Properties of Soils
- Phase Diagram
(i) Soil mass is in general a three-phase system composed of solid, liquid and gaseous matter in a blended form with each other.
But in phase diagram – for understanding, these three matters are shown separately.
(ii) In supersaturated, state with change in water content volume of voids changes hence volume of soil changes.
The diagrammatic representation of the different phases in a soil mass is called the "phase diagram".
- Water content
w = (W_{w}/W_{s}) x 100
where, W_{W} = Weight of power
W_{S }= Weight of solids
There can be no upper limit to water content, i.e. w ≥ 0 - Void ratio
e = V_{v}/V_{s}
where, Vv = Volume of voids
V = Total volume of soil
Porosity cannot exceed 100% i.e.,
0 < n < 100
Void ratio is more important engineering property. - Degree of Saturation
S = (V_{w}/V_{v}) x 100
where, V_{w} = Volume of water
V_{v} = Volume of voids
0 ≤ S≤ 100
for perfectly dry soil : S = O
for Fully saturated soil : S = 100% - Air Content
V_{a} = Volume of air
S_{r} + a_{c} = 1 - % Air Void
%n_{a} = (Volume of air/Total volume) x 100 = (V_{a}/V) x 100
n_{a} = n.a_{c}
Unit Weight
- Bulk unit weight
γ = W/V = (W_{s}+W_{w})/(V_{s}+V_{w}+V_{a})
Thus Bulk unit weight is total weight per unit volume. - Dry Unit Weight is the weight of soil solids per unit volume.
γ_{d} = W_{s/}V
Dry unit weight is used as a measure of denseness of soil. More dry unit weight means more compacted soil. - Saturated unit weight: It is the ratio of total weight of fully saturated soil sample to its total volume.
γ_{sat} = W_{sat}/V
(i) Submerged unit weight or Buoyant unit weight (γ): It is the submerged weight of soil solids per unit volume.
γ' = γ_{sat}-γ_{w}
γ_{sat} = unit wt. of saturated soil
γ = unit wt. of water
(ii) Unit wt. of solids:
γ_{s} = W_{s}/V_{s}
γ is roughly 1/2 of saturated unit weight.
Specific Gravity
- True/Absolute Special Gravity, G
(i) Specific gravity of soil solids (G) is the ratio of the weight of a given volume of solids to the weight of an equivalent volume of water at 4℃.
G = W_{s}/V_{s}.γ_{w} = γ_{s}/γ_{w}
G = 2.6 to 2.75 for inorganic solids
= 1.2 to 1.4 for organic solids
(ii) Apparent or mass specific gravity (G_{m}): Mass specific gravity is the specific gravity of the soil mass and is defined as the ratio of the total weight of a given mass of soil to the weight of an equivalent volume of water.
Gm = (W/V.γ_{w}) = (γ or γ_{d }or γ_{sat})/γ_{w}
where, γ is bulk unit wt. of soil
γ = γ_{sat} for saturated soil mass
γ = γ_{d }for dry soil mass
G_{m} < G
In India, G is reported at 27℃,
- Relative density (I_{D})
To compare the degree of denseness of two soils.
I_{D} ∞ Shear strength ∝ (1/Compressibility)
A. when particles are arranged in cubical array
e_{max} = 91%, n_{max} = 47.6%
B. When particles are arranged in prismoidal array (Rhomohedral Array)
e_{min} = 35%, n_{min} = 25.9% - Relative Compaction
Indicate: Degree of denseness of cohesive + cohesionless soil
R_{c} = γ_{D}/γ_{Dmax}
Relative Density
Indicate: Degree of denseness of natural cohesionless soil
Some Important Relationships
- Relation between γ_{d}, γ
γ_{d} = γ/(1+w) ,
V_{s} = V/(1+e) & W_{s} = W/(1+w) - Relation between e and n
n = e/(1+e) or e = n/(1-n) - Relation between e, w, G and S:Se = w. G
- Bulk unit weight (γ) in terms of G, e, w and γw γ, G, e, Sr, γw
{Se = w. G} - Saturated unit (γ_{sat}.) weight in terms of G, e & γwSr = 1
- Dry unit weight γd in terms of G, e and γwSr = 0
- Submerged unit weight (γ') in terms of G, e and γw
γ = γ_{sat} - γ_{w} =
- Relation between degree of saturation (s) w and G
Methods for determination of water content
- Oven Drying Method
(i) Simplest and most accurate method
(ii) Soil sample is dried in a controlled temperature (105-110℃)
(iii) For organic soils, temperature is about 60℃. Soil having gyprum, temperature
(iv) Sample is dried for 24 hrs.
