Content uploaded by Saurabh Sanjay Deshpande
Author content
All content in this area was uploaded by Saurabh Sanjay Deshpande on Apr 14, 2016
Content may be subject to copyright.
“Towards Global Technological Excellence”
GOVERNMENT COLLEGE OF ENGINEERING, AMRAVATI 444604
(An Autonomous Institute of Government of Maharashtra)
“Towards Global Technological Excellence”
A
Seminar Report
On
TENSILE STRENGTH OF SOIL
Submitted By:
SAURABH S. DESHPANDE
(ID: 15056011)
First Year, M. Tech.
(Geotechnical Engineering)
Guide
Dr. A. I. Dhatrak
Associate Professor
DEPARTMENT OF C
IVIL ENGINEERING
GOVERNMENT COLLEGE OF ENGINEERING, AMRAVATI 444604
(An Autonomous Institute of Government of Maharashtra)
APRIL - 2016
“Towards Global Technological Excellence”
TENSILE STRENGTH OF SOIL
IVIL ENGINEERING
GOVERNMENT COLLEGE OF ENGINEERING, AMRAVATI 444604
(An Autonomous Institute of Government of Maharashtra)
G
OVERNMENT COLLEGE OF ENGINEERING, AMRAVATI 444604
(An Autonomous Institute of Government of Maharashtra)
This is to certify that the seminar report entitled, “
being submitted here with for the award of M.Tech
M
r. Saurabh S. Deshpande
same has not been submitted elsewhere for the award of any degree.
Dr. A. I.
Dhatrak
(Guide)
Civil Engineering Department,
Govt. College of Engineering,
Amravati
i
OVERNMENT COLLEGE OF ENGINEERING, AMRAVATI 444604
(An Autonomous Institute of Government of Maharashtra)
DEPARTMENT
OF CIVIL ENGINEERING
CERTIFICATE
This is to certify that the seminar report entitled, “Tensile Strength of Soil
being submitted here with for the award of M.Tech
.
, is the result of the work completed by
r. Saurabh S. Deshpande
, under m
y guidance within the four walls of the institute and the
same has not been submitted elsewhere for the award of any degree.
Dhatrak
Dr.
(Guide)
Civil Engineering Department,
Civil Engineering Department
Govt. College of Engineering,
Govt. College of Engineering,
Amravati
OVERNMENT COLLEGE OF ENGINEERING, AMRAVATI 444604
(An Autonomous Institute of Government of Maharashtra)
OF CIVIL ENGINEERING
Tensile Strength of Soil
”, which is
, is the result of the work completed by
y guidance within the four walls of the institute and the
same has not been submitted elsewhere for the award of any degree.
S. P. Tatewar
(Guide)
(Head)
Civil Engineering Department
Govt. College of Engineering,
Amravati
ii
DECLARATION
I hereby declare that the seminar entitled “Tensile Strength of Soil”, has been carried
out and written by me under the guidance of Dr. A. I. Dhatrak, Associate Professor,
Department of Civil Engineering, Government College of Engineering, Amravati. This work
has not been previously formed the basis for the award of any degree or diploma or certificate
nor has been submitted elsewhere for the award of any degree or diploma.
Place: Amravati SAURABH S. DESHPANDE
(ID: 15056011)
Date:
iii
ACKNOWLEDGMENT
It gives me the feeling of immense pleasure in bringing out the seminar entitled
“Tensile Strength of Soil” and I want to take this opportunity to thank everybody who has
been involved in my seminar work from initiation and made it success for me.
I express my deep sense of gratitude and sincere regards to my respected guide
Dr. A. I. Dhatrak. His timely guidance and friendly discussion had helped me in selecting this
topic and completing seminar work.
I would like to thank Civil Engineering Department for providing me the internet
facilities at proper time to complete my seminar work. I would also like to thank Head of
Department Dr. S. P. Tatewar for allowing me to deliver this seminar.
I would like to thank the Principal, Prof. D. J. Chaudhary, Government College of
Engineering, Amravati for providing all the facilities at the right period of time.
Finally, I would like to thank all those who directly or indirectly helped me during my
seminar work.
Saurabh S. Deshpande
(15056011)
First Year, M. Tech.
(Geotechnical Engineering)
Govt. College of Engineering, Amravati
iv
CONTENTS
Chapter
No.
Title Page No.
Certificate i
Declaration ii
Acknowledgment iii
1 Introduction
1.1 General 1
1.2 Necessity 3
1.2 Determination of Tensile strength of soil 3
2 Tensile Strength Characteristics of Soil
2.1 Tensile characteristics of clayey soil 5
2.1.1 Effect of water content 6
2.1.2 Effect of dry density 10
2.2 Tensile characteristics of moist sand 11
3 Matric Suction and Tensile Strength of Soil
3.1 Matric suction 15
3.2 Relationship between tensile strength and matric suction 16
4 Methods for Determination of Tensile Strength
4.1 Indirect methods
4.1.1 Brazilian tensile test 18
4.1.2 Flexure beam test 19
4.1.3 Double punch test 20
4.1.4 Unconfined penetration test 22
4.2 Direct method 24
5 Conclusions 27
References 28
1
CHAPTER 1
INTRODUCTION
1.1 General
The behavior of soils in tension is a subject of great interest, not only for geotechnical
engineers, but also for other branches of engineering, such as agricultural or mining, where
the main object is connected with tillage or with resistance during soil excavation. From the
geotechnical engineering point of view, the interest with respect to the tensile strength of
soils is very often connected with the different tensile cracks that can develop in earth
structures, such as embankment dams, slopes, retaining walls from reinforced soil, or with a
capping clay sealing system of sanitary landfills [10].
