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1.
Fracture network modelling plays an important role in many application areas in which the behaviour of a rock mass is of interest. These areas include mining, civil, petroleum, water and environmental engineering and geothermal systems modelling. The aim is to model the fractured rock to assess fluid flow or the stability of rock blocks. One important step in fracture network modelling is to estimate the number of fractures and the properties of individual fractures such as their size and orientation. Due to the lack of data and the complexity of the problem, there are significant uncertainties associated with fracture network modelling in practice. Our primary interest is the modelling of fracture networks in geothermal systems and, in this paper, we propose a general stochastic approach to fracture network modelling for this application. We focus on using the seismic point cloud detected during the fracture stimulation of a hot dry rock reservoir to create an enhanced geothermal system; these seismic points are the conditioning data in the modelling process. The seismic points can be used to estimate the geographical extent of the reservoir, the amount of fracturing and the detailed geometries of fractures within the reservoir. The objective is to determine a fracture model from the conditioning data by minimizing the sum of the distances of the points from the fitted fracture model. Fractures are represented as line segments connecting two points in two-dimensional applications or as ellipses in three-dimensional (3D) cases. The novelty of our model is twofold: (1) it comprises a comprehensive fracture modification scheme based on simulated annealing and (2) it introduces new spatial approaches, a goodness-of-fit measure for the fitted fracture model, a measure for fracture similarity and a clustering technique for proposing a locally optimal solution for  fracture parameters. We use a simulated dataset to demonstrate the application of the proposed approach followed by a real 3D case study of the Habanero reservoir in the Cooper Basin, Australia.  相似文献   

2.
非等轴颗粒付林图解   总被引:3,自引:0,他引:3  
非等轴颗粒付林图解由直线a=1、b=1、a=b和曲线a2b=1、ab2=1分割成10个微区,并对应于不同的ex、ey、ez组合和应变类型。这些直线和曲线分别对应于特殊的ex、ey、ez组合和岩石应变类型。岩石的应变类型有18种。函数a.b的表征方程有4种类型,并分别表征直线a=1/k1和b=1/k2所分割的4个区间。a,b表征方程的确定取决于岩石总的变形行为。此图解可用于非等轴颗粒标志体应变测量和应变类型的确定和图示,文章给出了应用实例.   相似文献   

3.
Spatial fracture intensity (P 32, fracture area by volume) is an important characteristic of a jointed rock mass. Although it can hardly ever be measured, P 32 can be modeled based on available geological information such as spatial data of the fracture network. Flow in a mass composed of low-permeability hard rock is controlled by joints and fractures. In this article, models were developed from a geological data set of fractured andesite in LanYu Island (Taiwan) where a site is investigated for possible disposal of low-level and intermediate-level radionuclide waste. Three different types of conceptual models of spatial fracture intensity distribution were generated, an Enhanced Baecher’s model (EBM), a Levy–Lee Fractal model (LLFM) and a Nearest Neighborhood model (NNM). Modeling was conducted on a 10 × 10 × 10 m synthetic fractured block. Simulated flow was forced by a 1% hydraulic gradient between two vertical xz faces of the cube (from North to South) with other boundaries set to no-flow conditions. Resulting flow vectors are very sensitive to spatial fracture intensity (P 32). Flow velocity increases with higher fracture intensity (P 32). R-squared values of regression analysis for the variables velocity (V/V max) and fracture intensity (P 32) are 0.293, 0.353, and 0.408 in linear fit and 0.028, 0.08, and 0.084 in power fit. Higher R 2 values are positively linked with structural features but the relation between velocity and fracture intensity is non-linear. Possible flow channels are identified by stream-traces in the Levy–LeeFractal model.  相似文献   

