VM163

VM163
Groundwater Seepage (Permeability Analogy)

Overview

Reference:	D. R. J. Owen, E. Hinton, A Simple Guide to Finite Elements, Pineridge Press Ltd., Swansea, U. K., 1980, pg. 89, article 7.4.
Analysis Type(s):	Thermal Analysis (ANTYPE = 0), with Analogous Seepage Variables
Element Type(s):	2D Thermal Solid Elements (PLANE55)
Input Listing:	vm163.dat

Test Case

An opened top and bottom circular steel caisson separates a low level excavation from the surrounding ground. Determine the groundwater seepage flow rate q beneath the caisson for fully saturated soil. The pressure head is T₁with respect to a datum T_o at the bottom of the caisson. Show the pressure contours and the flow path.

Figure 228: Groundwater Seepage Problem Sketch

Material Properties

Geometric Properties

k = permeability = 0.864 m/day

a = 3.5 m

b = 8 m

c = 10 m

h = 3 m

T_o = 0 m (at Y = 7 m)

T₁ = 3 m (at Y = 10 m)

Analysis Assumptions and Modeling Notes

The thermal analysis, which solves the Laplace equation, is used to solve this problem since the seepage flow is also governed by the Laplace equation. The following mental substitution of input and output variables (thermal : flow) are used:

(temperature : flow potential (or pressure head))
(heat flow rate : fluid flow rate)
(thermal conductivity : permeability coefficient)

The bottom and side of the model are assumed to be far enough away from the caisson to be treated as impermeable.

Results Comparison

	Target	Mechanical APDL [1]	Ratio
q, m³/day (per radian)	8.6	8.6	1.0

POST1 results for q are on a full circumference basis.

Figure 229: Pressure Contours

Figure 230: Flow Gradients