void ratio correlations
TRANSCRIPT
CORRELATIONS OF VOID RATIO
Presented By: Muhammad Ali Rehman
Soil
Void Ratio
INTRODUCTION
Soil
To a Geotechnical Engineer,
Soil is considered to be a
three-phase material
composed of, solid (mineral
particle), water & air.
Void Ratio
Total volume of a soil sample canbe expressed as:
V = Vs + Vv
V = Vs + Vw + Va
The ratio of volume of voids to the volume of solids is known as void ratio.
e = Vv/Vs
Void Ratio
Value of void ratio depends on:
the volumetric changes of the soil.
the consistency
packing of soil.
Void ratio characterizes the compactness of the soil.
Void ratio of loose soil is higher than that of dense soil.
Can be determined only from undisturbed samples.
Typical Void ratio value for
Dense gravel: 0.3
Loose sand: 0.6
Clays: 0.5 < to <1.0.
Correlations
Porosity
Void ratio is usually used in parallel with soil
porosity.
Porosity is the ratio of volume of voids to the total
volume.
e = 𝑛
1−𝑛
Or
n = 𝑒
1+𝑒
Unit Weight
The relation of Dry Unit Weight with void ratio:
𝛾𝑑 = 𝐺𝑠𝛾𝑤
1+𝑒
e = 𝐺𝑠𝛾𝑤
𝛾𝑑− 1
Moisture content, Dry Density
S.e = 𝐺𝑠. 𝑤𝑛
𝑤𝑛 = 𝑆.𝑒
𝐺𝑠
e = 𝐺𝑠. 𝑤𝑛 (if S=1)
𝜌𝑑 = 𝐺𝑠.𝜌𝑤
1+𝑒(𝜌𝑤 = 1000 kg/𝑚3)
emax & emin
The maximum and minimum void ratios for granular soils
depend on several factors, such as:
Grain size
Grain shape
Fine contents, Fc (that is, fraction smaller than 0.075 mm)
emax is the void ratio of soil in loosest state
emin is the void ratio of soil in densest state
emax & emin
The amount of non-
plastic fines present in
a given granular soil
has a great influence
on emax and emin.
Influence of fines on void ratio
of Nevada Sand, Lade et al.
(1998)
emax & emin
Miura et al. (1997) determined the maximum and
minimum void ratios of a larger number of clean
sand samples.
emax ≈ 1.62emin
emax & emin
Cubrinovski and Ishihara (2002) and Patra et al.
(2010).
emax & emin
Cubrinovski & Ishihara (2002) studied the variation
of emax and emin for very large number of soils.
Clean Sand (Fc = 0 to 5%)
emax = 0.072 + 1.53emin
Sands with fines (5 < Fc ≤ 15%)
emax = 0.25 + 1.37emin
Sands with fines (15 < Fc ≤ 30%)
emax = 0.44 + 1.21emin
Silty soils (30 < Fc ≤ 70%)
emax = 0.44 + 1.32emin
emax & emin With Mean Grain Size
Plot of emax - emin versus the mean grain size (D50):
Cubrinovski and Ishihara (2002)
Relative Density
Relative density is commonly used to indicate the in situ denseness or looseness of granular soil.
Dr = 𝑒𝑚𝑎𝑥 − 𝑒
𝑒𝑚𝑎𝑥 −𝑒𝑚𝑖𝑛
Dr = relative density (usually in percentage)
e = in situ void ratio
emax = void ratio of soil in loosest state
emin = void ratio of soil in densest state
Shear Modulus
The small-strain shear modulus of soils, Gmax, is an important parameter for many geotechnical design applications, including site characterization, settlement analyses, seismic hazard analyses, and site response analysis and soil-structure interaction.
Hardin (1978) suggested that Gmax for clays depends on the in situ (or applied) stress (σ'), void ratio (e), and OCR.
The effects of OCR are, to a large extent, taken into account by the effect of void ratio and could be neglected, (Leroueil and Hight, 2003).
Shear Modulus
Hardin (1978) and
Hight & Leroueil (2003):
Void Ratio, e
Hydraulic Conductivity
One of the most important and useful parameter in the study of percolation process in porous media, consolidation & settlement of soils and foundation, water regime in stratified deposits, and other geotechnical problem.
