Thursday, December 22, 2016

Consolidation Settlement of Clay - Time Factor and coefficient of Consolidation- Single and Double Drainage

One of the main factor of rate of consolidation and the time of the consolidation is the single or the double drainage. When there is a double drainage, i.e. drainage from both of the opposite faces, the drainage path becomes half of the total thickness of the clay layer. In such cases the time of settlement decreases significantly. The following example illustrates the same.

Example:  (a) A 20 mm clay layer with double drainage reaches the 90% of total consolidation in 30 minutes. Find out the coefficient of consolidation.
If the same clay has a thickness of 10mm, find out the time it would take to reach 90% consolidation with (b)  single drainage (c) Double drainage. Draw the settlement curve/consolidation curve in each case.

Solution: For solution please zoom into the picture below.


Thank You!

Tuesday, October 18, 2016

Expression for permeability of an Unconfined Aquifer.


In pumping out test, the water is pumped out through a tube well, until a steady state is reached. The water table around the well turns into a cone of depression. The maximum depression along the centre line of the well is known as the drawdown(d).

Following assumptions are made:

  1. Flow follows the Darcy's law.
  2. Flow is laminar.
  3. Soil mass is isotropic and homogeneous.
  4. Well penetrates the aquifer to reach the impervious bed.
  5. Steady flow along the soil.
  6. Co-efficient of permeability is constant throughout.
  7. Natural water ground regime doesn't change.
Also it is assumed that the slope of the hydraulic line is small and so it can be taken as the tangent of the angle, in place of sine of the angle. 
or i = dz/dr

Consider flow through a cylindrical surface at a distance of 'r' and of depth 'z'. Further equation are given in the image below.

Flow can be estimated to a rough value using the influence radius of the well. Influence radius is the radius of the circle along which the effect of the pumping are observed. It varies from 150m to 300m. According the Sichardt, it can be found as follows. 
  R = 3000*d*(k)^0.5    , here d = Drawdown, k = permeability.

Further, permeability can be calculated using the influence radius as given in the formula in the image below.


Reference :  Buy the book online from the link given below.  Book Title: "Soil Mechanics and Foundation Engineering" by Dr. K R Arora.

Friday, October 7, 2016

Lateral Thrust on a Wall at rest against a Soil Backfill


A lateral thrust is applied by the soil backfilled behind a wall at rest, this thrust is known as the lateral thrust at rest. Walls which are restricted against any movements or moment come under this category. Example can be a basement wall, which is topped with a RCC slab, and therefore restricts its movement. The amount of thrust on the wall depends upon the properties of the soil.

Density of the soil, angle of friction, degree of the consolidation and the level of the water table are the major factors which govern the magnitude of the lateral thrust.

Example: A 10 m high basement wall, behind which is filled a soil with density 19.7 kN/m3, c=0,
OCR= 2, πœ™ = 35°, π›Ύπ‘‘ = 19.7 kN/m3. Find the lateral thrust and its location from base.


Fig. Lateral Thrust diagram for wall at rest. 
πΎπ‘œ = 1 - sinπœ™ = 1 - sin35° = 0.426

πΎπ‘œ(overconsolidated) = πΎπ‘œ(normally consolidated )√OCR
πΎπ‘œ(overconsolidated) = 0.426√2 = 0.602

At any depth z
    𝜎′𝑣  = z.𝛾𝑑,   [pore water pressure u= 0)
    𝜎′β„Ž = πΎπ‘œ*𝜎′𝑣
Depth,  z= 0
    𝜎′𝑣  = 0,  πœŽ′β„Ž = 0
Depth,  z= H=10 m
     πœŽ′𝑣  = 10*19.7 = 197 kN/m2,
     πœŽ′β„Ž = 0.602*197 = 118.594 kN/m2

Lateral Thrust = Area of the lateral stress diagram.  = 1/2 (10*118.59) = 592.97 kN

Lateral thrust acts at the centroid of the lateral stress diagram, i.e. at a height of H/3 from base.
H/3 = 10/3 = 3.333 m from base.


Friday, September 2, 2016

When and why the mat or raft foundations are used?

Q. When and why the mat or raft foundations are used?

Mat or raft foundations are type of the shallow foundations, which covers the entire area beneath a structure and provides support to all the columns and walls. It is also a type of the combined footing where all the footings are combined in the following cases:

  1. When the columns are so close such that their footings nearly touch each other.
  2. When the soil is weak and having the low bearing capacity.
  3. Where chances of differential settlement exist due to either the existence of the different soils or variation of the moisture content.
  4. or where there is a large variation in the loading in the adjacent columns.

reference: 'Analysis and design of substructures' by Swami Saran.


Saturday, May 2, 2015

Failure Criteria for Rockmasses

Hi there!

As we know, rock-masses are the complex structures. Failure of the rock-mass occur by the development of the fractures or slip surfaces, when the stresses get increased from the strength of the rock mass.
The failure process in rock-mass is complex, and mathematically difficult to quantify. Four failure criteria are:

  1. Coulomb's Criteria
  2. Mohr's Criteria
  3. Hoek and Bray Criteria
  4. Griffith's Criteria.
First three uses empirical approach, and have considerable value for the design of excavation, while the last one has value for understanding the fracture initiation in the rock.

