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The unidirectional consolidation theory of soils is widely used in certain conditions and approximate calculations. The multidirectional theory of soil consolidation is more reasonable than the unidirectional theory in practical applications but is much more complicated in terms of index determination and solution. To address the above problem, in this paper, we propose a deep learning method using physics-informed neural networks (PINN) to predict the excess pore water pressure of two-dimensional soil consolidation. In the proposed method, (1) a fully connected neural network is constructed; (2) the computational domain, partial differential equation (PDE), and constraints are defined to generate data for model training; and (3) the PDE of two-dimensional soil consolidation and the model of the neural network are connected to reduce the loss of the model. The effectiveness of the proposed method is verified by comparison with the numerical solution of PDE for two-dimensional consolidation. Moreover, the FEM and the proposed PINN-based method are applied to predict the consolidation of foundation soils in a real case of Sichuan Railway in China, and the results are quite consistent. The proposed deep learning approach can be used to investigate large and complex multidirectional soil consolidation. [ABSTRACT FROM AUTHOR]

PM 2.5 is one of the most severe types of air pollution that threatens human health. Its emissions have a notable spillover effect once released into the atmosphere and transported. In domestic trade, PM 2.5 emissions can be indirectly imported from external regions. Thus, regional inequity caused by PM 2.5 needs to be integrated and comprehensively estimated. Based on PM 2.5 emissions/concentrations grid maps and an input-output model, this study first examined the temporal-spatial changes in PM 2.5 emissions/concentrations across China. Additionally, a detailed relationship between PM 2.5 emissions and concentrations was examined at multiple scales, both temporal and spatial. Finally, this study developed a new approach with which to evaluate regional inequity. The results show that PM 2.5 emissions and concentrations increased between 1990 and 2012 and 1998 and 2016, respectively; the increase was more obvious for PM 2.5 emissions. Spatially, a rapid increase in PM 2.5 emissions was observed in the North China Plain and the Sichuan Basin. Between 1998 and 2012, the distribution of PM 2.5 concentrations was similar to that of emissions; however, between 2013 and 2016, 46.6% of the total area showed a decrease, mainly in the central and southern parts of China. Relationship analysis revealed that PM 2.5 emissions and concentrations are closely correlated in both time and space. There was obvious regional inequity among provinces; developed regions always imported considerably more PM 2.5 emissions from undeveloped regions than they exported. Overall, the regional inequity estimation framework shows that provinces along the coastline, especially developed provinces, have advantages under the regional inequity estimation framework, while most of the inland regions have disadvantages, especially in the west and north. • China's PM 2.5 emissions and concentration both increase obviously on the whole. • China's east is the hot region for PM 2.5 pollutions • Provincial PM 2.5 emissions has a tight connection with the concentration. • The innovatively designed model for inequity checking is simple and effective. • Most of the coastline provinces take advantages in regional inequity. [ABSTRACT FROM AUTHOR]