Phase Relationship Diagram
Phase Relationship Diagram
Phase Relationship Diagram
In a mass of soil, there are three physical components: solid, water, and air. A
phase relationship diagram is normally used to represent the relationship as
follows:
Definitions:
Phase Relationships:
Volume-volume relationship:
air content:
Weight-weight relationship:
Weight-Volume relationship:
Watch! (Videos):
Solution of Unit Weight and Its Conversion from Metric Units to SI and
US Units
Solution of Soil Compaction Check Via The Voids Ratio
Solution of The Value of The Moisture When Fully Saturated
Requirements:
Determine moist unit weight of soil, dry unit weight of soil, and water content.
Problem solving technique:
1. Moist unit weight gt= Wt / Vt (Wt = 100 lbs, Vt=1 ft3, are given)
2. Dry unit weight, gd = Ws / Vt (Weight of solid is weight of soil after dried
in oven ,Ws = 80 lbs, Vt=1 ft3, are given)
3. Water content, w (%) = Ww/Ws (Ws = 80 lbs , weight of water, W w not
known)
4. Find weight of water, from phase relationship diagram, Ww = Wt – Ws.
Solution:
Requirements:
Determine moist unit weight of soil, dry unit weight of soil, and water content.
Solution:
Requirements:
Solution:
Requirements:
Solution:
Question:
A contractor has compacted the base course for a new road and found that the
mean value of the test samples shows w = 14.6%, Gs = 2.81, and γ = 18.2
kN/m3. The specifications require that e < 0.80. Has the contractor complied
with the specifications?
Solution:
For formulas of soil phase relationships read Soil Phase Relationships article.
Thus
Question:
A cohesive soil sample was taken from an SPT and returned to the laboratory
in a glass jar. It was found to weigh 140.5 grams. The sample was then placed
in a container of V = 500 cm3 and 423 cm3 of water were added to fill the
container. From these data, what was the unit weight of the soil in kN/m 3 and
pcf?
Solution:
For formulas of soil phase relationships read Soil Phase Relationships article.
Notice that the 140.5 grams is a mass. Therefore, the ratio of mass to volume
is the density rho
for conversion from SI units to US units:
Question:
Solution:
For formulas of soil phase relationships read Soil Phase Relationships article.
but
rearranging
or
therefore
(2) Again, in a fully saturated soil:
Thus
or
See the full table of typical values of cohesive intercept "C" of soils here
See the full table of typical values of friction angle "φ" of soils here
Temperature
where
C = Celsius degree
F = Fahrenheit degree
K = Kelvin degree
R = Rankine scale
Water Pressure Gradient
1000 kg/m3 = 1.0 kg/dm3 = 1.0 g/cm3 = 62.4 pcf = 8.34 lb/gal = 350 lb/bbl
Sands: 115 ~ 135 pcf ( 18 ~ 21 kN/m3 up to 22 kN/m3 with some gravel content)
From e = 2 (extremely soft, weak clays) to e = 0.7 (very stiff clays). There are
extreme examples of softer clays (with e as high as 5) and stiffer clays.
Silica sands: 28 ~ 36
Clays: 15 ~ 30
As low as 5-7 degrees for smectites. For low confining stress levels and/or large
sand content it can be as high as critical-state friction angle.
Undrained: v = 0.5
Typical Values of Atterberg Indices
Ca/Cc = 0.02 ~ 0.07 (lower values for shale and mudstone; higher values for
peat)
Soil K
Gravel 10-3 to 1 m/s
Sand 10-7 to 10-2 m/s
Silt 10-9 to 10-5 m/s
Clay 10-13 to 10-9 ms
The cohesion intercept is a term used in describing the shear strength soils. Its
definition is mainly derived from the Mohr-Coulomb failure criterion and it is
used to describe the non-frictional part of the shear resistance which is
independent of the normal stress. In the stress plane of Shear stress-effective
normal stress, the soil cohesion is the intercept on the shear axis of the Mohr-
Coulomb shear resistance line.
"Granular soil" means gravel, sand, or silt (coarse-grained soil) with little or no
clay content. Granular soil has no cohesive strength. Some moist
granular soils exhibit apparent cohesion. Granular soil cannot be molded when
moist and crumbles easily when dry.
