4. Flow of Water Through Soils Explained: Hydraulic Conductivity, Darcy’s Law & Permeability Tests
The water flow (SEEPAGE) characteristics are very important in many applications of earthworks and structures such as earth dams, levees, embankments, underground structures, excavations, etc.
Hydraulic heads and Water flow:
Consider a water flow through a soil specimen filled in a clean pipe as shown below:
Because of the water-level difference between the left-side and the right- side of the pipe, water flows from left to right. The water level difference is called total head loss Δh which is a source of energy, to create a flow. Classic Bernoulli’s equation is used to define the flow of water through soil masses.
ht = hz + hp + hv
= z + u/ gw + v2/2g
Where: ht = total head
hz = elevation head
hp = pressure head
hv = velocity head
u = pore water pressure
v = flow velocity
The velocity head term v2/2g is neglected in most soil mechanics cases since this value is quite small in comparison with the values of other terms. Also, it is very important to define the datum to use the above written equation and could be chosen at any elevation, and all the heads are defined relative to datum.
Head loss is an energy loss. When water flows in soils, it must flow through many small passages in void sections of soils. This creates frictional resistance on the surface of particles. Flow energy is transmitted to frictional resistance on particle surfaces and then may be lost in hear generation, although it may not be easy to measure the temperature rise due to this energy transfer.
Permeability:
· Is the ease with which water can flow through any medium, and is a soil property which describes quantitatively as one must know how much water is flowing through a soil per unit time.
· Knowledge of permeability is essential in settlement of buildings, yield of wells, seepage through and below earth structures as it controls the hydraulic stability of soil masses.
· It is also required in design of filters used to prevent piping in hydraulic structures and subgrade drainage, rate of consolidation of compressible soils.
Darcy (1856) proposed equation for calculating the velocity of flow of water through a soil:
v = k.i
q = v.A = k.i.A
Q = q.t = k.i.A.t
Where,
v= Darcy or discharge velocity of water flow through porus media (cm/sec)
k= hydraulic conductivity of soil or coefficient of permeability(cm/sec)
i= hydraulic gradient = Δh/L
Δh = total head loss or piezometric head difference between two sections
L= distance between the sections which are always perpendicular to the direction of flow.
Q = total amount of flow (m3) for a period t (second)
q = flow rate of water (m3/s)
Note: the discharge velocity is not the true velocity of water flow but is rather an average velocity in the flow direction through the porus media. Since water can flow only in the void section of the media, the true velocity of water is called seepage velocity and is represented as vs=v/n where n is the porosity of soil.
The equation is valid for a wide range of soils. However, with materials like clean gravel and open-graded rockfills, the law breaks down because of the turbulent nature of flow through them.
The value of the hydraulic conductivity of soils varies greatly. In the laboratory, it can be determined by means of constant-head or falling-head permeability tests. The constant head test is more suitable for granular soils. Table 1.9 provides the general range for the values of k for various soils. In granular soils, the value depends primarily on the void ratio. In the past, several equations have been proposed to relate the value of k to the void ratio in granular
soil.
Coefficient of Permeability:
· Core sections of earth and rockfill dams utilize clay materials as impervious layers to control seepage. On the other hand, high-permeable gravels and sands are used as filtering materials in many applications.
Coefficient of permeability divided by porosity is called coefficient of percolation (Kp) = K/n
Determination of Coefficient of Permeability:
1. Laboratory Methods: The instruments used are permeameters
a. Constant-head permeability test (suitable for pervious soil: sand)
b. Variable-head permeability test ((suitable for less pervious soil: clay)
2. Field Methods
a. Pumping -out tests (influence large area around the pumping well and give an overall value of the coefficient of permeability of soil deposit).
b. Pumping -in tests (influence small area around the hole and gives an overall value of the coefficient of permeability of soil deposit).
3. Indirect Methods
Results from various tests:
Permeability of Stratified Soil:
· Actually, in the field soil is present in the form of different stratum which has different permeabilities.
· For the calculation of discharge average values of permeabilities are found out: average horizontal coefficient of permeability, (kH) when the flow is parallel to the strata and the average vertical coefficient of permeability (KV) when the flow is normal to strata.
 |
Note: It is assumed that within each stratum, the permeability is same for both horizontal and vertical flow.
Unit 4
ReplyDeleteQ1.
With the reference to standard laboratory practices and field methods, critical difference between the constant-head and variable-head permeability tests in term of testing procedure; The constant-head and variable-head permeability tests are based on Darcy's law but differ in procedure, calculation, and soil suitability. In the constant-head test, a steady water head is maintained and volume of water flowing through a soil sample in a given time is measured,making it suitable for course soils like sands and gravels here flow is rapid and easy to record. In contrast, the variable-head test allows the water level in a standpipe to fall over time, and permeability calculate from the rate of head loss and this is more appropriate for fine-grained soils like silts and clays where flow is very slow and difficult to measure directly.
