂缝模型的水力压裂数值计算方法,模拟了含有不同包裹体分布的岩石试件的水力压裂传播特点。     

Analysis of support requirements for a shallow diversion tunnel at Guledar dam site, Turkey

Engineering geological properties and support design of a planned diversion tunnel at Guledar dam site, which was located at the North of Ankara, Turkey were studied in this article. The main purpose of the construction of the planned tunnel is to regulate, drainage and to provide water for irrigation purposes. The diversion tunnel runs mainly through formations of limestone, sandstone and diabase. Rock masses at the site were characterized using Rock Mass Rating (RMR), Rock Mass Quality (Q), Rock Mass Index (RMi) and Geological Strength Index (GSI). RMR, Q, RMi and GSI were determined by using field data and mechanical properties of intact rock samples, measured in the laboratory. Support requirements for the planned diversion tunnel were determined accordingly in terms of the rock mass classification systems. Recommended support systems by empirical methods were also analyzed using 2D Finite Element method. Calculated parameters based on empirical methods were used as input parameters in the finite element models. The results from both methods were compared with each other. This comparison suggests that more reliable support design could be achieved by using the finite element method together with the empirical methods.     

Insights into the high-pressure behavior of kaolinite from infrared spectroscopy and quantum-mechanical calculations

The high-pressure behavior of Keokuk kaolinite has been studied to 9.5 GPa by infrared spectroscopy using synchrotron radiation. The kaolinite-I → kaolinite-II and kaolinite-II → kaolinite-III transformations have clear spectroscopic expression, with discontinuities coinciding with the transformation pressures bracketed by X-ray diffraction (Welch and Crichton in Am Mineral 95:651–654, 2010). The experimental spectra have been interpreted from band assignments derived from density functional theory for the structures of kaolinite-II and kaolinite-III, using as starting models the ab initio structures reported by Mercier and Le Page (Acta Crystallogr A B64:131–143, 2008, Mater Sci Technol 25:437–442, 2009) and unit-cell parameters from Welch and Crichton (Am Mineral 95:651–654, 2010). The relaxed theoretical structures are very similar to those reported by Mercier and Le Page (Acta Crystallogr A B64:131–143, 2008, Mater Sci Technol 25:437–442, 2009) in their theoretical investigation of kaolinite polytypes at high pressure. The vibrational spectra calculated from the quantum-mechanical analysis allow band assignments of the IR spectra to be made and provide insights into the behavior of different OH environments in the two high-pressure polytypes. The single perpendicular-interlayer OH group of kaolinite-III has a distinctive spectroscopic signature that is diagnostic of this polytype (ν = 3,595 cm⁻¹ at 9.5 GPa) and is sensitive to the compression/expansion of the interlayer space. This OH group also has a distinctive signature in the calculated spectra. The spectra collected on decompression are those of kaolinite-III and persist largely unchanged to 4.6 GPa, except for a continuous blue shift of the 3,595 cm⁻¹ band to 3,613 cm⁻¹. Finally, kaolinite-I is recovered at 0.6 GPa, confirming the kaolinite-III → kaolinite-I transformation previously observed by X-ray diffraction, and the irreversibility of the kaolinite-II → kaolinite-III transformation. The ambient spectra collected at the start and finish of the experiment are those of kaolinite-I, and start/finish band frequencies agree to within 6 cm⁻¹.     

A study of the factors and processes involved in the sedimentation of Tarbela reservoir,Pakistan

This study concerns Tarbela dam reservoir which is a major resource of Pakistan in terms of electricity generation and irrigation supplies. Rapid filling of reservoir due to sediment transported and deposited by Indus River is described and analysed in this article. Causes of sediment deposition and their impact on dam’s function and life are studied. The main characteristic parameters of the site are presented. The morphological evolution of the reservoir bed induced by dam construction, between the year 1974 when the River bed was in its original state before dam construction, and the situation of the river bed after the deposition of the sediment in the year 2006, is examined. A numerical model developed in this study (Khawaja and Sanchez in Tarbela dam: a numerical model for sediment management in the reservoir; coastal and maritime mediterranean conference, 1st edn, Hammamet, pp 111–114, 2009) allows obtaining the above-stated provisional evolution of the reservoir over the coming years. Finally, five potential remedial solutions are thoroughly discussed.     

A multi-domain decomposition-based Fourier finite element method for the simulation of 3D marine CSEM measurements

We introduce a multi-domain decomposition Fourier finite element (MDDFFE) method for the simulation of three-dimensional (3D) marine controlled source electromagnetic measurement (CSEM). The method combines a 2D finite element (FE) method in two spatial dimensions with a hybrid discretization based on a Fourier FE method along the third dimension. The method employs a secondary field formulation rather than the total field formulation. We apply the MDDFFE method to several synthetic marine CSEM examples exhibiting bathymetry and/or multiple 3D subdomains. Numerical results show that the use of the MDDFFE method reduces the problem size by as much as 87 % in terms of the number of unknowns, without any sacrifice in accuracy.     

Quantitative risk assessment of landslides with direct simulation of pre-failure to post-failure behaviors

Most previous studies on the quantitative risk assessment (QRA) of landslides focused on the probability of slope failure at the pre-failure stage and adopted empirical models for consequence analysis. The conventional approaches simplify the relationship between the pre-failure state and the post-failure behavior and cannot reasonably account for the effects of uncertainty on the entire landslide process. In this paper, an efficient QRA method that involves the direct simulation of the entire landslide process is proposed. A QRA formula that considers the probability of only those landslides that can impact the element at risk is used. The coupled Eulerian–Lagrangian method is used to simulate the entire landslide process and to identify slopes that can impact the element at risk and determine the failure consequences. The subset simulation method is adopted to efficiently estimate the probability of landslide impact, and parameter uncertainty is considered. Two case histories of landslides are investigated. First, the 2011 Baqiao loess landslide in Xi’an, China, is investigated, and the results of the proposed method are compared with those of the conventional approaches. Second, the proposed method is applied to assess the risk of the 2015 Ganjingzi landslide in the Three Gorges Reservoir. The effects of the risk mitigation works are also discussed.