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10/16/2015
Aj. Suriyah 1
CE 371 Soil Mechanics
Suriyah Thongmunee, Ph.D.
Compressibility and Consolidation
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Compressibility and Consolidation
2
Lecture Outline:
1. Elastic Settlement
2. Consolidation Settlement
3. One-Dimensional Consolidation
4. Consolidometer and Standard Test
5. Pressure-Void Ratio Curves
6. Determination of Preconsolidation Pressure
7. Computation of Consolidation Settlement
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Compressibility and Consolidation
Soil engineering problems are of two types. The first type includes all cases wherein there is no possibility of the stress being sufficiently large to exceed the shear strength of the soil, but the settlement due to the imposed stress is greater than allowable settlement. The second type includes cases in which there is danger of shearing stresses exceeding the shear strength of the soil
3
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Compressibility and Consolidation
When structures are built on soils, they transfer loads to the subsoil through the foundations. The effect of the loads is felt by the soil normally up to a depth of about two to three times the width of the foundation.
As a result, the soil within this depth gets compressed due to the imposed stresses. The compression of the soil mass leads to the decrease in the volume of the mass which results in the settlement of the structure.
4
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Compressibility and Consolidation
The settlement of structure is caused by (a) deformation of soil particles (b) relocations of soil particles (c) expulsion of water or air from the void spaces.
The settlement of the soil mass due to the imposed stresses may be almost immediate (elastic) or time dependent according to the permeability (consolidation) characteristics of the soil
In general, the soil settlement caused by loads may be divided into three categories: (1) Elastic settlement (2) Primary consolidation settlementand (3) Secondary consolidation settlement. The total settlement can be determined by summing up these settlement
5
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Compressibility and Consolidation
(1) Elastic settlement or immediate, which is caused by the elastic deformation of dry soil and of moist and saturated soils without any change in the moisture content. Elastic settlement calculations generally are based on equations derived from the theory of elasticity.
(2) Primary consolidation settlement, which is the result of a volume change in saturated cohesive soils because of expulsion of the water that occupies the void spaces.
(3) Secondary consolidation settlement, which is observed in saturated cohesive soils and is the result of the plastic adjustment of soil fabrics. It is an additional form of compression that occurs at constant effective stress.
6
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Compressibility and Consolidation
This chapter presents the fundamental principles for estimating the elastic and consolidation settlements of soil layers under superimposed loadings.
The total settlement of a foundation can then be given as
where
ST = Total settlement
Sc = Primary consolidation settlement
Ss = Secondary consolidation settlement
Se = Elastic settlement
7
When foundations are constructed on very compressible clays, the
consolidation settlement can be several times greater than the elastic
settlement.
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Elastic Settlement
Elastic, or immediate, settlement of
foundations (Se) occurs directly after the application of a load without a change in the moisture content of the soil.
The elastic settlement of a “flexible foundation” may be expressed as
8
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Elastic Settlement
9
The elastic settlement of a “rigid foundation” can be estimated as
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. 10
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. 11
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. 12
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Elastic Settlement
Due to the nonhomogeneousnature of soil deposits, the magnitude of Es may vary with depth. For that reason, Bowles (1987) recommended using a weighted average value of Es.
13
Typical value of Es
Typical value of ms
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 1
14
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 1
15
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Consolidation Settlement
“It is quite reasonable and rational to assume that the solid matter and the pore water are relatively incompressible under the loads usually encountered in soil mass”
16
The spring represents the mineral skeleton in actual soil mass, while the water below the piston is the pore water under saturated conditions in the soil mass
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Consolidation Settlement
17
This process is called “consolidation”.
The process opposite to consolidation is called
“swelling”.
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Consolidation Settlement
Consolidation may be due to one or more of the following factors:
1. External static loads from structure
2. Self-weight of the soil such as recently placed fills
3. Lowering of the ground water table
4. Desiccation
5. Permeability of soil
6. Skeleton of soil
18
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
One-Dimensional Consolidation
19
Based on the consolidation process, we can analyze the strain of a saturated clay layer subjected to a stress increase.
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. 20
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Consolidometer and Standard Test
The compressibility of a saturated clay is determined by means of the apparatus as shown in below figure. This apparatus is well known as oedometer.
21
2-5 cm in height and 6-10 cm in dia.
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Consolidometer and Standard Test
The main purpose of the consolidation test is to determine the magnitudeand rate of settlement.
• Loads are applied in steps in such a way that successive load intensity is twice the preceding load.
• Commonly used load intensities are 25, 50, 100, 400, 800 and 1600 kN/m2.
• Each load is allowed to stand until compression has practically ceased (≤24hr.)
• The dial reading are taken at elapsed times of ¼, ½, 1, 2, 4, 8, 15, 30, 60, 120, 240, 480, 1440 minutes from the time of new increment of load is put on the sample.
• After completion of greatest load, the load is removed in the steps to provide data for plotting the expansion curve of the soil.
• Required data of soil sample are %wbefore, %wafter, Gs, T˚, A and H.
22
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Consolidometer and Standard Test
The general shape of deformation of the specimen against time for a given load increment is shown in Figure.
23
Initial compression, which is caused mostly by preloading.
Primary consolidation,
Secondary consolidation, which occurs after complete dissipation of the excess pore water pressure, when some deformation of the specimen takes place because of the plastic readjustment of soil fabric.
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Consolidometer and Standard Test
Moreover, we could obtain 2 relationships
1. The relationship between void ratio (settlement) and effective stress for estimating preconsolidation pressure (Pc), compression index (Cc) and swelling index (Cs).
2. The relationship between deformation (settlement) and time for estimating coefficient of consolidation (Cv).
24
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Pressure-Void Ratio Curves
The pressure and void curve can be obtained if the void ratio of the sample at the end of each increment of load is determined.
Next is step-by-step procedure for obtaining the pressure-void curve.
25
1Calculate the height of solids, Hs, in soil specimen using the equation
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Pressure-Void Ratio Curves
26
2Calculate the initial height of void, Hv, in soil specimen as
3Calculate the initial void ratio, e, in soil specimen as
4After completion of each increment load, calculate the change of void and new void ratio if the deformation is ΔH1.