"Cohesive soil" means clay (fine-grained soil), or soil with a high clay content,
which has cohesive strength. Cohesive soil does not crumble, can be excavated
with vertical sideslopes, and is plastic when moist. Cohesive soil is hard to
break up when dry, and exhibits significant cohesion when submerged.
Cohesive soils include clayey silt, sandy clay, silty clay, clay and organic clay.
Cohesion [kPa]
Description USCS Specific Reference
min max
value
Well graded gravel, sandy gravel,
GW - - 0 [1],[2],[3],
with little or no fines
Poorly graded gravel, sandy gravel, [1],[2],
GP - - 0
with little or no fines [3],
Silty gravels, silty sandy gravels GM - - 0 [1],
Clayey gravels, clayey sandy
GC - - 20 [1],
gravels
Well graded sands, gravelly sands, [1],[2],
SW - - 0
with little or no fines [3],
Poorly graded sands, gravelly [1],[2],
SP - - 0
sands, with little or no fines [3],
Silty sands SM - - 22 [1],
Silty sands - Saturated compacted SM - - 50 [3],
Silty sands - Compacted SM - - 20 [3],
Clayey sands SC - - 5 [1],
Clayey sands - Compacted SC - - 74 [3],
Clayey sands -Saturated compacted SC - - 11 [3],
Loamy sand, sandy clay Loam -
SM, SC 50 75 [2],
compacted
Loamy sand, sandy clay Loam -
SM, SC 10 20 [2],
saturated
Sand silt clay with slightly plastic
SM, SC - - 50 [3],
fines - compacted
Sand silt clay with slightly plastic
SM, SC - - 14 [3],
fines - saturated compacted
Inorganic silts, silty or clayey fine
ML - - 7 [1],
sands, with slight plasticity
Inorganic silts and clayey silts -
ML - - 67 [3],
compacted
Inorganic silts and clayey silts -
ML - - 9 [3],
saturated compacted
Inorganic clays, silty clays, sandy
CL - - 4 [1],
clays of low plasticity
Inorganic clays, silty clays, sandy
CL - - 86 [3],
clays of low plasticity - compacted
Inorganic clays, silty clays, sandy
clays of low plasticity - saturated CL - - 13 [3],
compacted
Mixture if inorganic silt and clay -
ML-CL - - 65 [3],
compacted
Mixture if inorganic silt and clay -
ML-CL - - 22 [3],
saturated compacted
Organic silts and organic silty clays
OL - - 5 [1],
of low plasticity
Inorganic silts of high plasticity -
MH - - 10 [1],
compactd
Inorganic silts of high plasticity -
MH - - 72 [3],
saturated compacted
Inorganic silts of high plasticity MH - - 20 [3],
Inorganic clays of high plasticity CH - - 25 [1],
Inorganic clays of high plasticity -
CH - - 103 [3],
compacted
Inorganic clays of high plasticity -
CH - - 11 [3],
satrated compacted
Organic clays of high plasticity OH - - 10 [1],
ML, OL, MH,
Loam - Compacted 60 90 [2],
OH
ML, OL, MH,
Loam - Saturated 10 20 [2],
OH
ML, OL, MH,
Silt Loam - Compacted 60 90 [2],
OH
ML, OL, MH,
Silt Loam - Saturated 10 20 [2],
OH
Clay Loam, Silty Clay Loam - ML, OL, CL,
60 105 [2],
Compaced MH, OH, CH
Clay Loam, Silty Clay Loam - ML, OL, CL,
10 20 [2],
Saturated MH, OH, CH
OL, CL, OH,
Silty clay, clay - compacted 90 105 [2],
CH
OL, CL, OH,
Silty clay, clay - saturated 10 20 [2],
CH
Peat and other highly organic soils Pt - -
REFERENCES
Practicing engineers:
1. Soil mechanics
Soil mechanics is a branch of soil physics and engineering
mechanics that describes the behavior of soils. It differs from fluid
mechanics and solid mechanics in the sense that soils consist of a
heterogeneous mixture of fluids (usually air and water) and particles
(usually clay, silt, sand, and gravel) but soil may also contain organic
solids and other matter.
2. Geotechnical investigation
Geotechnical engineers and engineering geologists perform geotechnical
investigations to obtain information on the physical properties of soil and
rock underlying (and sometimes adjacent to) a site to design earthworks
and foundations for proposed structures, and for repair of distress to
earthworks and structures caused by subsurface conditions.
