Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue.In this context,we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e.0°,30°,45°,60°,and 90°),under multiple levels of direct shearing for the first time.The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior.Under a low shear stress,the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations,and the increase depends on the bedding orientation and creep time.Under high shear stress conditions,the creep compliance of shale is minimal when the bedding orientation is 0°,and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°,45°,60°,and 90°.The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation.A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed.The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate.The applicability of the five classical empirical creep models is quantitatively evaluated.It shows that the logarithmic model can well explain the experimental creep strain and creep rate,and it can accurately predict long-term shear creep deformation.Based on an improved logarithmic model,the variations in creep parameters with shear stress and bedding orientations are discussed.With abovementioned findings,a mathematical method for constructing an anisotropic shear creep model of shale is proposed,which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.

Non-equal-interval direct optimizing Verhulst model that x(n) be taken as initial value and its application

To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) of X(0) as the starting condition of the grey differential model. It optimizes a modified β value and the background value, and takes two times fitting optimization. The new model extends equal intervals to non-equal-intervals and is suitable for general data modelling and estimating parameters of the direct Verhulst GM(1,1). The new model does not need to pre-process the primitive data, nor accumulate generating operation (AGO) and inverse accumulated generating operation (IAGO). It is not only suitable for equal interval data modelling, but also for non-equal interval data modelling. As the new information is fully used and two times fitting optimization is taken, the fitting accuracy is the highest in all existing models. The example shows that the new model is simple and practical. The new model is worth expanding on and applying in data processing or on-line monitoring for tests, social sciences and other engineering sciences.

On establishment of novel constitutive model for directionally solidified nickel-based superalloys utilizing machine learning methods

To enhance the accuracy of mechanical simulation in the directional solidification process of turbine blades for heavy-duty gas turbines,a new constitutive model that employs machine learning methods was developed.This model incorporates incremental learning and transfer learning,thus improves the predictive accuracy and generalization performance.To account for the anisotropy of the directionally solidified alloy,a deformation direction parameter is added to the model,enabling prediction of the stress-strain relationship of the alloy under different deformation directions.The predictive capabilities of both models are evaluated using correlation coefficient(R),average relative error(δ),and value of relative error(RE).Compared to the traditional model,the machine learning constitutive model achieves higher prediction accuracy and better generalization performance.This offers a new approach for the establishment of flow constitutive models for other directionally solidified and single-crystal superalloys.

基于粒子群算法最优化Verhulst模型的开采残余下沉预测

矿区开采引起的残余下沉稳定时间长、潜在危害大,有必要准确地预测矿区地表的残余下沉。鉴于传统的残余下沉Verhulst模型建模误差大、适用性弱,在建模过程中以数据序列的首个数据保持不变导致预测效果差的缺陷,以直接离散Verhulst模型为基础,引入粒子群算法寻求模型迭代初始值的最优解,建立基于粒子群算法优化的矿区开采残余下沉直接离散Verhulst模型,并以山西阳泉和山东兖州矿区两个时间尺度的地表残余下沉监测数据集进行实例验证,最后利用MATLAB App Designer工具实现模型算法的可视化。结果表明:基于粒子群算法优化的直接离散Verhulst模型的矿区开采残余下沉预测精度和稳定性增益明显,所开发的计算工具具有正确性和有效性。

Study of the pressure transient behavior of directional wells considering the effect of non-uniform flux distribution