Friday, April 17, 2015

Tunneling in weak Rocks by Singh and Goel

 This book by Bhawani Singh and Rajnish K. Goel is a very easy to read and useful book for the students of the UG and PG courses of Geo-technical Engineering. I got this book from my course teacher, and it is very helpful.

In this post, I want to share with you the quotes those are written in the book, at the bottom of every title line at the start of the new chapter.
I loved these quotes, and they somehow motivated me to read this book.

1. (Chapter No.1 INTRODUCTION)
"College is where you learn how to learn" - Socrates (470 - 399 B.C.)

2. (Chapter No.2  Applications of Geophysics in tunneling and site survey activities)
"And so Geology once considered mostly a descriptive and historical science has in recent years taken on the aspect of an applied science. Instead of being largely speculative as perhaps it used to be, geology has become factual, quantitative, and immensely practical. It became so first in mining as an aid in the search for metals; then in the recovery of fuels and the search for the oil; and now in engineering in the search for the more perfect adjustment of man's structure to nature's limitations and for greater safety in public works." -  Charles P. Berkey, Pioneer Engineering Geologist. 

3. (Chapter No.3 Terzaghi's Rock Load Theory)
"The Geological engineer should apply theory experimentation but temper them by putting them into the context of the uncertainty of nature. Judgement enters through engineering." - Karl Terzaghi

4. (Chapter No.4 Rock Mass Rating (RMR))
"Effectiveness of knowledge through research(E) is E = mc^2; where m is the mass of knowledge and c is communication of knowledge by publications."   - Z.T. Bieniawski

5. (Chapter No.5  Rock Mass Quality Q)
"Genius is 99 percent perspiration and 1 percent inspiration." - Bernard Shaw

6. (Chapter No.6  Rock Mass Number)
 " My attention is now entirely concentrated on rock mechanics, where my experience in applied soil mechanics can render useful services. I am more and more amazed about the blind optimism with which the younger generation invades this field, without paying any attention to the inevitable uncertainties in the data on which their theoretical reasoning is based and without making serious attempts to evaluate the resulting errors."     - Annual summary in Terzaghi's Diary

7. (Chapter No.7 Strength of Discontinuities)
"Failure is success if we learn from it."  - Malcom S. Forbes

8.(Chapter No.8 Strength enhancement of rock mass in tunnels)
 "The behaviour of microscopic systems is generally described by non linear laws. (The non-linear laws may explain irreversible phenomena like instabilities, dualism, unevolving societies, cycles of growth and decay of societies. The linear laws are only linear approximation of the non-linear laws at a point in time and space.)"    -  Ilya Prigogine, Nobel Laureate

In this book,  there are 29 chapters in total, I think it would be a length post to write all of the quotes in one post, let me know if you want the others. If you want to buy the book, go to the Amazon link I have given above. 


Monday, February 9, 2015

Rock Quality Designation (RQD)

Rock Quality Designation  was introduced by D.U. Deere (1964) (Practical Approach to Civil Engineering by Singh and Goel) as an index of assessing rock quality quantitatively. RQD is a modified per cent core recovery which incorporated only sound rock core pieces that are 100 mm or greater in length along the core axis.

RQD  = (Sum of core pieces >= 10 cm)/ total drill length *100

Following are the methods of obtaining RQD :

a. Direct Method

International Society for Rock Mechanics(ISRM) recommends a core size of at least NX (size 54.7 mm) drilled with double-tube core barrel using a diamond bit. All the artificial fractures should be ignored while calculating the core length for RQD.
The relationship between RQD and engineering quality of the rock mass as proposed by Deere in 1968 is given as below:

S.No.          RQD (%)           Rock Quality
 1.                 <25                      Very Poor
 2.                 25-50                   Poor
 3.                 50-75                   Fair
 4.                 75- 90                  Good
 5.                 90- 100              Excellent

RQD determination - Direct Method ( Photo credit- A Practical Approach to Civil Engineering by Singh and Goel)
b. Indirect Method:
1. Seismic Method : The seismic survey method makes use of the elastic properties of strata that affect the velocity of the seismic waves travelling through them. This method is cheap, rapid and relatively easy to apply. We can find out the following information from this method:
a) Location and configuration of bed rock and geological structures in the subsurface.
b) The effect of discontinuities in rock mass may be estimated by comparing the in-situ compressional wave velocity with laboratory sonic wave velocity of intact drill core obtained from the same rock mass.
                RQD(5) = (Vi/Vl)^2 * 100
Where, Vi is the in-situ compressional wave velocity and Vl is compressional wave velocity in the intact rock core.

2. Volumetric Joint Count Method:
The RQD can be determined by counting the number of joints(discontinuities) per unit volume Jv.  A simple relationship(given by Palmstrom, 1982), RQD = 115 - 3.3*Jv , can be used to convert Jv into RQD for clay free rock masses.

Here Jv is the number of joints per cubic meter of the rock mass.
There are few other methods, which I shall cover up in the upcoming posts.

Thank You!