This document provides an overview of one-dimensional consolidation and settlement of fine-grained soils. It discusses key concepts such as effective stress, loading history, consolidation parameters, and the virgin consolidation line. An experiment is described to illustrate the basic concepts using a saturated clay sample between porous stones. Excess pore water pressures and soil settlement are monitored over time under applied loads. Primary consolidation involves water drainage and load transfer, while secondary compression involves ongoing fabric adjustment.
Introduction
Geostatic Stresses
Boussinesqâs Equation
Vertical Stresses Under A Circular Area
Vertical Stresses Under A Rectangular Area
Equation Point Load Method
Newmarkâs Influence Chart
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Geotechnical Engineering-II [Lec #17: Bearing Capacity of Soil]Muhammad Irfan
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Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Bearing capacity of shallow foundations by abhishek sharma ABHISHEK SHARMA
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elements you should know about bearing capacity of shallow foundations are included in it. various indian standards are also used. Bearing capacity theories by various researchers are also included. numericals from GATE CE and ESE CE are also included.
This ppt is more useful for Civil Engineering students.
I have prepared this ppt during my college days as a part of semester evaluation . Hope this will help to current civil students for their ppt presentations and in many more activities as a part of their semester assessments.
I have prepared this ppt as per the syllabus concerned in the particular topic of the subject, so one can directly use it just by editing their names.
Introduction
Geostatic Stresses
Boussinesqâs Equation
Vertical Stresses Under A Circular Area
Vertical Stresses Under A Rectangular Area
Equation Point Load Method
Newmarkâs Influence Chart
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Geotechnical Engineering-II [Lec #17: Bearing Capacity of Soil]Muhammad Irfan
Â
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Bearing capacity of shallow foundations by abhishek sharma ABHISHEK SHARMA
Â
elements you should know about bearing capacity of shallow foundations are included in it. various indian standards are also used. Bearing capacity theories by various researchers are also included. numericals from GATE CE and ESE CE are also included.
This ppt is more useful for Civil Engineering students.
I have prepared this ppt during my college days as a part of semester evaluation . Hope this will help to current civil students for their ppt presentations and in many more activities as a part of their semester assessments.
I have prepared this ppt as per the syllabus concerned in the particular topic of the subject, so one can directly use it just by editing their names.
Regarding Types of Foundation, Methods, Uses of different types of foundation at different soil properties. Methods of construction of different types of foundation, Codal Provisions etc.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Geotechnical Engineering-II [Lec #1: Shear Strength of Soil]Muhammad Irfan
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Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Methods to Determine the Immediate or Elastic Settlement (اÙÙØšÙØ· اÙÙÙرÙ)BahadarKhan8
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In this lecture I have Described the different methods to compute the immediate settlement in soils.
The methods described are Janbu & Bjerrum Method, Schmertmann's Method and Timoshinko & Goodier Method.
To watch videos please use the links below:
https://youtu.be/HULeW5TbyNw
https://youtu.be/8r0xfRoydk8
https://youtu.be/XplqYVOhPwg
TERZAGHIâS BEARING CAPACITY THEORY
DERIVATION OF EQUATION TERZAGHIâS BEARING CAPACITY THEORY
TERZAGHIâS BEARING CAPACITY FACTORS
Download vedio link
https://youtu.be/imy61hU0_yo
Geotechnical Engineering-II [Lec #22: Earth Pressure at Rest]Muhammad Irfan
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Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
This slide will help you to determine the immediate settlement for flexible foundation i.e. isolate footing and rigid foundation i.e. matt or raft foundation. To be more clear about the topic a numerical problem with the solution is given.
This presentation is all about consolidation of soil and it's importance in Civil Engineering, co-efficients of consolidation, methods of determining co-efficient of consolidation, Terzaghi's Spring Analogy, Terzaghi's Theory
Regarding Types of Foundation, Methods, Uses of different types of foundation at different soil properties. Methods of construction of different types of foundation, Codal Provisions etc.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Geotechnical Engineering-II [Lec #1: Shear Strength of Soil]Muhammad Irfan
Â
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Methods to Determine the Immediate or Elastic Settlement (اÙÙØšÙØ· اÙÙÙرÙ)BahadarKhan8
Â
In this lecture I have Described the different methods to compute the immediate settlement in soils.
The methods described are Janbu & Bjerrum Method, Schmertmann's Method and Timoshinko & Goodier Method.
