Runout distance

The focus is first set to the runout distances and how they are affected by the different earth pressure coefficients. In general, the runout distance shows different effects of using the active and passive coefficient depending on the values of the Voellmy friction coefficients 𝜇 and 𝜉. Hence, configuration of these parameters will influence how the earth pressure coefficient affects runout distance. Figure 58 includes a scenario in which the debris flow crashes into the end wall, and the effect of 𝜆 on runout is hence difficult to evaluate. This is shown as a straight horizontal line at 4.96 m, which is equal to the total runout length of the numerical model.

When the friction parameter 𝜇 is set to 0.03 in Figure 58, using passive earth pressure coefficients results in stabilization of the runout distances at a higher value than runout distance resulting from the isotropic earth pressure coefficient, 𝜆 = 1.0. All values of 𝜉 when 𝜇 = 0.03 result in an initial increasing effect of the earth pressure coefficient 𝜆 on runout distances. There is little change in effect as 𝜆 is increased beyond the initial

passive value, 𝜆 = 2.0. The overall effect of the passive values of 𝜆 is a spike to the runout distances. The active earth pressure coefficients cause a decrease in runout lengths as their values get lower. Hence the effect of the active earth pressure coefficient, 𝜆, on runout lengths when 𝜇 is low is a reduction, independent of the value of 𝜉.

Figure 58 Variations in runout depending on λ when μ = 0.03.

As the value of the friction parameter 𝜇 is increased to 𝜇 = 0.05 and 𝜇 = 0.08 in Figure 59 and Figure 60, the variation of the runout lengths as a function of 𝜆 changes. When the value of the coefficient 𝜇 is low, it does not seem like 𝜉 affects how 𝜆 influenced the runout lengths. When the earth pressure coefficient takes passive values, 𝜆 > 1.0, for higher values of 𝜇, the initial increase in runout from the isotropic condition is still

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present. The effect of 𝜆-passive on the runout lengths however, changes as the earth pressure coefficient is increased further 𝜆 > 2.0. When 𝜉 = 500 𝑚/𝑠² the runout lengths continue to increase as a function of the increasing passive 𝜆. For 𝜉 = 1000 𝑚/𝑠², the behavior is similar as described for 𝜇 = 0.03, as runout lengths stabilize around 4 m. For the highest value of 𝜉 = 1500 𝑚/𝑠², the passive earth pressure coefficients, 𝜆 > 2.0, result in the runout lengths decreasing as 𝜆 continues to increase. The behavior of the runout based on the active coefficients is little affected by the variations in the turbulence coefficient 𝜉.

Figure 59 Variations in runout depending on λ when μ = 0.05.

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Figure 60 Variations in runout depending on λ when μ = 0.08.

The effect that changing the earth pressure coefficient has on the runout distance, also varies somewhat with the value of the friction parameter 𝜇, as can be seen from Figure 61 to Figure 63.

The effect of the passive earth pressure coefficient changes little with 𝜇 when 𝜇 = 0.05 and 𝜇 = 0.08 for 𝜉 = 500 𝑚/𝑠². The main change in the effect of the passive 𝜆 appears when 𝜇 is reduced to a value of 0.03. As stated before, these runout distances stabilize for further increase of the passive earth pressure coefficient after an initial increase from the isotropic case.

For the active values of 𝜆 at 𝜉 = 500 𝑚/𝑠³, 𝜇 = 0.05 and 𝜇 = 0.08, there is an increase in runout lengths as 𝜆 gets smaller, from the value of the runout lengths produced with an isotropic earth pressure coefficient 𝜆 = 1.0. The curve is steepest for 𝜇 = 0.08 which shows that the effect of 𝜆 is the greatest for this value of 𝜇. As 𝜇 reduces to 0.05, the effect of the active 𝜆 is slightly reduced as the slope of the curve gets less steep. When 𝜇 = 0.03, the active behavior is changed considerably. Instead of the active behavior increasing runout lengths, they are now decreased for smaller values of 𝜆.

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Figure 61 Variations in runout depending on λ when 𝜉=500 m/s².

For higher values of the turbulence parameter 𝜉, the variations of the runout distance dependent on the passive values of 𝜆, don’t change much with 𝜇. The effect of the active coefficient still changes for the different values of 𝜇, as 𝜉 = 1000 𝑚/𝑠². Effects of the active earth pressure coefficients on the runout distances remain the same as stated for 𝜉 = 500 𝑚/𝑠² when 𝜇 is changing.

Figure 62 Variations in runout depending on λ when ξ=1000 m/s².

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As 𝜉 = 1500 𝑚/𝑠², it is important to notice the special case for 𝜇 = 0.03, when the flow crashed into the end wall which is discussed earlier in this section. The effect on the runout distance in this case is hence not considered for the following explanations.

The effect of the passive earth pressure coefficient on the runout distance is not altered for a changing value of 𝜇, which corresponds well to the statements made for 𝜉 =

500 𝑚/𝑠² and 𝜉 = 1000 𝑚/𝑠². The runout distances decrease as a result of an increase in the passive earth pressure coefficients after the initial increase for this value of 𝜉. This effect does not change with 𝜇.

The same yields for the effect of the active earth pressure coefficient on the runout distance. Both values of 𝜇 produce similar increase in runout distance due to 𝜆 getting smaller. Runout distances change little with the value of 𝜇.

Figure 63 Variations in runout depending on λ when ξ=1500 m/s².

In all cases, passive value increases the runout distance initially, while runout distances for active coefficients initially are only increased for 𝜇 = 0.03 or 0.05.

Additionally, the heights of the deposits in the runout zone are also decreased for the introduction of both the active and passive coefficients compared to the isotropic state as seen in Figure 64 to Figure 66.

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Figure 64 Height in deposited material when 𝜆 = 1.0. 𝜇 = 0.05 and 𝜉 = 500𝑚/𝑠².

Figure 65 Height in deposited material when 𝜆 = 0.82. 𝜇 = 0.05 and 𝜉 = 500𝑚/𝑠².

Figure 66 Height in deposited material when 𝜆 = 4.0. 𝜇 = 0.05 and 𝜉 = 500𝑚/𝑠².

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