(v) For sandy soils, complete drying can be achieved in 4 to 6 hrs.
(vi) Water content is calculated as:
where, W_{1} = weight of container
W_{2 }= weight of container + moist sample
W_{3 }= weight of container + dried sample
Weight of water = W_{2 }– W_{3}
Weight of solids = W_{3 }– W_{1} - Pycnometer Method
(i) quick method
(ii) capacity of pycnometer = 900 m/.
(iii) this method is more suitable for cohesionless soils.
(iv) used when specific gravity of soil solids is known
(v) Let W_{1} = Wt. of empty dried pycnometer bottle
W_{2 }= Wt. of pycnometer + Soil
W_{3} = Wt. of pycnometer + Soil + Water
W_{4 }= Wt. of pycnometer + Water.(W_{1}, W_{2}, W_{3} and W_{4} are in anticlockwise order) - Calcium Carbide Method/Rapid moisture Meter Method Field Method
(i) Quick method (requires 5 to 7 minutes); but may not give accurate results.
(ii) The reaction involved is
CaC_{2} + 2H_{2}O → C_{2}H_{2} ↑ + Ca(OH)_{2}
(iii) Soil sample weights 4-6 gms.
(iv) The gauge reads water content with respect to total mass of soil. i.e., w_{r} = W_{w}/(W_{s})_{wet}
(In this equipment pressure calibrated against water content with respect to total mass)
(v) Actual water content w = (w_{r}/(1-w_{r})) x 100%w_{r} is moisture content recorded, expressed as fraction of moist wt. of solid.
w is actual water content. - Sand Bath Method (Field Method)
(i) quick, field method
(ii) used when electric oven is not available.
(iii) soil sample is put in a container & dried by placing it in a sand bath, which is heated on the kerosene store.
(iv) water content is determined by using same formula as in oven drying method. - Torsion Balance Moisture Meter Method
(i) quick method for use in laboratory.
(ii) Infrared radiations are used for drying sample.
(iii) Principle: The torsion wire is prestressed accurately to an extent equal to 100% of the scale reading. Then the sample is evenly distributed on the balance pan to counteract the prestressed torsion and the scale is brought back to zero. As the sample dries, the loss in weight is continuously balanced by the rotation of a drum calibrated directly to read moisture% on wet basis. - Alcohol Method
(i) It is a quick method adopted in field.
(ii) Should not be used for organic soil and soils containing calcium compound.
Determination of specific gravity of soil solids
- Pycnometer method is used.
- Instead of pycnometer, Density bottle (50 ml) OR Flask (500 ml) can also be used.
Let, W_{1} = Weight of empty pycnometer
W_{2 }= Weight of pycnometer + soil sample (oven dried)
W_{3 }= Weight of pycnometer + soil soilds + water
W_{4 }= Weight of pycnometer + water
Methods for the determination of insity unit weight
1. Core-Cutter Method
- Used in case of cohesive soils.
- Cannot be used in case of hard and gravelly soils.
γ = W/V - The method consists of driving a core-cutter (Volume = 1000 cc) into the soil and removing it, the cutter filled with soil is weighted. Volume of cutter is known from its dimensions and in situ unit weight is obtained by dividing soil weight by volume of cutter.
- If water content is known in the laboratory, the dry unit weight can also be computed.
γ_{d }= γ/(1+w)
2. Sand Replacement Method
- Used in case of hard and gravelly soils.
- A hole in ground is made. The excavated soil is weighted. The volume of hole is determined by replacing it with sand. Insitu unit weight is obtained by dividing weight of excavated soil with volume of hole.