4.
This is the second paper in a series dedicated to studies of the X-ray binary Cyg X-1 in the HeII λ 4686 Å line using 3D Doppler tomography. A detailed analysis of the tomogram constructed has made it possible for the first time to obtain information about the motions of gaseous flows including all three velocity components. The observations were obtained in June 2007 at the Terskol Branch of the Institute of Astronomy (Russia) and the National Astronomical Observatory of Mexico. The correctness of the tomographic results and their discussion is analyzed. The results are compared with a 2D Doppler tomogram reconstruction. Model-atmosphere computations of HeII λ 4686 Å line profiles are used to estimate the influence of absorption features of the Osupergiant on the emission structure in the tomogram. The correctness of the 3D solutions is confirmed by the good agreement between the original sequence of spectral data and a control data set computed using the constructed 3D Doppler tomogram. Tomograms constructed using the data of each of the two observatories are compared. The results of the reconstruction for inclinations of the system of 40° and 45° essentially coincide. The maximum absorption (corresponding to the O supergiant) and emission structural features in the 3D tomogram are located in its central (V x , V y ) section, where the velocity component perpendicular to the orbital plane V z is zero. The emission is generated mainly in the outer part of the accretion structure, close to the supergiant. A gaseous stream from the Lagrangian point L1 with its motion close to the orbital plane can be distinguished. Its maximum velocity reaches 800 km/s. The identification of an emission structure with V z ~ 300 km/s and with V x , V y in the velocity interval corresponding to the donor star was unexpected. Its presence may indicate, for example, an outflow of matter from a magnetic pole of the supergiant.  相似文献   

5.
Present work provides in-situ structural data at a fine temperature scale from RT to the melting point of nitratine, NaNO3. From the analysis of log e 33 versus log t plots, it is possible to prove that an univocal indication on the R \( \overline{3} \) c (low temperature, LT) → R \( \overline{3} \) m (high temperature, HT) transition mechanism cannot be obtained because of the relevant role played by the arbitrary assumptions required for defining the c 0 dependence from temperature of the HT phase. This is due to the occurrence of excess thermal expansion for the HT phase. A significantly better fit for an Ising-spin structural model over a non-Ising rigid-body one has been obtained for the LT phase. Moreover, the Ising model led to a smooth variation of the oxygen site x fractional coordinate throughout the transition. The structure of the HT polymorph has been successfully refined considering an oxygen site at x, 0, ½, with 50% occupancy. Such model was the only acceptable one from the crystal chemical point of view as the alternative model (oxygen site at x, y, z with 25% occupancy) led to unrealistically aplanar \( {\text{NO}}_{3}^{ - } \) groups.  相似文献   

6.
Given the direction cosines a i = (a 1 i , a 2 i , a 3 i )corresponding to a set of pspherically projected fabric poles, an initial estimate x′ = (x1, x2, x3, x4)for the angular radius x4,and direction cosines of the center of the least-squares small circle which minimizes the sum of the squares of the angular residuals $$r = \sum\limits_p {\left[ {x_4 - \cos ^{ - 1} \left( {a_1^i x_1 + a_2^i x_2 + a_3^i x_3 } \right)} \right]} ^2 $$ can be iteratively improved by taking xj+1 = xj + Δxwhere xj is the value of xat the jth iteration and $$\Delta x = - H_j^{ - 1} \left[ {q_j + x_j \left( {x'_j H_j^{ - 1} x_j } \right)\left( {q_j - x'_j H_j^{ - 1} q_j } \right)} \right],$$ where As an initial approximation for xwe have found it convenient to ignore the fact that the data are constrained to lie on the surface of the reference sphere and to use the parameters of a least-squares plane through the given poles. Generalization of this approach to fitting variously constrained great and small circles is easily made. The relative merits of differently constrained fits to the same data can be tested approximately if it is assumed that the errors in the location of the poles are isotropic and normally distributed. It is thus possible to statistically assess the relative significance of conflicting structural models which predict different geometrical patterns of fabric elements.  相似文献   

7.
This paper presents an approach to modelling fracture networks in hot dry rock geothermal reservoirs. A detailed understanding of the fracture network within a geothermal reservoir is critically important for assessments of reservoir potential and optimal production design. One important step in fracture network modelling is to estimate the fracture density and the fracture geometries, particularly the size and orientation of fractures. As fracture networks in these reservoirs can never be directly observed there is significant uncertainty about their true nature and the only feasible approach to modelling is a stochastic one. We propose a global optimization approach using simulated annealing which is an extension of our previous work. The fracture model consists of a number of individual fractures represented by ellipses passing through the micro-seismic points detected during the fracture stimulation process, i.e. the fracture model is conditioned on the seismic points. The distances of the seismic points from fitted fracture planes (ellipses) are, therefore, important in assessing the goodness-of-fit of the model. Our aims in the proposed approach are to formulate an appropriate objective function for the optimal fitting of a set of fracture planes to the micro-seismic data and to derive an efficient modification scheme to update the model parameters. The proposed objective function consists of three components: orthogonal projection distances of the seismic points from the nearest fitted fractures, the amount of fracturing (fitted fracture areas) and the volumes of the convex hull of the associated points of fitted fractures. The functions used in the model update scheme allow the model to achieve an acceptable fit to the points and to converge to acceptable fitted fracture sizes. These functions include two groups of proposals: one for updating fracture parameters and the other for determining the size of the fracture network. To increase the efficiency of the optimization, a spatial clustering approach, the Distance-Directional Transform, was developed to generate parameters for newly proposed fractures. A simulated dataset was used as an example to evaluate our approach and we compared the results to those derived using our previously published algorithm on a real dataset from the Habanero geothermal field in the Cooper Basin, South Australia. In a real application, such as the Habanero dataset, it is difficult to determine definitively which algorithm performs better due to the many uncertainties but the number of association points, the number of final fractures and the error are three important factors that quantify the effectiveness of our algorithm.  相似文献   

