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U.S. Army Corps of Engineers
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US Army Corps of EngineersInstitute for Water Resources, Risk Management Center
Internal Erosion Suite

Vertical Triangular Crack

Method of Analysis​

The method of analysis is the same as that described for the Cylindrical Pipe worksheet in the Method of Analysis section.

Critical Shear Stress and Initial Crack Dimensions​

The critical shear stress and initial crack dimensions are the same as that described for the Vertical Rectangular Crack worksheet in the Critical Shear Stress and Initial Crack Dimensions section.

Core Geometry​

The core geometry is the same as that described for the Vertical Rectangular Crack worksheet in the Core Geometry section.

Hydraulic Shear Stress​

The hydraulic shear stress on the surface of the vertical triangular crack from flow of water in the crack is the same as that described for the Vertical Rectangular Crack worksheet in the Hydraulic Shear Stress section, but using a different equation. Equation calculates the hydraulic shear stress on the isosceles triangular surface of the vertical triangular crack.

τ=γwW6DL(H13−H23)(H1+H2)1+W24D2\tau = \frac{\gamma_{w}W}{6DL} \frac{(H_{1}^{3} - H_{2}^{3})}{(H_{1}+H_{2})\sqrt{1+ \frac{W^2}{4D^2}}}

Likelihood of Initiation of Concentrated Leak Erosion​

The likelihood of initiation of concentrated leak erosion is the same as that described for the Cylindrical Pipe worksheet in the Likelihood of Initiation of Concentrated Leak Erosion section, but using a different equation and crack width instead of pipe diameter.

Headwater Level for Initiation of Concentrated Leak Erosion​

The headwater level for initiation of concentrated leak erosion is the same as that described for the Cylindrical Pipe worksheet in the Headwater Level for Initiation of Concentrated Leak Erosion section, but using a different equation and crack width instead of pipe diameter.

Critical Crack Width for Initiation of Concentrated Leak Erosion​

The critical crack width at the top of the core for initiation of concentrated leak erosion is the same as that described for the Vertical Rectangular Crack worksheet in the Critical Crack Width for Initiation of Concentrated Leak Erosion section, but using a different equation. Equation calculates the critical crack width at the top of the core for initiation of concentrated leak erosion for each headwater level and the specified crack depth from the top of the core.

Wcr=τc(H1+H2)γw2(H13−H23)236D2L2−τc2(H1+H2)24D2W_{cr} = \frac{\tau_{c}(H_{1}+H_{2})}{\sqrt{ \frac{\gamma_{w}^{2}(H_{1}^{3} - H_{2}^{3})^2}{36D^{2}L^{2}} - \frac{\tau_{c}^{2}(H_{1}+H_{2})^{2}}{4D^2} }}
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