Influence of joint spacing and rock characteristics on the toppling stability of cut rock slope through a simplified limit equilibrium method

Toppling failure of rock mass/soil slope is an important geological and environmental problem.Clarifying its failure mechanism under different conditions has great significance in engineering.The toppling failure of a cutting slope occurred in a hydropower station in Kyushu,Japan illustrates that the joint characteristic played a significant role in the occurrence of rock slope tipping failure.Thus,in order to consider the mechanical properties of jointed rock mass and the influence of geometric conditions,a simplified analytical approach based on the limit equilibrium method for modeling the flexural toppling of cut rock slopes is proposed to consider the influence of the mechanical properties and geometry condition of jointed rock mass.The theoretical solution is compared with the numerical solution taking Kyushu Hydropower Station in Japan as one case,and it is found that the theoretical solution obtained by the simplified analysis method is consistent with the numerical analytical solution,thus verifying the accuracy of the simplified method.Meanwhile,the Goodman-Bray approach conventionally used in engineering practice is improved according to the analytical results.The results show that the allowable slope angle may be obtained by the improved Goodman-Bray approach considering the joint spacing,the joint frictional angle and the tensile strength of rock mass together.

Data-driven methods for predicting the representative temperature of bridge cable based on limited measured data

Cable-stayed bridges have been widely used in high-speed railway infrastructure.The accurate determination of cable’s representative temperatures is vital during the intricate processes of design,construction,and maintenance of cable-stayed bridges.However,the representative temperatures of stayed cables are not specified in the existing design codes.To address this issue,this study investigates the distribution of the cable temperature and determinates its representative temperature.First,an experimental investigation,spanning over a period of one year,was carried out near the bridge site to obtain the temperature data.According to the statistical analysis of the measured data,it reveals that the temperature distribution is generally uniform along the cable cross-section without significant temperature gradient.Then,based on the limited data,the Monte Carlo,the gradient boosted regression trees(GBRT),and univariate linear regression(ULR)methods are employed to predict the cable’s representative temperature throughout the service life.These methods effectively overcome the limitations of insufficient monitoring data and accurately predict the representative temperature of the cables.However,each method has its own advantages and limitations in terms of applicability and accuracy.A comprehensive evaluation of the performance of these methods is conducted,and practical recommendations are provided for their application.The proposed methods and representative temperatures provide a good basis for the operation and maintenance of in-service long-span cable-stayed bridges.

Methodology Validation of Microbial Limit Test of Bupi Qiangli Ointment

[Objective] This study was conducted to establish a microbial limit test method for Bupi Qiangli Ointment. [Method] The conventional method and medium dilution method were used for bacterial, mold and yeast counting in sample recovery test. [Result] The medium dilution method （1：10 test solution, 0.5 ml/plate） could effectively eliminate the inhibition effect of the Bupi Qiangli Ointment, and the recovery of Staphylococcus aureus was greater than 70% in the 3 batches of samples; and the conventional method exhibited the recoveries of E. coil, Bacillus subtilis, Candida albicans and Aspergillus greater than 70% in the 3 batches of samples. [Conclusion] Due to Bupi Qiangli Ointment has strongly antibacterial effect on Staphylococcus au- reus, the medium dilution method was used for bacterial counting, and the conventional method was used for mold and yeast counting; and the conventional method was used for controlled bacterium examination of E. coll.

LIMITED MEMORY BFGS METHOD BY USING LINEAR INDEPENDENT SEARCH DIRECTIONS

The degree of numerical linear independence is proposed and discussed. Based on this linear independence theory, a modified limited memory BFGS method is deve loped. Similar to the standard limited memory method, this new method determines the new update by applying the updating formula m times to an initial positive diagonal matrix using the m previous pairs of the change in iteration and gradient. Besides the most recent pair of the change, which guarantees the quadratic termination, the choice of the other ( m -1) pairs of the change in the new method is dependent on the degree of numerical linear independence of previous search directions. In addition, the numerical linear independence theory is further discussed and the computation of the degree of linear independence is simplified. Theoretical and numerical results show that this new modified method improves efficiently the standard limited memory method.

ELASTIC MODULUS REDUCTION METHOD FOR LIMIT LOAD EVALUATION OF FRAME STRUCTURES

A new strategy for elastic modulus adjustment is proposed based on the element bearing ratio （EBR）,and the elastic modulus reduction method （EMRM） is proposed for limit load evaluation of frame structures. The EBR is defined employing the generalized yield criterion,and the reference EBR is determined by introducing the extrema and the degree of uniformity of EBR in the structure. The elastic modulus in the element with an EBR greater than the reference one is reduced based on the linear elastic finite element analysis and the equilibrium of strain energy. The lower-bound of limit-loads of frame structures are analyzed and the numerical example demonstrates the flexibility,accuracy and effciency of the proposed method.

