# Electrical analogy seepage models

a. The laws governing flow of fluids through porous media and flow of electricity through pure resistance are mathematically similar. Thus, it is feasible to use electrical models to study seepage flows and pressure

 note: bottom of all wells SEALED С I. E. INSULATED IN MODEL).

 U. S. Army Corps of Engineers

 Figure 4-26. Shape factors for wells of various penetrations centered inside a circular source.

 Impervious SECTIONAL FLOW NET (ARTESIAN) (a)

 PLAN FLOW NET (b)

SECTIONAL FLOW NET

PLAN FLOW NET

DRAWDOWN AT ANY POINT

N = TOTAL NUMBER OF EQUI POTENTIAL DROPS BETWEEN FULL HEAD, H, AND HEAD AT EXIT, h

e ’ e

ne = NUMBER OF EQUIPOTENTIAL DROPS FROM EXIT TO POINT AT WHICH HEAD, h, IS DESIRED

h_ IS SHOWN IN FIG. 4-1 О

SEE FIG. 4-29 FOR HEAD CORRECTION FACTORS,

(Modified from “Foundation Engineering, " G. A. Leonards, ed., 1962, McGraw-Hill

Book Company. Used with permission of McGraw-Hill Book Company.)

Figure 4-27. Flow and drawdown to slots computedfromflow nets.

distribution for various seepage conditions. Both two – and three-dimensional models can be used to solve seepage problems.

b. Darcy’s law for two-dimensional flow of water

(previously identified as equation (1) in fig. 4-27) through soil can be expressed for unit length of soil formations as follows:

q = kH’£ (4-3)

CONSTRUCT PLAN FLOW NET. SPACE WELLS PROPORTIONAL TO FLOW LINES. COMPUTE TOTAL FLOW

tosyStEmFROM EQ 5 FO r ARTESIAN FLOW OR EQ 6 FOR GRAVITY FLOW (FIG. 4-28). ass U ME IN EQ 5

H’-H-h. See fig. 4-20, b(c; 4-22, b; AND 4-26 FOR EXPLANATION OF TERMS.

О

ARTESIAN FLOW

FLOW TO EACH WELL

(5 =*

WHERE П – NUMBER OF WELLS INTHE SYSTEM

DRAWDOWN AT WELLS

FULLYPENETRATING

l w / п і, a

H-h =-— -3F+—In——

w bO 277 2777

PARTIALLYPENETRATING

WHERE (7 IS OBTAINED FROM FIG. 4-21 t

a

HEAD INCREASES MIDWAY BETWEEN AND DOWNSTREAM OF WELLS MAY BE COMPUTED FROM EQUATIONS

GIVEN IN FIG. 4-20 AND 4-21.

GRAVITY FLOW

FLOW TO EACH WELL

USE EQ 1

DRAWDOWN AT FULLY PENETRATING WELL

HEAD INCREASES MIDWAY BETWEEN AND DOWNSTREAM OF WELLS MAY BE COMPUTED FROM EQUATIONS GIVEN IN FIG. 4-22.

t THE AVERAGE WELL SPACING MAY BE USED TO COMPUTE 0 ,0 , AND THE DRAWDOWN AT A N D

a m

BETWEEN WELLS.

U. S. Army Corps of Engineers

Figure 4-28. Flow and drawdown to wells computed from flow-net analyses

where

q = rate of flow к = coefficient of permeability H’ = differential head

f = shape factor dependent on the geometry of the system

C, Ohm’s law expresses the analogous condition for steady flow of electricity through a medium of purere-

sistance as follows:

where

I = rate of flow of electricity E = potential difference or voltage p — specific resistance of electrolyte

Since the permeability in fluid flow is analogous to the reciprocal of the specific resistance for geometrically similar mediums, the shape factors for Darcy’s law and Ohm’s law are the same.

d. A two-dimensional flow net can be constructed using a scale model of the flow and drainage system made of a conductive material representing the porous media (graphite-treated paper or an electrolytic solu­tion), copper or silver strips for source of seepage and drainage, and nonconductive material representing impervious flow boundaries, The electrical circuit con­sists of a potential applied across the model and a Wheatstone bridge to control intermediate potentials on the model (fig. 4-29). The flow net is constructed by tracing lines of constant potential on the model, thus establishing the flow-net equipotential lines after which the flow lines are easily added graphically. A

flow net constructed using an electrical analogy model may be analyzed in the same manner as one con­structed as in paragraph 4-3.

e. Equipment for conducting three-dimensional electrical analogy model studies is available at the WES. The equipment consists basically of a large plexiglass tank filled with diluted copper sulfate solu­tion and having a calibrated, elevated carrier assembly for the accurate positioning of a point electrode probe anywhere in the fluid medium. A prototype is simu­lated by fabricating appropriately shaped and sealed source and sink configurations and applying an elec­trical potential across them. The model is particularly useful for analyzing complex boundary conditions that cannot be readily analyzed by two-dimensional tech­niques.

 SEE PARAGRAPH 4-3 FOR EXPLANATION OF TERMS AND PROCEDURE FOR DETERMINING f

 TO D. C. POWER SUPPLY

U. S. Army Corps of Engineers