Let $i≥2$, $Δ≥0$, $1≤ a≤ b-Δ$, $n>\frac{(a+b)(ib+2m-2)}{a}+n'$ and $δ(G)≥\frac{b^{2}}{a}+n'+2m$, and let $g,f$ be two integer-valued functions defined on $V(G)$ such that $a≤ g(x)≤ f(x)-Δ≤ b-Δ$ for each $x∈ V(G)$. In this article, it is determined that $G$ is a fractional $(g,f,n',m)$-critical deleted graph if $\max\{d_{1},d_{2},···,d_{i}\}≥\frac{b(n+n')}{a+b}$ for any independent subset $\{x_{1},x_{2},..., x_{i}\}\subseteq V(G)$. The result is tight on independent set degree condition.

The focal point of this study is to assess the efficacy of a state-of-the-art optimization technique namely, particle swarm optimization (PSO) for enhancing the performance of the artificial neural network (ANN) in modeling the seismic landslides at Ludian districts, China. Twelve geological and hydrological landslide-conditioning factors namely, elevation, lithology, slope degree, slope aspect, stream power index, peak ground acceleration, topographic wetness index, distance to river, distance to road, distance to fault, normalized difference vegetation index and plan curvature were considered within a geographic information system (GIS). After achieving the optimal structure of the multilayer perceptron neural network, the PSO algorithm was applied to improve its efficiency. The landslide susceptibility maps were generated in a GIS environment and area under the curve (AUC) criterion was used to assess the integrity of employed predictive models. The results showed that after applying the PSO algorithm, AUC experiences a significant increase from 0.765 to 0.825 in the validation phase. Moreover, respective AUCs of 0.812 and 0.828 obtained for the training phase of ANN and PSO-ANN reveal the efficiency of the proposed algorithm in improving the ANN accuracy.

The diffusion progress of grout is hindered by groundwater, which means the diffusion distance cannot reach the designed values required in engineering for water plugging or reinforcement. In this study, based on the generalized Darcy’s law and the continuity equation of steady column penetration, a column diffusion mechanism for Bingham fluid, considering the displacement effect of grout on groundwater, is proposed. This diffusion mechanism is then validated by the penetration grouting experiments that have been previously performed. The influences of the grouting pressure, groundwater pressure, water–cement ratio and penetration coefficient of porous media on the diffusion radius are analyzed. Based on the Comsol Multiphysics platform, a three-dimensional numerical simulation program for this mechanism is developed using computer programming technology. Numerical simulations of the penetration and diffusion morphology of Bingham cement grout in porous media are then carried out. The results show that the theoretical calculation values of diffusion radius obtained from this mechanism are closer to the experimental values than those obtained from the column penetration grouting theory of Bingham fluid, without considering the displacement effect. The results of this study can provide theoretical support for practical grouting engineering.

Fluctuations in reservoir water levels exert a strong triggering effect on landslides along reservoir banks, constituting a long-term concern in the safe operation of hydroelectric projects and in the prevention and management of geological disasters. While existing research has investigated the impact of periodic water level changes on the deformation of reservoir bank landslides, observation and detection of such deformation are challenging, with noticeable gaps in understanding how these deformations respond to water level changes during the water impoundment period. To address this, our study targets the Baihetan Reservoir, leveraging 567 ascending and descending LiCSAR data and LiCSBAS (the small-baseline subset within LiCSAR) technology to construct a time series of ground deformations in the study area from 2019 to 2023. The TLCC (Time Lag Cross Correlation) model was employed to examine the time-lag response pattern of reservoir bank landslide deformations to reservoir water level changes during the impoundment period. Our findings indicate a clear time-lag response in reservoir bank landslide deformations to water level changes during the impoundment process. The rise in water levels emerged as a primary factor influencing the instability of reservoir bank landslides. During the half-year impoundment period of the Baihetan Reservoir, a time lag of 5–7 days was observed between landslide deformations and increases in water levels, with landslides on the eastern and western banks exhibiting differing time-lag response patterns. Our study illuminates the time-lag effect between water level changes during reservoir impoundment and reservoir bank landslide deformation monitoring. By proposing a quantitative analysis methodology utilizing LiCSBAS technology and the TLCC model, our findings can inform decision-making in the field of disaster prevention and reduction in reservoir engineering.

As urban construction has been leaping forward recently, large-scale land subsidence has been caused in Kunming due to the special hydrogeological conditions of the city; the subsidence scope has stretched out, and the subsidence rate has been rising year by year. As a consequence, Kunming’s sustainable development has seriously hindered. The PS-InSAR (Persistent Scatterer Interferometric Synthetic Aperture Radar) and the SBAS-InSAR (Small Baseline Subsets Interferometric Synthetic Aperture Radar) technologies were adopted to process the descending Sentinel-1A data stacks from July 2018 to November 2020 to monitor the land subsidence of Kunming, so as to ensure the sustainable development of the city. Moreover, the causes were analyzed. As revealed by the results, (1) the overall subsidence trend of Kunming was large in the south (Dian lakeside), whereas it was relatively small in the north. The significant subsidence areas showed major distributions in Xishan, Guandu and Jining district. The maximal average subsidence rates of PS-InSAR and SBAS-InSAR were −78 mm/a and −88 mm/a, respectively. (2) The ground Subsidence field of Kunming was analyzed, and the correlation coefficient R² of the two methods was reported as 0.997. In comparison with the leveling data of the identical period, the root mean square error (RMSE) is 6.5 mm/a and 8.5 mm/a, respectively. (3) Based on the urban subway construction data, geological structure, groundwater extraction data and precipitation, the causes of subsidence were examined. As revealed by the results, under considerable urban subways construction, special geological structures and excessive groundwater extraction, the consolidation and compression of the ground surface could cause the regional large-area subsidence. Accordingly, the monthly average precipitation in Kunming in the identical period was collected for time series analysis, thereby indicating that the land subsidence showed obvious seasonal variations with the precipitation. The results of this study can provide data support and facilitate the decision-making for land subsidence assessment, forecasting and construction planning in Kunming.