Overhanging rock slope by design:An integrated approach using rock mass strength characterisation,large-scale numerical modelling and limit equilibrium methods

Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlights an integrated approach of designing overhanging rock slopes where the relative dimensions of the slope exceed the scale of fracturing and the rock mass failure needs to be considered rather than kinematic release of individual blocks. The key to the method is a simplified limit equilibrium(LE) tool that was used for the support design and analysis of a multi-faceted overhanging rock slope. The overhanging slopes required complex geometries with constantly changing orientations. The overhanging rock varied in height from 30 m to 66 m. Geomechanical modelling combined with discrete fracture network(DFN)representation of the rock mass was used to validate the rock mass strength assumptions and the failure mechanism assumed in the LE model. The advantage of the simplified LE method is that buttress and support design iterations(along with sensitivity analysis of design parameters) can be completed for various cross-sections along the proposed overhanging rock sections in an efficient manner, compared to the more time-intensive, sophisticated methods that were used for the initial validation. The method described presents the development of this design tool and assumptions made for a specific overhanging rock slope design. Other locations will have different geological conditions that can control the potential behaviour of rock slopes, however, the approach presented can be applied as a general guiding design principle for overhanging rock cut slope.

Lateral Bearing Capacity of Modified Suction Caissons Determined by Using the Limit Equilibrium Method

The modified suction caisson(MSC) adds a short-skirted structure around the regular suction caissons to increase the lateral bearing capacity and limit the deflection. The MSC is suitable for acting as the offshore wind turbine foundation subjected to larger lateral loads compared with the imposed vertical loads. Determination of the lateral bearing capacity is a key issue for the MSC design. The formula estimating the lateral bearing capacity of the MSC was proposed in terms of the limit equilibrium method and was verified by the test results. Parametric studies on the lateral bearing capacity were also carried out. It was found that the lateral bearing capacity of the MSC increases with the increasing length and radius of the external skirt, and the lateral bearing capacity increases linearly with the increasing coefficient of subgrade reaction. The maximum lateral bearing capacity of the MSC is attained when the ratio of the radii of the internal compartment to the external skirt equals 0.82 and the ratio of the lengths of the external skirt to the internal compartment equals 0.48, provided that the steel usage of the MSC is kept constant.

A New Curve Fitting Method for Forming Limit Experimental Data

The forming limit curve （FLC） can be obtained by means of curve fitting the limit strain points of different strain paths. The theory of percent regression analysis is applied to the curve fitting of forming limit experimental data.Forecast intervals of FLC percentiles can be calculated. Thus reliability and confidence level can be considered. The theoretical method to get the limits of limit strain points distributing region is presented, and the FLC position can be adjusted according to practical requirement. Method for establishing FLC with high reliability using small samples is presented at the same time. This method can make full use of the current experimental data and the previous data.Compared with the traditional method that can only use current experimental data, fewer specimens are required in the present method to obtain the same precision and the result is more accurate with the same number of specimens.

A LIMITED MEMORY QUASI-NEWTON METHOD FOR LARGE SCALE PROBLEM

We study how to use the SR1 update to realize minimization methods for problems where the storage is critical. We give an update formula which generates matrices using information from the last m iterations. The numerical tests show that the method is efficent.

A Generalized Limit Equilibrium Method for the Solution of Active Earth Pressure on a Retaining Wall

In this paper, a generalized limit equilibrium method of solving the active earth pressure problem behind a retaining wall is proposed.Differing from other limit equilibrium methods, an arbitrary slip surface shape without any assumptions of pre-defined shapes is needed in the current framework, which is verified to find the most probable failure slip surface. Based on the current computational framework, numerical comparisons with experiment, discrete element method and other methods are carried out. In addition, the influences of the inclination of the wall, the soil cohesion, the angle of the internal friction of the soil, the slope inclination of the backfill soil on the critical pressure coefficient of the soil, the point of application of the resultant earth pressure and the shape of the slip surface are also carefully investigated. The results demonstrate that limit equilibrium solution from predefined slip plane assumption, including Coulomb solution, is a special case of current computational framework. It is well illustrated that the current method is feasible to evaluate the characteristics of earth pressure problem.