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Pressure-Void Ratio Curves
If all of effective stress and corresponding void ratio are determined. Then, we can plot void ratio in normal scale and effective stress in log scale.
27
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 2
28
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 2
29
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Pressure-Void Ratio Curves for sand
it has no consolidation tests of sand because the compression of sand is instantaneous. 90% of compression has taken place within a period of less than 2 minutes.
30
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Pressure-Void Ratio Curves for clay
Consolidation tests are usually conducted on samples of clay. Because the compression of clay under external load is time-dependent compression due to the discharge rate of pore water in the soil sample.
The compressibility of characteristics of clay depend on many factors in previous topic.
The most important factors are
1. whether the clay is normally consolidated or overconsolidated.
2. Whether the clay is sensitive or insensitive.
31
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
?
Pressure-Void Ratio Curves
A soil in the field at some depth has been
subjected to a certain maximum effective past pressure in its geologic history. This maximum effective past pressure may be equal to or lessthan the existing effective overburden pressure at the time of sampling.
During the soil sampling, the existing effective overburden pressure is also released, which results in some expansion.
32
Steeper slope
Flat slope
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Pressure-Void Ratio Curves
When this specimen is subjected to a
consolidation test, a small amount of settlement will occur when the applied effective pressure is less than the maximum effective past pressure.
When the effective pressure on the specimen becomes greater than the maximum effective past pressure, the change in the void ratio is much larger, and the e–log s ’ relationship is practically linear with a steeper slope.
33
Steeper slope
Flat slope
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Determination of Preconsolidation Pressure
1. By visual observation, establish point a, at which
the e–log s ’ plot has a minimum radius of curvature.
2. Draw a horizontal line ab.
3. Draw the line ac tangent at a.
4. Draw the line ad, which is the bisector of the angle bac.
5. Project the straight-line portion gh of the e–log s plot back to intersect line ad at f. The abscissa of point f is the
preconsolidation pressure, sc.
34
The maximum effective past pressure or well known as preconsolidationpressure can be determined from the laboratory e–log s ’ plot
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. 35
Determination of Preconsolidation Pressure
Empirical relationship
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. 36
Determination of Preconsolidation Pressure
Empirical relationship
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Normally Consolidated and Overconsolidated
The ratio of the preconsolidation pressure,sC, to the present effective
overburden pressure, s’, is called the overconsolidation ratio (OCR).
37
The OCR leads us to the two basic definition of clay based on stress history.
- Normally consolidated clay, whose present that the present effective overburden pressure is the maximum past pressure (OCR = 1).
- Overconsolidated clay, whose present that the present effective overburden pressure is less than that which the soil experienced in the past (OCR > 1).
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Overconsolidation of a clay may have been caused due to some of the following factors.
1. Weight of an overburden of soil which has eroded.
2. Weight of a continental ice sheet that melted
3. Desiccation of layers close to the surface
Experience (Murthy) indicates that the natural moisture content is commonly close to the liquid limit for normally consolidated clay whereas for overconsolidated clay the natural moisture content is close to the plastic limit.
38
Normally Consolidated and Overconsolidated
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. 39
Normally Consolidated and Overconsolidated
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Pressure-Void Ratio Curves : av and mv
40
Coefficient of Compressibility
Coefficient of Volume Compressibility
σ
e
ee
am
oo
vv Δ
Δ•
+1
1=
+1=
o
ov σσ
ee
σ
ea
-
-=
Δ
Δ=
1
1
De
Dp
eo
e1
σo σ1
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Pressure-Void Ratio Curves : Cc and Cr
41
Δ+
Δ=
σ
σσlog
eCc
Δ+
Δ=
σ
σσlog
eCr
Normally consolidation
recompression
Over consolidation
De
s s+Ds
Preconsolidation
Pressure, sc
sc
Recompression
Index, Crrebound
Compression
Index, Cc
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Calculation of settlement: ODPC
42
So,
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Calculation of settlement: e-p
• From coefficient of volume compressibility
* mv is not constant value
43
σ
e
ee
am
oo
vv Δ
Δ•
+1
1=
+1=
σme
ev
o
Δ=+1
Δ
HσmS vc Δ=∴
De
Dp
eo
e1
σo σ1
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 3.1
44
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. 45
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Calculation of settlement: e-log p
• For normally consolidated clay (after s’o)
• For overconsolidation clay (before s’o)
46
s’o
Cc
Cr
Cr
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Cc and Cr by empirical formulas
47
Skempton (1944)
Rendon-Herrero (1983)
Nagaraj and Murty (1985)
Cc
Cs
or
Cr Nagaraj and Murty (1985)
Kulhawy and Mayne (1990)
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 3.2
48
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 3.2 : Part a
49
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 3.2 : Part b
50
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 3.2 : Part c
51
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 4
52
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 4 : part a
53
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 4 : part b
54
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 4 : part c
55
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Secondary Consolidation Settlement
Secondary consolidation settlement is the settlement of soil due to the plastic adjustment of soil fabrics.
The secondary compression index can be defined as
56
The magnitude of the secondary consolidation can be calculated as
p
α'α
'αs e
CCwhere
t
tlogHCS
+1==
1
2
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Secondary Consolidation Settlement
57
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 5
58
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. 59
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Time Rate of Consolidation
The total settlement caused by primary consolidation resulting from an increase in the stress on a soil layer can be calculated by the use of the equations as follows.
However, they do not provide any information regarding the rate of primary consolidation.
60
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Time Rate of Consolidation
Terzaghi (1925) proposed the first theory to consider the rate of
one-dimensional consolidation for saturated clay soils. The mathematical
derivations are based on the following six assumptions (also see Taylor, 1948):
1. The clay–water system is homogeneous.
2. Saturation is complete.
3. Compressibility of water is negligible.
4. Compressibility of soil grains is negligible (but soil grains rearrange).
5. The flow of water is in one direction only (that is, in the direction of
compression).
