Mapping Detailed Soil Property Using Small Scale Soil Type Maps and Sparse Typical Samples

Soil type maps at the scale of I Z 1 000 000 are used extensively to provide soil spatial distribution information for soil erosion assessment and watershed management models in China. However, the soil property maps produced through conventional direct linking method usually suffer low accuracy as well as the lack of spatial details within a soil type polygon. This paper presents an effective method to produce detailed soil property map based on representative samples which were extracted from each polygon on the 1 ： 1 000 000 soil type map. The representative sample of each polygon is defined as the location that can represent the largest area within the polygon. The representativeness of a candidate sample is determined by calculating the soil-forming environment condition similarities between the sample and other locations. Once the representative sample of each polygon has been chosen, the property values of the existing typical samples are assigned to the corresponding representative samples with the same soil type. Finally, based on these representative samples, the detailed soil property map could be produced by using existing digital soil mapping methods. The case study in XuanCheng City, Anhui Province of China, demonstrated the proposed method could produce soil property map at a higher level of spatial details and accuracy： 1） The soil organic matter （SOM） map produced based on the representative samples can not only depict the detailed spatial distribution of SOM within a soil type polygon but also largely reduce the abrupt change of soil property at the boundaries of two adjacent polygons. 2） The Root Mean Squared Error （RMSE） of the SOM map based on the representative samples is 1.61, and it is 1.37 for the SOM map produced by using conventional direct linking method. Therefore, the proposed method is an effective approach to produce spatial detailed soil property map with higher accuracy for environment simulation models.

New judging model of fuzzy cluster optimal dividing based on rough sets theory

To investigate the judging problem of optimal dividing matrix among several fuzzy dividing matrices in fuzzy dividing space, correspondingly, which is determined by the various choices of cluster samples in the totality sample space, two algorithms are proposed on the basis of the data analysis method in rough sets theory： information system discrete algorithm （algorithm 1） and samples representatives judging algorithm （algorithm 2）. On the principle of the farthest distance, algorithm 1 transforms continuous data into discrete form which could be transacted by rough sets theory. Taking the approximate precision as a criterion, algorithm 2 chooses the sample space with a good representative. Hence, the clustering sample set in inducing and computing optimal dividing matrix can be achieved. Several theorems are proposed to provide strict theoretic foundations for the execution of the algorithm model. An applied example based on the new algorithm model is given, whose result verifies the feasibility of this new algorithm model.

Representative elementary volume analysis of polydisperse granular packings using discrete element method

The representative elementary volume （REV） for three-dimensional polydisperse granular packings was determined using discrete element method simulations. Granular mixtures of various sizes and particle size distributions were poured into a cuboid chamber and subjected to uniaxial compression, Findings showed that the minimum REV for porosity was larger compared with the REV for parameters such as coordination number, effective elastic modulus, and pressure ratio. The minimum REV for porosity and other parameters was found to equal 15,10, and 5 times the average grain diameter, respectively. A study of the influence of sample size on energy dissipation in random packing of spheres has also confirmed that the REV size is about 15 times the average grain diameter. The heterogeneity of systems was found to have no effect on the REV for the parameters of interest for the narrow range of coefficient of uniformity analyzed in this paper. As the REV approach is commonly applied in both experimental and numerical studies, determining minimum REV size for polydisperse granular packings remains a crucial issue.