During the production,the fluid in the vicinity of the directional well enters the wellbore with different rates,leading to non-uniform flux distribution along the directional well.However,in all existing studies,it is oversimplified to a uniform flux distribution,which can result in inaccurate results for field applications.Therefore,this paper proposes a semi-analytical model of a directional well based on the assumption of non-uniform flux distribution.Specifically,the direction well is discretized into a carefully chosen series of linear sources,such that the complex well trajectory can be captured and the nonuniform flux distribution along the wellbore can be considered to model the three-dimensional flow behavior.By using the finite difference method,we can obtain the numerical solutions of the transient flow within the wellbore.With the aid of Green's function method,we can obtain the analytical solutions of the transient flow from the matrix to the wellbore.The complete flow behavior of a directional well is perfectly represented by coupling the above two types of transient flow.Subsequently,on the basis of the proposed model,we conduct a comprehensive analysis of the pressure transient behavior of a directional well.The computation results show that the flux variation along the direction well has a significant effect on pressure responses.In addition,the directional well in an infinite reservoir may exhibit the following flow regimes:wellbore afterflow,transition flow,inclined radial flow,elliptical flow,horizontal linear flow,and horizontal radial flow.The horizontal linear flow can be observed only if the formation thickness is much smaller than the well length.Furthermore,a dip region that appears on the pressure derivative curve indicates the three-dimensional flow behavior near the wellbore.

A statistical damage-based constitutive model for shearing of rock joints in brittle drop mode

Some rock joints exhibit significant brittleness,characterized by a sharp decrease in shear stress upon reaching the peak strength.However,existing models often fail to accurately represent this behavior and are encumbered by numerous parameters lacking clear mechanical significance.This study presents a new statistical damage constitutive model rooted in both damage mechanics and statistics,containing only three model parameters.The proposed model encompasses all stages of joint shearing,including the compaction stage,linear stage,plastic yielding stage,drop stage,strain softening stage,and residual strength stage.To derive the analytical expression of the constitutive model,three boundary conditions are introduced.Experimental data from both natural and artificial rock joints is utilized to validate the model,resulting in average absolute relative errors ranging from 3%to 8%.Moreover,a comparative analysis with established models illustrates that the proposed model captures stress drop and post-peak strain softening more effectively,with model parameters possessing clearer mechanical interpretations.Furthermore,parameter analysis is conducted to investigate the impacts of model parameters on the curves and unveil the relationship between these parameters and the mechanical properties of rock joints.Importantly,the proposed model is straightforward in form,and all model parameters can be obtained from direct shear tests,thus facilitating the utilization in numerical simulations.

灰色Verhulst-时间序列组合模型在沉降监测中的应用

针对传统单一的灰色模型、时间序列模型在进行沉降监测数据模型存在精度较低的问题,本文提出了一种灰色Verhulst模型和时间序列模型的组合优化模型。首先,对灰色Verhulst模型、时间序列模型的基本理论进行阐述;其次,建立了灰色Verhulst-时间序列模型,即以灰色Verhulst模型得到的样本数据拟合值作为时间序列模型进行预测的样本值;最后,通过以某建筑物沉降监测点为例进行计算并进行灰色Verhulst模型、时间序列模型以及灰色Verhulst-时间序列模型的预测结果对比。实验结果表明,灰色Verhulst-时间序列组合优化模型的预测精度最高,均方差为0.3275 mm,验证了该组合模型更贴合建筑物沉降的变形趋势。

基于灰色Verhulst模型的矿区地表沉降预测研究

灰色Verhulst模型是灰色系统理论模型的重要组成之一,对“S”形曲线具有良好的表现能力。针对灰色Verhulst模型在矿区地表沉降预测中的适用性问题,以灰色Verhulst模型为矿区地表沉降预测模型,以某煤矿综采工作面地表沉降监测数据为数据源,选取其中2个点(M36和M79)开展了灰色Verhulst模型地表沉降预测研究。同时,以后验差比C、小误差概率P和预测值平均相对误差综合进行模型预测精度评价。结果表明:M36和M79号点的预测结果P值均为1,C值分别为0.22和0.07,模型等级均为优秀。M36和M79号点的预测结果平均相对误差分别为1.18和0.27,与C、P值保持一致。灰色Verhulst模型可对地下采煤引起的地表移动初始期、活跃期和衰退期三个阶段开展全周期预测,是矿区地表沉降预测的适用性模型。

Cloud-Verhulst hybrid prediction model for dam deformation under uncertain conditions