6. Darcy’s law is valid.
61
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Time Rate of Consolidation
62
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Time Rate of Consolidation
63
Using Darcy’s law, we have
The rate of change in the volume of the soil element is equal to the rate of change in the volume of voids.
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Time Rate of Consolidation
64
The change in the void ratio is caused by the increase of effective stress (i.e., a decrease of excess pore water pressure). Assuming that they are related linearly, we have
av = coefficient of compressibility
mv = coefficient of volume compressibility
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Time Rate of Consolidation
65
Unit : L2/t
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Time Rate of Consolidation
is the basic differential equation of Terzaghi’s consolidation theory and can be solved with the following boundary conditions:
66
where m = an integer
M = (π/2)(2m +1)uO = initial excess pore water pressureTv = time factor = cvt / H2
dr
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Time Rate of Consolidation
67
Because consolidation progresses by the dissipation of excess pore water pressure, the degree of consolidation at a distance z at any time t is
∑∞
0=
-
2
32-1=
m
TM
drz
veH
Mzsin
MU ( )
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Time Rate of Consolidation
68
However, for analysis of settlement in general case, the average settlement of the clay layer are mainly considered. The degree of consolidation at time t can be written as
100×=c
)t(c
S
SU
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. 69
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 6
70
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 7
71
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 7
72
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 7
73
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Determination of Coefficient of Consolidation
Logarithm of Time Method
74
50
2
v
50
t
2
H196.0
C
196.0T
Final Compression
=
=
t 4t t50
d50
d100
=
=
Initial
Compression
Primary
Consolidation
Secondary
ConsolidationFinal Compression
U = 0.5¯
ds
U = 1.0¯
U = 0¯
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Determination of Coefficient of Consolidation
Square Root of Time Method
75
Initial
Compression
Primary
Consolidation
100 หนวย 15 หนวย
Secondary
Consolidation
U = 0¯
U = 0.9¯
U = 1.0¯
t90
90
2
v
90
t
2
H848.0
C
848.0T
ds
d90
d100
100
90
dd
dd
s100
s90
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 7
76
Using the logarithm-of-time method and square-root-time, determine cv. The average height of the specimen during consolidation was 2.24 cm, and it was drained at the top and bottom.
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 7.1 using log-of time
77
0.01 0.1 1 10 100 1000 10000
0.54
0.52
0.50
0.48
0.46
0.44
0.42
0.40
0.38
sett
lem
ent
(cm
)
time (min)
=
=
t 4t
t50
d50
d100
U = 0.5¯
ds
U = 1.0¯
U = 0¯
19 min
( )
sec
cm.c
min
cm.c
/..c
t
H.c
.T
v
v
v
drv
24
2
2
50
2
50
10×1702=
0130=
19
2242×1960=
1960=
1960=
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Example 7.2 using square-root-of time
78
0 10 20 30 40 50
0.54
0.52
0.50
0.48
0.46
0.44
0.42
0.40
0.38
sett
lem
ent
(cm
)
square root time (min)
100 หนวย15 หนวย
U = 0¯
U = 0.9¯
U = 1.0¯
t90ds
d90
8.5 min
( )
sec
cm.c
min
cm.c
..
/..c
t
H.c
.T
v
v
v
drv
24
2
2
90
2
90
10×4532=
01470=
58×58
2242×8480=
8480=
8480=
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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Quiz 1
79
Calculate the total settlement at center of the footing as shown below by using the data of clay layer from the example 7.1.1. After 5 year2. After 15 years of construction.
Very stiff layer
Loose to dense layerEs = 30000 kN/m2
Normal consolidation clay900=020= 0 .e,.cα
Es = 4000 kN/m2
μs = 0.30
“Education is the best provision for the journey to old age.”
Aristotle
อางอง
• Braja M. Das :"Principles of Geotechnical Engineering 5th Edition
• V.N.S. Murthy : Geotechnical Engineering
• เอกสารการสอน อ.อนรทธ ธงไชย
• รปภาพจาก Google images
3/14/2015
Soil Mechanics .......... Suriyah 1
Soil Mechanics
Suriyah Thongmunee, Ph.D.
Shear Strength of Soil
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Shear Strength of Soil
2
Lecture Outline:
1. Mohr-Coulomb Failure Criterion
2. Direct Shear Test
3. Triaxial Test
4. Unconfined Compression Test
5. Vane Shear Test
3/14/2015
Soil Mechanics .......... Suriyah 2
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Shear Strength of Soil
The “shear strength” of a soil mass is the internal resistance per
unit area that the soil mass can offer to resist failure and sliding along any plane inside it. One must understand the nature of shearing resistance in order to
analyze soil stability problems, such as bearing capacity, slope stability, and lateral pressure on earth-retaining structures.
3
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Mohr-Coulomb Failure Criterion
Mohr (1900) presented a theory for rupture in materials that contended that a material fails because of a critical combination of
normal stress and shearing stress and not from either maximum normal or shear stress alone.
For most soil mechanics problems, Coulomb (1776) approximated the
shear stress on the failure plane as a linear function of the normal stress.
4
or
3/14/2015
Soil Mechanics .......... Suriyah 3
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Mohr-Coulomb Failure Criterion
The equations are expressions of shear strength based on total stress and effective stress.
c’ = 0 (sand and inorganic silt)
≈ 0 (normally consolidated clays)
> 0 (Overconsolidated clays)
The angle of friction, φ’, is sometimes referred to as the drained angle of friction.
5
or
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Mohr-Coulomb Failure Criterion
6
3/14/2015
Soil Mechanics .......... Suriyah 4
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Inclination of the Failure Plane
7
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Determination of Shear Strength Parameters
There are several methods now available to determine the shear strength parameters (i.e., c, φ, c’, φ’) of various soil specimens in the laboratory. They are as follows:
• Direct shear test
• Triaxial test
• Unconfined Compression Test
• Van shear test (field test)
8
3/14/2015
Soil Mechanics .......... Suriyah 5
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Direct Shear Test
9
Direct shear test can be either stress
controlled or strain controlled.In stress-controlled tests, the shear force
is applied in equal increments until the specimen fails. The failure occurs along the plane of split of the shear box. After the application of each incremental load, the shear displacement of the top half of the box and The change in the height of the specimen are measured by a horizontal dial gauge and vertical dial gauge, respectively.
