<p> In 2014, in the Kanto-Koshin region many buildings were severely damaged by heavy rainfall after snowfall, a phenomenon called rain-on-snow.</p><p> Hence, to estimate rain-on-snow load on the roof, we are proposing a two-dimensional snow cover model. By observing recorded data, we assumed the model consists of three snow layers, the uppermost unsaturated layer does not contain much water, while the middle layer is a capillary force layer containing a large amount of water. The second layer does not cause outflow due to capillary force. The bottom is an outflow layer in which the water moves along the roof. The load was determined as the sum of the weights of three layers.</p><p> The thickness of the three layers is determined by the following method. First, several formulas were already existed for calculating the thickness of the capillary force layer, but the obtained values by these formulas are different from the measured values in Nagaoka this time. On the other hand, as indicated by conventional formula, we were able to confirm a tendency of inverse correlation between the thickness and particle size, the thickness of the layer increasing as the particle size decreasing. Here, depending on the particle size, we adopted 0.3 to 1.5 cm thickness of the capillary force layer. Second, the thickness of the outflow layer was obtained from the rainfall intensity, roof span, roof gradient and particle size. Third, the thickness of the unsaturated layer was the one obtained by subtracting the thicknesses of capillary force layer and the outflow layer from the overall thickness. To calculate the total thickness of all layers, we defined the density increment and the modified density increment. Since they showed a positive correlation regardless of snow condition, roof span or roof, we used this correlation to determine the total thickness.</p><p> We used two types of density in this model; unsaturated density and saturated density. Unsaturated density showed a strong correlation with the initial density in the experiment so we calculated unsaturated density using initial density in this model. The saturated layer density was approximately 850 kg/m³ regardless of the snow condition, roof span or roof gradient, so we adopted this value.</p><p> In estimating the transition of the increase in rain-on-snow load during rainfall, the amount of runoff from the bottom layer affects the estimation accuracy. In this calculation model, we used Darcy's law which is often used in the civil engineering field. In order to use this rule, the value of the permeability was required, which was obtained by the formula proposed by Shimizu.</p><p> Comparing the estimated values using this model with the measured values in Nagaoka and Shinjo, they matched with high accuracy even in various environments with different snow conditions and roof shapes. Through our model, we were able to obtain quite a similar result to not just measured values but also to of an actual phenomenon. By assuming the capillary force layer, we succeeded in modeling of the actual phenomenon, where snow on the top end of the roof holds water the phenomenon cannot be described by the formula proposed by Colbeck. It was also confirmed that our model could be performed with high accuracy even when there was granular snow whose properties were significantly different from other snow.</p>
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