To watch videos please use the links below:
https://youtu.be/HULeW5TbyNw
https://youtu.be/8r0xfRoydk8
https://youtu.be/XplqYVOhPwg
TERZAGHIâS BEARING CAPACITY THEORY
DERIVATION OF EQUATION TERZAGHIâS BEARING CAPACITY THEORY
TERZAGHIâS BEARING CAPACITY FACTORS
Download vedio link
https://youtu.be/imy61hU0_yo
Geotechnical Engineering-II [Lec #22: Earth Pressure at Rest]Muhammad Irfan
Â
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
This slide will help you to determine the immediate settlement for flexible foundation i.e. isolate footing and rigid foundation i.e. matt or raft foundation. To be more clear about the topic a numerical problem with the solution is given.
This presentation is all about consolidation of soil and it's importance in Civil Engineering, co-efficients of consolidation, methods of determining co-efficient of consolidation, Terzaghi's Spring Analogy, Terzaghi's Theory
This presentation includes Definition of Permeability, measurement of Permeability, Validity of Darcy's law, Darcy's Law, Methods of Finding Permeability, factors affecting permeability, Permeability of Stratified Soil
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Forklift Classes Overview by Intella PartsIntella Parts
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Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Student information management system project report ii.pdfKamal Acharya
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Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologistâs survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
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A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
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This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
2. 1. Introduction
ï¶ Load applied to soil from super structure through foundation
develops stress in the soil, cause compression of soil (volume
change).
ï¶ The contact pressure is not uniform, non- uniform compression is
occur, that causes tilting, example is leaning tower of Pisa, Italy.
ï¶ Under load, all soils will settle, causing settlement of structures
founded on or within them, related to displacement structures
undergo.
ï¶ If the settlement is not kept to a tolerable limit, the desired use of
the structure may be impaired and the design life of the structure
may be reduced.
ï¶ Structures may settle :
ï uniformly or
ï Non- uniformly : is called differential settlement
and is often the crucial design consideration.
ï¶ The total settlement usually consists of three parts
ï immediate or elastic compression
ï primary consolidation
ï secondary compression
3. 2. Basic Concepts
ï¶ Assumption on consolidation settlement development are:
ïA homogeneous, saturated soil.
ïThe soil particles and the water to be incompressible.
ïVertical flow of water.
ïThe validity of Darcyâs law.
ïSmall strains.
ï¶ conduct a simple experiment to establish the basic concepts of the
1D- consolidation settlement of fine-grained soils.
ï¶ Let us take a thin, soft, saturated sample of clay and place it
between porous stones in a rigid, cylindrical container whose
inside wall is frictionless (figure below. Next slide)
ï¶ The porous stones facilitate drainage of the pore water from the
top and bottom faces of the soil.
ï¶ The top half of the soil will drain through the top porous stone
and the bottom half will drain through the bottom porous stone.
4. 2. Basic Concepts
ï¶ A platen on the top of the top porous stone transmits applied loads to
the soil.
ï¶ Expelled water is transported by plastic tubes to a burette.
ï¶ A valve is used to control the flow of the expelled water into the
burette.
Fig. Experimental setup for illustrating basic concepts on
consolidation.
5. ï¶ Three pore water transducers are mounted in the side wall of the
cylinder to measure the excess pore water pressure near the porous
stone at the top (A), at a distance of one-quarter the height (B), and
at the mid-height of the soil (C).
ï¶ A displacement gauge with its stem on the platen keeps track of the
vertical settlement of the soil.
ï¶ We will assume that the pore water and the soil particles are
incompressible and the initial pore water pressure is zero.
ï¶ The volume of excess pore water that drains from the soil is then a
measure of the volume change of the soil resulting from the
applied loads.
ï¶ Since the side wall of the container is rigid, no radial displacement
can occur.
ï¶ The volume of excess pore water that drains from the soil is then a
measure of the volume change of the soil resulting from the
applied loads.
ï¶ Since the side wall of the container is rigid, no radial displacement
can occur.
2. Basic Concepts
6. ï¶ The lateral and the circumferential strains are then equal to zero
(ðð= ðð = 0) and the volumetric strain (ðð = ðð§ + ðð + ðð) is
equal to the vertical strain ðð§ =
âð§
ð»ð
where âð§ is the change in
height or thickness and ð»ð is the initial height or thickness of the
soil.
1. Instantaneous Load
2. Basic Concepts
fig. Instantaneous or initial excess pore water pressure when a vertical
load is applied
7. ïapply a load P to the soil through the load platen and keep the valve
closed.
