Evaluating the Performance of Protective Barriers against Debris Flows Using Coupled Eulerian Lagrangian and Finite Element Analyses
Abstract
:1. Introduction
2. Methodology
2.1. Coupled Eulerian–Lagrangian Method (CEL)
2.2. Rheological Model of Debris Flow
3. Validation and Investigation
3.1. Model Validation
3.2. Estimating Flow Velocities at Different Locations on Hobart Rivulet Terrain
3.2.1. Study Area
3.2.2. Simulation and Estimation
3.3. Simulation of Boulder–Barrier Interactions
3.3.1. Identifying the Weakest I-Beam Post of the Barrier
3.3.2. Effect of Boulder Impact Velocity
3.3.3. Effect of Boulder Impact Height
3.3.4. Effect of Boulder Size
3.3.5. Effect of Boulder Orientation
4. Benchmark Simulations of Flow–Boulder–Barrier Interactions
4.1. Parameters and Simulations
4.2. Results, Analysis, and Comparison
5. Conclusions
- The CEL model is validated by simulating experimental debris flow tests from Ng et al. [52] using the Bingham model. The good agreement between the CEL model and experimental data suggests accurate predictions of flow velocities, boulder velocities, and impact forces. Subsequent examinations of debris flow velocities along the Hobart Rivulet using a 3D CEL model reveal distinct flow dynamics. Beginning at 3 m/s, flow velocities surged downstream, stabilising at 7 m/s, 12 m/s, 14 m/s, and 16 m/s, indicating increasing momentum and turbulence downstream. These findings provide a foundation for subsequent investigations into boulder-barrier interactions, with a designated velocity of 12 m/s used for the structural effect analysis in Section 3.3, and the release of boulders at a specific location for benchmark simulation in Section 4.
- By accounting for the dynamic nature of debris flows and various impact scenarios, the simulations of boulder–barrier interactions are conducted to assess the performance of I-beam post barriers in Hobart Rivulet. The study identifies weak points in the protective structure using the failure ratio, which measures the proportion of elements failing upon impact. The results show minimal variation in impact forces across different posts, but significant differences in failure ratios, pinpointing FN9 and BN3 as the weakest, with FN9 being critical due to its front-row position.
- The simulation results of boulder–barrier interactions also reveal that higher boulder velocities strongly correlate with increased failure ratios and impact forces, while varying impact heights reveal that the middle sections of the posts are more vulnerable. Additionally, larger boulders result in higher failure ratios, while different impact orientations lead to varying structural damages, with orientation (b) yielding the highest failure ratio and orientation (c) the highest impact force.
- Numerical models conducted for different boulder sizes (0.5 m, 1.5 m, and 2.5 m) highlight the effectiveness of the CEL model in capturing the complex interactions between debris flow, boulders, and the I-beam barrier on a real rivulet terrain. The findings indicate that larger boulders significantly increase the failure ratio and impact force on the barrier, with failure ratios stabilising at approximately 4%, 65%, and 80% for boulder sizes of 0.5 m, 1.5 m, and 2.5 m, respectively. Notably, the CEL model stands out for handling multiple boulders without assuming impact locations or orientations. Moreover, there is a noticeable difference in the velocities of smaller boulders, indicating the sensitivity of FE models to size variations. The comparative analysis using FE models shows good agreement with CEL results, although the FE models predict slightly higher impact forces and different failure distributions. This complementarity provides valuable insights into the utility of both approaches in enhancing structural resilience and optimising barrier design against debris flow impacts.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Material Parameter | Constitutive Model | Density ρ (kg/m3) | (Pa) | (Pa·s) | Poisson’s Ratio ν | Young’s Modulus E (kPa) |
---|---|---|---|---|---|---|
Debris flow | Bingham | 1500 | 100 | 100 | - | - |
Hobart Rivulet Terrain | Rigid body | - | - | - | - | - |
Barrier * | Linear elastic | 7850 | - | - | 0.25 | 2 108 |
Boulder * | Rigid body | 2880 | - | - | - | - |
Beam Type | ||
---|---|---|
Classification | UC200-59 | 150PFC |
t1 (mm) | 14.2 | 9.5 |
t2 (mm) | 14.2 | 9.5 |
t3 (mm) | 9.5 | 6 |
b1 (mm) | 205 | 75 |
b2 (mm) | 205 | 75 |
y (mm) | 105 | 75 |
h (mm) | 210 | 150 |
Post Beam Type | Flange Beam Type | s1 (m) | s2 (m) | s3 (m) | s4 (m) | s5 (m) | s6 (mm) | H * (m) | |
---|---|---|---|---|---|---|---|---|---|
Minimum | Maximum | ||||||||
UC200-59 | 150PFC | 1.5 | 0.75 | 0.95 | 12.205 | 1.5 | 150 | 3.31 | 3.78 |
Geometry | Test No | Reference Size SR (m) | Volume (m3) | Mass (tons) |
---|---|---|---|---|
S1 | 0.5 | 0.1 | 0.3 | |
S2 | 1 | 0.8 | 2.3 | |
S3 | 1.5 | 2.7 | 7.6 | |
S4 | 2 | 6.3 | 18.1 | |
S5 | 2.5 | 12.3 | 35.3 | |
S6 | 3 | 21.2 | 61.1 |
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Sha, S.; Dyson, A.P.; Kefayati, G.; Tolooiyan, A. Evaluating the Performance of Protective Barriers against Debris Flows Using Coupled Eulerian Lagrangian and Finite Element Analyses. Sustainability 2024, 16, 7332. https://doi.org/10.3390/su16177332
Sha S, Dyson AP, Kefayati G, Tolooiyan A. Evaluating the Performance of Protective Barriers against Debris Flows Using Coupled Eulerian Lagrangian and Finite Element Analyses. Sustainability. 2024; 16(17):7332. https://doi.org/10.3390/su16177332
Chicago/Turabian StyleSha, Shiyin, Ashley P. Dyson, Gholamreza Kefayati, and Ali Tolooiyan. 2024. "Evaluating the Performance of Protective Barriers against Debris Flows Using Coupled Eulerian Lagrangian and Finite Element Analyses" Sustainability 16, no. 17: 7332. https://doi.org/10.3390/su16177332