Compared to the compressive or shear strength of soil, its tensile strength is generally
assumed to be zero, or insignificant, in geotechnical engineering practice because of its
relatively small value and lack of a satisfying laboratory technique. The tensile strength of
soil is, however, an important parameter in the design of geo-systems, where tensile cracks
contribute to progressive erosion or landslides in excavation, slopes, dams, highway
embankments, riverbanks, hydraulic barriers, and other earth structures [3]. Fig. 1.1 shows a
tensile crack that developed close to a rock-fill dam crest parallel to its longitudinal axis.
Fig. 1.1 Longitudinal Crack on the Surface of the Clay Core Rock-fill Dam
2
Very often, a tensile crack can be observed at the top of the slope as a first sign of the
potential danger of a slope stability problem as shown in Fig. 1.2.
Fig. 1.2 Tensile Crack at the upper part of the Slope
Fig. 1.3 shows a large tensile crack observed very close behind the zone of
reinforcement for a high retaining wall made from reinforced soil.
Fig. 1.3 Tensile crack behind the zone of reinforcement of a retaining wall
The presence of tensile cracks in soil can significantly affect its mechanical and
hydraulic properties. For example, the overall strength and bearing capacity of a soil
containing cracks are often much less than those of intact soil. The cracks can also create
preferential flow paths that may significantly increase soil hydraulic conductivity. As a result,
3
the performance of soil involved in various engineering disciplines (geotechnical, geological,
and environmental engineering) could be significantly affected by cracks. There is evidence
that cracking at the crest area of the slopes usually triggers the initiation of slope failure. To
prevent such effects of tensile cracking and reveal the relevant cracking mechanisms, a
comprehensive understanding of soil tensile strength characteristics is essential [9].
1.2 Necessity
Tensile strength of soil is a major mechanical parameter controlling the development
of tensile cracking, which is commonly encountered in many earth structures e.g., dams,
hydraulic barriers, slopes, runway subgrades, river banks, highway and railway
embankments, especially when subjected to desiccation, differential settlement, or other
external loads. The tension cracks occurring in soil affect its compressibility, its time rate of
consolidation, its strength, and the rate at which water can re-enter. Thus, much geotechnical
construction is affected directly or indirectly by the presence of cracks in a soil mass. A soil
with cracks is more compressible than an intact version of the same soil at the same water
content.
However, wetting and drying cycles lead to increasing over-consolidation towards the
surface, and this reduces the compressibility. A cracked soil has much higher hydraulic
conductivity than the same soil at the same water content but in an intact state. Thus
consolidation can be expected to proceed much more quickly [8]. Therefore it is very
important to understand the behavior of tensile strength characteristics of soil and also to
study the tensile strength determination of soil for recognizing the probability of tensile crack
development.
1.3 Determination of Tensile Strength of Soil
There are two categories of methods that can be used to measure soil tensile
strength, namely indirect and direct methods. The indirect method allows developing
correlations between various parameters for determining the soil tensile strength, including
the Brazilian tensile test [4], Flexure beam test [4], Double punch test [1], and Unconfined
penetration test [3].
In these tests, specimens are split under point or linear compression loads. Various
hypotheses were proposed to calculate the tensile strength. Particularly, the tensile strength
was essentially determined by assuming that tensile stress distributes uniformly on the failure
plane. As a result, these methods are more suitable for brittle and elastic materials (stiff,
highly compacted, or chemical stabilized soils) than for ductile materials (soft and wet clayey
soils).
4
For the direct method, the tensile strength of soil is usually determined by uniaxial
tensile tests [9], [7]. The tensile load is directly applied to the two ends of a soil specimen.
Such tests are generally preferred, as the tensile stress and strength can be directly obtained.
Both the tensile load and displacement can be controlled, depending on test device. However,
it has been shown that direct tensile tests are difficult to perform due to problems of specimen
preparation and specimen fixing during tension. Development of new test setups and
methodologies are therefore needed to improve the efficiency of these direct tests.
5
CHAPTER 2
TENSILE STRENGTH CHARACTERISTICS OF SOIL
One of the explanations given for the existence of the tensile strength in soil is the
cohesion between particles. The physical mechanisms attributing to the cohesion of soil
include the following: (i) Van Der Waals attraction at or near particle contacts; (ii) Electrical
double-layer repulsion between platy clay particles and attraction near face-to-edge contacts;
(iii) Cementation due to solute precipitation and (iv) Capillary attraction due to the existence
of water bridges or bodies between particles. The tensile strength characteristics of clayey
soil were studied by Tang et al. (2015)9 the same are discussed below [9].