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Direct Shear Test
In strain-controlled tests, a constant rate of shear displacement is applied to one-half of the box by a motor that acts through gears. The constant rate of shear displacement is measured by a horizontal dial gauge. The resisting shear force of the soil corresponding to any shear displacement and The volume change of the specimen during the test can be measured by proving ring and dial gauge.
The advantage of the strain-controlled tests is that in the case of dense sand, peak shear resistance (that is, at failure) as well as lesser shear resistance (that is, at a point after failure called ultimate strength) can be observed and plotted.
10
3/14/2015
Soil Mechanics .......... Suriyah 6
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Direct Shear Test : each normal stress
11
At large shear displacement, the void ratios of loose and dense sands become practically the same, and this is termed the “critical void ratio”.
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Direct Shear Test : various normal stresses
12
3/14/2015
Soil Mechanics .......... Suriyah 7
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Drained Direct Shear Test on Saturated Sand and Clay
13
Similar to the ultimate shear strength in the case of sand, at large shearing displacements, we can obtain the residual shear strength of clay (τr) in a drained test.
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Direct Shear Test
14
Skempton (1964)
3/14/2015
Soil Mechanics .......... Suriyah 8
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Ex. of DSTs
15
Test no. Normal weight
(kg)
Shear force
(kg)
Cross section area
(cm ×××× cm.)
Normal Stress
(kN/m2)
Shear Stress
(kN/m2)
1 4 5.80 5.5 ×××× 5.5 13 17.5
2 8 6.94 5.5 ×××× 5.5 26 22.4
3 12 8.10 5.5 ×××× 5.5 39 26.2
4 16 9.60 5.5 ×××× 5.5 52 31.0
Determine shear strength of soil from direct shear test results as shown in below table and find principle stress of Test No.2
222
11
222
11
kN/m 17.5 )01.0((5.5)
000)(9.81)(1/1 5.8
A
T
kN/m 13 m/cm) 01.0(cm) (5.5
kN/1000N) N/kg)(1 kg)(9.81 (4
A
P
===
===
τ
σ
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Ex. of DSTs
100
40 50 60 70 803020
10
20
30
40
50
From Figure, it was found thatc = 13 ton/m2ϕ = 19.2 deg
Principle stress can be determined by drawing graph as shown or calculating using below equations
where
3/14/2015
Soil Mechanics .......... Suriyah 9
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
General Comment on DST
• Simple and economical for sandy soil but not fail along the weakest plane
• Shear stress distribution over shear plane is not uniform
• Interface friction angle between soil and foundation material can be easily determined by DST --- Similar equation with shear strength of soil
17
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
General Comment on DST
18
3/14/2015
Soil Mechanics .......... Suriyah 10
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Triaxial Shear Test
• What is Triaxial Shear Test?Shear test that confining pressure is considered
and applied by compression of fluid in camber. Axial load is applied via vertical loading ram.
• It has 2 ways for applying the vertical stress until soil specimen is failed.
o Stress Control – measure deformationo Strain Control – measure vertical stress
19
Most reliable methods for
determining shear strength
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Triaxial Shear Test
• Standard types of triaxial tests1. Consolidated-drained test or drained test (CD test)
2. Consolidated-undrained test (CU test)
3. Unconsolidated-undrained test (UU test)
20
∆∆∆∆u= 0ττττ
σσσσn
∆∆∆∆u= 0
σσσσn
∆∆∆∆u= 0 ∆∆∆∆u>
0
ττττσσσσn σσσσn
∆∆∆∆u> 0 ∆∆∆∆u> 0ττττ
σσσσnσσσσn
C,φ
Ccu, φcu
Cuu, φuu
3/14/2015
Soil Mechanics .......... Suriyah 11
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Triaxial Shear Test
Triaxial shear test is the test of saturated soil (%Sr =100)
21
How to saturate and
check %Sr
When the saturated soil specimen is firstly subjected the confining pressure, the pore pressure increases suddenly. The ratio of pore pressure and confining pressure is defined as B parameter. It is used to check the degree of soil saturation. Theoretical values of B at complete saturation are shown in below table.
B = Skempton’s pore pressure parameter
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Consolidated-drained test (CD test)
22
CD test procedure
• Saturates the specimen
• Checks %Sr
• Applies confining pressure
• Open drainage gage
• Waits until uc≈ 0 and record volume change
• Slowly applies deviator stress and record volume change
Typical test results
3/14/2015
Soil Mechanics .......... Suriyah 12
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Consolidated-drained test (CD test)
23
CD test results of normally consolidated soil
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Consolidated-drained test (CD test)
24
CD test results of overconsolidated soil
For overconsolidated soil, the strength parameter will consist of friction and cohesion parameters. These parameters can be determined by conducting at least 2 tests with different confining pressure.
