10
2 Similarity of Model Experiments
2.2 Purpose and Significance
The proposed method predicts the sediment retained by check dams based on rainfall,
land cover and geological conditions in the prototype catchment before the check
dams are constructed. Suppose that a small watershed on the Loess Plateau would
be managed, and rainfall-erosion data before construction of the check dams were
available. To predict the erosion while a check dam system is being constructed, we
assume that other erosion factors, e.g., rainfall, erosion material, and plant cover,
would be similar to those before the check dams were constructed.
The researchers should consider the similarity of the cumulative effect while
designing the downscaled model experiment for soil conservation. For the erosion
controlled by check dams, the cumulative effect for at least one year by the check
dam may be considered rather than the motion process of each soil particle. In fact,
the annual sediment yield in the small watersheds on the Loess Plateau is primarily
generated by a few strong rainstorms; that is, the short and intense rainfall events
are responsible for 60–90% of the total soil loss over a 1-year period. Since the
cumulative effect of check dams to retain sediment is of concern and not the temporal
evolution of the slopes or gullies, a downscaled model experiment must ensure that
the ratio of the prototype soil loss after rainfall events to model soil loss after the same
rainfalls, namely the scale number of the soil loss, remains constant. In this instance
the scale number of the soil loss could be pre-calibrated. Thus, the amount of soil
loss in the model watershed after constructing check dams represent the prototype
soil loss. In this study, four criteria are utilized to ensure that the scale number of the
soil loss remains constant. Firstly, the initial dimensions of the landform required
by the geometrical similarity, including those of the check dams, are scaled down
according to the dimensions of the prototype watershed with the same proportion
in the horizontal and vertical orientations. Secondly, for the similarity of erosion
form, the simulated soil similar to that of the prototype is used, and the model
rainfall intensity exceeds the soil erosion threshold. Thirdly, the rainfall duration
was determined by the Froude number (Fr) similarity. Finally, for the similarity of
the rainfall-erosion, the relationship between the rainfall and erosion in the model
experiment corresponds to that of the prototype. The proposed method provides the
quantitative proportion of soil loss between the prototype and model using similarity
criteria. Nevertheless, it does not strictly meet the similar situation in the conventional
scale model experiment. Thus, the proposed method is defined as the semi-scale
physical model experimental method (SSPM).
The SSPM was tested using two downscaled experiments (Fig. 2.1). A large scale
model, the Model B, at 1:60 of the prototype landform, was used as the simulated prototype watershed. Two small scale models, Model Da and Model Db, with different
erosion rates but the same geometrical size, each at 1:240 of the prototype landform,
were employed to simulate the hydraulic process in Model B. Data from these three
models are comparable because the experimental devices and observation measures
in the small scale models are consistent with those in the Model B. Moreover, an
2 Similarity of Model Experiments
2.2 Purpose and Significance
The proposed method predicts the sediment retained by check dams based on rainfall,
land cover and geological conditions in the prototype catchment before the check
dams are constructed. Suppose that a small watershed on the Loess Plateau would
be managed, and rainfall-erosion data before construction of the check dams were
available. To predict the erosion while a check dam system is being constructed, we
assume that other erosion factors, e.g., rainfall, erosion material, and plant cover,
would be similar to those before the check dams were constructed.
The researchers should consider the similarity of the cumulative effect while
designing the downscaled model experiment for soil conservation. For the erosion
controlled by check dams, the cumulative effect for at least one year by the check
dam may be considered rather than the motion process of each soil particle. In fact,
the annual sediment yield in the small watersheds on the Loess Plateau is primarily
generated by a few strong rainstorms; that is, the short and intense rainfall events
are responsible for 60–90% of the total soil loss over a 1-year period. Since the
cumulative effect of check dams to retain sediment is of concern and not the temporal
evolution of the slopes or gullies, a downscaled model experiment must ensure that
the ratio of the prototype soil loss after rainfall events to model soil loss after the same
rainfalls, namely the scale number of the soil loss, remains constant. In this instance
the scale number of the soil loss could be pre-calibrated. Thus, the amount of soil
loss in the model watershed after constructing check dams represent the prototype
soil loss. In this study, four criteria are utilized to ensure that the scale number of the
soil loss remains constant. Firstly, the initial dimensions of the landform required
by the geometrical similarity, including those of the check dams, are scaled down
according to the dimensions of the prototype watershed with the same proportion
in the horizontal and vertical orientations. Secondly, for the similarity of erosion
form, the simulated soil similar to that of the prototype is used, and the model
rainfall intensity exceeds the soil erosion threshold. Thirdly, the rainfall duration
was determined by the Froude number (Fr) similarity. Finally, for the similarity of
the rainfall-erosion, the relationship between the rainfall and erosion in the model
experiment corresponds to that of the prototype. The proposed method provides the
quantitative proportion of soil loss between the prototype and model using similarity
criteria. Nevertheless, it does not strictly meet the similar situation in the conventional
scale model experiment. Thus, the proposed method is defined as the semi-scale
physical model experimental method (SSPM).
The SSPM was tested using two downscaled experiments (Fig. 2.1). A large scale
model, the Model B, at 1:60 of the prototype landform, was used as the simulated prototype watershed. Two small scale models, Model Da and Model Db, with different
erosion rates but the same geometrical size, each at 1:240 of the prototype landform,
were employed to simulate the hydraulic process in Model B. Data from these three
models are comparable because the experimental devices and observation measures
in the small scale models are consistent with those in the Model B. Moreover, an