2.1 Tensile Characteristics of Clayey Soil
Fig. 2.1 shows the typical tensile curves (tensile load-displacement) of the specimens
compacted at a water content of 16.5% and dry density of 1.5 Mg/m3. The results of repeated
tests were also presented. As can be seen, the tensile patterns of the parallel specimens (T1
and T2) were similar, indicating good consistency of specimen preparation and test
procedures. The tensile load increased monotonically with increasing displacement before the
peak load was reached. After that, the tensile load decreased sharply, indicating that tensile
cracking had occurred at the specimen neck, as shown in Fig. 2.1. According to the maximum
tensile loads determined from the tensile curves, the average tensile strength of each test
group was calculated.
Fig. 2.1 Typical Tensile Curves for Two Repeated Soil Samples
6
Currently, the quantitative understanding of the roles and magnitudes of each of the
first three mechanisms in tensile behavior of soils is not well established. Most of the
research in recent decades has mainly focused on the quantitative understanding of the
relationship between capillary attraction and tensile strength of unsaturated soils by
examining water retention mechanisms or mechanical interactions between two particles. In
recent years, the suction stress characteristic curve has been proposed to represent the state of
stress in unsaturated soil, and suction stress was considered as the dominant parameter
controlling soil tensile strength [6], [5].
Mechanically, suction stress originates from the available interaction energy at the
soil solid surface that can be conceptualized to exist in the forms of van der Waals and
double-layer forces, surface tension, and tensile pore water pressure. As indicated by Lu et al.
(2009)5, a macroscopic continuum representation of suction stress is the tensile stress that can
be simply determined from the direct tensile test. According to the Mohr-Coulomb (M-C)
shear failure criterion, if it is assumed that the ratio of shear stress to normal stress in the
tensile stress regime remains the same in the compressive stress regime, i.e., tan ϕ, then the
uniaxial tensile strength measured by the direct tensile test can be logically considered as the
mobilization of isotropic bonding stress (cohesion) when the maximum principal stress
remains zero [5].
In other words, failure occurs not because the applied stress reaches the bonding
strength, but because the ratio of shear stress to normal stress at a point reaches tan ϕ. In the
case of homogeneous and isotropic soil, no shear stress develops at any point in any direction
when soil fails under isotropic tensile stress. The isotropic tensile strength of soil is
independent of the internal friction angle. Lu et al. (2006)6 and Lu et al. (2009)5 defined the
isotropic tensile strength as a part of suction stress, and they developed a theory for
describing the tensile strength of unsaturated granular media derived by considering the
suction stress [6], [5].
2.1.1 Effect of water content
For soils that are either completely dry or saturated, tensile strength is often
considered as a material constant or part of the shear strength. For soils under partially
saturated conditions, tensile strength is known as a function of suction and significantly
depends on water content [7]. In the past several decades, although the tensile strength of
compacted soil has been quantitatively investigated by either the indirect or direct methods
discussed, the water contents of the test specimens were usually concentrated in a narrow
7
range around the optimum value determined from the Proctor curve. Information on the
tensile strength within a broader range of compaction water contents is relatively limited.
In the study done by Tang et al. (2015)9, according to the measured tensile strength σt
at different water contents w or degrees of saturation S, the tensile strength characteristic
curves (TSCC, σt versus w or S) were determined for the specimens compacted at different
dry densities (1.5, 1.6, and 1.7 Mg/m3) as shown in Fig. 2.2 (a and b), respectively. Three
distinct curves can be seen for the three different dry densities, but all the curves show similar
features and peak values can be observed. The results indicated that the σt depends
significantly on w or S at a given dry density. With the increase of w or S, the σt increased
quickly before critical water content wc or critical degree of saturation Sc is reached, which
corresponds to the peak value of σt.
Fig.2.2 Measured Tensile Strength Characteristic Curves of Specimens as a Function of
(a) Water Content and (b) Degree of Saturation
8
As shown in Fig. 2.2, both the wc and Sc were only slightly influenced by dry density
and could be assumed negligible. The average value of wc (11.5%) and Sc (45.2%) was used
in the discussion sections by the above mentioned researchers. Beyond this point, a
decreasing trend in σt was observed with further increases in w or S. For example, the average
σt of the specimens compacted at a dry density of 1.5 Mg/m3 increased from 12.93 to the
peak value of 33.77 kPa as the water content increased from 4.3 to 12.5%, and then decreased
gradually to 17.90 kPa at a water content of 28.5% (about 96% saturation). Generally, the
increase rate of σt at the dry side (w lower than wc) was higher than the decrease rate at the
wet side (w larger than wc).
Moreover, the decrease rate of σt dropped gradually with further increase of water
content, showing that the tensile strength at high degree of saturation (i.e., S > 80%) was not
significantly sensitive to the variation of water content, while tends to reach a residual tensile
strength at saturation. The preceding observation showed an important conceptual change to
the previous theories or findings wherein the tensile strength decreased monotonically with a
decrease in suction or increase in water content or degree of saturation, because that was only
true for soil within the wet side, where the corresponding degree of saturation was relatively
high as shown in Fig. 2.2 (b). However, for the soil within the dry side of wc, the tensile
strength increased with an increase in water content or degree of saturation (or decrease in
suction) until a peak value is reached. This significant dependence of tensile strength on
water content or degree of saturation for compacted clayey soil was explained by considering
both the microstructure and the capillary bonding forces between the particles.