3. Water Displacement Method
- Suitable for cohesive soils only, where it is possible to have a lump sample.
- A regular shape, well trimmed sample is weighted. (W_{1}). It is coated with paraffin wax & again weighted (W_{2}). The sample is now placed in a metal container filled with water upto the brim. Let the volume of displaced water be V_{m}. Then volume of uncoated specimen is calculated as,
V = V - (W_{2}-W_{1})/γ_{P}
where, = unit wt. of paraffin wax
Thus, bulk unit wt. of soil - Sands + Gravels: Bulky grains
Bulk grains classified as – angular, Subangular, Sub rounded, rounded, well rounded
Higher angularity ∝ Higher Shear Strength - Clay Minerals: Flaky grains
Grain size distribution
- Sieve Analysis: (For Coarse Grained Soils)
The fraction retained on 4.75 mm sieve is called the gravel fraction which is subjected to coarse sieve analysis.
The material passing 4.75 mm sieve is further subjected to fine sieve analysis if it is sand or to a combined sieve and sedimentation analysis if silt and clay sizes are also present. - Coarse Sieves: 4.75 mm, 10 mm, 20 mm, 80 mm.
- Fine Sieves: 75 μ, 150 μ, 212 μ, 425 μ, 600 μ, 1 mm, 2 mm.
- Concept of "Percentage finer"
% retained on a particular sieve = (Weight of soil retained on that sieve/Total weight of soil taken) x 100
Cumulative % retained = sum of % retained on all sieves of larger sizes and the % retained on that particular sieve."Percentage finer" than the sieve under reference = 100% - Cumulative % retained. - Sedimentation Analysis
According to stokes law, the terminal velocity is given by,
= density of grains (g/cm^{3})
= density of water (g/cm^{3})
μ = viscosity of water
g = acceleration due to gravity (cm/s^{2})
D = Diameter of grain (cm)
If 'h' the height through which particle falls in time 't', then h/t = k.D^{2}
∴ - Pipette Method
In this method, the weight of solids per cc of suspension is determined directly by collecting 10 cc of soil suspension from a specified sampling depth.
If m_{d} = dry mass (obtained after drying the sample) then, mass present in unit vol. of pipette
If M_{d} = total mass of soil dissolved in total volume of water (V) then mass/unit volume
= M_{d}/V
Therefore, % finer is given by = %
N = m_{d}N_{p}/m_{d}N
In m is the mass of dispersing agent dissolved in the total volume V, then actual % finer,
- Hydrometer Method
In this method the weight of solids present at any time is calculated indirectly by reading the density of soil suspension. - Calibration of Hydrometer
Establishing a relation between the hydrometer reading R_{H} and effective depth (H_{e}).
The effective depth is the distance from the surface of the soil suspension to the level at which the density of soil suspension is being measured.Effective depth is calculated as
H_{e} = H_{1} + 1/2(h - V_{H}/A_{J})
where, H_{1} = distance (cm) between any hydrometer reading and neck.
h = length of hydrometer bulb
V_{H} = volume of hydrometer bulb
A_{J} = area of the cross section of the jar.
Reading of Hydrometer is related to sp. gr. or density of soil suspension as:
G_{SS} = 1 + (R_{H}/1000)
Thus a reading of R_{H} = 25 means, G_{ss} = 1.025 and a reading of R_{H} = -25 means, G_{ss} = 0.975% finer is given as:
where, G = sp. gr. of soil solids
R_{H} = final corrected value of hydrometer
V = Total volume of soil suspension
W = weight of soil mass dissolved. - Corrections to Hydrometer Reading
(i) Meniscus correction: (C_{m})
Hydrometer reading is always corresponding to the upper level of meniscus.
Therefore, meniscus correction is always positive (+C_{m}).
(ii) Temperature correction: (C_{t})
Hydrometers are generally calibrated at 27℃. If the test temperature is above the standard (27℃) the correction is added and, if below, it is subtracted.
(iii) Dispersing/Defloculating agent correction: (C_{d})
The correction due to rise in specific gravity of the suspension on account of the addition of the defloculating agent is called Dispersing agent correction (C_{d}).
C_{d} is always negative.