ïno excess pore water can drain from the soil, the change in volume
of the soil is zero(âð = 0)
ï¶ The pore water carries the total head i.e.âð¢ð = âðð§ =
ð
ðŽ
or more
appropriately the change in mean total stress, âð =
âðð§+2âðð
3
Where âð¢ð = ðððð¡ððð ðððð ð€ðð¡ðð ðððð ð ð¢ðð
âðð§ = ðâðððð ðð ð¡âð ððððððð ð£ððð¡ðððð ð ð¡ððð ð
âðð = ðâððððð ðð ð¡âð ðð ð¡âð ðððððð ð ð¡ððð ð
ï¶ For our thin soil layer, we will assume that the initial excess pore
water pressure will be distributed uniformly with depth so that at
every point in the soil layer, the initial excess pore water pressure
is equal to the applied stress. For example if the
âðð§ = 100ððð, ð¡âðð âð¢ð = 100ððð
2. Basic Concepts
8. 2. Consolidation Under a Constant Load: Primary Consolidation
ï open the valve and allow the initial excess pore water to drain.
2. Basic Concepts
Excess pore water pressure distribution and settlement
during consolidation.
9. ï The total volume of soil at time ð¡1 decreases by the amount of
excess pore water that drains from it as indicated by the change in
volume of water in the burette.(fig. above)
ï At the top and bottom of the soil sample, the excess pore water
pressure is zero because these are drainage boundaries.
ï The decrease of initial excess pore pressure at the middle of the soil
(position C) is the slowest because a water particle must travel from
the middle of the soil to either the top or bottom boundary to exit the
system.
ï Most of the settlement of soil âð§ with time ð¡, occurs shortly after
the valve was opened and not linear.
ï Before the valve opened, an initial hydraulic head(
âð¢ð
ðŸð€
) was created
by the applied vertical stress.
ï When the valve opened, the initial excess pore water forced out of
the soil by this initial hydraulic head and with time, the initial
hydraulic decreases and, consequently, smaller amount of excess
pore water are forced out.
2. Basic Concepts
10. ï¶ We call the initial settlement response, soon after the valve was
opened, the early time response or primary consolidation.
ï¶ Primary consolidation is the change in volume of the soil caused by
the expulsion of water from the voids and the transfer of load from
the excess pore water pressure to the soil solid particles
3. Secondary Compression
ï Primary consolidation ends with âð¢ = 0
ï The later time settlement response is called secondary compression
or creep.
ï Secondary compression is the change in volume of fine-grained soils
caused by the adjustment of the soil fabric (internal structure) after
primary consolidation has been completed.
ï The rate of settlement from secondary compression is very slow
compared with primary consolidation.
ï In reality, the distinction is not clear because secondary compression
occurs as part of the primary consolidation phase especially in soft
clays.
2. Basic Concepts
11. 4. Drainage Path
ï It is the longest vertical path taken by water to exit the soil.
ï If we allowed the soil to drain on the top and bottom faces (double
drainage) ,the length of the drainage path, ð»ðð,is
ð¯ð ð =
ð¯ðð
ð
=
ð¯ð + ð¯ð
ð
where ð»ðð£ is the average height and ð»0 and ð»ð are the initial and final
heights, respectively, under the current loading.
ï If drainage were permitted from only one face of the soil, then
ð»ðð = ð»ðð£
5. Rate of Consolidation
ï The rate of consolidation for a homogeneous soil depends on the
soilâs permeability, the thickness, and the length of the drainage
path.
2. Basic Concepts
12. 6. Effective Stress Changes
According to the principle of the effective stress:
âðð
â²
= âð â âð
ïŒ Increases in vertical stresses lead to soil settlement caused
by changes to the soil fabric.
ïŒ As time increases, the initial excess water pressure
continues to dissipate and the soil continues to settle.
ïŒ After some time the initial excess pore water pressure in
the middle of the soil reduces to approximately zero and
the rate of decrease of the volume of the soil becomes very
small, and from the principle of effective stress all of the
applied vertical stress is transferred to the soil; i.e.
âðð
â²
= âðð
2. Basic Concepts
13. 7. Void Ratio and Settlement Changes Under a Constant Load
ï The initial volume (specific volume) of a soil is ðœ = ð + ðð where
ðð =initial void ratio.
ï Any change in volume of the soil âðœ is equal to the change in
void ratio âð .
