Stress Path Method in Geomechanics geotechnical

The concept of a stress path in geotechnical engineering refers to the trajectory that stress states follow within a soil element during loading, unloading, or shearing processes, typically represented in stress space such as p-q (mean stress vs. deviator stress) or σ₁-σ₃ (major vs. minor principal stresses). Stress paths are crucial for understanding soil behavior under various conditions, especially in triaxial testing, where they help visualize how soil transitions from initial to failure states. A stress path can be drained or undrained, active or passive, and its orientation and curvature reveal critical insights into soil strength, stiffness, dilatancy, and failure mechanisms. For example, in an undrained triaxial test on saturated clay, the stress path tends to move vertically in p-q space due to constant volume, while in drained conditions, it may curve depending on pore pressure dissipation. Engineers use stress paths to predict deformation, assess stability, and design foundations, slopes, and earth structures. The initial stress condition, loading direction, and boundary constraints all influence the path, making it a dynamic tool for interpreting soil response. Stress paths also aid in numerical modeling and finite element analysis, where realistic simulation of soil behavior under complex loading is essential. In practical applications, such as embankment construction or excavation, understanding the stress path helps anticipate potential failure zones and optimize reinforcement strategies. Moreover, stress path analysis supports the development of constitutive models like the Modified Cam Clay, which rely on stress history and path-dependent behavior. By integrating laboratory data, field observations, and theoretical frameworks, stress path methodology bridges the gap between soil mechanics and geotechnical design, offering a powerful lens to evaluate performance under real-world conditions.

1. Dr.Ch.Nageshwar Rao,
Professor, CE,VNRVJIET
STRESS PATH
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2. Stress path
Drained (ESP)& Undrained Stress path
(TSP)
Stress path with respect to different initial
state of the soil
Stress path for different practical situations
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3. Stress Point
State of stress at a point in soil mass can be represented by a Mohr
circle in a τ-σ coordinate system. Some times it is convenient to
represent that state of stress by a stress point whose coordintes are
shown in fig
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4. What is Stress path?
Stress path is used to represent the successive states of stress
in a test specimen of soil during loading or unloading
Series of Mohr circles can be drawn to represent the successive
states of stress, but it is difficult to represent number of circles in
one diagram
t - σ plane q-p plane
The successive states of stress can be represented by a series
of stress points and a locus of these points (in the form of
straight or curve) is obtained. The locus is called stress path
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5. Stress path
• A convenient way of plotting triaxial test data is through diagrams
called stress paths.
•Stress path = line that connects a series of point, each of which
represents a successive stress state experienced by a soil specimen
during the process of a test
•Lamb (1964) suggested a new coordinate system of p’ versus q’
where,
Stress path = diagrams/graphs of stress
changes

6. Stress path
A stress path is a line connecting a series of points, each
point representing a successive stress state experienced by a
soil specimen during the progress of a test
Why draw stress paths? Very often in geotechnical
engineering practice, if you understand the complete stress
path of your problem, you are well along the way towards the
solution of that problem
Because, soil’s behaviour is influenced by previous stress
histories, as well as the current status and process. It is a way
of describing the soil’s past and where it is heading toward.
Results of triaxial tests can be represented by diagrams called
stress paths.
There are several ways in which the stress path can be drawn
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1.Stress path in / space
2.Stress path in 
1/
3 space
3.Stress path in t’/s’ space
4.Stress path in q’/p’ space
TYPES OF STRESS PATH

8. The stress path can be drawn as:
Total stress path (TSP)
Effective stress path (ESP)
Stress path of total stress minus static pore water pressure
(TSSP)
 
If in a field situation, static ground water table exists, initial pore
water pressure u
0 
will act on the sample. Thus, the static pore
water pressure will be equal to u
0. The effective stress
coordinates of the stress points on p'-q' plane can be obtained as:
P’={(σ
v-u) + (σ
h-u)}/2 = (σ’
v + σ’
h)/2
q’={(σ
v-u) - (σ
h-u)}/2 = (σ’
v- σ’
h)/2= (σ
v- σ
h)/2
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9. Different stress paths
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65. Procedure for Plotting Stress Paths
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66. Ex.Two cylindrical specimens, A and B, of a soil were
loaded as follows.
Both specimens were isotropically loaded by a stress of
200 kPa under drained conditions.
Subsequently, the radial stress applied on specimen A
was held constant and the axial stress was
incrementally increased to 440 kPa under undrained
conditions.
The axial stress on specimen B was held constant and
the radial stress incrementally reduced to 50kPa under
drained conditions.
Plot the total and effective stress paths for each
specimen assuming the soil is a linear, isotropic, elastic
material. Calculate the maximum excess pore water
pressure in specimen A.
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70. A reconstituted triaxial specimen of dry sand is
consolidated isotropically to an effective confining pressure
of 200 Kpa, and then loaded in drained triaxial compression
to a deviator stress (σ1-σ3) of 200 kPa, at that point the
specimen is subjected to a harmonic deviator stress that
oscillates between 100 and 300 . Plot the total and
estimated effective stress paths.
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