8.
To study the behavior of macrocomponents and admixtures during the fractional crystallization of sulfide melts and the influence of As on noble metals in this process, we performed a quasi-equilibrium directional crystallization of melt of composition (at.%): Fe—35.5, Ni—4.9, Cu—10.4, and S—48.3, with admixtures of Pt, Pd, Rh, Ru, Ir, Au, Ag, As, and Co (each 0.1 at.%), which imitates the average (by Cu contents) compositions of massive ores at the Noril'sk Cu-Ni deposits. The following sequence of phase formation from melt has been established: mss (zone I) / mss + iss (zone II) / iss (zone III) (mss is (FezNi1–z)S1+δ, iss is (FexCuyNi1–xy)zS1–z); it corresponds to the distribution of main elements along the sample (primary zoning). Distribution curves for macrocomponents in zones I and II of the sample were constructed, as well as the dependencies of their partition coefficients (k) between solid solutions and sulfide melt on the fraction of crystallized melt. The secondary (mineral) zoning resulted from subsolidus phase transformations has been revealed. Five subzones have been recognized: mss + cp (Ia) / mss + cp + pn (Ib) / mss + pc + pn (IIa) / mss + pc + pn + bn (IIb) / pc + bn + pn + unidentified microphases (III). Admixture species in the sample were studied: (1) admixtures dissolved in primary solid solutions and in main minerals resulted from solid-phase transformations and (2) admixtures forming their own mineral phases. The partition coefficients of Co, Rh, and Ru (mss/L), Ru, Ir, and Rh (mss/cp), and Co, Rh, and Pd (mss/pn) were determined. Minerals of noble metals have been recognized: Pt3Fe, PtFe, Au, (Ag,Pd), (Au,Pt), Ag, Ag3Cu, Au3(Cu,Ag,Pd,Pt), etc., and the regularities of their distribution in the sample have been established. It is shown that some noble-metal admixtures are prone to interact with As. Mineral arsenides and sulfoarsenides of noble metals produced during fractional crystallization have been recognized: PtAs2, Pd3As, (RhAsS), (IrAsS), and (Ir,Rh)AsS. The discovered drop-like inclusions of noble-metal arsenides suggest the separation of the initial sulfide-arsenide melt into two immiscible liquids. By indirect features, the micromineral inclusions are divided into primary, crystallized from melt, and secondary, produced in solid-phase reactions. The results of study are compared with literature experimental data obtained by the isothermal-annealing method and with the behavior of noble metals and As during the formation of zonal massive orebodies at the Noril'sk- and Sudbury-type deposits.  相似文献   

9.
The scientific community is confident that warming of the Earth’s climate is unequivocal. Sea-level rise, which poses potential threats to coastal areas, is one of the most recognised possible impacts of this climate change. The nonlinearities, complexities, and spatial and temporal lags are common characteristics of coastal processes driven by human and natural interaction. With the acknowledgement of the complexity and dynamic nature of coastal systems, this paper introduces a spatial–temporal assessment framework, for addressing both the temporal and spatial variations, when assessing the vulnerability of natural and human systems in coastal areas. The framework is based upon a combination of system dynamics (SD) modelling and geographical information systems by taking into account spatial (x, y, z) and temporal (t) dimensions. The strategy of the adopted approach is to use the loose coupling approach by which a spatial model component is incorporated into a SD model component through a data converter.  相似文献   