The corrected hydrometer reading is given by
(R_{H}) = R_{H} + C_{m}±C_{t}-C_{a} - Grain Size Distribution Curves Curve-1: Well graded soil: good representation of grain sizes over a wide range and its gradation curve is smooth.
Curve-2: Poorly graded soil/ Uniform gradation:
It is either an excess or a deficiency of certain particle sizes or has most of the particles about the same size.
Curve-3: Gap graded soil: In this case some of the particle sizes are missing.
Curve-4: Predominantly coarse soil.
Curve-5: Predominantly fine soil.
The diameter D_{10} corresponds to 10% of the sample finer in weight on the Grain size distribution curve. This diameter D_{10} is called effective size.
Similarly, D_{30} and D_{60} are grain dia. (mm) corresponding to 30% fine and 60% finer.
The shape parameters related to these are:
(i) Coefficient of Uniformity C_{u} = D_{60}/D_{10}
(ii) Coefficient of Curvature
(a) for a soil to be well graded: [1 < C_{c} < 3] and [Cu > 4] for gravels:
[C_{u} > 6] for sands.
(b) Cu = 1 for uniform soils/poorly graded soils.
Consistency of clays: Atterberg limits
LL = W_{I }= liquid limit
PL = W_{p} = plastic limit
SL = W_{s} = Shrinkage limit
V_{1} = Volume of soil mass at LL
V_{p} = Volume of soil mass at PL
V_{d} = Volume of soil mass at SL
V_{s} = Volume of solids
Plasticity Index (I_{p})
It is the range of moisture content over which a soil exhibits plasticity.
I_{p} = W_{L} - W_{p}
W_{L} = water content at LL
W_{p} = water content at PL
If PL ≥ LL, I_{p} is reported as zero.
Soil classification related to plasticity index:
Relative Consistency or Consistency – index (I_{c})
To study behaviour saturated fine grained soil at its natural water content I_{C} = (W_{L}-W_{N})/(I_{P})
If I_{C} < 0, the natural water content of soil (w_{N}) is greater than w_{L} and the soil mass behaves like a liquid, but only upon disturbance.
If I_{C} > 1, soil is in semi solid state and will be very hard or stiff.
- Liquidity Index (I_{L})
I_{L} = (W_{N }- W_{P}) / (I_{P})
For a soil in plastic state I_{L} varies from 0 to 1.
- Flow Index (I_{f})
I_{f }= (W_{1 }- W_{2}) / log10(N_{2 }/ N_{1})
- Toughness Index (I_{t})
I_{T} = I_{P }/ I_{F}
For most of the soils: 0 < I_{T} < 3
When I_{T} < 1, the soil is friable (easily crushed) at the plastic limit. - Shrinkage Ratio (SR)
where, V_{1} = Volume of soil mass at water content w1%.
V_{2} = volume of soil mass at water content w2%.
V_{d} = volume of dry soil mass
Now, at SL, w_{2} = w_{s} and V_{2} = V_{d}
If w_{1} & w_{2} are expressed as ratio,
Stress-strain curve for different consistency states
- Unconfined Compressive Strength (q_{u})
Defined as the load per unit area at which an unconfined prismatic or cylindrical specimen of standard dimensions of a soil fails in a simple compression test.
q_{u} = 2 x shear strength of a clay soil (under undrained condition).
q_{u} is related to consistency of clays as:
- Sensitivity (S_{t}): It is defined as the ratio of the unconfined compressive strength of an undisturbed specimen of the soil to the unconfined compressive strength of a specimen of the same soil after remolding at unaltered water content.
S_{t} = (q_{u})undisturbed/(q_{u})remoulded
S_{t }≤ 1: in case of stiff clay having cracks and fissures.
Soil classification based on sensitivity:
- Thixotropy: It is the property of certain clays by virtue of which they regain, if left alone for a time, a part of the strength lost due to remoulding, at unaltered moisture content.
Higher the sensitivity, larger the thixotropic hardening.
- Active
Activity of clay = Plasticity index/%by weight finer 2μ
Activity based classification of clays
Volume change during swelling or shrinkage = (I_{p} and % clay) of Activity