TESTING DETERMINE THE PERMEABILITY COEFFICIENT SOILD PERMEABILITY

TESTING DETERMINE THE PERMEABILITY COEFFICIENT SOILD PERMEABILITY

TESTING DETERMINE THE PERMEABILITY COEFFICIENT SOILD PERMEABILITY

26/05/2021

The permeability coefficient along with the water release coefficient are the most important parameters of the aquifer. It is an important input parameter in the design of groundwater pumping system

DETERMINATION OF absorbent coefficient

1. General

Water can move individually in rock without filling all holes and voids in the form of individual drops and streams. The infiltration of rainwater through the aeration zone to the groundwater table is an example of free infiltration.

In the case of soil pores filled with water and water moving due to hydrostatic pressure from a place of high pressure to a place of low pressure is called groundwater infiltration

1.1 Bernoulli equation – seepage energy

Based on the Bernoulli equation, we have the water column h of a liquid element as the energy of water per unit weight. Considering a water particle acted upon by a pressure u, with a velocity v at a depth z, we have the water column:

where: h = height of water column

                   u = pressure

                   v = velocity

                   g = acceleration due to gravity

                   w  = density of water

And   is a constant that is determined when we choose a normal surface. If the
Bernoulli equation is applied to groundwater flow, the first term of
the above equation can be ignored because the velocity of groundwater flow is very small. We have
the hydraulic equation for groundwater that can be rewritten as:

If the water element moves, energy is lost, which is the water column loss. The above equation gives two important conclusions:

  • There is only flow between two points if there is a difference in the head of water between those two points
  • In an equilibrium fluid, the head at two points in the liquid is the same regardless of the depth.

The difference in head between two points A and B can be expressed as follows:

Or can also be represented as:

where:

                   i = hydraulic gradient

                   L = distance between two points A and B

Based on the change of velocity v with respect to the hydraulic gradient i, the flow in the soil pores can be laminar, turbulent or in an intermediate state. Laminar flow when the flow forms parallel layers without mixing, turbulent flow is the flow that consumes a certain amount of energy due to the mixing of water layers. Between these two states is a transitional flow. This is shown in detail in the following figure:

1.2 Darcy's law of permeability

Darcy's experiment: Water is put into a tube filled with sand, the water level is kept at a fixed level. After percolating the tank with sand, the water level in this tank is also kept at a fixed level.

In 1856, from experiments conducted Darci established the relationship:

K is called the permeability coefficient or water permeability coefficient of the rock.

Dividing both sides of the above equation by the area of ​​the cylinder (F) we get the permeability rate:

In the above formula when i=1 (slope angle 45 0 ) we have k=v. Thus, the permeability coefficient is equal to the seepage rate when the hydraulic slope is 1 .

The above equation shows a linear relationship of the seepage velocity v with the hydraulic gradient i. According to Darcy's law, the seepage velocity is proportional to the hydraulic gradient i. Darcy's law is consistent with laminar motion which is very common in natural conditions. Therefore, this law is often called the Basic Law of Groundwater Permeation.

Note: the rate read in this experiment (permeation rate) is the conversion rate, because the permeation flow area in the formula is taken as the cylinder area, but in reality the water only moves through the pores. void of rock. To get the actual velocity of water in the soil we need to divide the flow rate Q by the pore area.

where n is the porosity of the rock.

This formula shows that the real rate of movement of groundwater is always greater than the rate of infiltration.

Gravity water in the pores of clay is
obstructed by the water shells surrounding the soil particles , so only with a certain value of hydraulic gradient will the water
begin to move, this gradient is called hydrodynamic gradient. The initial force is denoted 0 .

When the permeability coefficient is very large, the permeability law is broken, the flow changes to turbulent flow, so Darcy's law is no longer valid.

  1. The permeability coefficient is inferred from the mechanical properties

2.1 Relation k- loose grain soil

2.1.1 Permeability coefficient according to Hazen

For soils with fairly uniform grains (gravel, very clean sand), the permeability coefficient can be determined according to Hazen's formula published in 1930 as follows:

Where:         k (cm/s)

                   C coefficient from 1~1.5

                   D 10   soil grain diameter at which 10% of soil particles are less than this value (mm)

The reliability of this formula is quite low, experimentally proven by Carrier in 2003.

2.1.2 Carrier permeability coefficient corrected from Kozeny-Carman

The Kozeny equation gives quite good results (quite complicated). Carrier in 2003 has been corrected to make it easy to use in practice.

Where: SF form factor in the range of 6-8

                   D li is the size of the large floor hole (cm)

                   D si is the small floor hole size (cm)

                   f i is the percentage between the 2 exchanges (%)

(Refer to page 175 [1] )

2.1.3 According to Champuis published in 2004

Proposed empirically and based on ink formula 2.2

2.1.4 Amer and Awad (1974)

Based on laboratory experimental results, Amer and Awad (1974) published the relationship k with fine particles. The formula takes into account the viscosity coefficient of water, for simplicity at 20 0 C we have the formula:

Where: C u : homogeneity coefficient

                   D 10 : hole diameter (mm) at which 10% of particles pass

2.1.5 US Navy (1971)

Based on laboratory testing, US Deparment of Navi provides an empirical correlation between k (ft/min) and D 10 for fine-grained soils with a homogeneity coefficient Cu from 2 to 12 and D 10 /D 5 < 1.4 . Correlation chart

2.2 Relationship in k-stick soil

Many authors have studied the permeability coefficient in cohesive soil environment. More details refer [1]

For example, Tavenas, and NNK (1983) have shown the relationship between the porosity coefficient and the permeability coefficient of clay. PI-plasticity index, CF- clay content (0.3, 0.4,…..~30%, 40%).

  1. Experiment to determine the permeability coefficient in the room

Determination of the permeability coefficient of soil is the direct application of Darcy's law, in which case the following methods are available in the laboratory:

- Determined by the constant water column method, usually applied to well-permeable soils.

- Determined by the method of variable water column, usually applied to weakly permeable soils.

3.1 Constant water column method cột

A soil sample of cross section S, length L, is fitted to a laboratory permeability meter. The two ends of the soil sample are attached to porous, permeable rock.

The constant head test is to keep the water column difference (h) between the two sides of the soil core constant throughout the experiment, measure the amount of water (Q) flowing through the core during a period of time (t). .

According to Darcy's law:

3.2 Method of variable water column

Water in a pipe of area s will flow through the soil, initially at an initial height h 1 at time t=0. Water begins to flow through the soil sample, at time t=t 2 , we measure h 2

  1. Test to determine the permeability coefficient at the wall

4.1 Experimental suction pumping method

The suction pump experiment system includes a central pump well, monitoring wells, and pump flow meter.

Basic steps:

- Measure the groundwater level before pumping in the wells

- Carry out the suction pump bơm

- Measure the lowering of the water level over time, according to the flow.

Recorded data are processed according to a number of separate methods

4.2 Water column method

  1. Coefficient of longitudinal and transverse permeability thấm

Most soils are anisotropic in terms of permeability. In sedimentary soils, the magnitude of k varies depending on the direction of infiltration. There are two components, namely longitudinal permeation v and transverse permeation h . The magnitude of these two components depends on many factors, such as the form of the sediment.

Some research results on h / k v ratio for fine-grained soil have been published:

Equivalent permeability coefficient:

Equivalent transverse permeability

Equivalent longitudinal permeability

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