Let's suppose there this a soil with the configuration shown in the following figure, where $L_1$ and

$L_2$ are the lengths of each section, $k_1$ and $k_2$ are the permeabilities, $"$e$"$ is the thickness, $h_1,h_2$

and $h_3$ are the hydraulic potentials at the indicated points and $Q$ is the flow through the ground:

Complete the following:

Obtain the expression of the equivalent permeability of the system $(k_{eq})$ based on the

parameters presented.

Knowing the following data, $L_1=6m,L_2=8m,h_2=5m,e=3m,Q=0\mathrm{.}0003\frac{m^3}{s},k_1=$

$5{10}^{-5}\frac{m}{s}$ and $k_2=1{10}^{-4}\frac{m}{s},$ determine the values of: $h_1,h_3,$ the hydraulic gradient

in section $1(i_1)$ and in section $2(i_2),$ the equivalent gradient $(i_{eq})$ and the equivalent

permeability of the system $(k_{eq}).$ A particular soil is made up of an upper layer of sand $3$ meters thick and a lower layer of clay $7$

meters thick. Beneath the clay is a completely impermeable rock substrate. The permeability of

the sand layer is $k_{\text{s}\text{a}\text{n}\text{d}}=5{10}^{-5}\frac{m}{s}$ and the permeability of the clay layer is $k_{\text{s}\text{a}\text{n}\text{d}}=5{10}^{-8}\frac{m}{s}.$

Complete the following:

Calculate the equivalent horizontal permeability.

Calculate the equivalent vertical permeability.

Assuming there is a horizontal flow and a vertical flow with the same constant gradient $($i

$=$ cte.$)$:

Which flow rate will be greater, the vertical or the horizontal?

In what proportion? A fellow geologist has provided us with the following data of a rock mass on which the

foundation for the piles of a viaduct will be designed:

$"$ Uniaxial compressive strength of the rock matrix: $30$MPa.

$,RQD=80\%.$

$"$ Spacing of discontinuities of $1$ meter.

$"$ Conditions of discontinuities:

$"$ Length: $5$ meters.

Aperture: Greater than $5mm(>5mm).$

$"$ Roughness: Slightly rough.

$"$ Filling: Hard and thicker than $5mm(>5mm).$

$"$ Alteration: Very altered.

$"$ Seepage in the mass: slightly damR.