3/14/2015
Soil Mechanics .......... Suriyah 13
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Ex. of CD test
25
From the CD-Test results of sand sample, please calculate 1. Internal friction angle, ϕ, 2. Angle between failure plane and principle plane, θ,3. Normal stress, σn, and shear stress, τn, on failure plane
σ3= 276 kN/m2
(Δσd)f = 276 kN/m2
s3
s3
s3
Deviator Stress kN/m2
Axial Strain
Cell pressure = 276 kN/m2
276
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Ex. of CD test
26
2
d311
233
kN/m 552 276 276
)(
kN/m 276
=+=
∆+====
fσσσσσσ
φστ tan n=
01-
31
31
5.19)333.0(sin '
0.333 276552
276 - 552
2''
2''
OA
AB ' sin
==
=+
=
+
−
==
φ
σσ
σσ
φ
R
OA
B
o
o
o
o
7.542
5.1945
2
'45
=+=
+= φθ
kN/m 130 54.7) (2sin 2
276 - 552 '
kN/m 368 57.4) (2 cos 2
276 - 552
2
276 552
2 cos 2
''
2
'' '
2f
2
3131
=×=
=×++=
−++=
τ
θσσσσσ n
φφφφ
++++= =
3/14/2015
Soil Mechanics .......... Suriyah 14
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Consolidated-undrained test (CU test)
27
CU test procedure
• Saturates the specimen
• Checks %Sr
• Applies confining pressure
• Waits until uc≈ 0 and record volume change
• Closed drainage gage
• Applies deviator stress and record pore pressure
A = Skempton’s pore pressure parameter
/
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Consolidated-undrained test (CU test)
28
CD test results
Typical test results
Loose sand
Or NC soil
Dense sand
Or OCR soil Decreases due to dilation of soil
3/14/2015
Soil Mechanics .......... Suriyah 15
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Consolidated-undrained test (CU test)
29
CD test results of normally consolidated soil
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Consolidated-undrained test (CU test)
31
CD test results of overconsolidated soil
3/14/2015
Soil Mechanics .......... Suriyah 16
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Unconsolidated-undrained test (UU test)
32
//
CU test procedure
• Saturates the specimen
• Checks %Sr
• Closed drainage gage
• Applies confining pressure and record pore pressure
• Applies deviator stress and record pore pressure
UU test method is appropriate for fully saturated
cohesive soil.
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
CD & CU & UU tests
33
CD : Q
CU : P
UU : R
3/14/2015
Soil Mechanics .......... Suriyah 17
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Unconfined Compression Test (UC test)
34
• Special test of UU test with confining pressure is zero
• Value of Cu slightly lower Cu obtained from UU test
• Fully saturated cohesive soil with completely undrained
• Rapid loading
• Useful in practice : test preparation and testing is fast
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Ex. of CU and UC test
35
From CU test result of clay sample, please calculate
1. Total stress strength envelope, ϕ,2. Effective stress strength envelope, ϕ’,3. Angle of failure plane of sample 1, θ,4. Unconfined compressive strength of
sample 2 , qu,
Test No.
σ3
(kPa)(∆σd)f(kPa)
∆uf
(kPa)σ1
(kPa)σ’3(kPa)
σ’1(kPa)
1 200 150 140 350 60 210
2 400 300 280 700 120 420
0
01-
31
31
1-
01-
31
31
1-
8.15
8.15 400700
400 - 700 sin
2
2 sin
8.15 200350
200 - 350 sin
2
2 sin
=
=+
=
+
−
=
=+
=
+
−
=
avgφ
σσ
σσ
φ
σσ
σσ
φ
3/14/2015
Soil Mechanics .......... Suriyah 18
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Ex. of CU and UC test
36
From CU test result of clay sample, please calculate
1. Total stress strength envelope, ϕ,2. Effective stress strength envelope, ϕ’,3. Angle of failure plane of sample 1, θ,4. Unconfined compressive strength of
sample 2 , qu,
Test No.
σ3
(kPa)(∆σd)f(kPa)
∆uf
(kPa)σ1
(kPa)σ’3(kPa)
σ’1(kPa)
1 200 150 140 350 60 210
2 400 300 280 700 120 420
01-
31
31
7.33)556.0(sin '
0.556 60210
60 - 210
2''
2''
' sin
==
=+
=
+
−
=
φ
σσ
σσ
φ
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Ex. of CU and UC test
37
From CU test result of clay sample, please calculate
1. Total stress strength envelope, ϕ,2. Effective stress strength envelope, ϕ’,3. Angle of failure plane of sample 1, θ,4. Unconfined compressive strength of
sample 2 , qu,
Test No.
σ3
(kPa)(∆σd)f(kPa)
∆uf
(kPa)σ1
(kPa)σ’3(kPa)
σ’1(kPa)
1 200 150 140 350 60 210
2 400 300 280 700 120 420
θθθθ
σ'1
σ'3
62°°°°
o61.8 2
33.7 45
2
' 45
oo
o
=+=
+= φθ
3/14/2015
Soil Mechanics .......... Suriyah 19
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Ex. of CU and UC test
38
From CU test result of clay sample, please calculate
1. Total stress strength envelope, ϕ,2. Effective stress strength envelope, ϕ’,3. Angle of failure plane of sample 1, θ,4. Unconfined compressive strength of
sample 2 , qu,
Test No.
σ3
(kPa)(∆σd)f(kPa)
∆uf
(kPa)σ1
(kPa)σ’3(kPa)
σ’1(kPa)
1 200 150 140 350 60 210
2 400 300 280 700 120 420
kPaq
q
u
fdu
30031
=∆=−= σσσ
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Sensitivity and Thixotropy of Clay
After UC test, the collapsed soil is remolded and tasted again. The UC strength will reduce greatly. This property is called “Sensitivity”
Degree of sensitivity is ratio of undisturbed and remolded UC strength. Some clay turn to viscos fluid (high sensitivity) is called “Quick clay”
39
Mos
t cl
ayH
ighl
y floc
cule
nt
mar
ine
clay
Rosenqvist (1953)
3/14/2015
Soil Mechanics .......... Suriyah 20
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Sensitivity and Thixotropy of Clay
Why the UC strength of soil reduces ?
because the clay particle structure was destructed during remolding.
After remolding, the soil is kept for a while. Then, the UC test of the soil is again carried out. The UC strength of soil will be greater then that of the remolded soil. This phenomenon is called “Thixotropy”.
40
Most soil is partially
thixotropic material. Its
behavior is shown here
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Related researches on Thixotropy
Seed and Chan (1959) carried out the shear strength tests of three compacted soil with water content near the plastic limit to study the thixotropic strength regain.
it was founded that the tendency of thixotropic strength regain is exponential
growth. Moreover, the strength of all compacted soil developed more than 10%
within one week.
41
3/14/2015
Soil Mechanics .......... Suriyah 21
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Strength Anisotropy in Clay
So, UU shear strength of saturated soil can vary, depending direction of applied load. It can be called
“strength anisotropy”. It is caused by the nature of the deposition of the cohesive soils, and subsequent consolidation.
