A New Approach for the Calculation of Slope Failure Probability with Fuzzy Limit-State Functions

This study presents an innovative approach to calculating the failure probability of slopes by incorporating fuzzylimit-state functions,a method that significantly enhances the accuracy and efficiency of slope stability analysis.Unlike traditional probabilistic techniques,this approach utilizes a least squares support vector machine(LSSVM)optimized with a grey wolf optimizer(GWO)and K-fold cross-validation(CV)to approximate the limit-statefunction,thus reducing computational complexity.The novelty of this work lies in its application to one-dimensional(1D),two-dimensional(2D),and three-dimensional(3D)slope models,demonstrating its versatility andhigh precision.The proposed method consistently achieves error margins within 3%of Monte Carlo simulation(MCS)results,while substantially reducing computation time,particularly for 2D and 3D models.This makes theapproach highly practical for real-world engineering applications.Furthermore,by applying fuzzy mathematics tohandle uncertainties in geotechnical properties,the method offers a more realistic and comprehensive understandingof slope stability.As water is the main factor influencing the stability of slopes,this aspect is investigatedby calculating the phreatic line after the change in water level.Relevant examples are used to show that the failureprobability of a slope under water wading condition can increase by more than 20%(increase rates in 1D,2D and3D conditions being 25%,27%and 31%,respectively)compared with the natural condition.The influence ofdiverse fuzzy membership functions—linear,normal,and Cauchy—on failure probability is also considered.Thisresearch not only provides a strategy for better calculation of the slope failure probability but also pioneers theintegration of computational intelligence,fuzzy logic and fluid-dynamics in geotechnical engineering,presentingan innovative and efficient tool for slope stability analysis.

AN APPLICATION OF EXTENSION THEORY TO THE EVALUATION OF SLOPE STABILITY

The slope stability is affected by multiple factors. Thecomprehensive evaluation of the slope stability is a complicateproblem. The principles of extension theory have been used in thispaper to establish the matter-element model for the evaluation ofslope stability. The quantitative evaluated results have been giventhrough the calculation of the matter-element dependent degree.

Concept Development and Implementation of Family Care/Caring Theory in Concentric Sphere Family Environment Theory

Caring is directed toward a variety of things. One of them is thought to be the concept of “family caring” aimed at families. This study attempts to clarify family caring and develop Family Care/ Caring Theory (FCCT), with the aim of implementing it in conjunction with an existing family nursing theory, the Concentric Sphere Family Environment Theory (CSFET). In Japan and in Hong Kong, family ethnography (including formal interviews) was conducted. As a result, the item “family health care nurses and their colleagues” was added to the family external environment of the CSFET. In the family environment, evidence was obtained to the effect that the family system unit is cared for by the nursing professional, and conversely the family system unit cares for the nursing professional, in a circular transaction. Observing the two-dimensional plane formed by the structural distance and functional distance, family caring assumes a structure of concentric circles, and according to transactions, the structural distance and functional distance between the nursing professional and family system unit are gradually approached, and through deepening of mutual trust maintain an appropriate distance. Moreover observing the three-dimensional space-time continuum which is created through addition of the temporal distance, family caring forms a helical structure. As transactions are repeated along the temporal axis, the family system unit’s self-actualization of other individuals and the self-actualization of the nursing professional are realized. Through these processes, a family care/caring relationship is reinforced and established. This is the concept of FCCT. Through future utilization in clinical settings this will be empirically substantiated, and it will be necessary to continue making creative corrections and revisions.

Effect of graph generation on slope stability analysis based on graph theory

Limit equilibrium method （LEM） and strength reduction method （SRM） are the most widely used methods for slope stability analysis. However, it can be noted that they both have some limitations in practical application. In the LEM, the constitutive model cannot be considered and many assumptions are needed between slices of soil/rock. The SRM requires iterative calculations and does not give the slip surface directly. A method for slope stability analysis based on the graph theory is recently developed to directly calculate the minimum safety factor and potential critical slip surface according to the stress results of numerical simulation. The method is based on current stress state and can overcome the disadvantages mentioned above in the two traditional methods. The influences of edge generation and mesh geometry on the position of slip surface and the safety factor of slope are studied, in which a new method for edge generation is proposed, and reasonable mesh size is suggested. The results of benchmark examples and a rock slope show good accuracy and efficiency of the presented method.