10.
Manganoan lipscombite (Fe x /2+ , M y /2+ ) Fe 3?(x +y)/3+ [OH)3?(x+y)(PO4)2] was synthesized from pure chemicals. From the study of the Mn2+/Fe2+ atomic ratio by Mössbauer spectra, solubility, and electrokinetic properties, it was found that the crystal structure of lipscombite is not changed substantially by the manganese substitution. The unit cell parameters were determined from Guinier-Hägg X-ray diffraction patterns, which are identical for both synthetic ferrous-ferric and manganoan lipscombite. The two compounds crystallize in the tetragonal system with a=5.3020±0.0005 Å and c=12.8800±0.0005 Å.  相似文献   

11.
The results of a 3D Doppler tomography analysis for the X-ray binary system Cyg X-1 in the HeII λ 4686 Å line are presented. Information about the motions of gaseous flows outside the orbital plane has been obtained for the first time. Line profiles obtained in June 2007 on the 2-m telescope of the Terskol Branch of the Institute of Astronomy (Russia) and on the 2.1-m telescope of the National Astronomical Observatory of Mexico were used. A detailed analysis of these spectral data is presented: the distribution of the data in time, distribution of orbital phases for the projections, comparison of the line profile shapes for the data from two observatories. The geometry of the total transfer function obtained in the reconstruction is considered. The possibility of applying the profiles obtained to realize 3D tomography is justified. The resolution of the constructed 3D tomogram in velocity space is 60 × 60 × 40 km/s for V x , V y , V z . Fifteen cross sections for 15 different V z values perpendicular to the orbital plane are presented. The intensity distributions corresponding to the velocities of gaseous structures in the binary system are obtained. The reconstruction was realized using the radio-astronomical approach, developed for solving problems in tomography with a limited number of projections.  相似文献   

12.
In this paper, we study the problem of constructing a smooth approximant of a surface defined by the equation z = f(x 1, x 2), the data being a finite set of patches on this surface. This problem occurs, for example, after geophysical processing such as migration of time-maps or depth-maps. The usual algorithms to solve this problem are picking points on the patches to get Lagrange's data or trying to get local junctions on patches. But the first method does not use the continuous aspect of the data and the second one does not perform well to get a global regular approximant (C 1 or more). As an approximant of f, a discrete smoothing spline belonging to a suitable piecewise polynomial space is proposed. The originality of the method consists in the fidelity criterion used to fit the data, which takes into account their particular aspect (surface's patches): the idea is to define a function that minimizes the volume located between the data patches and the function, and which is globally C k. We first demonstrate the new method on a theoretical aspect and numerical results on real data are given.  相似文献   

13.
(Ca x ,Sr1?x )ZrO3 and Ca(Sn y ,Zr1-y )O3 solid solutions were synthesized by solid-state reaction at high temperature before to be studied by powder X-ray diffraction and Raman Spectroscopy. Diffraction data allow the distortion of the ABO3 perovskite structure to be investigated according to cations substitution on A and B-sites. It is shown that distortion, characterized by Φ, the tilt angle of BO6 octahedra, slightly increases with decreasing y content in Ca(Sn y ,Zr1?y )O3 compounds and strongly decreases with decreasing x content in (Ca x ,Sr1?x )ZrO3 compounds. Such results are discussed in view of the relative A and B cation sizes. Raman data show that vibrational spectra are strongly affected by the cation substitution on A-site; the frequencies of most vibrational modes increase with increasing x content in (Ca x ,Sr1?x )ZrO3 compounds, i.e. with the decreasing mean size of the A-cation; the upper shift is observed for the 358 cm?1 mode (?ν/?r = ?60.1 cm?1/Å). On the other hand, the cation substitution on B-sites, slightly affect the spectra; it is shown that in most cases, the frequency of vibrational modes increases with increasing y content in Ca(Sn y ,Zr1?y )O3 compounds, i.e. with the decreasing mean size of the B-cation, but that two modes (287 and 358 cm?1) behave differently: their frequencies decrease with the decreasing mean size of the B-cation, with a shift respectively equal to +314 and +162 cm?1/Å. Such results could be used to predict the location of different elements such as trivalent cations or radwaste elements on A- or B-site, in the perovskite structure.  相似文献   