Uncertainties existing in the process of dam deformation negatively influence deformation prediction. However, existing deformation pre- diction models seldom consider uncertainties. In this study, a cloud-Verhulst hybrid prediction model was established by combing a cloud model with the Verhulst model. The expectation, one of the cloud characteristic parameters, was obtained using the Verhulst model, and the other two cloud characteristic parameters, entropy and hyper-entropy, were calculated by introducing inertia weight. The hybrid prediction model was used to predict the dam deformation in a hydroelectric project. Comparison of the prediction results of the hybrid prediction model with those of a traditional statistical model and the monitoring values shows that the proposed model has higher prediction accuracy than the traditional sta- tistical model. It provides a new approach to predicting dam deformation under uncertain conditions.

A Study on Sulfate Optical Properties and Direct Radiative Forcing Using LASG-IAP General Circulation Model

The direct radiative forcing （DRF） of sulfate aerosols depends highly on the atmospheric sulfate loading and the meteorology, both of which undergo strong regional and seasonal variations. Because the optical properties of sulfate aerosols are also sensitive to atmospheric relative humidity, in this study we first examine the scheme for optical properties that considers hydroscopic growth. Next, we investigate the seasonal and regional distributions of sulfate DRF using the sulfate loading simulated from NCAR CAM-Chem together with the meteorology modeled from a spectral atmospheric general circulation model （AGCM） developed by LASG-IAP. The global annual-mean sulfate loading of 3.44 mg m-2 is calculated to yield the DRF of -1.03 and -0.57 W m-2 for clear-sky and all-sky conditions, respectively. However, much larger values occur on regional bases. For example, the maximum all-sky sulfate DRF over Europe, East Asia, and North America can be up to -4.0 W m-2. The strongest all-sky sulfate DRF occurs in the Northern Hemispheric July, with a hemispheric average of -1.26 W m-2. The study results also indicate that the regional DRF are strongly affected by cloud and relative humidity, which vary considerably among the regions during different seasons. This certainly raises the issue that the biases in model-sinmlated regional meteorology can introduce biases into the sulfate DRF. Hence, the model processes associated with atmospheric humidity and cloud physics should be modified in great depth to improve the simulations of the LASG-IAP AGCM and to reduce the uncertainty of sulfate direct effects on global and regional climate in these simulations.

Progress on modeling and simulation of directional solidification of superalloy turbine blade casting

Directional solidified turbine blades of Ni-based superalloy are widely used as key parts of the gas turbine engines.The mechanical properties of the blade are greatly influenced by the final microstructure and the grain orientation determined directly by the grain selector geometry of the casting.In this paper,mathematical models were proposed for three dimensional simulation of the grain growth and microstructure evolution in directional solidification of turbine blade casting.Ray-tracing method was applied to calculate the temperature variation of the blade.Based on the thermo model of heat transfer,the competitive grain growth within the starter block and the spiral of the grain selector,the grain growth in the blade and the microstructure evolution were simulated via a modified Cellular Automaton method.Validation experiments were carried out,and the measured results were compared quantitatively with the predicted results.The simulated cooling curves and microstructures corresponded well with the experimental results.The proposed models could be used to predict the grain morphology and the competitive grain evolution during directional solidification.

Distributed modeling of direct solar radiation on rugged terrain of the Yellow River Basin

Due to the influences of local topographical factors and terrain inter-shielding, calculation of direct solar radiation （DSR） quantity of rugged terrain is very complex. Based on digital elevation model （DEM） data and meteorological observations, a distributed model for calculating DSR over rugged terrain is developed. This model gives an all-sided consideration on factors influencing th a resolution of 1 km × 1 km for thDSR. Using the developed model, normals of annual DSR quantity wie Yellow River Basin was generated, with DEM data as the general characterization of terrain. Characteristics of DSR quantity influenced by geographic and topographic factors over rugged terrain were analyzed thoroughly. Results suggest that： influenced by local topographic factors, i.e. azimuth, slope and so on, and annual DSR quantity over mountainous area has a clear spatial difference; annual DSR quantity of sunny slope （or southern slope） of mountains is obviously larger than that of shady slope （or northern slope）. The calculated DSR quantity of the Yellow River Basin is provided in the same way as other kinds of spatial information and can be employed as basic geographic data for relevant studies as well.

