Phase Relations of Soils: Soil-Water Relationship | Soil Mechanics - Civil Engineering (CE) PDF Download

Properties of Soils

1. 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".
   
2. 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
3. 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.
4. 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%
5. Air Content
    V_a = Volume of air
   S_r + a_c = 1
6. % Air Void
   %n_a = (Volume of air/Total volume) x 100 = (V_a/V) x 100
   n_a = n.a_c

Unit Weight

1. 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.
2. 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.
3. 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

1. 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℃,
   
2. 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%
3. 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

1. Relation between γ_d, γ
   γ_d = γ/(1+w) ,
   V_s = V/(1+e) & W_s = W/(1+w)
2. Relation between e and n
   n = e/(1+e) or e = n/(1-n)
3. Relation between e, w, G and S:Se = w. G
4. Bulk unit weight (γ) in terms of G, e, w and γw γ, G, e, Sr, γw
   
    
   {Se = w. G}
5. Saturated unit (γ_sat.) weight in terms of G, e & γwSr = 1
   
6. Dry unit weight γd in terms of G, e and γwSr = 0
   
7. Submerged unit weight (γ') in terms of G, e and γw
   γ = γ_sat - γ_w =
   
8. Relation between degree of saturation (s) w and G
   

Methods for determination of water content

1. 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 gypsum, 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, W₁ = weight of container
   W₂ = weight of container + moist sample
   W₃ = weight of container + dried sample
   Weight of water = W₂ – W₃
   Weight of solids = W₃ – W₁
2. 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 W₁ = Wt. of empty dried pycnometer bottle
   W₂ = Wt. of pycnometer + Soil
   W₃ = Wt. of pycnometer + Soil + Water
   W₄ = Wt. of pycnometer + Water.(W₁, W₂, W₃ and W₄ are in anticlockwise order)
3. 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
   CaC₂ + 2H₂O → C₂H₂ ↑ + 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.
4. 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.
5. 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.
6. 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

1. Pycnometer method is used.
2. Instead of pycnometer, Density bottle (50 ml) OR Flask (500 ml) can also be used.
   Let, W₁ = Weight of empty pycnometer
   W₂ = Weight of pycnometer + soil sample (oven dried)
   W₃ = Weight of pycnometer + soil soilds + water
   W₄ = Weight of pycnometer + water

Methods for the determination of in sity 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. (W₁). It is coated with paraffin wax & again weighted (W₂). 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 - (W₂-W₁)/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/cm³)
   = density of water (g/cm³)
  μ = viscosity of water
  g = acceleration due to gravity (cm/s²)
  D = Diameter of grain (cm)
  If 'h' the height through which particle falls in time 't', then h/t = k.D²
  ∴
• 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_dN_p/m_dN
  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 = H₁ + 1/2(h - V_H/A_J)
  where, H₁ = 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/Deflocculating agent correction: (C_d)
  The correction due to rise in specific gravity of the suspension on account of the addition of the deflocculating 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 D₁₀ corresponds to 10% of the sample finer in weight on the Grain size distribution curve. This diameter D₁₀ is called effective size.
  Similarly, D₃₀ and D₆₀ are grain dia. (mm) corresponding to 30% fine and 60% finer.
  The shape parameters related to these are:
  (i) Coefficient of Uniformity C_u = D₆₀/D₁₀ 
  (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
V₁ = 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 = (W₁ - W₂) / log10(N₂ / N₁)

• 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, V₁ = Volume of soil mass at water content w1%.
  V₂ = volume of soil mass at water content w2%.
  V_d = volume of dry soil mass
  Now, at SL, w₂ = w_s and V₂ = V_d
  
  If w₁ & w₂ 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