ï Volumetric strain ðð=
âð
ð
=
âð
1+ðð
ï For one-dimensional consolidation, ðºð = ðºð
ï A relationship between settlement and the change in the void
ratio can be written as ðºð =
âð
ð¯ð
=
âð
ð+ðð
, âð = ð¯ð â
âð
ð+ðð
ï denote ððð for primary consolidation settlement rather than
âð
ððð= ð¯ð â
âð
ð + ðð
2. Basic Concepts
14. ï The void ratio at any time under load P is
ð = ðð â âð = ðð â
âð§
ð»
1 + ðð = ðð 1 â
âð§
ð»
â
âð§
ð»
ï For a saturated soil,ðð = ð€ðºð then, ð = ð€ðºð 1 â
âð§
ð»
â
âð§
ð»
2. Basic Concepts
8. Effects of Vertical Stresses on Primary Consolidation
15. ï By applying additional loads to the soil and for each load increment
we can calculate the final void ratio from ð = ðð 1 â
âð§
ð»
â
âð§
ð»
and
plot the results as shown by segment AB in figure (a)
ï The segment AB is called the virgin consolidation line or normal
consolidation line (NCL) & plotted from soil data test.
ï At point where soil reaches equilibrium under the previous loading
step to the vertical effective stress, ðâ²ð§ð,let us unload the soil
incrementally.
ï When an increment of load is removed, the soil will start to swell
by absorbing water from the burette.
ï The void ratio increases but the increase is much less than the
decrease in void ratio from the same magnitude of loading that was
previously applied.
ïŒ Now let us reload the soil after unloading it to ðâ²ð§ð .
ïŒ The reloading path CD is convex compared with the concave
unloading path, BC.
2. Basic Concepts
16. ï¶ We will represent the unloading-reloading path by an average
slope BC and refer to it as the recompression line or the
unloading-reloading line (URL).
ï¶ The path BC represents the elastic response while the path AB
represents the elastoplastic response of the soil.
ï¶ Loads that cause the soil to follow path BC will produce elastic
settlement.
ï¶ Loads that cause the soil to follow path AB will produce
settlements that have both elastic and plastic (permanent)
components.
ï¶ Unloading and reloading the soil at any subsequent vertical
effective stress would result in a soilâs response similar to paths
BCDE.
2. Basic Concepts
17. 9. Primary Consolidation Parameters
ï The primary consolidation settlement of the soil (settlement that
occurs along path AB in Figure can be expressed through the
slopes of the curves.
ï Two slopes for primary consolidation are coefficient of
compression or compression index,
ðð = â
ððâðð
ð¥ðšð
ððð
â²
ððð
â²
=
âð
ð¥ðšð
ððð
â²
ððð
â²
and
modulus of volume compressibility,
ðŠð¯ = â ðºð³ ðâ ðºð ð
ðâ²
ð ðâ ðð
â²
ð
= âðºð
ðâ²
ð ðâ ðð
â²
ð
2. Basic Concepts
18. ï Similarly, the slope BC in Figure the recompression
index, ð¶ð, which we can express as:
ðð = â
ððâðð
ð¥ðšð
ððð
â²
ððð
â²
=
âðð
ð¥ðšð
ððð
â²
ððð
â²
ï The slope BC in Figure the modulus of volume
recompressibility, ðððand is expressed as
ððð = â ðºð³ ðâ ðºð ð
ðâ²
ð ðâ ðð
â²
ð
=
âðºðð
ðâ²
ð ðâ ðð
â²
ð
From Hookeâs law:
ðžð
â²
=
âðð§
â²
âðð§
ð¡âðð , ðð£ð =
1
ðžð¶
â²
2. Basic Concepts
19. 10. Effects of Loading History
ï¶ If a soil were to be consolidated to stresses below its past maximum
vertical effective stress, then settlement would be small because the
soil fabric was permanently changed by a higher stress in the past.
ï¶ However, if the soil were to be consolidated beyond its past
maximum effective stress, settlement would be larger for stresses
because the soil fabric undergo further change from a current loading
ï¶ The practical significance of this soil behavior is that if the loading
imposed on the soil by a structure is such that the vertical effective
stress in the soil does not exceed its past maximum vertical effective
stress, the settlement of the of the structure would be small,
otherwise significant permanent settlement would occur.
ï¶ The preconsolidation stress defines the limit of elastic behavior.