Comprehensive analysis of slope stability and determination of stable slopes in the Chador-Malu iron ore mine using numerical and limit equilibrium methods

One of the critical aspects in mine design is slope stability analysis and the determination of stable slopes. In the Chador- Malu iron ore mine, one of the most important iron ore mines in central Iran, it was considered vital to perform a comprehensive slope stability analysis. At first, we divided the existing rock hosting pit into six zones and a geotechnical map was prepared. Then, the value of MRMR （Mining Rock Mass Rating） was determined for each zone. Owing to the fact that the Chador-Malu iron ore mine is located in a highly tectonic area and the rock mass completely crushed, the Hoek-Brown failure criterion was found suitable to estimate geo-mechanical parameters. After that, the value of cohesion （c） and friction angle （tp） were calculated for different geotechnical zones and relative graphs and equations were derived as a function of slope height. The stability analyses using numerical and limit equilibrium methods showed that some instability problems might occur by increasing the slope height. Therefore, stable slopes for each geotechnical zone and prepared sections were calculated and presented as a function of slope height.

Hermite WENO-based limiters for high order discontinuous Galerkin method on unstructured grids

A novel class of weighted essentially nonoscillatory （WENO） schemes based on Hermite polynomi- als, termed as HWENO schemes, is developed and applied as limiters for high order discontinuous Galerkin （DG） method on triangular grids. The developed HWENO methodology utilizes high-order derivative information to keep WENO re- construction stencils in the von Neumann neighborhood. A simple and efficient technique is also proposed to enhance the smoothness of the existing stencils, making higher-order scheme stable and simplifying the reconstruction process at the same time. The resulting HWENO-based limiters are as compact as the underlying DG schemes and therefore easy to implement. Numerical results for a wide range of flow conditions demonstrate that for DG schemes of up to fourth order of accuracy, the designed HWENO limiters can simul- taneously obtain uniform high order accuracy and sharp, es- sentially non-oscillatory shock transition.

A new slope optimization design based on limit curve method

A new method is proposed for slope optimization design based on the limit curve method, where the slope is in the limit equilibrium state when the limit slope curve determined by the slip-line field theory and the slope intersect at the toe of the slope. Compared with the strength reduction (SR) method, finite element limit analysis method, and the SR method based on Davis algorithm, the new method is suitable for determining the slope stability and limit slope angle (LSA). The optimal slope shape is determined based on a series of slope heights and LSA values, which increases the LSA by 2.45°-11.14° and reduces an invalid overburden amount of rocks by 9.15%, compared with the space mechanics theory. The proposed method gives the objective quantification index of instability criterion, and results in a significant engineering economy.

The height-width ratio limited value for rubber bearing isolated structure computed by uniform design method

Rubber isolation is the most mature control technology in practical application, and is widely used by short rigid buildings. However, many high isolation buildings have been built around the world in recent years, which do not follow the existing criterions and codes. Many researchers began to research the special problems caused by larger height-width ratio isolation structures. The overturning effect of high height-width ratio structures with rubber bearing is firstly studied. Considering the main factors, such as the height-width ratio of structures, type of site, the designed basic acceleration of ground motion and the decouple factor in horizon, computing experiment is defined with the Uniform Design Method, which is also known as designing isolation structure. The forces of the bearing under edge of structures based on the position of the rubber bearing are calculated. The result indicates that the rubber bearings will lose its functionality under very high tension and compressing force of earthquake motion in horizon and vertical, when the height-width ratio is over a certain value. Thus, based on the calculation result of isolation structures defined in the uniform design method, regression analysis is conducted, and also the rubber edge force regression formula are gotten, which has higher correlation and smaller standard deviation. This formula can be used to roughly calculate whether the pull force occurs at the edge of the building. By the edge bearings of isolation structure minimum force formula, the height-width ratio limited value of the isolation structure is deducted when rubber bearing has minimum force of zero.

A Method Combining Numerical Analysis and Limit Equilibrium Theory to Determine Potential Slip Surfaces in Soil Slopes

This paper describes a precise method combining numerical analysis and limit equilibrium theory to determine potential slip surfaces in soil slopes. In this method, the direction of the critical slip surface at any point in a slope is determined using the Coulomb’s strength principle and the extremum principle based on the ratio of the shear strength to the shear stress at that point. The ratio, which is considered as an analysis index, can be computed once the stress field of the soil slope is obtained. The critical slip direction at any point in the slope must be the tangential direction of a potential slip surface passing through the point. Therefore, starting from a point on the top of the slope surface or on the horizontal segment outside the slope toe, the increment with a small distance into the slope is used to choose another point and the corresponding slip direction at the point is computed. Connecting all the points used in the computation forms a potential slip surface exiting at the starting point. Then the factor of safety for any potential slip surface can be computed using limit equilibrium method like Spencer method. After factors of safety for all the potential slip surfaces are obtained, the minimum one is the factor of safety for the slope and the corresponding potential slip surface is the critical slip surface of the slope. The proposed method does not need to pre-assume the shape of potential slip surfaces. Thus it is suitable for any shape of slip surfaces. Moreover the method is very simple to be applied. Examples are presented in this paper to illustrate the feasibility of the proposed method programmed in ANSYS software by macro commands.