42
For construction of embankment, Lateritic soil is filled and compacted in construction area. Due to that process, it may change the direction of major principle stress acting on soil element beneath the embankment as shown in figure.
วรยา ฉมอRอย, 2553
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Strength Anisotropy in Clay
some soil particles can orient perpendicular or parallel to major principle stress that can be cause the soil strength variation with direction.
Casagrande and Carrillo (1944) proposed the relationship between strength and direction.
43Based on Loh and Holt, 1974
3/14/2015
Soil Mechanics .......... Suriyah 22
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
Vane Shear Test
Vane shear test is commonly used to determine the undrained shear strength of soft cohesive soils. The test results is fairly reliable.
The vane is pushed into the soil and torque is, then, applied at head of vane rod with uniform speed. The maximum torque to cause soil failure is used to estimate Cu by using below equation.
44
Soil covers top blade3u R 28
3T Cor
πτ =
Soil is not cover top blade 3u R 26
3T Cor
πτ =
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. ………. Suriyah Thongmunee, Ph.D.
HW.
45
Test No.σσσσ3
(kPa)
(∆σ∆σ∆σ∆σd)f
(kPa)
1 25 85
2 60 101
3 105 113
4 154 163
From the CD-Test results of sand sample, please calculate 1. Internal friction angle, ϕ, and cohesion, c, for test 1 & 22. Internal friction angle, ϕ, and cohesion, c, for test 2 & 33. Internal friction angle, ϕ, and cohesion, c, for test 3 & 44. Draw Mohr-Coulomb of each test and each failure envelope in the same graph
3/14/2015
Soil Mechanics .......... Suriyah 23
“Education is the best provision for the journey to old age.”
Aristotle
อ<างอง
• Braja M. Das :"Principles of Geotechnical Engineering 5th Edition• V.N.S. Murthy : Geotechnical Engineering• วรยา ฉมนRอย (2553) ผลกระทบของความไมaสมนยตaอพฤตกรรมการรบแรงเฉอนของดนเหนยวกรงเทพ,
วารสารวทยาศาสตรnและเทคโนโลย ปqท 18 ฉบบท 4• เอกสารการสอน อ.อนรทธn ธงไชย• รปภาพจาก Google images
10/18/2015
Aj.Suriyah 1
Soil Mechanics
Suriyah Thongmunee, Ph.D.
Lateral Earth Pressure I
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Lateral Earth Pressure I
2
Lecture Outline:
1. Introduction
2. At rest, active and passive pressure
3. Earth pressure at rest
4. Rankine’s theory of active pressure
5. Rankine’s theory of passive pressure
10/18/2015
Aj.Suriyah 2
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Introduction
3
Knowledgeof
lateral forcesthat act
betweenSoiland
Structuresis
Needed
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
At rest, active and passive pressure
4
Consider a soil element located at a depth zclosed to frictionless wall in below figure. The soil element is subjected to a effective overburden pressure, σ’o, and a effective horizontal
pressure, σ’h.
The ratio of σ’h to σ’o is defined as earth pressure coefficient, K.
3 possible cases may arise depending on the movement of soil mass or retaining wall
10/18/2015
Aj.Suriyah 3
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
At rest, active and passive pressure
5
If the wall does not move to the right or to the left compared with its initial position, the soil element will be in a state of static equilibrium. In the case, the σ’h is referred to as the at-rest earth pressure and the K is referred to as the at-rest earth pressure coefficient.
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
At rest, active and passive pressure
6
If the wall moves to the left compared with its initial position, the soil mass BC will reach a state of plastic equilibrium. In the case, the σ’h is referred to as the active earth pressure and the K is referred to as the active earth pressure coefficient.
10/18/2015
Aj.Suriyah 4
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
At rest, active and passive pressure
7
If the wall moves to the right compared with its initial position, the soil mass BC will also reach a state of plastic equilibrium. In the case, the σ’h is referred to as the passive earth pressure and the K is referred to as the passive earth pressure coefficient.
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
At rest, active and passive pressure
8
hp = Kpv
ho = Kov
ha = Kav
10/18/2015
Aj.Suriyah 5
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
At rest, active and passive pressure
9
Change of horizontal stress due to the wall
movement
v is constant
h decreases when soil mass expands (wall move away)
h increases when soil mass is compressed
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Earth pressure at rest
At rest earth pressure coefficient, Ka, and overburden effective stress,o, are necessary for computing the horizontal effective stress. Ka can be determined by below equation
10
-------------Loose sand
Dense sand
10/18/2015
Aj.Suriyah 6
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Ex.1
11
if wall is static, calculate the lateral force, P0, per unit length of the wall. Also, determine the location of the resultant force from point c
Determine σ’o Determine σ’h Determine u
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. 12
Ex.1if wall is static, calculate the lateral force, P0, per unit length of the wall.
Also, determine the location of the resultant force from point c
Z
10/18/2015
Aj.Suriyah 7
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Rankine’s theory of active pressure
13
)/(K
σK)/(
σ σ
c
)/(
σ σ
)/(c)/(σσ
oa
vaov
ha
oov
ha
oohav
245tan
1
245tan
0c ; sscohesionle is soil if
)2/45tan(
2
245tan
245tan2245tan
2
2
2
2
ha= 3
v = 1 avaha Kc σ K σSo 2 ,
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Rankine’s theory of active pressure
14
avaha Kc σ K σSo 2 , What happened ??
This area is subjected the tension force. However, soil is weak when subjected the tension force. consequently, tension crack will occur easily in this part.
So, engineer usually analyzes this kind of problem after tension crack occurs
10/18/2015
Aj.Suriyah 8
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. 15
Ex.2A retaining wall with saturated clay backfill is shown in below figure.