14.
In history matching and sensitivity analysis, flexibility in the structural modelling is of great importance. The ability to easily generate multiple realizations of the model will have impact both on the updating workflow in history matching and uncertainty studies based on Monte Carlo simulations. The main contribution to fault modelling by the work presented in this paper is a new algorithm for calculating a 3D displacement field applicable to a wide range of faults due to a flexible representation. This gives the possibility to apply this field to change the displacement and thereby moving horizons and fault lines. The fault is modelled by a parametric format where the fault has a reference plane defined by a centre point, dip and strike angles. The fault itself is represented as a surface defined by a function z = f(x,y), where x, y and z are coordinates local to the reference plane, with the z-axis being normal to the plane. The displacement associated with the fault outside the fault surface is described by a 3D vector field. The displacement on the fault surface can be found by identifying the intersection lines between horizons and the fault surface (fault lines), and using kriging techniques to fill in values at all points on the surface. Away from the fault surface the displacement field is defined by a monotonic decreasing function which ensures zero displacement at a specified distance from the fault. An algorithm is developed where the displacement can be increased or decreased according to user-defined parameters. This means that the whole displacement field is changed and points on horizons around the fault can be moved accordingly by applying the modified displacement field on them. The interaction between several faults influencing the same points is taken care of by truncation rules and the ordering of the faults. The method is demonstrated on a realistic synthetic case based on a real reservoir.  相似文献   

15.
For petrological calculations, including geothermobarometry and the calculation of phase diagrams (for example, PT petrogenetic grids and pseudosections), it is necessary to be able to express the activity–composition (ax) relations of minerals, melt and fluid in multicomponent systems. Although the symmetric formalism—a macroscopic regular model approach to ax relations—is an easy-to-formulate, general way of doing this, the energetic relationships are a symmetric function of composition. We allow asymmetric energetics to be accommodated via a simple extension to the symmetric formalism which turns it into a macroscopic van Laar formulation. We term this the asymmetric formalism (ASF). In the symmetric formalism, the ax relations are specified by an interaction energy for each of the constituent binaries amongst the independent set of end members used to represent the phase. In the asymmetric formalism, there is additionally a "size parameter" for each of the end members in the independent set, with size parameter differences between end members accounting for asymmetry. In the case of fluid mixtures, for example, H2O–CO2, the volumes of the end members as a function of pressure and temperature serve as the size parameters, providing an excellent fit to the ax relations. In the case of minerals and silicate liquid, the size parameters are empirical parameters to be determined along with the interaction energies as part of the calibration of the ax relations. In this way, we determine the ax relations for feldspars in the systems KAlSi3O8–NaAlSi3O8 and KAlSi3O8–NaAlSi3O8–CaAl2Si2O8, for carbonates in the system CaCO3–MgCO3, for melt in the melting relationships involving forsterite, protoenstatite and cristobalite in the system Mg2SiO4–SiO2, as well as for fluids in the system H2O–CO2. In each case the ax relations allow the corresponding, experimentally determined phase diagrams to be reproduced faithfully. The asymmetric formalism provides a powerful and flexible way of handling ax relations of complex phases in multicomponent systems for petrological calculations.  相似文献   

16.
A series of fluoride perovskites related to neighborite was investigated using X-ray and neutron diffraction techniques, and Rietveld profile refinement of powder diffraction data. The series (Na1? x K x )MgF3 comprises orthorhombic (Pbnm, a?≈? , b?≈? , c?≈?2a p , Z=4) perovskites in the compositional range 0?≤?x?≤?0.30, tetragonal perovkites (P4/mbm, a?≈? , c?≈?a p , Z=2) in the range 0.40?≤?x?≤?0.46, and cubic phases (Pmm, Z=1) for x?>?0.50. The structure of the orthorhombic neighborite is derived from the perovskite aristotype by rotation of MgF6 octahedra about the [110] and [001] axes of the cubic subcell. The degree of rotation, measured as a composite tilt Φ about the triad axis, varies from 18.2° at x=0 to 11.2° at x=0.30 (as determined from the fractional atomic coordinates). Orthorhombic neighborite also shows a significant displacement of Na and K from the “ideal” position (≤0.25?Å). The tetragonal members of the neighborite series exhibit only in-phase tilting about the [001] axis of the cubic subcell (φ) ranging from 4.5° to 4.8° (determined from the atomic coordinates). The solid solution (Na1? x K x )MgF3, shows a regular variation of unit-cell dimensions with composition from 3.8347?Å for the end-member NaMgF3 (reduced to pseudocubic subcell, a p ) to 3.9897?Å for KMgF3. This variation is accompanied by increasing volumes of the A-site polyhedra, whereas the volume of MgF6 octahedra initially decreases (up to x=0.40), and then increases concomitantly with K content. The polyhedral volume ratio, V A /V B , gradually increases towards the tetragonal structural range, in agreement with diminishing octahedral rotation in the structure. The P4/mbm-type neighborite has an “anomalous” polyhedral volume ratio (ca. 5.04) owing to the critical compression of MgF6 polyhedra.  相似文献   