DEPENDENCE OF PREDICTION MODEL OF FORMING LIMIT STRAINS ON FORMING METHOD AND MECHANICAL PROPERTIES OF SHEET METALS

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Development of Finite Element Limiting Analysis Method and Its Applications in Geotechnical Engineering

The Finite Element Limiting Analysis Method(LELAM) has the advantage of combining a numerical analysis method with traditional limiting equilibrium methods.It is particularly applicable to the analysis and design of geotechnical engineering.In the early 20th century,FELAM has been developed vigorously in domestic geotechnical engineering over international common finite element procedures.It has made great achievements in basic theory research and computational precision,thus broadening the application fields in practical projects.In order to gradually make innovations in geotechnical design methods,some of our research results are presented,mainly including geotechnical safety factor definitions,the principles for use of the method concerned,the overall failure criterion,the deduction and selection of the yield criterion,and the measurement to improve the computational precision,etc..The application field has been broadened from two-dimensional to three-dimensional,from soil slope to jointed rock slope and foundation,from stable seepage to non-stable seepage,from slope and foundation to tunnel.This method has also been used in search of many hidden sliding surfaces of complex landslides,conducting the structural support design considering the interaction between the soil and the structure,and computing simulation foundation bearing plates load tests,etc..

PREDICTION FOR FORMING LIMIT OF AL2024T3 SHEET BASED ON DAMAGE THEORY USING FINITE ELEMENT METHOD

This paper presents the application of anisotropic damage theory to the study of forming limit diagram of A12024T3 aluminum alloy sheet. In the prediction of limiting strains of the aluminum sheet structure, a finite element cell model has been constructed. The cell model consists of two phases, the aluminum alloy matrix and the intermetallic cluster. The material behavior of the aluminum alloy matrix is described with a fully coupled elasto-plastic damage constitutive equation. The intermetallic cluster is assumed to be elastic and brittle. By varying the stretching ratio, the limiting strains of the sheet under biaxial stretching have been predicted by using the necking criterion proposed. The prediction is in good agreement with the experimental findings. Moreover, the finite element cell model can provide information for understanding the microscopic damage mechanism of the aluminum alloy. Over-estimation of the limit strains may result if the effect of material damage is ignored in the sheet metal forming study.

LOWER BOUND LIMIT ANALYSIS OF THREE-DIMENSIONAL ELASTOPLASTIC STRUCTURES BY BOUNDARY ELEMENT METHOD

Based on the lower bound theorem of limit analysis, a solution procedure for limit analysis of three_dimensional elastoplastic structures was established using conventional boundary element method (BEM). The elastic stress field for lower bound limit analysis was computed directly by three_dimensional boundary element method (3_D BEM). The self_equilibrium stress field was constructed by the linear combination of several self_equilibrium “basis vectors” which can be computed by elastic_plastic incremental iteration of 3_D BEM analysis. The lower bound limit analysis problem was finally reduced to a series of nonlinear programming sub_problems with relatively few optimal variables. The complex method was used to solve the nonlinear programming sub_problems. The numerical results show that the present solution procedure has good accuracy and high efficiency.

Hybrid LEAP modeling method for long-term energy demand forecasting of regions with limited statistical data

An accurate long-term energy demand forecasting is essential for energy planning and policy making. However, due to the immature energy data collecting and statistical methods, the available data are usually limited in many regions. In this paper, on the basis of comprehensive literature review, we proposed a hybrid model based on the long-range alternative energy planning (LEAP) model to improve the accuracy of energy demand forecasting in these regions. By taking Hunan province, China as a typical case, the proposed hybrid model was applied to estimating the possible future energy demand and energy-saving potentials in different sectors. The structure of LEAP model was estimated by Sankey energy flow, and Leslie matrix and autoregressive integrated moving average (ARIMA) models were used to predict the population, industrial structure and transportation turnover, respectively. Monte-Carlo method was employed to evaluate the uncertainty of forecasted results. The results showed that the hybrid model combined with scenario analysis provided a relatively accurate forecast for the long-term energy demand in regions with limited statistical data, and the average standard error of probabilistic distribution in 2030 energy demand was as low as 0.15. The prediction results could provide supportive references to identify energy-saving potentials and energy development pathways.