# Development of a Practical Evaluation Method for Tsunami Debris and Its Accumulation
## 2 Practical Method for Evaluating Tsunami Debris Accumulation and Thickness

Table 1: Volume of residual accumulated debris; estimated debris volume from washed away and totally destroyed buildings; its residual rate. Figure 6: The relationship between \(P_{\text{db}}\) and \(L^{\star}\) in each analysis area—from [PERSON] et al. [6]. by narrow valleys surrounded by mountainous terrain, \(i_{\text{M}}\) was relatively large near the inundation boundary. The relatively steep mountainous terrain blocked the tsunami flow and caused debris to accumulate, as reported by [PERSON] et al. [1]. In addition, \(NDT\) was high when 0.0 < \(D\)* < 8 and 25% < \(i_{\text{M}}\) < 125% (Figure 7b). These high \(NDT\) values were also considered to be related to land use, because residential areas are mainly in areas with relatively small \(i_{\text{M}}\). The relationships between each of these parameters and \(NDT\) are difficult to interpret systematically and there are no clear trends; these are features of a complex system. The practical evaluation model for debris accumulation, developed by [PERSON] et al. [12], consists of two independent evaluation models, one for \(P_{\text{db}}\) and the other for \(NDT\). A stochastic model for \(P_{\text{db}}\) was constructed by a logistic regression in which the explanatory values were \(AS\), \(L\), and \(SI\), as follows:  
\[P_{\text{db}}=\frac{1}{[1+\exp(-\phi)]} \tag{1}\]  
\[\Phi=0.43 AS-0.11L_{*}+0.87 SI-1.61 \tag{2}\]  
The predictive accuracy of \(P_{\text{db}}\) > 0.5 determined with Equations (1) and (2) was 70%. \(NDT\) was assumed to be a power function of \(AS\), \(L\), \(D\), \(i_{\text{M}}\), and \(SI\), and Equation (3) was obtained by fitting the function to the observed data, as follows:  
\[NDT=0.0009 AS^{-0.014}\ D_{*}^{0.12}\ i_{M}^{0.38}SI^{0.29}\pm\sigma_{NDT} \tag{3}\]  
\(\sigma_{NDT}\) as of 0.48 \(\times\) 10\({}^{-4}\), the standard deviation included in the regression value of the predicted \(NDT\). The predicted \(NDT\) ranged from 0.5 to 3.0 times the observed value. It was applicable for 0.49 < \(AS\) < 2.13, 0 < \(L^{*}\) < 1, 0 < 7 m, 0 < \(D\) < 10, 0 < \(i_{\text{M}}\) < 200, and 0 < \(SI\) < 2.25. Both the observed and calculated value of \(NDT\) tended to increase as \(L\)* approached the inundation boundary (\(L\)* \(\approx\) 1) (Figure 8). For example, in Figure 8, the observed and calculated distributions of accumulated debris thickness in Otsuchi are  
Figure 7: (**a**) Relationships among \(i_{\text{M}}\), \(L^{*}\), and \(NDT\). (**b**) Relationships among \(i_{\text{M}}\), \(D^{*}\), and \(NDT\). Each figure from [PERSON] et al. [6]. compared (Figure 9). The accumulated debris thickness was calculated using Equation (3) with the observed values of each parameter (_AS_, \(L\), \(D\), _i_M, and _SI_), and the probability of debris accumulation was calculated using Equations (1) and (2) with uniform random numbers, where the mean of 100 trials was used as the representative value. In the calculated results, the accumulation of debris was seen around the inundation boundary and buildings, but local increases in debris thickness in the observed distribution were not reproduced. Rather, the debris tended to be deposited thinly over a wider area than was the case in the observed distribution. Estimation of the Total Amount of Tsunami Debris in the Target Area by a Tsunami Fragility Function  
The evaluation model expressed by Equations (1)-(3) is used to predict where tsunami debris is likely to accumulate and its thickness. To convert _NDT_ obtained by Equation (3) to the actual debris thickness, _DT_, the total volume of woody debris produced by the tsunami in the analysis area must be known. In this study, we estimated the total volume  
Figure 8: Observed and calculated _NDT_ in relation to \(L^{\star}\). Figure 9: Observed and calculated tsunami debris accumulation thickness in Otsuchi. Each figure from [PERSON] et al. [6]. of woody debris by using a tsunami fragility function for wooden buildings under the assumption that most of the woody debris was derived from wooden buildings damaged by the tsunami.