TRANSFORMATION OF ANISOTROPIC SOIL CONDITIONS. TO ISOTROPIC SOIL CONDITIONS

 

E-l. General. All of the analytical methods for computing seepage through a permeable deposit are based on the assumption that the permeability of the deposit is isotropic. However, natural soil deposits are stratified to some degree, and the average permeabil­ity parallel to the planes of stratification is greater than the permeability perpendicular to these planes. Thus, the soil deposit actually possesses anisotropic permeability, with the permeability in the horizontal direction usually the greatest. To construct a flow net or make a mathematical analysis of the seepage through an anisotropic deposit, the dimensions of the deposit and the problem must be transformed so that the permeability is isotropic. Each permeable stratum of the deposit must be separately transformed into iso­tropic conditions. If the seepage flows through more than one stratum (isotropically transformed), the analysis can be made by a flow net constructed to ac­count for permeability of the various strata.

E-2. Anisotropic stratum. A homogeneous, anisotropic stratum can be transformed into an iso­tropic stratum in accordance with the following equa­tion:

 

mine the required length_of well screen W to achieve an effective penetration W in a stratified aquifer, the following procedure can be used. This method is used in analyses to determine penetration depths needed to obtain required discharge from partially penetrating wells or wellpoints. Each stratum of the previous foun­dation or aquifer with thickness d and horizontal and vertical permeability coefficients kh and kv, respective­ly, is first transformed using equation (E-l) into an isotropic layer of thickness d, where

= a ^TT

The transformed coefficient of permeability of each stratum from equation (E-2) is к = Vkhkv

The thickness of the equivalent homogeneous isotropic aquifer is

m=n

D = I dm (E-3)

m=l

where n equals the number of strata in the aquifer.

The effective permeability of the transformed aquifer is

  TRANSFORMATION OF ANISOTROPIC SOIL CONDITIONS. TO ISOTROPIC SOIL CONDITIONS

where

у = transformed vertical dimension у = actual vertical dimension kh = permeability in the horizontal direction kv = permeability in the vertical direction The horizontal dimensions of the problem would re­main unchanged in this transformation. The permea­bility of the transformed stratum, to be used in all equations for flow or drawdown, is as follows:

_ к = /Ш (E-2)

where к equals the transformed coefficient of permea­bility.

E-3. Effective well penetration. In a strati­fied aquifer, the effective well penetration usually dif­fers from that computed from the ratio of the length of well screen to total thickness of aquifer. To deter-

 

(E-4)

  TRANSFORMATION OF ANISOTROPIC SOIL CONDITIONS. TO ISOTROPIC SOIL CONDITIONS

E-l

 

TRANSFORMATION OF ANISOTROPIC SOIL CONDITIONS. TO ISOTROPIC SOIL CONDITIONSTRANSFORMATION OF ANISOTROPIC SOIL CONDITIONS. TO ISOTROPIC SOIL CONDITIONS