At low water contents (on the dry side of wc, Fig. 2.2), most of the water was trapped
in intra-aggregate pores, while small amounts of water form a limited number of water-
bridges at the aggregate-aggregate contact points as shown in Fig. 2.3. These bridges resulted
in capillary bonding forces between the aggregates, giving rise to both cohesion and tensile
strength. The compacted specimens at this stage were located in the region of intra-aggregate
governing suction. Although the soil suction was high, it contributed less to the inter-
aggregate force as well as tensile strength. Moreover, the water trapped in inter-aggregate
pores (water-bridges) was disconnected and characterized as a pendular regime, where
suction stress increased with an increase in degree of saturation [5]. As the water content
increased, more and more water-bridges were developed in the contact points.
After water-bridges resided in all the possible contact points among the aggregates,
suction stress and tensile strength reached its maximum value, which corresponded to the
critical water content wc or critical degree of saturation Sc as shown in Fig. 2.2 and 2.3.
9
Fig.2.3 Conceptual Illustration of Soil Water Retention States, Microstructure Features, and
Tensile Strength Characteristics of Clayey Soil and Sand
With a further increase in water content, a decreasing trend in tensile strength was
observed after its peak value (wet side of wc, Fig. 2.2). This phenomenon was explained by
considering the following factors: (i) the size and number of inter-aggregate pores in soil
specimens decreased because the aggregate structure at low water content changed gradually
to an aggregate-dispersed structure (Fig. 2.3); (ii) capillary bonding forces developed by the
bridge system gradually disappeared because the trapped pore water between aggregates
started to transform from disconnected to a connected state, and that regime was known as
the funicular regime and (iii) suction and cohesion between clay particles also decreased
concurrently.
The tensile strength of soil at this stage was probably dominated by both the
cohesions between aggregates and between clay particles as shown in Fig. 2.3. As the
specimen neared full saturation, the aggregates were subdivided into individual small clay
particles and the inter-aggregate pores disappeared. The specimen showed an evident
dispersed structure, where the pores were almost filled with water and only few disconnected
air bubbles were trapped as shown in Fig. 2.3. That stage was known as the capillary regime,
where suction was very low and did not contribute much to the tensile strength. As indicated
by Lu et al. (2009)5, suction stress and tensile strength of sand in a capillary regime generally
reduced to zero when the sand was sufficiently wet [5]. However, for compacted clayey soil,
a residual tensile strength was observed as shown in Fig. 2.2. The measured tensile strength
within this regime was mainly dominated by cohesion between clay particles such as van der
10
Waal forces, particle surface forces, etc., which were unlike the capillary bonding forces
developed at the dry side of wc and not sensitive to variation of water content.
It was noted that, especially if the specimen is saturated or near saturation, pore water
pressure is likely to develop during the tension test due to two processes: dilatancy and
application of the tensile force itself. Both processes would cause negative pore water
pressure generation, and also an increase in suction as the specimen is stretched.
Consequently, the measured tensile strength would be overestimated, and depend on tensile
rate accordingly. In the investigation done by above mentioned researchers, only one tensile
rate (0.5 mm/min) was employed. The effect of the tensile rate on suction and tensile strength
is beyond the scope of this study.
2.1.2 Effect of dry density
From the results shown in Fig. 2.4, it was seen that tensile strength was significantly
affected by dry density ρd. With the increase in ρd, there was an increase in σt even though the
specimens were compacted at the same water content. For example, at a water content of
4.3%, the average tensile strength increased by 73.2 and 200.5% as ρd increased from 1.5 to
1.6 and from 1.5 to 1.7 Mg/m3, respectively. A high dry density had a positive effect on
tensile strength. This was because higher ρd leaded to more contacts between soil aggregates
and particles, hence increasing the number of water-bridges, which caused higher measured
tensile strength.
This phenomenon was more pronounced at low water content. Fig. 2.4 shows the
average increase percent of σt at different water contents as the specimen’s dry density
increased from 1.5 to 1.6 Mg/m3 and from 1.6 to 1.7 Mg/m3, respectively.
Fig. 2.4 Effect of Dry Density on Tensile Strength of Clayey Soil
11
The increase percent at the dry side of wc (w lower than 11.5%) was generally higher
than that at the wet side. This was expected since the water was mainly trapped in intra-
aggregate pores at low compaction water content. Soil specimens were located in the intra-
aggregate governing suction region, where the water retention state and capillary bonding
force was slightly affected by mechanical effects except the number of water-bridges.
However, as the specimen was compacted at high water content, the increase of ρd could
result in both the rise of macroscopic degree of saturation and the decrease of suction levels,
and consequently counter-balance part of the contribution of dry density to the tensile
strength.
