What you’ll learn

What is Permeability in Geotechnical Engineering?

Permeability in geotechnical engineering is how water flows through soil and rock masses. It’s an ability of the soil or a rock to transmit liquid through its interconnected void spaces.

The Permeability of the soil depends on several factors:

Grain Size Distribution
Void Ratio
Degree of Saturation
Soil Structure

Bernoulli’s Energy Equation

Why is there Bernoulli’s Energy Equation in Geotechnical Engineering?

Wondering why there’s Bernoulli Energy Equation when we’re dealing with Geotechnical Engineering? Well, when we analyze permeability, we’re dealing with the movement of water from points of higher hydraulic head to lower hydraulic head. The Bernoulli equation helps us understand this energy.

$E = \frac{v^2}{2g}+\frac{p}{\gamma}+z$

This equation can be modified into simpler terms because since the seepage velocity is small, the term velocity head can be neglected.

$h = \frac{p}{\gamma}+z$

Hydraulic Gradient

$i= \frac{\Delta h}{L}$

Darcy’s Law

According to Henry Darcy in 1856, the velocity of a flow is directly proportional to the hydraulic gradient and the permeability of the soil.

He formulated this equation:

$v = ki$

where:
v = discharge velocity
k = hydraulic conductivity
i = hydraulic gradient

For calculating actual discharge:

since

$Q = Av \to Q = Aki$

$Q = kiA$

where:
Q = total discharge rate
A = cross-sectional area perpendicular to the flow

Hydraulic Conductivity

Soil Type	k (cm/s)
Clean Gravel	100 – 1
Coarse Sand	1.0 – 0.01
Fine Sand	0.01 – 0.001
Silty Clay	0.001 – 0.00001

where:
$c$ = a constant that varies from 1.0 to 1.5
$D_{10}$ = effective size in mm

mainly used for fairly uniform sand

where:
$k$ = hydraulic conductivity at void ratio
$k_{0.85}$ = k at void ratio 0.85

Constant Head Test

The constant head test is used to determine the coefficient of permeability, mainly for course-grained soils where maintaining a constant water level is feasible.

$k = \frac{VL}{hAT}$

where:
k = coefficient of permeability
V = volume of water collected
L = length of soil
h = constant head difference
A = cross-sectional area of
t = time period for collection

Why is it called “constant head”?

Because the water level difference between the inlet and outlet remains unchanged during the test

Falling Head Test

The falling head test is a lab method we use to measure how easily water can move through fine-grained soils, like silts or clays.

Think of it as watching water slowly seep down through a narrow pipe, while keeping track of how fast the water level drops over time.

$k = \frac{aL}{AT}ln\frac{h_1}{h_2}$

where:
a = area of the standpipe
A = area of the specimen
$h_1$ = head at time, $t_1$
$h_2$ = head at time, $t_2$

Aquifers

The stratum of the soil in which water from the underground is present.

Unconfined Aquifer

Unconfined aquifers have a free water surface and are open to atmospheric pressure at the top.

$k = \frac{Qln \frac{r_1}{r_2}}{\pi(h^2_1-h^2_2)}$

where:
k = coefficient of permeability
Q = rate of discharge

Confined Aquifer

A confined aquifer is a layer of water-bearing rock or sediment trapped between two impermeable layers, often called aquitards or aquicludes.

$k = \frac{Qln \frac{r_1}{r_2}}{2\pi t(h_2-h_1)}$

Transimissibility of Aquifer

$T =kt= \frac{Qln}{2\pit(h_2-h_1)}\frac{r_1}{r_2}$

‌

Flow Through Layers of Aquifers

Equivalent Hydraulic Conductivity in Parallel Flow

$k_{eq}= \frac{k_1+k_2}{H_1+H_2}$

Equivalent Hydraulic Conductivity in Perpendicular Flow

$\frac{L}{k_{eq}}= \frac{L_1}{k_1} + \frac{L_2}{k_2}$

References:

EE. (2020, April 5). Unconfined Aquifer – Permeability of soil – Field test. Elementary Engineering. https://elementaryengineeringlibrary.com/civil-engineering/soil-mechanics/unconfined-aquifer-permeability-of-soil-field-test/

Darcy’s Law – Definition, Applications, Properties & Limitations. (n.d.). Testbook. https://testbook.com/physics/darcys-law

‌Das, B. M. (2013). Fundamentals of geotechnical engineering. Cengage Learning.

‌

CH 2 : ATTERBERG LIMITS