Exploring frequency–size relationships of piping-related collapse sinkholes in different morphoclimatic environments.

Piping is a soil erosion process that occurs in almost all morphoclimatic zones and in a widevariety of sediment types. It plays a considerable role in badlands evolution. Pipes(subsurface tunnels) and the associated internal mechanical erosion transfer sedimentfrom hillslopes to channels providing subsurface slope–channel connectivity. Tothe best of our knowledge, this process is not included in soil erosion models andit is not considered in sedimentary budget assessments. However, soil loss ratesrelated to piping may reach significant values, ranging from below 1 t ha−1 y−1, asreported in the US, to 33 t ha−1 y−1 in the Loess Plateau, China, and with a maximumof 550 t ha−1 y−1 in Spain. Therefore, there is a need to better understand thisprocess. This study explores the frequency-size distribution of pipe collapses (PCs) through theconstruction of empirical cumulative frequency curves. The analysis has been performed withfield-based inventories of PCs from two different morphoclimatic environments: one area inthe semi-arid Ebro Depression, NE Spain and 4 areas in the temperate BieszczadyMts., SE Poland. This morphometric study allows us to check for the first time iffrequency–size relationships of PCs follow a power-law as it is proven for many naturalphenomena. PCs developed when the upward propagation of cavity roofs by collapse processes(i.e., stoping) reached the surface, resulting in collapse sinkholes with vertical ornearly vertical walls. There was only subsurface connection between them and theassociated gully/valley systems. These landforms are initiated by piping erosion andthe foundering of the undermined pipe roofs. However, PCs may have a complexmulti-episodic evolution. Once a PC is formed, it may change its size and geometry bymass-wasting processes acting on their walls and by coalescence with adjacent holes. Intotal, more than 720 PCs were analyzed (335 in Spain and 389 in Poland). Thefrequency–size relationships were based on the major axis (m) and area (m2) ofPCs. The cumulative frequency curves of empirical data in the different areas show a similarpattern and high goodness of fit (R2: 0.91-0.98). The cumulative frequency-size distributionfollows a negative power-law for medium-size PCs. However, some differences can be noted.For instance, PCs in NE Spain show larger dimensions suggesting that mechanical factorssuch as the strength of the sediments play a decisive role, controlling the minimum size ofthe collapses (geomorphic threshold) and the frequency-size distribution of eacharea. Exploring the magnitude-frequency relationships of PCs provides relevant informationabout the impact of piping on hillslope denudation and landscape evolution. It also offerscritical quantitative data for subsidence hazard assessment. The study is supported by the National Science Centre, Poland within the first author’sproject SONATINA 1 (DEC-2017/24/C/ST10/00114) and by the Institute of Geography andSpatial Management of the Jagiellonian University in Kraków, Poland (K/DSC/005466). [ABSTRACT FROM AUTHOR]