case study on terzaghi’s theory

1. Case study on terzaghi’s theory
Group members:
1. Bhavik Kalariya (14soecv11023)
2. Arjun mandaliya (14soecv11030)
3. Kinjal marakana (14soecv11032)

2. Intoduction
Terzaghi's Principle states that when a rock is subjected to a stress, it
is opposed by the fluid pressure of pores in the rock.
More specifically, Karl von Terzaghi's Principle, also known as
Terzaghi's theory of one-dimensional consolidation, states that all
quantifiable changes in stress to a soil [compression, deformation,
shear resistance] are a direct result of a change in effective stress. The
effective stress σ ′ is related to total stress σ and the pore pressure u
by the relationship.
Total stress is equal to the sum of effective stress and pore water
pressure.

3. Introduction
• Objective:
The following objectives are set forth to achieve the aim of the research:
i. To develop consolidation equipment that could be used to run rapid consolidation using
constant rate of strain consolidation method.
ii. To compare the result of the compression characteristic of the soil, coefficient of
consolidation (cv) and compression index (cc) obtained from CRS test to the results
of conventional oedometer test.
iii. To establish the new criteria of acceptance for Constant Rate of Strain consolidation test.
• Scope:
i. Disturbed samples are collected from Kluang, Gemas and Air Papan, Johor . Kaolin soil was
used as the control sample for the study.
ii. The specimens used for the study is remoulded sample. In the case all the disturbed soil
samples were dried and grinded into powder and remoulded from slurry under 100, 200 and 300 kPa
pre-consolidation pressure using self made remoulded sampler equipment.
iii. Conventional oedometer test and the Constant Rate of Strain consolidation test will be
conducted to a maximum of 8.5 kN and 1100 kPa vertical pressure respectively.

4. Introduction
• Materials:
A porous medium or a porous material is a solid (often called matrix) permeated by an
interconnected network of pores (voids) filled with a fluid (liquid or gas).
Usually both solid matrix and the pore network (also known as the pore space) are assumed to be
continuous, so as to form two interpenetrating continua such as in a sponge.
Many natural substances such as rocks, soils, biological tissues, and man made materials such as
foams and ceramics can be considered as porous media.

5. Assumptions
1. The soil is homogenous (uniform in composition throughout) and
isotropic(show same physical property in each direction).
2. The soil is fully saturated (zero air voids due to water content being
so high).
3. The solid particles and water are incompressible.
4. Compression and flow are one-dimensional (vertical axis being the
one of interest).
5. Strains in the soil are relatively small.
6. The coefficient of permeability and the coefficient of volume
compressibility remain constant throughout the process.

6. Terzaghi’s formula
Terzaghi's Bearing capacity equations:
• Strip footings:
Qu = c Nc + γD Nq + 0.5 γB Nγ
• Square footings:
Qu = 1.3 c Nc + γD Nq + 0.4 γB Nγ
• Circular footings:
Qu = 1.3 c Nc + γD Nq + 0.3 γB Nγ

7. Literature view
Sr. no. Author Year Title Publish
1. Darshana Perera April 24, 2016 Analytical model for
vacuum
consolidation
incorporating soil
disturbance caused
by mandrel-driven
drains
14 November 2016
2. Caihui Zhu March 22, 2016. Prediction and
analysis of surface
settlement due to
shield tunneling for
Xi’an Metro
14 November 2016.
3. Muniram Budhu October 22, 2011. Design of shallow
footings on heavily
overconsolidated
clays
20 January 2012.

8. Summary(conclusion)
1. Analytical model for vacuum consolidation incorporating soil
disturbance caused by mandrel-driven drains :
When vacuum preloading is applied with vertical drains, the rate of
consolidation can be increased, and the stability of an embankment is
enhanced due to the inward lateral movement.
The aim of this study is to develop an analytical solution for vacuum
preloading that accurately captures the more realistic variations in
compressibility and permeability in actual ground conditions as a result
of drain installation.

9. Summary(conclusion)
2. Prediction and analysis of surface settlement due to shield
tunneling:
This estimation method is able to take into account the support pressure
of the shield head at the tunnel face, the lining support pressure around
the tunnel opening, the filling effect of tail grouting, yawing, and
pitching of the shielding machine, and the long-term deformation of the
remoulded surrounding soil.
It is suggested that the new estimation method can be used effectively in
estimating the Surface Settlement induced by the shield tunneling
method.

10. Summary(conclusion)
3. Design of shallow footings on heavily overconsolidated clays:
This method pro-vides a unified analysis rather than two separate
analyses to determine the limit bearing capacity and settlement of
shallow foundations. It represents the soil consistently. In comparison,
the conventional method treats the soil mass below the bottom of the
footing as a rigid –perfectly plastic body for the determination of the
failure (collapse) load and then treats that same soil as an elastic
material for the calculation of settlement.
This method can be extended to dense coarse-grained soils, the
difficulty is in defining an overconsolidation ratio for these soils .

11. Results and discussion
1. Evaluation of Load Bearing Capacity of Foundations with
Different Vertical Crosssectional Shapes

12. Result and discussion

13. Result and discussion

14. Result and discussion
• From the figures, it is observed that the load bearingcapacity of T shape foundation is generally
higher than those of rectangular and wedge shapes. The lowest load bearing capacity was observed
with rectangular shape. The relatively higher load bearing capacity recorded with T and wedge
shapes is attributed to additional resistance offered by the soil above their bases from the
compression by their flanges.
• From fig. 5, it is observed that for rectangular shape foundation, the load-settlement curve is linear
up to 0.5 kN load, after which the settlement begins rapid increase with subsequent load
increments. But for wedge and T shape foundations,rapid increase in settlement with subsequent
load applications begin after 0.62 kN load. This observation is attributed to additional resistance
offered by the soil above the bases of T and wedge shapes from the compression by their flanges.
Note that the difference in the patterns of the curves becomes more defined after these defined
loads.

15. Result and discussion
2. ULTIMATE BEARING CAPACITY AND SETTLEMENT FOR
RECTANGULAR FOOTINGS
• For depth of sand cushion of 900mm for rectangular footing of sizes
100mmx125mm,100mmx150mm 100x175mm 100x200mm, ultimate bearing capacity values are
found to be95.49 kN/m², 104.71kN/m², 109.64kN/m²and 114.81kN/m² respectively. As compared
to100mmx125mm rectangular footing, the percentage increase in the ultimate bearing capacity for
100x150mm, 100x175mm and 100x200mm rectangular footing are found to be9.65%,14.81% and
20.23 % respectively. Thus it indicates that as footing size increases, ultimate bearing capacity goes
on increasing.
• For rectangular footing of size 100x125mm,100x150mm,100x175mm and100x200mm depth of
sand cushion below the footing Dsc= 900mm, the values of settlements goes on increasing. The
percentage increase as compare to 100x125mm rectangular footing are found to be 4.60%,31.79%
and 37.93% respectively. Thus it indicates that as footing size increases, settlement also increases.

16. References
1) http://eprints.utm.my
2) https://en.wikipedia.org/wiki/Poromechanics
3) http://www.nrcresearchpress.com
4) http://www.rroij.com
5) http://www.academia.edu