9:30 AM - 9:45 AM
[HGM03-03] Development of “steady-state” landforms in geomorphic experiments and the concept of “threshold hillslope”
Keywords:geomorphic experiment, steady state, permeability, fluvial erosion, slope failures, threshold hillslope
The development of experimental landforms by uplift and rainfall erosion starting from a flat surface at the ground level commonly progresses to the steady-state, in which erosion attains equilibrium with uplift to keep relatively stable height and similar landforms. The sequence of this process of landform development can be divided into 3 stages, namely, the valley encroaching stage (stage 1), the mountain growth stage (stage 2), and the dynamic equilibrium stage (stage 3). In stage 1 fluvial erosion with the development of valley systems proceeds and average height of the uplifted area increases linearly with uplift at a slightly lower rate. Valleys continue to develop into stage 2, in which slopes grow high enough to induce slope failures and sediments produced by slope failures are quickly carried away through valley systems. Mountains grow, but the rate of surface rise in the uplifted area gradually declines in this stage. The average height then stops continuously increasing in stage 3 and starts to change around a certain height as maintaining similar landforms.
Two runs of experimental landform development, with the same uplift rate (0.36 mm/h for 960 hours) and different rainfall intensity (40 - 50 and 80 - 90 mm/h) on the same material (a mixture of fine sand and kaolinite 10 : 1 by weight and permeability of 10-3 cm/s order), showed the common process to reach steady-state landforms. The same serrate shape of graphs showing the change in average height of the uplifted area indicates the way how similar average height and landforms are maintained through stage 3, although the difference in rainfall intensity resulted in the development of different landforms, a higher massive mountain and lower separated ridges. The periodic rapid decrease followed by the gradual increase in average height of the uplifted area apparently reflects the observed cyclic occurrence of landslide concentration and the following period of uplift with basic erosion by sporadic slope failures and fluvial transportation. The repetition of this process works to limit the average surface height within a certain range and to keep landforms similar during stage 3. This interpretation of the process to maintain steady-state landforms seems to nicely fit in with the concept of threshold hillslope model of landscape evolution, which explains steady state landscapes in tectonically active mountain belts from the balance between rates of uplift and river incision through adjustment of landslide erosion rates on threshold hillslopes. The average value of cell slope steeper than the angle of repose of dry material used in the experiments (ca., 34°), which is designated as mean cell slope of steeper cluster here, can be assumed to indicate the readiness of slopes to collapse. The parameter, cell slope, is defined as the gradient of the steepest line connecting two points among four vertices of a grid cell, and is considered to represent the slope gradient of each grid. The values of mean cell slope of steeper cluster in stage 3 of both runs, which changed with time (and uplift) as shown also by serrate shaped graphs, are plotted within a relatively narrow band of 45° - 54°, suggesting that mean cell slope of steeper cluster in the dynamic equilibrium stage may represent the inherent threshold hillslope of the material used in these runs, regardless of rainfall intensity. The values of mean cell slope of steeper cluster in 11 other runs of experiments with the same material under various experimental conditions are all within the range of 45°- 60° after slope failures become dominant in the erosion process, regardless of uplift rate, rainfall intensity, width of depositional area, and permeability adjusted by the degree of compaction. This suggests that mean cell slope of steeper cluster of 45°- 60° is to represent the threshold hillslope proper to the 10 : 1 mixture of fine sand and kaolinite. Expressing the threshold hillslope in an area by an average value with a certain range is considered more appropriate than by a particular slope gradient. This is because defining a particular threshold hillslope in the area is impractical even in the simplified experiment due to the diversity in conditions of individual slopes. Slope conditions, such as shape and size, the behavior of infiltrated water, and local condition of material, are more or less different on each slope; and moreover, the nature and magnitude of triggering events can be different at each time. If mean cell slope of steeper cluster increases into the range of threshold hillslope, landslide concentration would possibly occur, and this possibility or frequency would increase as the value of this parameter increases towards the upper limit.
Two runs of experimental landform development, with the same uplift rate (0.36 mm/h for 960 hours) and different rainfall intensity (40 - 50 and 80 - 90 mm/h) on the same material (a mixture of fine sand and kaolinite 10 : 1 by weight and permeability of 10-3 cm/s order), showed the common process to reach steady-state landforms. The same serrate shape of graphs showing the change in average height of the uplifted area indicates the way how similar average height and landforms are maintained through stage 3, although the difference in rainfall intensity resulted in the development of different landforms, a higher massive mountain and lower separated ridges. The periodic rapid decrease followed by the gradual increase in average height of the uplifted area apparently reflects the observed cyclic occurrence of landslide concentration and the following period of uplift with basic erosion by sporadic slope failures and fluvial transportation. The repetition of this process works to limit the average surface height within a certain range and to keep landforms similar during stage 3. This interpretation of the process to maintain steady-state landforms seems to nicely fit in with the concept of threshold hillslope model of landscape evolution, which explains steady state landscapes in tectonically active mountain belts from the balance between rates of uplift and river incision through adjustment of landslide erosion rates on threshold hillslopes. The average value of cell slope steeper than the angle of repose of dry material used in the experiments (ca., 34°), which is designated as mean cell slope of steeper cluster here, can be assumed to indicate the readiness of slopes to collapse. The parameter, cell slope, is defined as the gradient of the steepest line connecting two points among four vertices of a grid cell, and is considered to represent the slope gradient of each grid. The values of mean cell slope of steeper cluster in stage 3 of both runs, which changed with time (and uplift) as shown also by serrate shaped graphs, are plotted within a relatively narrow band of 45° - 54°, suggesting that mean cell slope of steeper cluster in the dynamic equilibrium stage may represent the inherent threshold hillslope of the material used in these runs, regardless of rainfall intensity. The values of mean cell slope of steeper cluster in 11 other runs of experiments with the same material under various experimental conditions are all within the range of 45°- 60° after slope failures become dominant in the erosion process, regardless of uplift rate, rainfall intensity, width of depositional area, and permeability adjusted by the degree of compaction. This suggests that mean cell slope of steeper cluster of 45°- 60° is to represent the threshold hillslope proper to the 10 : 1 mixture of fine sand and kaolinite. Expressing the threshold hillslope in an area by an average value with a certain range is considered more appropriate than by a particular slope gradient. This is because defining a particular threshold hillslope in the area is impractical even in the simplified experiment due to the diversity in conditions of individual slopes. Slope conditions, such as shape and size, the behavior of infiltrated water, and local condition of material, are more or less different on each slope; and moreover, the nature and magnitude of triggering events can be different at each time. If mean cell slope of steeper cluster increases into the range of threshold hillslope, landslide concentration would possibly occur, and this possibility or frequency would increase as the value of this parameter increases towards the upper limit.