The development of mountainous towns is limited by the terrain and landforms, resulting in an urban expansion model dominated by new city construction. The geographical spatial manifestation of this model is that the construction of new cities is far from the main urban area and urban construction land gradually expands toward higher slopes (i.e., gradient expansion of construction land). Although gradient expansion solves the problem of land resource scarcity in mountainous towns, it also increases the risk of geological disasters, such as land subsidence. Exploring the law of gradient expansion and identifying disaster risks are paramount. This study selected three new cities with severe gradient expansion as typical case areas and used DEM to obtain the gradient expansion areas of the new areas from 2017 to 2022. Based on Sentinel-1A SAR data from 2016 to 2020, SBAS InSAR technology was used to obtain surface deformation information in order to reveal the spatial correlation between gradient expansion and land subsidence in new areas.
The results showed that, from 2017 to 2022, the gradient expansion phenomenon in Yan'an New Area, Liangjiang New Area, and Lanzhou New Area was significant, with gradient expansion areas accounting for 53.5%, 51.0%, and 45.2%, respectively. Yan'an New Area, which was most severely affected by terrain, had the highest proportion of gradient expansion areas, and the gradient expansion speed was consistent with the urban expansion speed trend.
The maximum settlement velocities in Yan'an New Area, Liangjiang New Area, and Lanzhou New Area were 28, 30, and 29 mm/a, respectively. Settlement mostly occurred at the beginning of the expansion of the new area, and there were different scale-gradient expansion areas around the settlement area.
The intensity of gradient expansion was positively correlated with the rate of land subsidence, and the clustering distribution of areas with high gradient expansion intensity and high ground subsidence rate indicated that urban gradient expansion accelerated the occurrence of land subsidence in the expansion area. This study had positive significance in exploring the correlation between urban gradient expansion and land subsidence, and in promoting the sustainable development of mountainous cities.