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[DAY-3] GATE 2021 | Civil Engineering Key Notes and Formulas – Soil Mechanics Part – 3

Sep 22, 2020
• The elevation head (hz) of any point is its height above the datum line. The height of water level in the standpipe above the datum is the piezometric head (h). h = hz + hw
• Darcy’s law states that there is a linear relationship between flow velocity (v) and hydraulic gradient (i) for any given saturated soil under steady laminar flow conditions.
• If the rate of flow is q (volume/time) through cross-sectional area (A) of the soil mass, Darcy’s Law can be expressed as
v = q/A = k.i
where k = permeability of the soil
i = Dh/L
Dh = difference in total heads
L =
length of the soil mass
• The flow velocity (v) is also called the Darcian velocity or the superficial velocity.
• It is different from the actual velocity inside the soil pores, which is known as the seepage velocity, vS.
• Seepage velocity is always greater than the superficial velocity, and it is expressed as:

where AV = Area of voids on a cross section normal to the direction of flow
n = porosity of the soil

• Permeability (k) is an engineering property of soils and is a function of the soil type. Its value depends on the average size of the pores and is related to the distribution of particle sizes, particle shape and soil structure.

• The ratio of permeabilities of typical sands/gravels to those of typical clays is of the order of 106. A small proportion of fine material in a coarse-grained soil can lead to a significant reduction in permeability.

• For different soil types as per grain size, the orders of magnitude for permeability are as follows:

Soil

k (cm/sec)

Gravel

100

Coarse sand 100 to 10-1
Medium sand 10-1 to 10-2
Fine sand 10-2 to 10-3
Silty sand 10-3 to 10-4
Silt 1 x 10-5
Clay

10-7 to 10-9

• In soils, the permeant or pore fluid is mostly water whose variation in property is generally very less. Permeability of all soils is strongly influenced by the density of packing of the soil particles, which can be represented by void ratio (e) or porosity (n).
• In sands, permeability can be empirically related to the square of some representative grain size from its grain-size distribution. For filter sands, Allen Hazen in 1911 found that » 100 (D10)2 cm/s where D10= effective grain size in cm.
• Kozeny-Carman equation for laminar flow in saturated soils.
• For silts and clays, the Kozeny-Carman equation does not work well, and log k versus e plot has been found to indicate a linear relationship.

For clays, it is typically found that

where Ckis the permeability change index and eis a reference void ratio.