17.
《Applied Geochemistry》1998,13(5):543-552
The accumulation chamber methodology allows one to obtain reliable values of the soil CO2 flux, ϕsoil CO2, in the range 0.2 to over 10 000 g m−2 d−1, as proven by both laboratory tests and field surveys in geothermal and volcanic areas. A strong negative correlation is observed between Δϕsoil CO2t and ΔPatmt. Maps of classes of log ϕsoil CO2 for the northern sector of Vulcano Island, Solfatara of Pozzuoli, Nea Kameni Islet and Yanbajain geothermal field evidence that active faults and fractures act as uprising channels of deep, CO2-rich geothermal or magmatic gases. The total diffuse CO2 output was evaluated for each surveyed area.  相似文献   

18.
A new catalog of 8382 close quasar-galaxy pairs is presented. The catalog was composed using published catalogs of quasars and active galactic nuclei containing 11358 objects, as well as the LEDA catalog of galaxies, which contains on the order of 100 thousand objects. Based on these new data, the dependence of the number of pairs on a=z G /z Q is analyzed, where z G and z Q are the redshifts of the galaxy and quasar, respectively, revealing an excess of pairs with a<0.1 and a>0.9. This means that the galaxies in pairs are preferably located close to either the observer or the quasar and avoid intermediate distances along the line of sight to the quasar. Computer simulations demonstrate that it is not possible to explain this number of pairs with the observed distribution in a as the result of chance positional coincidences with a uniform spatial distribution of galaxies. Data on globular clusters show that the excess of pairs with a<0.1 and a>0.9 is consistent with the hypothesis that we are observing distant compact objects that are strongly gravitationally lensed by transparent lenses with a King mass distribution located in the halos of nearby galaxies. The Hubble diagram for galaxies and quasars is presented. Observational tests of the mesolensing hypothesis are formulated.  相似文献   

19.
The presence of fractures in reservoir rocks causes scattering of seismic wave energy. In this paper, we utilize the finite-difference modelling technique to study these scattering effects to gain more insights into the effects and assess the validity of using anisotropic wave scattering energy as a diagnostic tool to characterize fractured hydrocarbon reservoirs. We use a simplified fractured reservoir model with four horizontal layers with a fractured-layer as the third layer. The fractures are represented by grid cells containing equivalent anisotropic medium by the use of the linear slip equivalent model. Our results show that the scattered energy, quantified through estimates of the seismic quality factor (Q) is anisotropic, exhibiting a characteristic elliptical (\(\cos 2\theta \)) variations relative to the survey azimuth angle \(\theta \). The fracture normal is inferred from the minor axis of the Q ellipse. This direction correlates with the direction of maximum wave scattering. Minimum wave scattering occurs in the fracture strike direction inferred from the major axis of the Q ellipse. These results provide more complete insights into anisotropic wave scattering characteristics in fractured media and thus, validate the practical utility of using anisotropic attenuation attribute as an additional diagnostic tool for delineation of fracture properties from seismic data.  相似文献   

20.
This paper investigates, using the random field theory and Monte Carlo simulation, the effects of random field discretization on failure probability, p f, and failure mechanism of cohesive soil slope stability. The spatial sizes of the discretized elements in random field Δx, Δy in horizontal and vertical directions, respectively, are assigned a series of combinational values in order to model the discretization accuracy. The p f of deterministic critical slip surface (DCSS) and that of the slope system both are analyzed. The numerical simulation results have demonstrated that both the ratios of Δy/λ y (λ y  = scale of fluctuation in vertical direction) and Δx/λ x (λ x  = scale of fluctuation in horizontal direction) contribute in a similar manner to the accuracy of p f of DCSS. The effect of random field discretization on the p f can be negligible if both the ratios of Δx/λ x and Δy/λ y are no greater than 0.1. The normalized discrepancy tends to increase at a linear rate with Δy/λ y when Δx/λ x is larger than 0.1, and vice versa for p f of DCSS. The random field discretization tends to have more considerable influence on the p f of DCSS than on that of the slope system. The variation of p f versus λ x and λ y may exhibit opposite trends for the cases where the limit state functions of slope failure are defined on DCSS and on the slope system as well. Finally, the p f of slope system converges in a more rapid manner to that of DCSS than the failure mechanism does to DCSS as the spatial variability of soil property grows from significant to negligible.  相似文献   

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