An approach for determination of lateral limit angle in kinematic planar sliding analysis for rock slopes

Planar sliding is one of the frequently observed types of failure in rock slopes.Kinematic analysis is a classic and widely used method to examine the potential failure modes in rock masses.The accuracy of planar sliding kinematic analysis is significantly influenced by the value assigned to the lateral limit angleγlim.However,the assignment ofγlim is currently used generally based on an empirical criterion.This study aims to propose an approach for determining the value ofγlim in deterministic and probabilistic kinematic planar sliding analysis.A new perspective is presented to reveal thatγlim essentially influences the probability of forming a potential planar sliding block.The procedure to calculate this probability is introduced using the block theory method.It is found that the probability is correlated with the number of discontinuity sets presented in rock masses.Thus,different values ofγlim for rock masses with different sets of discontinuities are recommended in both probabilistic and deterministic planar sliding kinematic analyses;whereas a fixed value ofγlim is commonly assigned to different types of rock masses in traditional method.Finally,an engineering case was used to compare the proposed and traditional kinematic analysis methods.The error rates of the traditional method vary from 45%to 119%,while that of the proposed method ranges between 1%and 17%.Therefore,it is likely that the proposed method is superior to the traditional one.

Development of a DFN-based probabilistic block theory approach for bench face angle design in open pit mining

In open pit mining,uncontrolled block instabilities have serious social,economic and regulatory consequences,such as casualties,disruption of operation and increased regulation difficulties.For this reason,bench face angle,as one of the controlling parameters associated with block instabilities,should be carefully designed for sustainable mining.This study introduces a discrete fracture network(DFN)-based probabilistic block theory approach for the fast design of the bench face angle.A major advantage is the explicit incorporation of discontinuity size and spatial distribution in the procedure of key blocks testing.The proposed approach was applied to a granite mine in China.First,DFN models were generated from a multi-step modeling procedure to simulate the complex structural characteristics of pit slopes.Then,a modified key blocks searching method was applied to the slope faces modeled,and a cumulative probability of failure was obtained for each sector.Finally,a bench face angle was determined commensurate with an acceptable risk level of stability.The simulation results have shown that the number of hazardous traces exposed on the slope face can be significantly reduced when the suggested bench face angle is adopted,indicating an extremely low risk of uncontrolled block instabilities.

Exactly Solvable Two-Parameter Models of Relativistic δ′s -Sphere Interactions in Quantum Mechanics

We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.

基于随机场理论的反倾斜坡变形演化特征研究

基于改进颗粒流的数值模拟方法,建立反倾斜坡土体参数的空间变异性模型,研究土体参数空间变异性对反倾斜坡变形演化过程的影响,对比分析确定性反倾斜坡变形演化和随机场理论反倾斜坡变形演化特征。结果表明:反倾斜坡变形演化分为坡脚初始剪切破坏、剪断面贯通坡体、倾倒破坏起始3个关键节点;土体参数的空间变异性导致反倾斜坡的破坏速度增加,坡脚裂缝和剪断面贯通速度加快;土体参数的空间变异性还使反倾斜坡的前缘和后缘破坏深度增加,而对剪切破坏面与节理面法向夹角、后缘张拉角的影响较小。

美国俄亥俄州残疾儿童教育联盟家长教育的理念与实践

美国俄亥俄州残疾儿童教育联盟基于爱普斯坦的交叠影响域理论和家校合作实践框架开展特殊儿童家长教育活动,活动主题涉及教养技能辅导、心理健康调适和社会资源支持三方面,活动开展方式主要是与社会机构开展合作、为家校合作建立渠道和搭建学习资源应用平台。借鉴上述经验,我国应构建家校社协同育人框架,提高特殊儿童家长教育质量;设计个性化的教育内容,重视特殊儿童家长教育需求;丰富家长学习形式,提升特殊儿童家长的教育参与意愿。