Kozney-Carman relation, (Kozney 1927 and Carman 1937):
k: hydraulic conductivity (m/s)
e: void ratio,
Ss: specific surface area (𝑚2/𝑔)
CF: shape factor { ≈ 0.2 (Taylor, 1948)}
γw = unit weight of water (N/𝑚3)
ρm = density of soil (kg/𝑚3)
μ = Viscosity of fluid (N.s/𝑚2)
Hydraulic Conductivity
Carrier (2003) has modified the Kozney-Carman
relation into:
k = 𝟏. 𝟗𝟗 × 𝟏𝟎𝟒 𝟏
𝑺𝑺
𝟐×
𝒆𝟑
𝟏+𝒆
Carrier (2003) further suggested that:
Hydraulic Conductivity
Taylor (1948) and Lambe & Whitman (1969)
proposed:
Ck: permeability change index i.e. the
slope of e versus log(k) plot
k0: hydraulic conductivity for
reference void ration e0
Hydraulic Conductivity
Samarasinghe et al. (1982) proposed an equation:
C: constant with same unit as k,
n: constant that depends on type
of soil and varies from 3.2 to 14.2
Hydraulic Conductivity
Variation in hydraulic conductivity with void ratio:
Mesri & Olson (1971)
Void Ratio-Pressure Plot
Typical plot of void ratio against effective pressure
(semi logarithmic scale)
e0: initial void ratio of specimen
e1: void ratio after consolidation caused
by pressure increment σ’1
e2: void ratio at the end of consolidation
caused by next increment of
pressure σ’2
Pre-consolidation Pressure
Cassagrande (1936) proposed a simple graphical method to determine the pre-consolidation pressure from laboratory e-logσ’ plot.
Draw a horizontal line ab.
Draw the line ac tangent at a.
Draw the line ad, which is thebisector of the angle bac.
Project the straight-line portiongh of the e-log σ’ plot back tointersect line ad at f.
The abscissa of point f is thepre-consolidation pressure (σ’c).
Pre-consolidation Pressure
Nagaraj & Murty (1985):
e0: in situ void ratio
eL: void ratio at liquid limit = 𝐿𝐿 (%)
100. 𝐺𝑠
Gs: specific gravity of soil
σ’0: in situ effective overburden pressure (kN/𝑚2)
Cc : Compression Index
Rendon-Herrero (1983) gave the relationship for the compression index in the form:
𝐶𝑐 = 0.141𝐺𝑠2 1+𝑒0
𝐺𝑠
2.38
𝐶𝑐 = 1.15(𝑒0- 0.27) by Nishida (1956) – all clays
𝐶𝑐 = 0.156𝑒0 + 0.0107) by Hough (1957) – All clays
𝐶𝑐 = 0.30(𝑒0- 0.27) by Hough (1957) – inorganic cohesive soils
𝐶𝑐 = 0.30(𝑒0- 0.27) by Hough (1957) – low plasticity soils
𝐶𝑐 = 0.208𝑒0 + 0.0083 by Hough (1957) – Chicago Clays
Variation of Void Ratio with Shearing
Displacement
At large shear displacement, the void ratios of loose and dense sands become practically the same, and this is termed the critical void ratio.
Variation of tan𝜙’ with Void Ratio
Acar, Durgunoglu, and Tumay (1982)
Figure shows the results of direct shear tests
conducted with a quartz sand and concrete,
wood, and steel as foundation
materials, with σ’ =100 (kN/𝑚2).
References
Principles of Geotechnical Engineering, 7th Ed, B.M. Das
An Introduction to Geotechnical Engineering, Robert D. Holtz, and William D. Kovacs
Soil Mechanics in Engineering Practice, 3rd Ed, Karl V. Terzaghi, Ralph B. Peck, and Gholamreza Mesri
Correlations between Shear Wave Velocity and Geotechnical Parameters in Norwegian Clays, J. S. L’Heureux and M. Long
S. M. Rezwan Hossain, MD. Abdul Qaiyum Talukder, Shariful Islam, MD. Rafiue Islam, “Significance of Silt Content and Void Ratio on the Hydraulic Conductivity of Sand-Silt Mixtures”, International Journal of Advanced Structures and Geotechnical Engineering ISSN 2319-5347, Vol. 02, No. 04, October 2013