Foreign Direct Investment with Chinese Characteristics:A Middle Path Between Ownership-Location-Internalization Model and Linkage-Leverage-Learning Model

The majority of multinational enterprises （MNEs） traditionally originate from developed countries. In the last ten years, however, there has been dramatic growth in foreign direct investment （FDI） from China. It is a comparatively new phenomenon that challenges the classic FDI theories. In this paper, we review the pros and cons of two important theories, known as the Owner- ship-Location-Internalization （0LI） model and Linkage-Leverage-Learning （LLL） model, and use the statistical data and company case studies from China to test the plausibility of these two models. We believe that neither of them suits totally： the OLI model is quite use- fill for understanding FDI from China to developing economies, while the LLL model is more powerful for explaining the FDI to de- veloped economies. We argue that the companies from China attain a very advantageous position as intermediates in the global economy They may catch up with the first movers if they integrate OLI-led and LLL-led FDI within one firm. This combination can bring to- gether the most advanced knowledge acquired in developed economies with the knowledge about adaptation needs and the needs for cost reduction in production as expressed in developing economies. It may also accelerate the knowledge transfer globally. We thus fill a gap in research into the geographical pattern of Chinese FDI and offer a deeper understanding of the internationalization of Chinese MNEs and revolving knowledge transfer.

Direct Climatic Effect of Dust Aerosol in the NCAR Community Atmosphere Model Version 3 (CAM3)

Direct climate responses to dust shortwave and longwave radiative forcing （RF） are studied using the NCAR Community Atmosphere Model Version 3 （CAM3）. The simulated RF at the top of the atmosphere （TOA） is-0.45 W m-2 in the solar spectrum and ＋0.09 W m-2 in the thermal spectrum on a global average. The magnitude of surface RF is larger than the TOA forcing, with global mean shortwave forcing of-1.76 W m-2 and longwave forcing of ＋0.31 W m-2 . As a result, dust aerosol causes the absorption of 1.1 W m-2 in the atmosphere. The RF of dust aerosol is predicted to lead to a surface cooling of 0.5 K over the Sahara Desert and Arabian Peninsula. In the meantime, the upper troposphere is predicted to become warmer because of the absorption by dust. These changes in temperature lead to a more stable atmosphere, which results in increases in surface humidity. The upward sensible and latent heat fluxes at the surface are reduced, largely balancing the surface energy loss caused by the backscattering and absorption of dust aerosol. Precipitation is predicted to decrease moderately on a global scale.

Direct modeling for computational fluid dynamics

All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes （NS） equations. The current computational fluid dynamics （CFD） focuses on the numerical solution of partial differential equations （PDEs）, and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numer- ical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require fur- ther expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional dis- tinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of con- structing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm develop- ment. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be mod- eled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct construction of dis- crete numerical evolution equations, where the mesh size and time step will play dynamic roles in the modeling process. With the variation of the ratio between mesh size and local particle mean free path, the scheme will capture flow physics from the kinetic particle transport and collision to the hydro- dynamic wave propagation. Based on the direct modeling, a continuous dynamics of flow motion will be captured in the unified gas-kinetic scheme. This scheme can be faithfully used to study the unexplored non-equilibrium flow physics in the transition regime.