3. Foundations
A building's foundation transmits loads from buildings and other
structures to the earth. Geotechnical engineers design foundations based
on the load characteristics of the structure and the properties of the soils
and/or bedrock at the site.
4. Lateral earth support structures
A retaining wall is a structure that holds back earth. Retaining walls
stabilize soil and rock from downslope movement or erosion and provide
support for vertical or near-vertical grade changes. Cofferdams and
bulkheads, structures to hold back water, are sometimes also considered
retaining walls.
5. Earthworks
Earthworks include excavation, filling, and compaction.
6. Ground Improvement
Ground Improvement is a technique that improves the engineering
properties of the treated soil mass. Usually, the properties modified are
shear strength, stiffness and permeability. Ground improvement has
developed into a sophisticated tool to support foundations for a wide
variety of structures. Properly applied, i.e. after giving due consideration
to the nature of the ground being improved and the type and sensitivity of
the structures being built, ground improvement often reduces direct costs
and saves time.
7. Slope stabilization
Slope stability is the potential of soil covered slopes to withstand and
undergo movement. Stability is determined by the balance of shear
stress and shear strength.
8. Offshore geotechnical engineering
Offshore (or marine) geotechnical engineering is concerned with
foundation design for human-made structures in the sea, away from
the coastline (in opposition to onshore or nearshore).
9. Geosynthetics
Geosynthetics are a type of plastic polymer products used in geotechnical
engineering that improve engineering performance while reducing costs.
The followings are almost the best geotehnical engineering journals, this list
does not include all journals
Fills on Clays:
Excess pore water pressures are created when fills are placed on clay or
silt. Provided the applied loads do not cause the undrained shear strength
of the clay or silt to be exceeded, as the excess pore water pressure
dissipates consolidation occurs, and the shear strength of the clay or silt
increases with time. For this reason, the factor of safety increases with
time under the load of the fill.
Cuts in Clay:
As a cut is made in clay the effective stress is reduced. This reduction will
allow the clay to expand and absorb water, which will lead to a decrease
in the clay strength with time. For this reason, the factor of safety of a cut
slope in clay may decrease with time. Cut slopes in clay should be
designed by using effective strength parameters and the effective
stresses that will exist in the soil after the cut is made.
Slaking - Shales, Claystones, Siltstones, etc.:
Sudden moisture increase in weak rocks can produce a pore pressure
increase in trapped pore air accompanied by local expansion and
strength decrease. The "slaking" or sudden disintegration of hard shales,
claystones, and siltstones results from this mechanism. If placed as rock
fill, these materials will tend to disintegrate into a clay soil if water is
allowed to percolate through the fill. This transformation from rock to clay
often leads to settlement and/or shear failure of the fill.
Soil friction angle is a shear strength parameter of soils. Its definition is derived
from the Mohr-Coulomb failure criterion and is used to describe the friction
shear resistance of soils together with the normal effective stress.
In the stress plane of Shear stress-effective normal stress, the soil friction angle
is the angle of inclination with respect to the horizontal axis of the Mohr-
Coulomb shear resistance line.
"Cohesive soil" means clay (fine-grained soil), or soil with a high clay content,
which has cohesive strength. Cohesive soil does not crumble, can be excavated
with vertical sideslopes, and is plastic when moist. Cohesive soil is hard to
break up when dry, and exhibits significant cohesion when submerged.
Cohesive soils include clayey silt, sandy clay, silty clay, clay and organic clay.
Typical values of soil friction angle for different soils according to USCS
References:
Correlation between SPT-N value and friction angle and Relative density
(Meyerhoff 1956)
SPT N3 Friction angle
Soi packing Relative Density [%]
[Blows/0.3 m - 1 ft] [°]
<4 Very loose < 20 < 30
4 -10 Loose 20 - 40 30 - 35
10 - 30 Compact 40 - 60 35 - 40
30 - 50 Dense 60 - 80 40 - 45
> 50 Very Dense > 80 > 45
Usually, the economics of the project dictates the type of test you would use for
determination of the friction angle. Nonetheless, the best test to determine the
friction angle of soil is the one that is more analogous to the problem at hand.
For example, if you are to determine bearing capacity of a square footing,
triaxial test is the best one.