Q2.The constant-head test is practical for high permeability soils in both lab and field while variable-head method is better for low permeability soils. Soil permeability is influenced by factors such as grain size, void ratio, soil structure, degree of saturation, fluid viscosity, chemical composition, compaction, and effective stress. Overall, permeability depends on both soil characteristics and flow conditions, and the testing method is chosen to match soil type and the ease of measuring water movement.
1. The constant-head test involves maintaining a steady water level and measuring the flow rate. This makes it ideal for coarse soils, such as sand. The variable-head test tracks the drop in water level over time and is better suited to fine soils, such as clay, where flow is slower. The calculations differ: the constant-head test uses k = QL/Aht, while the variable-head test uses k = aL/At. ln(h₁/h₂). In practice, pumping tests mimic the constant-head method for permeable soils and slug tests resemble the variable-head method for low-permeability conditions.
ReplyDelete2. Soil permeability depends on grain size, void ratio, structure, saturation, fluid viscosity, temperature, compaction and organic content.
Q1.
ReplyDeleteBoth the constant-head and variable-head permeability tests are derived from Darcy’s law, but they differ in their procedures, calculations, and soil applications. In the constant-head test, the water level is kept steady, and the amount of water passing through the soil sample within a fixed time is measured. This approach is most suitable for coarse-grained soils such as sands and gravels, where water movement is fast and easy to monitor. On the other hand, the variable-head test allows the water level in a standpipe to gradually drop, and permeability is determined from the rate of head reduction. This method is more appropriate for fine-grained soils like silts and clays, where flow occurs very slowly and direct measurement is difficult.
Q2.
The constant-head method is more practical for soils with high permeability, whether in laboratory or field conditions, whereas the variable-head test is better suited to soils with low permeability. The permeability of soil is affected by several factors, including particle size, void ratio, soil structure, degree of saturation, fluid viscosity, chemical properties, compaction, and effective stress. In general, permeability is controlled by both the inherent properties of the soil and the flow conditions, so the choice of test depends on the soil type and how easily water movement can be observed.
The constant-head and variable-head permeability tests differ in their procedure, governing principles, and calculation approach. The constant-head test is mainly used for coarse-grained soils such as sands and gravels, where water can flow easily. In this method, a constant water head is maintained throughout the test, and the volume of water discharged in a given time is measured. This test assumes steady-state flow conditions and applies Darcy’s law directly, giving a relatively quick and simple calculation of permeability.
ReplyDeleteIn contrast, the variable-head test is suited for fine-grained soils like silts and clays, where water flow is slow and maintaining a constant head is impractical. Here, water is allowed to flow from a standpipe and the drop in head is recorded over time. The flow is unsteady, so Darcy’s law is integrated over time.
While the constant-head test is quicker and simpler, the variable-head test is more sensitive to low flow rates and provides more accurate results for low-permeability soils. Overall, the choice between the two depends on soil type, expected permeability, and required accuracy.
The choice between the constant-head and variable-head permeability tests is primarily based on the soil’s permeability and the practicality of measuring flow. Sandy and gravelly soils have high permeability, meaning water flows through them quickly. For such soils, the constant-head test is more suitable because it can maintain a steady hydraulic head and collect a measurable discharge volume in a short time, which reduces the risk of measurement errors. This method works well under steady-state conditions and is efficient for soils where large quantities of water can flow continuously without significant head loss. On the other hand, fine-grained soils such as silts and clays have very low permeability, causing water to flow extremely slowly. In these cases, a constant-head test would require impractically long times to collect sufficient discharge for accurate measurement. The variable-head test overcomes this limitation by using a standpipe, allowing the head to gradually fall over time, which is easier to monitor and provides better sensitivity for very small flow rates.
Extending this understanding to field methods, a similar principle applies. For permeable soils, field pumping tests or constant-head infiltration tests are preferred, as they can maintain a steady flow and give reliable permeability values over a large volume of soil. For less permeable soils, methods such as falling-head tests in piezometers or in-situ permeability tests using packers are better suited, since they measure the change in head over time and do not rely on collecting large amounts of water. In summary, the constant-head approach is ideal where rapid, measurable flow is expected, while the variable-head approach is chosen for soils where slower seepage needs to be captured accurately—both in the lab and in the field.
2. Soil permeability is the ability of soil to transmit water and is influenced by several key factors. Grain size is the most important: coarse soils like sand and gravel have large pores and high permeability, while fine soils like clay have very small pores and low permeability. Soil structure, void ratio, and compaction affect the size and connectivity of pores—dense soils transmit less water than loose soils. Permeability also depends on the degree of saturation, with fully saturated soils allowing easier flow. Other factors include water temperature (affecting viscosity), impurities that may clog pores, and overburden stress, which reduces void space and lowers permeability. Together, these factors control how easily water flows through soil and must be considered in seepage and drainage design.