2.2 Tensile Characteristics of Moist Sand
It is well known that moist sand generally exhibits cohesion with a magnitude
dependent on the degree of wetness or saturation, particle size, particle-size distribution, and
porosity. Perhaps the most striking and persistent characteristic of moist sand behavior is the
nonlinear dependence of tensile strength on saturation or soil suction. Qualitatively, dry sand
has minimal tensile strength even though the interlocking of the sand could be strong. As
sand progressively wets toward full saturation, the degree of saturation increases, and soil
suction reduces [5].
However, the bonding stress isotropic tensile strength will rst increase up to a
maximum value depending on particle size and porosity, followed by a reduction to zero near
saturation or when the sand is suf ciently wet. A conceptual illustration of such up-and-down
behavior of tensile strength of sand is shown in Fig. 2.5.
Fig. 2.5 Interrelationship between Soil Water Retention Curve and Tensile Strength
Characteristics Curve for over the Entire Saturation Range
12
Because capillary water can be retained in three distinct regimes—pendular, funicular,
and capillary regimes—theoretical formulation of soil tensile strength has been challenging.
Nearly all the existing theories are based on consideration of water retention and capillary
force interactions between idealized two particle pairs in the pendular regime, and thus
cannot accurately describe tensile strength for multi-particle systems in the funicular regime.
For typical sand, the pendular regime represented up to about 20% saturation, the
funicular regime between approximately 20 and 90%, and capillary regime between
approximately 90 and 100%. Consequently, while most existing theories can quantitatively
predict the magnitude of tensile strength in the pendular regime, few of them can accurately
predict the occurrence of the maximum tensile strength or the variation of tensile strength in
the funicular and capillary regimes.
The theory presented by Lu et al. (2009)5 was used to predict tensile strength behavior
in all three water retention regimes [5]. This was illustrated first by considering three
idealized cases. Fig. 2.6 illustrates the tensile strength of three hypothetical ne sands as a
function of soil suction. All three ne sands had the same air-entry pressure of 1.67 kPa,
which caused 16.7 cm of capillary fringe above the water table under hydrostatic eld
conditions. For the ne sand with a narrow range of particle sizes, the pore size distribution
was also narrow (n=2.3). The maximum tensile strength was 1.23 kPa, which occured at
matric suction of 2.81 kPa or 43.6% of saturation (not shown in the gure). Tensile strength
reduced relatively slowly as matric suction increased after passing the peak value. At matric
suction of 100 kPa (0.5% of saturation), tensile strength still sustained about 0.48 kPa.
Fig. 2.6 Tensile strength of fine sand as a function of soil suction for different pore size
distribution
13
For the ne sand with a moderate particle size and pore-size distribution (n=4), the
maximum tensile strength was 1.03 kPa, which occurred at matric suction of 1.40 kPa or
73.8% of saturation. Tensile strength reduced quickly as matric suction increased after
passing the peak strength. Tensile strength was 0.01 kPa at matric suction of 22 kPa (or
saturation of 0.04%). Finally, for the ne sand with a wide particle-size and pore-size
distribution (n=8), the maximum tensile strength was 1.10 kPa, which occurred at matric
suction of 1.32 kPa or 83.0% of saturation. Tensile strength decreased very rapidly after the
peak value, and it reached 0.01 kPa at matric suction of 6 kPa or (saturation of 0.03%). It was
drawn from those three hypothetical cases that the magnitude of tensile strength was greatly
controlled by the air entry pressure parameter α, the peak tensile strengths occurred at very
similar matric suction values, but quite different saturations calculated for those three sands.
Accurate prediction of the maximum tensile strength and its occurrence was also
derived from the equation of suction stress which will be discussed later in the report.
The maximum magnitude of uniaxial tensile strength was given by:
() =
1
1
2
(2.1)
The corresponding degree of saturation was
() =
(2.2)
Where, n was identi ed to be valid for greater than 2, which was generally the case for sandy
materials. The dependence of the maximum tensile strength and degree of saturation on the
pore size spectrum parameter n, as described by above equations 2.1 and 2.2 is shown in
Fig. 2.7.
(a)
14
(b)
Fig. 2.7 Theoretical Functions for (a) The Magnitude of the Peak Tensile Strength as a
function of the Pore Size Spectrum Parameter n; (b) The Equivalent Degree of
Saturation for the Peak Strength as a function of the Pore Size Spectrum Parameter n
The theory predicted that the normalized maximum tensile strength was a down-and-
up function of the n parameter. The corresponding degree of saturation was an increasing
function of the n parameter and it could occur at any degree of saturation.
15
CHAPTER 3
MATRIC SUCTION AND TENSILE STRENGTH OF SOIL
Experiments have shown that the void spaces between the particles do not remain
indefinitely filled with water, and successively larger proportions of air gradually enter the
void spaces. Surface-tension effects at air-water-soil contacts inside the soil generate negative
pressures (or matric suctions) below atmospheric pressure in the remaining pore water. These
matric suctions produce two counteracting effects. One, at a selected point, the soil tends to
contract more or less isotropically, assuming at this stage that the pore water remains
interconnected and the pore air is discontinuous. This shrinkage produces vertical cracks
below horizontal drying surfaces. Two, the soil gains strength and provides increased
resistance to crack formation. Suctions can also arise from osmotic effects related to soil
chemistry. However, matric suction dominates below the immediate surface of a soil deposit,
and most workers assume that it drives shrinkage and cracking process during drying. It has
been proved that tensile strength of soil is the function of suction of soil [8].