基于场域理论的文化和旅游融合测度及机制研究——以安徽省为例

基于场域理论,运用物理学容量耦合模型测度文旅融合水平,采用灰色斜率相似关联度模型探讨文旅融合机制。结果显示:2012—2021年安徽省文游两大子系统发展水平及融合发展度总体水平较低,以中、低等级为主;社会环境变化引起两大子系统及融合系统的剧烈波动,旅游子系统波动更加激烈,文旅融合发展度阶段性特征明显,旅游子系统对融合系统的影响显著;文旅融合主要贡献力量源自文化子系统,而主要阻滞力量来自旅游子系统。提出该省应优化文旅融合供给侧场域、引领文旅融合需求侧场域和规范文旅场域惯习行动等对策。

季节性循环冻融下岩质边坡稳定性分析

为探究循环冻融对岩质边坡稳定性的影响,以中国东北某矿山受季节性循环冻融影响的岩质边坡为研究对象,考虑-5℃、-10℃、-15℃、-20℃4种冻融温度梯度,探究1,3,5,7次循环冻融下岩体力学特性劣化规律,并基于MSDP准则开展岩质边坡稳定性评价。研究结果表明:随着冻融温度梯度降低和循环冻融次数增加,试样内部冻缩加剧,试样抗压强度降低2.9%~20.3%,抗拉强度降低6.1%~24.8%,内聚力和内摩擦角分别降低6.5%~13.7%、2.2%~17.3%;当冻融温度梯度固定时,试样拉压力学性能随循环冻融次数增加出现大幅度降低,再次回升后趋于稳定,3次完整循环冻融下试样力学特性降幅最大。疲劳损伤作用下试样内部裂隙不断扩张发育,间断形的裂纹逐渐衍生贯通,裂纹数量随循环冻融次数的增加而增多,细观角度分析冻融对岩体强度劣化的实质是循环冻融下产生的疲劳损伤。基于MSDP准则下求算出的安全系数小于常规极限平衡法求算的安全系数。冻融温度-20℃、循环冻融7次时安全系数最低,循环冻融作用下,试样内部发生了不可逆的结构性损伤,试样强度劣化后抗滑力下降,边坡安全系数随之降低。计算结果可为循环冻融作用下岩质边坡稳定性评价提供参考。

INDENTATION OF A TRANSVERSELY ISOTROPIC PIEZOELECTRIC HALF-SPACE BY A RIGID SPHERE

This paper exactly analyzes the problem of a rigid sphereindenting a transversely isotropic piezoelectric half-space. Thepotential theory method is employed and generalized to included thepiezoelec- tric effect. By using the previous results of elasticity,an exact solution is derived. It is found that all the elastoelectricvariables can be expressed in terms of elementary functions.

Statistical Distribution of Surface Slope in A 3-D Ocean Wave Field

A joint probability density function (PDF) for surface slopes in two arbitrary directions is derived on the basis of Longuet Higgins's linear model for three-dimensionol (3-D) random wave field. and the correlation moments of surface slopes. as parameters in the PDF, are expressed in terms of directional spectrum of ocean waves. So long as the directional spectrum model is given, these parameters are determined. Since the directional spectrum models proposed so far are mostly parameterized by the wind speed and fetch, this allows for substituting these parameters with thc wind speed and fetch. As an example, the wind speed and fetch are taken to be 14 m ' s and 200 km, and the Hasselmann and Donclan directional spectra are, respectively, use to compute these parameters. Some novel results a reobtained. One of the increasing interesting results is that the variances of surface slope in downwind and cross-wind directions determined by the Donclan directional spectra are close to those measured by Cox and Munk (1954). Some discussions are made on these results.