ïFor stresses lower than the preconsolidation stress, the soil will
follow the URL and soil behave like an elastic material.
ïFor stresses greater than the preconsolidation stress the soil
would behave like an elastoplastic material.
2. Basic Concepts
20. 11. Overconsolidation Ratio
ï§ A soil whose current vertical effective stress or overburden effective
stress ðððis less than its past maximum vertical effective stress or
preconsolidation stress ðððis called as an over consolidated soil.
ï§ An over consolidated soil will follow a void ratio versus vertical
effective stress path similar to CDE during loading. (refer figure)
ï§ The degree of overconsolidation called, overconsolidation ratio, OCR,
is defined as ð¶ðªð¹ =
ððð
ððð
ï§ If OCR = 1, the soil is normally consolidated soil.
ï§ Normally consolidated soils follow paths similar to ABE (refer figure)
12.Possible and Impossible Consolidation Soil States
ï The normal consolidation line delineates possible from impossible soil
states.
ï Unloading of a soil or reloading it cannot bring it to soil states right of
the NCL, impossible soil states.
ï Possible soil states only occur on or to the left of the normal
consolidation line.
2. Basic Concepts
21. 3. Calculation of Primary Consolidation Settlement
1. Effects of Unloading/Reloading of a Sample Taken from Field
ï Consider a soil sample taken from the field at a depth z & assume the
groundwater level is at the ground surface.
ï The current vertical effective stress or overburden effective stress at z
is:ðð
â² = ðžððð â ðžð â ð³ = ðžâ²ð
a. Soil sample at a depth z below
ground surface.
b. Expected one-dimensional response.
22. ï The current void ratio can be found from ðŸð ðð¡
ï On a plot of e versus log ðâ² the current vertical effective stress
represented as in figure above
ï To obtain a sample, make a borehole and remove the soil above it.
ï The act of removing a soil reduces the total stress to zero; that is, the
soil is fully unloaded.
ï From the principle of effective stress ðð= ââðð
ï Since ð canât be -ve ,i.e., soil canât sustain tension â the pore water
pressure must be -ve.
ïŒ As the pore water pressure dissipates with time, volume changes
occur.
ïŒ If soil sample reload, the reloading path followed depends on the
OCR.
ïŒ If OCR=1 ,the path followed during reloading would be BCD
(Figure b) and the average slope ABC is Cr.
3. Calculation of Primary Consolidation Settlement
23. ï Once Ïzois exceeded, the soil follows the normal consolidation line,
CD, of slope Cc.
ï If OCR>1, the reloading path followed BEF because the soil is
reloaded beyond its preconsolidation stress before it behaves like a
normally consolidated line.
ï The average slope of ABE is Cr and the slope of EF is Cc.
ï The point E, marks the preconsolidation stress.
2. Primary Consolidation Settlement of Normally
Consolidated Fine-grained Soils
ï If a building constructed on a site consisting of a normally
consolidated soil, the increase in vertical stress due to the building at
depth z, where soil sample taken is âðð§
ï The final vertical stress is ðâ²ððð = ððð
â²
+ âðð
3. Calculation of Primary Consolidation Settlement
24. 3. Calculation of Primary Consolidation Settlement
ï The increase in vertical stress will cause the soil to settle following
the NCL and the primary consolidation settlement is:
ððð = ð»ð â
âð
1+ð
=
ð»ð
1+ð
ð¶ð log
ðððð
â²
ðð§ð
â² ; Where ðð¶ð = 1,
âð = ð¶ð â log
ðððð
â²
ðð§ð
â²
3. Primary Consolidation Settlement of Overconsolidated Fine-
grained Soils
ï If the soil is Overconsolidated, we have to consider two cases
depending on the magnitude of âðð§
ï§ Case-1 :In this case, consolidation occurs along the URL.
ððð = ð»ð â
âð
1 + ðð
=
ð»ð
1 + ðð
ð¶ð log
ðððð
â²
ðð§ð
; ðððð
â²
< ðð§ð
â²
ï§ Case-2 :In this case, we have to consider two equations, one
along the URL and the other along the NCL
ððð =
ð»ð
1 + ð
ðð« log
ððð
â²
ððð
â² + ðªð log
ðððð
â²
ððð
â² ; ðððð
â²
> ððð
â²
25. ððð =
ð¯ð
ð+ð
(ðð ð¥ðšð ð¶ðªð¹ + ðð ð¥ðšð
ðððð
â²
ððð
â² ); ðððð
â²
> ððð
â²
3. Calculation of Primary Consolidation Settlement
4. Procedure to Calculate Primary Consolidation Settlement
ï The procedure to calculate primary consolidation settlement is as follows:
1. Calculate the current vertical effective stress (ððð
â² ) and the current void ratio
(ðð) at the center of the soil layer for which settlement is required.