3.1 Matric Suction
The matric suction is a capillary component of free energy of soil suction. In suction
terms, it is the equivalent suction derived from the measurement of the partial pressure of the
water vapor in equilibrium with the soil water, relative to the partial pressure of the water
vapor in equilibrium with a solution identical in composition with the soil water. The matric
suction is the sum of pore-air pressure and pore-water pressure. The matric suction
component is commonly associated with the capillary phenomenon arising from the surface
tension of water [3].
The total suction corresponds to the free energy of the soil water, while the matric and
osmotic suctions are the components of free energy. In an equation form, this can be written
as
= ( – ) + л (3.1)
Where,
Ψ is the total suction.
– = matric suction
= pore-air pressure
= pore-water pressure
л = osmotic suction
16
Lu et al. (2009)5 developed a model and stated an equation showing the relation
between matric suction and tensile strength of soil [5]. The same is discussed below.
3.2 Relationship between Tensile Strength and Matric suction
Lu et al. (2009)5 developed a theory for the tensile strength of unsaturated sands
derived by considering the suction stress of Lu et al. (2006)6, defined as the isotropic tensile
stress that can be conceptualized as the isotropic tensile strength. According to the
relationships between suction stress and equivalent degree of saturation, and isotropic tensile
strength and uniaxial tensile strength, Lu et al. (2009)5 proposed the following two
expressions for estimating the uniaxial tensile strength of unsaturated sand in terms of soil
suction and equivalent degree of saturation, respectively [2]:
=2tan tan
(){1 + [()]}()
(3.2)
The tensile strength was then given by equation:
=2tan
()
1
(3.3)
Where,
σt = uniaxial tensile strength;
= internal friction angle determined at low normal stress level, i.e., less than 1 kPa,
= pore air pressure;
= pore water pressure;
Α = inverse value of the air-entry pressure;
n = pore size spectrum number; and
Se = equivalent degree of saturation, which was defined as degree of saturation S normalized
by the residual saturation
as follows:
=
(3.4)
Thus, above equation may be used to predict the uniaxial tensile strength of
unsaturated sands as a function of suction or degree of saturation if the parameters , α and
n are known. Generally, the latter two parameters, α and n, can be determined by the soil
water characteristic curve (SWCC).
Generally, for unsaturated sand, the tensile strength presented a nonlinear relationship
with saturation or soil suction. Dry sand usually had minimal tensile strength close to zero.
As sand progressively wetted toward full saturation, tensile strength would first increase up to
17
a peak value, which was followed by a reduction to zero near saturation or the sand was
sufficiently wet as shown in Fig. 2.5. Apparently, the TSCC of sand was significantly
different from that of compacted clayey soil, which presented evident residual tensile strength
near saturation as shown in Fig. 2.4 and 2.5. This was because; the suction stress of clayey
soil was not zero at saturated condition due to the presence of van der Waals and double-layer
forces. Meanwhile, the suction stress of sand at saturated condition was zero due to the
disappearance of tensile pore water pressure. For that reason, the tensile strength model
proposed by Lu et al. (2009)5, mainly based on the suction stress state of sand, would not be
directly applied to estimate the tensile strength of clayey soil at a relatively high degree of
saturation.
18
CHAPTER 4
METHODS FOR DETERMINATION OF TENSILE STRENGTH
Two categories of methods are used to measure the tensile strength of soil, namely
direct and indirect methods. The indirect methods relate the tensile strength with various
parameters such as compressive load, shear strength, etc. Whereas the direct method is a
simple measure for obtaining the tensile strength of soil. Both the categories are discussed
below.
4.1 Indirect Methods
4.1.1 Brazilian tensile test
The Brazilian tensile test [4], also referred to as diametrical compression test, is most
commonly used for testing the tensile properties of rock and concrete. In addition it has been
used to test the tensile strength of soils. A cylindrical disk specimen of soil, placed
horizontally, is subjected to a compressive force through two diametrically opposed rigid
platens. The compressive force generates a tensile stress, perpendicular to the compressive
force, along the plane between the two platens. The compressive force is increased until
failure occurs along this plane. Based on an assumption of linear elasticity, along the loaded
diameter the tensile stress, σx is constant and equal to;
=
л (4.1)
Where, ‘P’ is the maximum vertical load applied in the test, ‘d’ is the diameter of the sample
and ‘t’, its thickness or height. The shear stress is zero along the loading plane, therefore
and are the principal stresses.
As loading occurs the sample deforms at the loading interface, resulting in loading
conditions changing from point loading to distributed-loading. As a consequence of this the
stress distribution changes from the ideal tensile stress at the centre to a more complex
combined stress. Determination of a tensile strength relies on the assumptions of linearly
elastic behavior, which is not the case for soils. Fig. 4.1 shows the schematic representation
of the Brazilian tensile test and Fig. 4.2 shows the Brazilian test apparatus.