Determine 1. depth of tension crack 2. Pa before tension crack occurs 3. Pa
after tension crack occurs
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Rankine’s theory of passive pressure
16
hp= 1
v = 3
)/(K
Kσ)/( σ σ
)/(c)/(σσ
op
pvo
vhp
oovhp
245tan
245tan
0c ; sscohesionle is soil if
245tan2245tan
2
2
2
pa
pvphp
KKMoreover
Kc σ K σSo
1 ,
2 ,
10/18/2015
Aj.Suriyah 9
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Ex.3
17
Determine all lateral forces acting on sheet pile wall as shown in figure
SOIL 1
SOIL 2
= 18 kN/m3
c = 0 , = 38o
= 20 kN/m3
c = 10 kN/m2, = 28o
50kN/m2
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
aa K2.c. - .K vha
SOIL 1
SOIL 2
= 18 kN/m3
c = 0 , Ka= 0.24
= 20 kN/m3
c = 10 kN/m2, Ka=0.36
50kN/m2
18
Ex.3 Determine all lateral forces acting on sheet pile wall as shown in figure
10/18/2015
Aj.Suriyah 10
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
SOIL 1
SOIL 2
= 18 kN/m3
c = 0 , Kp= 4.17
= 20 kN/m3
c = 10 kN/m2, Kp = 2.78
pvhp Kc..2.K p
19
Ex.3 Determine all lateral forces acting on sheet pile wall as shown in figure
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
HW.
20
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Aj.Suriyah 11
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
HW.
21
“Education is the best provision for the journey to old age.”
Aristotle
อางอง
• Braja M. Das :"Principles of Geotechnical Engineering 5th Edition
• V.N.S. Murthy : Geotechnical Engineering
• เอกสารการสอน อ.อนรทธ ธงไชย
• รปภาพจาก Google images
10/18/2015
Aj.Suriyah 1
Soil Mechanics
Suriyah Thongmunee, Ph.D.
Bearing Capacity for shallow foundation
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Bearing Capacity
2
Lecture Outline:
1. Introduction
2. Bearing capacity failure
3. Modes of bearing capacity failure
4. Bearing capacity analysis
5. Bearing capacity equation
6. Factor of safety
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Aj.Suriyah 2
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Introduction
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Technical words• หนวยแรงแบกทาน (Bearing Pressure)• หนวยแรงแบกทานสงสด (Ultimate Bearing Capacity)• หนวยแรงแบกทานทยอมให (Allowable Bearing Capacity)• คาความปลอดภย (Safety Factor)
What is foundation ?? A lowest part of an architectural structure which transfers the loads from superstructure to soil layers beneath the superstructure
Introduction
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Aj.Suriyah 3
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Introduction
ขนตอน วตถประสงค ทฤษฎ ขอมล
ออกแบบขนาด/รปราง
(Proportional Design)
ใหฐานรากสามารถสงถายแรงกระทาจากโครงสรางใหดนรบไดอยางปลอดภย
• การวเคราะหหนวยแรงในมวลดน
• การวเคราะหการทรดตวชนดน
• การวเคราะหกาลง แบกทานชนดนฐานราก
• นาหนกบรรทกฐาน
ราก
• คณสมบตชนดนฐานราก
การออกแบบโครงสราง (Structural
design)
ใหฐานรากมความแขงแรง สามารถรบนาหนกบรรทกและแรงตานจากดนได
• การวเคราะหหนวยแรงภายในโครงสราง
• การวเคราะหกาลงรบแรงวสดโครงสราง (e.g. RC design)
• คณสมบตกาลงรบแรงวสดโครงสราง(e.g. คอนกรต/เหลก)
Design of foundation
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Introduction
6
Types of foundation• Shallow foundation
o Spread foundationo Wall foundationo Mat foundationo etc.
• Deep foundationo Bore pileo Driven pileo etc.
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Aj.Suriyah 4
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
หนวยแรงแบกทานสงสดททาใหมวลดนเกดการวบต
= กาลงแบกทาน
= Q3
Bearing capacity failure
Q1 < Q2 < Q3
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Modes of bearing capacity failure
Local Shear Failure
ดนฐานรากหลวม
Punching Shear Failure
ดนฐานรากหลวมมาก
General Shear Failure
ดนฐานรากแนน - แนนมาก
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Aj.Suriyah 5
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Modes of bearing capacity failure
o Density of soil
o Depth of foundation
Influencing factors
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Bearing capacity analysis
o Shear strength of soil, c, o Unit weight of soil,
o Depth of foundation, q = D
o Size and shape of foundation, B
Controlling factors of bearing capacity
สถานะสมดลพลาสตก:
/2) (45 tan 2 /2)(45 tan 231 c
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Aj.Suriyah 6
Ka = 1 / Kp
22/12/32/12/5
22/12/112/3
)(2)(4
1
)(2)(4
1
pppppult
pppppppult
qKKKcKKBq
qKKKcKKKBKq
γqcult NB qN cN q 2
1
22/12/32/12/5
22/12/112/3
)(2)(4
1
)(2)(4
1
pppppult
pppppppult
qKKKcKKBq
qKKKcKKKBKq
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Aj.Suriyah 7
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Bearing capacity analysis
Nc, Nq, N = Bearing Capacity Factors
= ขนอยกบคาสมประสทธมมเสยดทาน,
พจนท 1 = กาลงแบกทานจากคาสมประสทธกาลงรบแรงเฉอน, c
พจนท 2 = กาลงแบกทานจากอทธพลของนาหนกดนกดทบ, q
พจนท 3 = กาลงแบกทานจากอทธพลของนาหนกดนใตฐานราก, γ
Bearing capacity :
γqcult NB qN cN q 2
1
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Bearing capacity equation by other researchers
10/18/2015
Aj.Suriyah 8
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Bearing capacity equation by other researchers
ผวจย เงอนใข รปสมการ
Terzaghi -
Meyerhof แรงกระทาใน แนวดง แรงกระทาใน แนวเอยง
Hansen ทวไป
= 0
bgidsBNbgids Nq bgids cNq qqqqqqccccccult .5 0
qdsSq cuult )(1 5.14 c'
sBNNqscNq qccult 0.5
dsBNdsNqds cNq qqqcccult 0.5
idBNidNqid cNq qqqcccult 0.5
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
ปจจยทมอทธพล ตวประกอบ สมการทใช
สมประสทธมมเสยดทาน, Bearing Capacity Factors: Nc , Nq , N
Terzaghi, Meyerhof, Hansen
รปรางฐานราก Shape Factors: sc , sq , s Terzaghi, Meyerhof, Hansen
ความลกฐานราก, D Depth Factors: dc , dq , d Meyerhof, Hansen
มมเอยงของแนวแรงกระทา, i Inclination Factors: ic , iq , i Meyerhof, Hansen
มมเอยงของระนาบผวดน, Ground Factors: gc , gq , q Hansen
มมเอยงของระนาบฐานราก, Base Factors: bc , bq , b Hansen
Component factors in bearing capacity equation
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Aj.Suriyah 9
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Bearing Capacity Factors by Terzaghi
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Bearing Capacity Factors by Meyerhof
10/18/2015
Aj.Suriyah 10
