Simulation of landslide dam failure due to overtopping considering vertical soil particles distribution

Figures & data

Figure 1. Analysis of particle grading curve for landslide dams.

Figure 2. Procedure for obtaining spatial particle size.

Figure 3. Vertical and horizontal continuous expansion of the breach.

Figure 4. Stability calculation of breach slope.

Figure 5. The model calculation process of the mathematical model.

Figure 6. The (a) full extent, (b) cross-section, and (c) longitudinal section of the Tangjiashan landslide dam (Hu et al. 2010).

Figure 7. Grading analysis of Tangjiashan landslide dam.

Table 1. Conditions of Tangjiashan landslide dam.

Index	Value	Index	Value
Dam height (m)	103	Initial breach depth (m)	13
Crest width (m)	300	Initial breach width (m)	8
Dam length (m)	612	ρs (kg/m^3)	2216
U/S slope (V/H)	0.36	d50 (m)	Equation (29)
D/S slope (V/H)	0.24	c (kPa)	25^a
Reservoir storage (m^3)	1.5 × 10^8	φ (º)	22
Initial reservoir lever (m)	92.5	n0	40%
Initial downstream water lever (m)	0^a	Time step (s)	1

^a Assumed values.

Figure 8. The (a) cross-section, (b) longitudinal section of Baige landslide dam (Zhong et al. 2020b).

Figure 9. Grading analysis of Baige landslide dam.

Table 2. Conditions of Baige landslide dam.

Index	Value	Index	Value
Dam height (m)	96	Initial breach depth (m)	13.48
Crest width (m)	270	Initial breach width (m)	3
Dam length (m)	600	ρs (kg/m^3)	1854
U/S slope (V/H)	0.37	d50 (m)	Equation (30)
D/S slope (V/H)	0.18	c (kPa)	3
Reservoir storage (m^3)	7.57 × 10^8	φ (º)	32.8
Initial reservoir lever (m)	85.53	n0	37.5%
Initial downstream water lever (m)	0^a	Time step (s)	1

^a Assumed values.

Figure 10. Analysis of discharge coefficients.

Figure 11. The failure process of Tangjiashan landslide dam: (a) the discharge process; (b) the breach development; (c) the reservoir water level development.

Figure 12. The failure process of Baige landslide dam: (a) the discharge process; (b) the breach development; (c) the reservoir water level development.

Table 3. Comparison of breaching outcomes of Tangjiashan landslide dam.

	Qb (m^3/s)	B (m)	b (m)	Tp (h)	D (m)
Measured value	7500	186.2	83.8	15.1	35
Calculated value	7079	181.7	66.4	15.3	42.2
Relative error	−5.6%	−2.4%	−20.8%	1.3%	+20.6%

Table 4. Comparison of breaching outcomes of Baige landslide dam.

	Qb (m^3/s)	B (m)	b (m)	Tp (h)
Measured value	31,000.0	264.1	107.8	37.25
Calculated value	31,492.5	250.7	106.3	35.5
Relative error	+1.6%	−5.1%	−1.4%	−4.7%

Table 5. Comparison between calculated and measured data of Tangjiashan landslide dam breach.

Item	Qb (m^3/s)	B (m)	b (m)	Tp (h)	D (m)
Model by Zhong et al. (2018a)	6299.34	179.00	106.64	14.94	–
	−16.0%	−3.9%	+27.3%	−1.1%	–
Model by Chang and Zhang (2010)	6737	247	101	–	45
	−4.8%	+32.7%	+20.5%	–	+28.6%
Model proposed in this article	7079	181.7	66.4	15.3	42.2
	−5.6%	−2.4%	−20.8%	1.3%	+20.6%
Measured value	7500	186.2	83.8	15.1	35

Table 6. Comparison of measured and calculated data of Baige landslide dam breach.

Item	Qb (m^3/s)	B (m)	b (m)	Tp (h)
Model by Zhang et al. (2019)	34,348	337.4	139.8	38.32
	+10.8%	+27.8%	+29.7%	+2.9%
Model by Chen et al. (2020)	31,041.1	–	–	37.72
	+0.1%	–	–	+1.3%
Model proposed in this article	31,492.5	250.7	106.3	35.5
	+1.6%	−5.1%	−1.4%	−4.7%
Measured value	31,000.0	264.1	107.8	37.25

Figure 13. The failure process of Tangjiashan landslide dam under different median particle sizes: (a) discharge of breach; (b) development of breach.

Table 7. Influence of particle size on the dam breach process.

Cases	dsur,50 (mm)	Qp (m^3/s)	Tp (h)	B (m)	b (m)
1	11.45	9621.07	10.46	196.16	77.77
	−50%	+35.91%	−31.64%	+7.96%	+17.12%
2 (Prototype)	22.9	7079	15.3	181.7	66.4
	–	–	–	–	–
3	34.35	5009.10	22.00	171.23	59.18
	+50%	−29.24%	+43.78%	−5.76%	−10.87%

Figure 14. The failure process of Tangjiashan landslide dam under different particle distributions: (a) discharge of breach; (b) development of breach.

Table 8. Influence of particle distribution on the dam breach process.

Cases	Distribution	Qp (m^3/s)	Tp (h)	B (m)	b (m)
1 (Prototype)	Inverse grading	7079	15.3	181.7	66.4
		–	–	–	–
2	Uniform grading	5582.50	18.90	174.20	60.82
		−21.14%	+23.53%	−4.13%	−8.40%

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Data availability statement

The input parameters and output results of the breach model used for real-world dam break calculation in this article are available from the digital data repository in Zhao (2024).