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Efficient slope reliability analysis under soil spatial variability using maximum entropy distribution with fractional moments

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Journal of Rock Mechanics and Geotechnical Engineering 2024年第4期16卷 1140-1152页

作者： Chengxin Feng Marcos A.Valdebenito Marcin Chwała Kang Liao Matteo Broggi Michael Beer Institute for Risk and Reliability Leibniz University HannoverCallinstr.34Hannover30167Germany Chair for Reliability Engineering TU Dortmund UniversityLeonhard-Euler-Str.5Dortmund44227Germany Faculty of Civil Engineering Wrocƚaw University of Science and TechnologyWrocƚawPoland Faculty of Geosciences and Environmental Engineering Southwest Jiaotong UniversityChengdu610031China University of Liverpool Institute for Risk and UncertaintyPeach StreetLiverpoolL69 7ZFUnited Kingdom International Joint Research Center for Resilient Infrastructure & International Joint Research Center for Engineering Reliability and Stochastic Mechanics Tongji UniversityShanghaiChina

Spatial variability of soil properties imposes a challenge for practical analysis and design in geotechnical engineering.The latter is particularly true for slope stability assessment,where the effects of uncertainty are synthesized in the so-called probability of failure.This probability quantifies the reliability of a slope and its numerical calculation is usually quite involved from a numerical viewpoint.In view of this issue,this paper proposes an approach for failure probability assessment based on Latinized partially stratified sampling and maximum entropy distribution with fractional moments.The spatial variability of geotechnical properties is represented by means of random fields and the Karhunen-Loève expansion.Then,failure probabilities are estimated employing maximum entropy distribution with fractional moments.The application of the proposed approach is examined with two examples:a case study of an undrained slope and a case study of a slope with cross-correlated random fields of strength parameters under a drained slope.The results show that the proposed approach has excellent accuracy and high efficiency,and it can be applied straightforwardly to similar geotechnical engineering problems.

关键词： Slope random field Reliability analysis Maximum entropy distribution Latinized partial stratified sampling

random　field　characteristics　of　earthquake　occurrence　and　test　of　earthquake　occurrence　rate

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Earthquake Science 1994年第S1期7卷 91-94页

作者：高孟潭

The random field characteristics of earthquake occurrence is studied, the random field of earthquake occurrence is defined according to basic concepts of random field, and expectations of the random field are discussed. It is proved that this random field is inhomogeneous. The average of the random field can not be estimated from the spatial-distribution average. So, in order to overcome this shortcoming, and assistant random field is introduced.This assistant random filed is homogenous and ergodic. The average of this random field can be evaluated from spatial-distribution average. On the basis of these results, earthquake occurrence rate adopted by Chinese Seismic Zoning Map(1990 version) are tested by using recent 15 years data and recent 50 years data.

关键词： random field average occurrence rate ergodic

Glassy behaviour of random field Ising spins on Bethe lattice in external magnetic field

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Chinese Physics B 2011年第6期20卷 416-425页

作者： Khalid Bannora Galal Ismail Wafaa Hassan Mathematics Department Faculty of Science Zagazig University Mathematics and Physics Department Faculty of Engineering Port Said Branch of Suez Canal University

The thermodynamics and the phase diagram of random field Ising model （RFIM） on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field （B）. A Gaussian distribution of random field （hi） with zero mean and variance （hi2 = H2RF is considered. The free-energy （F）, the magnetization （M） and the order parameter （q） are investigated for several values of coordination number （z）. The phase diagram shows several interesting behaviours and presents tricritical point at critical temperature Tc = J/k and when HRF = 0 for finite z. The free-energy （F） values increase as T increases for different intensities of random field （HRE） and finite z. The internal energy （U） has a similar behaviour to that obtained from the Monte Carlo simulations. The ground state of magnetization decreases as the intensity of random field HRF increases, The ferromagnetic （FM） paramagnetic （PM） phase boundary is clearly observed only when z →∞. While FM PM-spin glass （SG） phase boundaries are present for finite z. The magnetic susceptibility （X） shows a sharp cusp at Tc in a small random field for finite z and rounded different peaks on increasing HRF.

关键词： random field replica trick coordination number order parameter susceptibility and phase diagram

Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field

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Chinese Physics B 2010年第10期19卷 525-533页

Phase diagram and thermodynamic parameters of the random field Ising model （RFIM） on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field （B）. The random field （hi） is assumed to be Gaussian distributed with zero mean and a variance （hi2） = HRF2. The free energy （F）, the magnetization （M） and the order parameter （q） are calculated. The ferromagnetic （FM） spin-glass （SG） phase transition is clearly observed. The critical temperature （Tc） is computed under a critical intensity of random field HRF = V/2/πJ. The phase transition from FM to paramagnetic （PM） occurs at TC = J/k in the absence of magnetic field. The critical temperature decreases as HRF increases in the phase boundary of FM-to-SG. The magnetic susceptibility （X） shows a sharp cusp at TC and the specific heat （C） has a singularity in small random field. The internal energy （U） has a similar behaviour to that obtained from the Monte Carlo simulation.