Deep learning-based key-block classification framework for discontinuous rock slopes

The key-blocks are the main reason accounting for structural failure in discontinuous rock slopes, and automated identification of these block types is critical for evaluating the stability conditions. This paper presents a classification framework to categorize rock blocks based on the principles of block theory. The deep convolutional neural network(CNN) procedure was utilized to analyze a total of 1240 highresolution images from 130 slope masses at the South Pars Special Zone, Assalouyeh, Southwest Iran.Based on Goodman’s theory, a recognition system has been implemented to classify three types of rock blocks, namely, key blocks, trapped blocks, and stable blocks. The proposed prediction model has been validated with the loss function, root mean square error(RMSE), and mean square error(MSE). As a justification of the model, the support vector machine(SVM), random forest(RF), Gaussian naïve Bayes(GNB), multilayer perceptron(MLP), Bernoulli naïve Bayes(BNB), and decision tree(DT) classifiers have been used to evaluate the accuracy, precision, recall, F1-score, and confusion matrix. Accuracy and precision of the proposed model are 0.95 and 0.93, respectively, in comparison with SVM(accuracy = 0.85, precision = 0.85), RF(accuracy = 0.71, precision = 0.71), GNB(accuracy = 0.75,precision = 0.65), MLP(accuracy = 0.88, precision = 0.9), BNB(accuracy = 0.75, precision = 0.69), and DT(accuracy = 0.85, precision = 0.76). In addition, the proposed model reduced the loss function to less than 0.3 and the RMSE and MSE to less than 0.2, which demonstrated a low error rate during processing.

Seismic ultimate bearing capacity of strip footings on slope

The influence of earthquake forces on ultimate bearing capacity of foundations on sloping ground was studied. A solution to seismic ultimate bearing capacity of strip footings on slope was obtained by utilizing pseudo-static analysis method and taking the effect of intermediate principal stress into consideration. Based on limit equilibrium theory, the formulae for computing static bearing capacity factors, Nq, Nc, Nγ, and dynamic bearing capacity factors, Nqd, Ned, Nγd, which are associated with surcharge, cohesion and self-weight of soils respectively, were presented. A great number of analysis calculations were carried out to obtain the relationship curves of the static and dynamic bearing capacity factors versus various calculation parameters. The curves can serve as the practical engineering design. The calculation results also show that when the values of horizontal and vertical seismic coefficients are 0.2, the dynamic bearing capacity factors Nqd, Ned and Nγd, in which the effects of intermediate principal stress are taken into consideration, increase by 4%-42%, 3%-27% and 34%-57%, respectively.

Analysis of blasting vibration signal of high steep anti-dip layered rock slope

Blasting is one of the most economical and efficient mining methods in open-pit mine production.However,behind the huge benefits,it poses a hidden threat to the quality of slope rock mass,stability of slope,and safety of nearby buildings.In order to explore the influence of blasting vibration on the stability of anti-dip layered rock slopes,herein,the site near the large-scale toppling failure area of Changshanhao gold mine stope of Inner Mongolia Taiping Mining Co.,Ltd.was selected for on-site blasting test and monitoring.The Peak Particle Velocity(PPV)measured at the monitoring point is located on the lower side of the maximum allowable vibration velocity curve that is prepared based on the allowable speed standard evaluation chart in the full frequency domain established by standards practiced in various countries such as German DIN4150,the USBM RI 8507,and Chinese GB6722-2014.This indicates that the blasting vibration has less influence on the location of the monitoring point.The vibration signals obtained in the blasting test were analyzed using the wavelet packet theory,and it was concluded that the blasting vibration signals measured in the anti-dip layered rock slope were mainly concentrated in two frequency bands of 0-80 Hz and 115-160 Hz.The sum of energy of the two frequency bands accounted for more than 99%,wherein,the energy contained in the 0-80 Hz frequency band accounted for more than 85%of the monitoring signals.The vibration signal with 0-80 Hz frequency band monitored at the slope toe was selected for the energy attenuation analysis.The results showed that the energy attenuation decreased in radial,vertical,and tangential directions.Further,the Energy Attenuation Rate per Meter(EARPM)was calculated.In conjunction with the site characteristics analysis,it was found that the energy attenuation rate was significantly affected by the rock mass characteristics of the structural plane.The slope reinforcement project can effectively reduce the absorption of vibration energy by the slope and increase slope stability.