Measurement of tensile strain profile is complex due to the presence of horizontal
strain associated with the compressive force through the effect of Poisson’s ratio. Meaning
the strain measurements in both the horizontal and vertical direction would be required at the
sample centre, due to the non-homogenous stress field, this would be difficult to successfully
achieve.
19
Fig. 4.1 Schematic of Brazilian Test
Fig. 4.2 Brazilian Test Apparatus
4.1.2 Flexure beam test
This test is also called as 3 point bending test [4]. It is commonly used in materials
engineering and for rock and concrete testing. It consists of a sample beam supported at two
points with a load applied at the midpoint. Under loading the beam deflects, with the extreme
compressive and tensile stress occurring at in the top and bottom fiber of the beam
20
respectively. Value for the extreme tensile stress are calculated by assuming linear elastic
behavior from the following
=
(4.2)
Where, ‘P’ is the applied load, ‘h’ is the height of the beam. ‘L’ is the length of the beam
from the midpoint to the support and ‘I’ is the moment of inertia for the beam. Fig. 4.3
represents the flexure beam test.
Fig. 4.3 Schematic of Flexure Beam Test
An alternative to 3 point bending test is the 4 point bending test. The additional
loading point creates a region of homogenous tensile stress between the loading arms. Instead
of above equation 4.2, knowledge of strain allows for calculation of the extreme tensile stress
by considering equilibrium of forces and moments.
=
(
(+ ) ) (4.3)
Where, ‘M’ is the applied bending moment and εc and εt are the extreme fiber compressive
and tensile strains respectively.
The radiographic strain measurement technique was replaced with particle image
velocimetry and high-capacity tensiometers were embedded in to the mid-span of the clay
beam to monitor the pore-water pressure. The presence of tensiometer was found to induce
cracking in approximately one third of the samples tested.
4.1.3 Double punch test
The double-punch test [1] may be briefly described as follows:
Using two steel discs (punch) centered on both top and bottom surfaces of a
cylindrical soil specimen, the vertical load is applied on the discs until the specimen reaches
failure. The tensile strength of the specimen can be calculated from the maximum load by the
theory of perfect plasticity. Fig. 4.4 shows the double punch test apparatus and mode of
failure of sample.
21
(a)
(b)
Fig. 4.4 (a) Double Punch Test Apparatus and (b) Mode of failure of sample
The plasticity developed previously for computing the bearing capacity of concrete
blocks or rocks was extended to soils and other stabilized materials. Further evaluation of the
effects of the compression-tensile strength ratio, friction angle of soil, and sample-punch size
related to the formula were used for computing the tensile strength of soils.
Two major assumptions were made in the theory. The first was that sufficient local
deformability of soils in tension and in compression did exist to permit the application of the
generalized theorems of limit analysis to soils idealized as a perfectly plastic material. The
second was that a modified Mohr-Coulomb failure surface was postulated as a yield surface
for soils.
22
Fig. 4.5 shows an ideal failure mechanism for a double-punch test on a cylinder
specimen.
Fig. 4.5 Failure Mechanism of a Double Punch Test
It consists of many simple tension cracks along the radial direction and two cone-
shaped rupture surfaces directly beneath the punches. The cone shapes move toward each
other as a rigid body and displace the surrounding material sideways.
Finally, the tensile strength of soil is given by the equation
=
() (4.4)
Where, ‘P’ is the load applied. The term ‘k’ is given by k = tan (2 +), ‘b’ is the radius of
specimen, ‘a’ is the radius of punch, ‘H’ is the height of specimen, ‘α’ is the angle of cone,
′′ is the angle of friction.
4.1.4 Unconfined penetration test
The unconfined penetration tests also called as indentation test is an indirect method
for tensile strength determination [3]. It uses a pair of cylindrical metal indenters, or punches,
to compress a cylindrical soil specimen. The tensile strength is computed through the
equation developed from the limit analysis. The test gives an applied compressive axial load
and indenter displacement curve. The maximum load is identified for further data reduction
23
to compute the tensile strength. The limitation of this test method is that a certain level of
brittleness of the specimen is required so that a split tension failure would occur. Fig. 4.6
shows the unconfined penetration testing apparatus.
Fig. 4.6 Unconfined Penetration Test Apparatus
By equating the external work with the internal work, an upper bound solution can be
obtained as follows:
л=
( )
+ tan(+Ø)(
– cot α) (4.5)
Where, pu is the upper bound axial compressive load that causes the split tension failure. ‘a’ is
the radius of the indenter, ‘b’ is the radius of the soil specimen, Ø is the internal frictional
angle of the soil, α is the developed angle underneath the indenter when failure occurs, qu is
the unconfined compressive strength while qt is the tensile strength to be determined. The
upper bound solution has a minimum value when -
= 0
Also,
л = [
tan (2α+ Ø) – 1] (4.6)
By equating above equations 4.5 and 4.6, following can be obtained:
24
cot = tan Ø + sec Ø 1+
(4.7)
Let p is the maximum compressive load applied from the test, which is less than the
upper bound load, . Therefore,
≤= [tan(2+ )] (4.8)
And the tensile strength is given by:
=
() (4.9)
Where, K = tan(2 + )
The value of K is challenging to determine in laboratory testing as it is a function of
the internal frictional angle of the soil, the unconfined compressive-tensile strength ratio, as
well as the size of the indenter.