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Bearing Capacity Factors by Hansen
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Factor Strip Circular Square
sc 1.0 1.3 1.3
sγ 1.0 0.6 0.8
Other Factors by Terzaghi
10/18/2015
Aj.Suriyah 11
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Bearing Capacity Factors by Meyerhof
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Bearing Capacity Factors by Hansen
H = Qh = horizontal component of the inclined loadV = Qu = vertical component of the inclined load
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Aj.Suriyah 12
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
How to choose the bearing capacity equation
Researcher Conditions
Terzaghi (1943) ระดบฐานรากอยไมลกจากผวดนมาก (D/B <1)
ดนรองรบฐานรากเปนดนเหนยว (= 0)
ฐานรากแบบแถบ จตรส กลม
แรงกระทาฐานรากอยในแนวดง
Meyerhof (1963) ระดบฐานรากอยลกจากผวดน (D/B >1)
ดนรองรบฐานรากมคาสมประสทธความตานทานแรงเฉอน c และ ฐานรากสเหลยมผนผา กวาง B ยาว L
แรงกระทาฐานรากอาจเอยงทามมกบแนวดง
Hansen (1970) ใชเหมอนสมการ Meyerhof ในทกกรณ และใชไดเพมในกรณตอไปน
ระดบผวดนอยในแนวเอยง หรอ ระดบฐานรากอยในแนวเอยง
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Factor of safety
A factor of safety, Fs, of about 3 or more is generally used to calculate the value of the allowable bearing capacity. An Fs of 3 or more is not considered too conservative because soils are neither homogeneous nor isotropic in nature.
There are two basic definitions of the allowable bearing capacity of shallow foundations. They are gross allowable bearing capacity, qall, and net allowable bearing capacity, qnet.
24where
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Aj.Suriyah 13
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Ex.1
25
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Ex.2
26
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Aj.Suriyah 14
“Education is the best provision for the journey to old age.”
Aristotle
อางอง
• Braja M. Das :"Principles of Geotechnical Engineering 5th Edition
• V.N.S. Murthy : Geotechnical Engineering
• เอกสารการสอน อ.อนรทธ ธงไชย
• รปภาพจาก Google images
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
HW.
28
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Aj.Suriyah 15
Kp =tan2 (45+ϕ/2)
Qh = horizontal component of the inclined loadQu = vertical component of the inclined load
10/18/2015
Aj.Suriyah 1
Soil Mechanics
Suriyah Thongmunee, Ph.D.
Slope stability I
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Lateral Earth Pressure I
2
Lecture Outline:
1. Introduction
2. Modes of slope failures
3. Factor of safety
4. Stability of infinite slopes
10/18/2015
Aj.Suriyah 2
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Introduction
What is earth slope? ……………………. is a ground surface that stands at an angle with the horizontal plane which can be natural or man-made.
3
Earth slope
Earth retaining structure
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Introduction
What is slope failure?
……………………. Is the downslope movement of soil mass in response to a gravitational stresses.
4
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Aj.Suriyah 3
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Modes of slope failures
It can be classified the slope failures into six major categories. They are
1. Fall. masses are detached from steep slope/cliff along surfaces with little or no shear displacement.
2.Topple. This is a forward rotation of soil and/or rock mass about an axis below the center of gravity of
mass being displaced.
5
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Modes of slope failures
3. Slide. Rotational slides (slumps): masses slide outwards and downwards on one or more concave-
upward failure surfaces that impart a backward tilt to the slipping mass, which sinks at the rear and heaves at the toe. Translational (planar) slides: movements occur along planar failure surfaces that may run more-or less parallel to the slope.
4. Spread. involve the fracturing and lateral extension of coherent rock or soil masses due to plastic flow or
liquefaction of subjacent material.
6
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Aj.Suriyah 4
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Modes of slope failures
5. Flow. slow to rapid movements of saturated or dry materials which advance by flowing like a viscous
fluid, usually following an initial sliding movement.
6. Complex. A complex slide involves one of the main types of movement followed by two or more of the
other main types of movement.
7
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Factor of safety
For analyzing slope stability, engineer has to determine the factor of safety. The factor of safety, or safety factor, FS, is generally defined as
8
When FS 1 ; slope failsWhen FS > 1 ; slope is stable
Generally, the safety factor of 1.5 with respect to strength is acceptable for design of slope stability
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Aj.Suriyah 5
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E. 9
Factor of safety
=
In case of cohesive soilϕ = 0
In case of cohesionless soilc = 0
So,
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Stability of infinite slopes without seepage
10
10/18/2015
Aj.Suriyah 6
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Stability of infinite slopes with seepage
11
sincosH satu
HH
H
wsat
22
2,
coscos
cos
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Ex.1
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Aj.Suriyah 7
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Ex.1
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Ex.2
14
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Aj.Suriyah 8
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
Ex.2
15
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.
HW.
16
10/18/2015
Aj.Suriyah 9
“Education is the best provision for the journey to old age.”
Aristotle
อางอง
• Braja M. Das :"Principles of Geotechnical Engineering 5th Edition
• V.N.S. Murthy : Geotechnical Engineering
• เอกสารการสอน อ.อนรทธ ธงไชย
• http://www.bgs.ac.uk/landslides/how_does_BGS_classify_landslides.html
• รปภาพจาก Google images