Direct Nitrous Oxide Emissions Related to Fertilizer-Nitrogen, Precipitation, and Soil Clay Fraction: Empirical Models

Direct nitrous oxide(N2O) emissions(DNEs) from croplands are required in national inventories of greenhouse gases. The Intergovernmental Panel on Climate Change(IPCC) guidelines provide an approach using direct emission factors(EFds) to estimate DNEs, which are constants for large regions. The goal of this paper is to establish empirical models to account for the temporal and spatial variations of EFds, which, apart from the nitrogen addition rate, also vary with a range of environmental factors, so as to enhance the accuracy of regional/national DNE estimates. Therefore, the seasonal/annual DNEs(n = 71) from upland croplands, which are the differences in N2 O emissions between fields with and without fertilizer-nitrogen addition, were used to statistically relate DNEs to regulating factors including the fertilizer-nitrogen addition rate(FN), and environmental(climate and soil) factors. The multivariate stepwise linear regression results showed positive combined effects of FN and clay fraction on DNEs(R2 = 0.61, p < 0.001). Furthermore, the nonlinear regression of FN, precipitation, and clay fraction was also adopted for prediction(R2 = 0.50, p < 0.001). Validation with an independent dataset(n = 31) suggested that both models were better predictors of DNEs than the IPCC model, which only depends on FN. These empirical models may provide simple but reliable approaches for compiling regional/national, and even global inventories of DNEs from croplands. However, both models were restricted to a limited sample size. Understandably, more field observations are still required to further validate the global applicability of these simple approaches.

Acoustic emission activity in directly tensile test on marble specimens and its tensile damage constitutive model

For understanding acoustic emission （AE） activity and accumulation of micro-damage inside rock under pure tensile state, the AE signals has been monitored on the test of directly tension on two kinds of marble specimens. A tensile constitutive model was proposed with the damage factor calculated by AE energy rate. The tensile strength of marble was discrete obviously and was sensitive to the inside microdefects and grain composition. With increasing of loading, the tensile stress-strain curve obviously showed nonlinear with the tensile tangent modulus decreasing. In repeated loading cycle, the tensile elastic modulus was less than that in the previous loading cycle because of the generation of micro damage during the prior loading. It means the linear weakening occurring in the specimens. The AE activity was corresponding with occurrence of nonlinear deformation. In the initial loading stage which only elastic deformation happened on the specimens, there were few AE events occurred; while when the nonlinear deformation happened with increasing of loading, lots of AE events were generated. The quantity and energy of AE events were proportionally related to the variation of tensile tangent modulus. The Kaiser effect of AE activity could be clearly observed in tensile cycle loading. Based on the theory of damage mechanics, the damage factor was defined by AE energy rate and the tensile damage constitutive model was proposed which only needed two property constants. The theoretical stress-strain curve was well fitted with the curve plotted with tested datum and the two property constants were easily gotten by the laboratory testing.

DYNAMIC PREDICION OF FOREST FUEL LOADS BY GREY VERHULST MODEL

The variation of fuel loads after a fire for three forest types, phododendron -Larix gmetinii forest, herb--Larix gmelinii forest and herb--Betula plalyphlla forest , in the northern forest area of Daxing’anling region was discussed. The dynamic models were developed by gray theory for estimating the fuels loads of arbor- shrub, herbs’ grass, litter, and semi-decomposed litter, inflamma ble fuel and the total fuels in each forest type. After a fire, the inflammabIe fuel loads in phododendron-- Larix gmelinii forest and in the herb- - Betula platyphlla fores was estimated at 10.958 t/hm2and 10.473 t/hm2 respectively’ by 13 years later. and that was 12.297 t/hm 2 in herb--Larix gmeliniiforest by 7 years later.. It was predicated that a big fire may occur after 10 years based on inflammable fuel biomass accumulated.

Mathematical model of the direct reduction of dust composite pellets containing zinc and iron

Direct reduction of dust composite pellets containing zinc and iron was examined by simulating the conditions of actual production process of a rotary hearth furnace （RHF） in laboratory. A mathematical model was constructed to study the reduction kinetics of iron oxides and ZnO in the dust composite pellets. It was validated by comparing the calculated values with experimental results. The effects of furnace temperature, pellet radius, and pellet porosity on the reduction were investigated by the model. It is shown that furnace temperature has obvious influence on both of the reduction of iron oxides and ZnO, but the influence of pellet radius and porosity is much smaller. Model calculations suggest that both of the reduction of iron oxides and ZnO are under mixed control with interface reactions and Boudouard reaction in the early stage, but only with interface reactions in the later stage.