4.2 Direct Method
For the direct method, the tensile strength of soil is usually determined by uniaxial
tensile tests [5]. The tensile load is directly applied to the two ends of a soil specimen. Such
tests are generally preferred, as the tensile stress and strength can be directly obtained. Both
the tensile load and displacement can be controlled, depending on test device. However, it
has been shown that direct tensile tests are difficult to perform due to problems of specimen
preparation and specimen fixing during tension.
Although direct measurement of tensile strength of ne-granular materials has been a
subject of study for many years, few methods are directly applicable to sands. For example,
the adhesive method that is widely used in material science requires the test materials to be
suf ciently strong to be bonded to the sample adapters. The Brazilian tensile splitting method
widely used for rocks requires the materials to be strong and brittle. Other direct stretching
methods suitable for clays cannot be used for sands since these methods are conducted with
no con ning stress. A direct tensile strength apparatus recently was developed to accurately
measure the tensile strength characteristics of unsaturated sands [9]. The method is simple in
principle, accurate in measurement, and reliable in obtaining repeatable tensile strength. The
basic idea was to use the weight generated by tilting a sample to split it. The apparatus, as
shown in Fig. 4.7, consisted of an adjustable table for sample tilting, a digital probe for tilting
angle measurement, detachable sample tubing, and a sample tubing mounting plate.
25
Fig. 4.7 Direct Tensile Test apparatus
26
An unsaturated sand sample was rst compacted or cored into the sample tubing
mounted on the sample mounting plate to a desired porosity and water content using a
vibration table. The sample tubing was then placed horizontally on a set of spherical ball
bearings that minimized friction between the sample tubing and the table. The sample tubing
comprised two detachable sections which were clamped together during sample preparation
and released prior to testing.
One section of the sample tubing was xed on to the table while the other section was
free to slide. The test was then followed by progressive inclination of the sample to increase
the pull force along the longitudinal direction of the sample by tilting the adjustable table.
The inclination angle was recorded during the test and the nal reading indicated the angle
when the sample broke into two halves. The measured inclination angle β, together with the
sample and tubing weight (the weight of the right half W) and geometrical con guration
(sample cross section area A), provided a simple and accurate determination of the tensile
strength of the sand, i.e.,
= /. (4.10)
Where, is the tensile strength of sand.
The test could be repeated for the same porosity and moist content for duplication or
be conducted for other sets of porosity and/or moisture content to obtain complete tensile
strength characteristics of the sand.
27
CHAPTER 5
CONCLUSIONS
After referring to various literatures available on tensile strength of soil and its
determination, following conclusions can be drawn:
1. To prevent effects of tensile cracking and reveal the cracking mechanism,
understanding of soil tensile strength characteristics is essential.
2. The tensile strength of compacted clayey soil depends significantly on compaction
water content.
3. The tensile strength increases with an increase in dry density. The contribution of
dry density at low water content is more pronounced than that at relatively high
water content.
4. Tensile strength of soil is a function of soil suction.
5. The direct method of determination of tensile strength offers a simple but effective
means for investigating the tensile characteristics of soil at different water
contents and dry densities.
28
REFERENCES
1. Fang H.Y., and Chen W.F., ‘Further study of double-punch test for tensile strength of
soils’, Fritz Laboratory Reports, Lehigh University, 1972
2. Fredlund D.G., and Rahardjo H., ‘Soil Mechanics for Unsaturated Soils’, John Wiley
& Sons, (65), 1993
3. Ge L., Yang K.H., ‘Tensile strength of lightly cemented sand through indentation
tests’, Proceedings of the 18th International Conference on Soil Mechanics and
Geotechnical Engineering, Paris, 2013
4. Khalili N., Russel A., and Khoshghalb A., ‘Unsaturated Soils: Research &
Applications’, CRC Press, 824-825, 2014
5. Lu N., Kim T.H., Sture S., and Likos W.J., ‘Tensile strength of unsaturated sand’, J.
Eng. Mech., 10.1061/ (ASCE) EM.1943-7889.0000054, 1410-1419, 2009
6. Lu N., and Likos W.J., ‘Suction stress characteristic curve for unsaturated soil’, J.
Geotech. Geoenviron. Eng., 10.1061/ (ASCE) 1090-0241, 132:2 (131), 131-142, 2006
7. Lu N., Wu B., and Tan C.P., ‘Tensile strength characteristics of unsaturated sands’, J.
Geotech. Geoenviron. Eng.,10.1061/(ASCE) 1090-0241, 133:2(144), 144-154, 2007
8. Morris P.H., Graham J., and Williams D.J., ‘Cracking in drying soils’, Can. Geotech.
J., 29 (2), 263-277, 1992
9. Tang C., Pei X., Wang D., Shi B., and Li J., ‘Tensile strength of compacted clayey
soil’, J. Geotech. Geoenviron. Eng., 10.1061/ (ASCE) GT.1943-5606.0001267, 133:2
(141), 2015
10. Vanicek I., ‘The importance of tensile strength in geotechnical engineering’, Acta
Geotechnica Solvenica, 5-17, 2013