关键词： random field mean field theory magnetization specific heat and phase diagram

Multiscale stochastic finite element method on random field modeling of geotechnical problems- a fast computing procedure

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Frontiers of Structural and Civil Engineering 2015年第2期9卷 107-113页

作者： Xi F. XU School of Civil Engineering Beo'ing Jiaotong University Beijing 100044 China

The Green-function-based multiscale stochastic finite element method (MSFEM) has been formulated based on the stochastic variational principle. In this study a fast computing procedure based on the MSFEM is developed to solve random field geotechnical problems with a typical coefficient of variance less than 1. A unique fast computing advantage of the procedure enables computation performed only on those locations of interest, therefore saving a lot of computation. The numerical example on soil settlement shows that the procedure achieves significant computing efficiency compared with Monte Carlo method.

关键词： multiscale finite element settlement perturbation random field geotechnical

An extended stochastic response surface method for random field problems

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Acta Mechanica Sinica 2007年第4期23卷 445-450页

作者： Shuping Huang Xinjian Kou Shanghai Jiaotong University,Shanghai 200240,China Shanghai Jiaotong University Shanghai China

An efficient and accurate uncertainty propagation methodology for mechanics problems with random fields is developed in this paper. This methodology is based on the stochastic response surface method （SRSM） which has been previously proposed for problems dealing with random variables only. This paper extends SRSM to problems involving random fields or random processes fields. The favorable property of SRSM lies in that the deterministic computational model can be treated as a black box, as in the case of commercial finite element codes. Numerical examples are used to highlight the features of this technique and to demonstrate the accuracy and efficiency of the proposed method. A comparison with Monte Carlo simulation shows that the proposed method can achieve numerical results close to those from Monte Carlo simulation while dramatically reducing the number of deterministic finite element runs.

关键词： Stochastic response surface Karhunen-Loeve expansion Polynomial chaos random field Stochastic finite elements

Magnetic properties of mixed Ising system with random field

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Chinese Physics B 2004年第12期13卷 2147-2152页

作者：梁雅秋魏国柱张起邱巍藏树良 DepartmentofPhysics LiaoningUniversityShengyang110036China CollegeofSciences NortheasternUniversityShenyang110006China//InternationalCenterforMaterialPhysicsChineseAcademyofSciencesShengyang110015China CollegeofSciences NortheasternUniversityShenyang110006China SchoolofChemicalScience&Engineering LiaoningUniversityShengyang110036China

A spin-1/2 and spin-3/2 mixed Ising system in a random field is studied by the use of effective-field theory with correlations. The phase diagrams and thermal behaviours of magnetizations are investigated numerically for the honeycomb lattice (z=3) and square lattice (z=4) respectively. The tricritical behaviours for both honeycomb and square lattices, as well as the reentrant behaviour for the square lattice are found.

关键词： mixed spins random field phase diagram magnetizations

Reliability analysis of excavated slopes in undrained clay

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Frontiers of Structural and Civil Engineering 2023年第11期17卷 1760-1775页

作者： Shuang SHU Bin GE Yongxin WU Fei ZHANG Key Laboratory of the Ministry of Education for Geomechanics and Embankment Engineering College of Civil and Transportation EngineeringHohai UniversityNanjing 210098China

A novel approach based on the upper bound theory is proposed to assess the stability of excavated slopes with spatially variable clay in undrained conditions.The proposed random limit analysis is a combination of the deterministic slope stability limit analysis together with random field theory and Monte Carlo simulation.A series of analyses is conducted to verify the potential application of the proposed method and to investigate the effects of the soil undrained shear strength gradient and the spatial correlation length on slope stability.Three groups of potential sliding surfaces are identified and the occurrence probability of each sort of failure mechanism is quantified for various slope ratios.The proposed method is found to be feasible for evaluating slope reliability.The obtained results are helpful in understanding the slope failure mechanism from a quantitative point of view.The paper could provide guidance for slope targeted local reinforcement.

关键词： slope stability spatial variability limit analysis random field clay

Numerical investigation of pile responses induced by adjacent tunnel excavation in spatially variable clays

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Underground Space 2022年第5期7卷 911-927页

作者： Xin Gu Fuyong Chen Wengang Zhang Qi Wang Hanlong Liu School of Civil Engineering Chongqing UniversityChongqingChina Key Laboratory of New Technology for Construction of Cities in Mountain Area Chongqing UniversityChongqingChina National Joint Engineering Research Center of Geohazards Prevention in the Reservoir Areas Chongqing UniversityChongqingChina

The pile responses induced by adjacent tunnel excavation have been a hot research topic in geotechnical engineering.Tunnel excavation may exert disturbance to the surrounding soil mass and then influence the adjacent pile foundations.In this paper,the random finite difference analysis considering the spatial variations of soil properties is conducted to explore the effect of tunnel excavation on the adjacent pile response by varying the distance of pile away from the tunnel centerline(D),the pile length(L),the pile diameter(d_(p)),the tunnel depth(h),and the anisotropic ratio between the horizontal and the vertical scales of fluctuation(δ_(x)/δ_(y)).A set of pile response curves are developed to assess the influence of tunnel excavation on the adjacent passive pile foundations in spatially variable clays and provide guidelines for the tunnel excavation in the complex constructed environment.

关键词： Pile response Tunnel excavation random field Spatially variable clays random finite difference analysis