The spatial effects of rural toilet retrofitting investment on farmers' medical and health expenditure in China.

Background: China stretches across a vast area, and different geographical environments and economic and social development conditions, along with learning imitation and factor flow among participants can lead to two major spatial characteristics of toilet retrofitting investment: spatial heterogeneity and spatial correlation. Methods: This study contributes to explore this topic by assessing the spatial heterogeneity and spatial correlation of toilet retrofitting investment on farmers' medical and health expenditure based on the spatial econometric model. Results: (1) There are significant spatial agglomeration characteristics of both the toilet retrofitting investment and farmers' medical and health expenditure in China. (2) At the national level, the rural toilet retrofitting investment will influence the farmers' medical and health expenditure, and the effect on the local area is greater than on the surrounding areas. (3) After taking into account the differences in natural geographical environment and social and economic development, China is divided into four regions: east, central, west and northeast. In terms of spatial effects within different regions, the intensity of the impact of toilet retrofitting investment on local farmers' medical and health expenditure is in the order of central > eastern > western > northeast. The improvement of people's livelihood in the eastern and central regions by toilet retrofitting investment would lead to imitation by surrounding regions, thus reflecting spillover effects, while in the western region, toilet retrofitting investment would trigger fierce competition in related industries and factor markets, manifesting the competition effect. (4) As for the spatial effects across different regions, the toilet retrofitting investment produces spillover effects in all four regions, among which the intensity of the influence effect is the greatest in the central-western region, followed by the west-northeast, and the influence effect in the east-west is not significant. Discussion: The comprehensive promotion of rural toilet retrofitting should not only focus on investment in the western and northeastern regions, but also strengthen regional communication and cooperation to improve rural residents' health and quality of life.

Method of Fatigue-Life Prediction for an Asphalt Mixture Based on the Plateau Value of Permanent Deformation Ratio.

Laboratory predictions for the fatigue life of an asphalt mixture under cyclic loading based on the plateau value (PV) of the permanent deformation ratio (PDR) were carried out by three-point bending fatigue tests. The influence of test conditions on the recovery ratio of elastic deformation (RRED), the permanent deformation (PD) and PDR, and the trends of RRED, PD, and PDR were studied. The damage variable was defined by using PDR, and the relation of the fatigue life to PDR was determined by analyzing the damage evolution process. The fatigue equation was established based on the PV of PDR and the fatigue life was predicted by analyzing the relation of the fatigue life to the PV. The results show that the RRED decreases with the increase of the number of loading cycles, and the elastic recovery ability of the asphalt mixture gradually decreases. The two mathematical models proposed are based on the change laws of the RRED, and the PD can well describe the change laws. The RRED or the PD cannot well predict the fatigue life because they do not change monotonously with the fatigue life, and one part of the deformation causes the damage and the other part causes the viscoelastic deformation. The fatigue life decreases with the increase of the PDR. The average PDR in the second stage is taken as the PV, and the fatigue life decreases in a power law with the increase of the PV. The average relative error of the fatigue life predicted by the fatigue equation to the test fatigue life is 5.77%. The fatigue equation based on PV can well predict the fatigue life.