Control of the photodetachment of H^-near a metallic sphere surface by an elastic interface

According to the closed-orbit theory, we study the influence of elastic interface on the photodetachment of H- near a metallic sphere surface. First, we give a clear physical description of the detached electron movement between the elastic interface and the metallic sphere surface. Then we put forward an analytical formula for calculating the photodetachment cross section of this system. Our study suggests that the photodetachment cross section of H is changed with the distance between the elastic interface and H^-. Compared with the photodetachment cross section of H^- near a metallic sphere surface without the elastic interface, the cross section of our system oscillates and its oscillation is strengthened with the decrease of the distance from the elastic interface to H^-. In additon, our calcuation results suggest that the influence of the elastic interface becomes much more significant when it is located in the lower half space rather than in the upper half space. Therefore, we can control the photodetachment of H^- near a metallic sphere surface by changing the position of the elastic interface. We hope that our work is conducive to the understanding of the photodetachment process of negative ions near interfaces, cavities and ion traps.

Enhanced KR-Fundamental Measure Functional for Inhomogeneous Binary and Ternary Hard Sphere Mixtures

An enhanced KR-fundamental measure functional （FMF） is elaborated and employed to investigate binary and ternary hard sphere fluids near a planar hard wall or confined within two planar hard walls separated by certain interval. The present enhanced KR-FMF incorporates respectively, for aim of comparison, a recent 3rd-order expansion equation of state （EOS） and a Boublfk＇s extension of Kolafa＇s EOS for HS mixtures. It is indicated that the two versions of the EOS lead to, in the framework of the enhanced KR-FMF, similar density profiles, but the 3rd-order EOS is more consistent with an exact scaled particle theory （SPT） relation than the BK EOS. Extensive comparison between the enhanced KR-FMF-3rd-order EOS predictions and corresponding density profiles produced in different periods indicates the excellent performance of the present enhanced KR-FMF-3rd-order EOS in comparison with other available density functional approximations （DFAs）. There are two anomalous situations from whose density profiles all DFAs studied deviate significantly; however, subsequent new computer simulation results for state conditions similar to the two anomalous situations are in very excellent agreement with the present enhanced KR-FMF-3rd-order EOS. The present paper indicates that （i） the validity of the ＂naive＂ substitution elaborated in the present paper and peculiar to the original KR-FMF is still in operation even if inhomogeneoas mixtures are being dealt with; （ii） the high accuracy and self-consistency of the third order EOS seem to allow for application of the KR-FMF-third order EOS to more severe state conditions; and （iii） the ＂naive＂ substitution enables very easy the combination of the original KR-FMF with future＇s more accurate but potentially more complicated EOS of hard sphere mixtures.

How to Extend the Bridge Density Functional Approximation to the Confined Non-hard Sphere Fluid

A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simple, quantitatively accurate in a wide range of coexistence phase and external field parameters. Especially, the DFT approach only needs a second order direct correlation function （DCF） of the coexistence bulk fluid as input, and is therefore applicable to the subcritical temperature region. The present theoretical method can be regarded as a non-uniform counterpart of the thermodynamic perturbation theory, in which it is not at the level of the free energy but at the level of the second order DCF.the National Natural Science Foundation of China （No. 20546004） and the Natural Science Foundation of Education Department of Hunan Province （No.04C711）.

Wave Scattering by a Submerged Sphere in Three-Layer Fluid

Using linear water wave theory,three-dimensional problems concerning the interaction of waves with spherical structures in a fluid which contains a three-layer fluid consisting of a layer of finite depth bounded above by freshwater of finite depth with free surface and below by an infinite layer of water of greater density are considered.In such a situation timeharmonic waves with a given frequency can propagate with three wavenumbers.The sphere is submerged in either of the three layers.Each problem is reduced to an infinite system of linear equations by employing the method of multipoles and the system of equations is solved numerically by standard technique.The hydrodynamic forces(vertical and horizontal forces)are obtained and depicted graphically against the wavenumber.When the density ratio of the upper and middle layer is made to approximately one,curves for vertical and horizontal forces almost coincide with the corresponding curves for the case of a two-layer fluid with a free surface.This means that in the limit,the density ratio of the upper and middle layer goes to approximately one,the solution agrees with the solution for the case of a two-layer fluid with a free surface.