MalcolmWoodruff/TerraPercolatio

MalcolmWoodruff`TerraPercolatio`

SeepageUnconfined

SeepageUnconfined [spec,opts]
	solves an unconfined seepage problem (earth dam, slope) with an iteratively located phreatic surface.

Details and Options

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spec is an

Association

: "Profile" -> counterclockwise polygon of the dam or slope cross-section; "UpstreamLevel" -> Hu and "DownstreamLevel" -> Hd (flow runs left to right); "Layers" -> {<|"Polygon"->..,"kx"->..,"ky"->..|>,...} for multiple materials, else give homogeneous "kx", "ky".

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The base (the minimum-y edge) is impermeable. For non-trivial profiles give "UpstreamFace" and "DownstreamFace" explicitly, as polylines ordered from the base upward; the free surface and the faces are assumed single-valued (x-monotone and y-monotone).

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Rainfall or surface infiltration is applied as a flux on the phreatic surface with "Rainfall" -> r (mm/day) or "Recharge" -> q (m/s, added to "Rainfall"); it raises the water table and pore pressures, or drains laterally to a boundary for drain-spacing design. The water table is capped at the ground surface, with the excess shed as runoff; "WaterTableDaylights" in the result reports whether that happened.

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The following options can be given:

"Name"	Automatic	Store the result under TerraPercolatio ["name"] as well as returning it.
"MeshSize"	Automatic	Maximum finite-element area used at each phreatic-surface iteration; Automatic scales with the saturated-region area.
"Points"	25	Number of stations used to represent the phreatic surface.
"Relaxation"	0.65	Under-relaxation factor applied to the phreatic-surface update at each iteration.
"MaxIterations"	100	Maximum number of phreatic-surface iterations before giving up.
"Tolerance"	Automatic	Mean phreatic-surface movement below which the iteration is taken as converged; Automatic scales with the head difference.
"Monitor"	False	True prints the iteration history (mean movement and exit-point elevation) as the free surface converges.
"Rainfall"	0.	Steady surface infiltration in millimetres per day, applied as a flux across the phreatic surface.
"Recharge"	0.	The same infiltration flux as "Rainfall", given directly in m/s and added to it.
"UpstreamNoFlow"	False	True makes the upstream face a mid-spacing no-flow divide for parallel-drain design; "UpstreamLevel" is then only the initial guess for the water-table apex.

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Returns the same keys as

SeepageSolve

, plus "PhreaticSurface" (list of points), "ExitPoint", "SaturatedRegion", "GroundSurface", "UnsaturatedZone", "UnsaturatedThickness" ({min,max} gap to the ground), "WaterTableDaylights", "Rainfall_mmday", "Converged" and "Iterations".

Examples

(11)

Basic Examples

(1)

Solve for unconfined seepage through a homogeneous earth dam:

In[1]:=

damSpec=Association["Profile"{{0.`,0.`},{52.`,0.`},{28.`,12.`},{24.`,12.`}},"UpstreamLevel"10.`,"DownstreamLevel"0.`,"kx"1.`*^-6,"ky"1.`*^-6];damSol=