How to Determine the Permeability of Stratified Soil Deposits?

The soil mass, in the field, consists of several layers of soil deposited one above the other. Each layer may have different coefficients of permeability. The average of permeability of the entire soil deposit depends on the direction of flow with respect to bedding planes. Transported soils usually exist in several layers, each layer with different permeability. For a three-layered soil deposit, the average permeability parallel to bedding planes lies closer to the intermediate permeability. The average permeability normal to bedding planes lies closer to the least permeability.

Two common cases of flow direction have been considered as follows:

1. Case 1 – Flow Parallel to Bedding Planes:

Figure 9.7 shows a soil profile with four layers having different perme­abilities with flow parallel to bedding planes. Let z_1, z₂ z₃ …, z_n be the thickness of soil layers 1, 2, 3,…, n, respec­tively, and k₁, k₂, k₃, …, k_n be the permeability in the horizontal direction of soil layers 1, 2, 3, …, n, respectively For flow parallel to bedding planes, the hydraulic gradient will be the same for all layers.

However, since v = ki and since k is different for different soil layers, the velocity of flow will be different in different layers. Let k_x = average permeability of soil deposit parallel to bedding planes and z = total thickness of the soil deposit (z₁ + z₂ + z₃ + … + z_n). Total discharge through the soil deposit –

q = kiA = k_xi (z × 1)

The sum of discharge through individual layers of soil deposit –

2. Case 2 – Flow Perpendicular to Bedding Planes:

Figure 9.8 shows a soil profile with four layers having differ­ent permeabilities with flow perpendicular to bedding planes. In this case, the velocity of flow (v₂) and hence the discharge (q_z) will be the same through all layers.

However, the hydraulic gradient and hence the head loss through each layer will be different. Let h₁, h₂, h₃,…, h_n be the head loss through layers 1, 2, 3,…,n and H be the total head loss. Then –

H = h₁ + h₂ + h₃ + …. + h_n …(9.16)

k_z is the average permeability of soil deposit perpendicular to bedding planes. Now –

Therefore,

Substituting these values in Eq. (9.16), we get –