26. 2. Calculate the applied vertical stress increase (âðð§) at the center of
the soil layer using the appropriate method.
3. Calculate the final vertical effective stress ðððð
â²
= ðð§ð
â² + âðð§
4. Calculate the primary consolidation settlement.
ï If the soil is normally consolidated (ð¶ðªð¹ = ð ), the primary
consolidation settlement is ððð =
ð¯ð
ð+ð
ðªð ððð
ðððð
â²
ððð
â² ;
ï If the soil is Overconsolidated and ðððð
â²
< ððð
â² the primary
consolidation settlement is ððð =
ð¯ð
ð+ð
ðªð ððð
ðððð
â²
ððð
â² ;
ï If the soil is Overconsolidated and ðððð
â²
> ððð
â² the primary
consolidation settlement is ððð =
ð¯ð
ð+ð
(ðð ð¥ðšð ð¶ðªð¹ + ðð ð¥ðšð
ðððð
â²
ððð
â² );
ï± The primary consolidation settlement be calculated using mv
ððð = ð»ððð£âðð§ð
ï± However, unlike Cc, which is constant, mv varies with stress
levels.
ï± Compute an average value of mv over the stress rangesðð§ð
â² ð¡ð ðððð
â²
3. Calculation of Primary Consolidation Settlement
27. Example
1. The soil profile at a site for a proposed office building consists of a
layer of fine sand 10.4 m thick above a layer of soft, normally
consolidated clay 2 m thick. Below the soft clay is a deposit of coarse
sand. The groundwater table was observed at 3 m below ground
level. The void ratio of the sand is 0.76 and the water content of the
clay is 43%. The building will impose a vertical stress increase of
140 kPa at the middle of the clay layer. Estimate the primary
consolidation settlement of the clay.
Assume the soil above the water table to be saturated, ð¶ð = 0.3 and
ðºð = 2.7
28. example
2. Assume the same soil stratigraphy as in example 1. But now the
clay is Overconsolidated with an ðð¶ð = 2.5, ð€ = 38%, ððð ð¶ð =
0.05. All other soil values given in Example 1 remain unchanged.
Determine the primary consolidation settlement of the clay.
3. Assume the same soil stratigraphy and soil parameters as in
Example 2 except that the clay has an overconsolidation ratio of 1.5.
Determine the primary consolidation settlement of the clay.
29. 4. Terzaghi's One-dimensional Consolidation Theory
1. Derivation of Governing Equation
ïŒ Assumptions to derive Terzaghiâs 1D consolidation Equation:
1. The soil is saturated, isotropic and homogeneous
2. Darcyâs law is valid.
3. Flow only occurs vertically.
4. The strains are small.
ïŒ The basic concepts:
1. The change in volume of soil(âð) is equal to the change of pore
water expelled (âðð)which is equal to the change in the volume
of the voids(âð
ð£)
2. At any depth, the change in vertical effective stress is equal to the
change in excess pore water pressure at that depth.i.e. ððð§ = ðð¢
30. ï For soil element in figure the
inflow of water is= ð£ððŽ
and the outflow over the elemental
thickness ðð§ is ð£ +
ðð£
ðð§
ðð§ ððŽ
ï the flow rate is the product of the
velocity and the cross-sectional
area normal to its (velocity)
direction.
4. Terzaghi's One-dimensional Consolidation Theory
ïThe change in flow is then
ðð£
ðð§
ðð§ ððŽ
ïThe rate of change in volume of water expelled, which is equal to the
rate of change of volume of the soil, must equal the change in flow
ðð
ðð¡
=
ðð£
ðð§
ðð§ ððŽ ⊠⊠⊠⊠⊠.
ðð¢
ðð¡
= ð¶ð£
ð2ð¢
ðð§
ï This equation describes the spatial variation of excess pore water
pressure (âð¢) with time (t) and depth (z)
31. 2. Solution of Governing Consolidation Equation Using Fourier
Series
ï¶ The solution of any differential equation requires a knowledge of
the boundary conditions.
ï¶ By specification of the initial distribution of excess pore water
pressures at the boundaries, we can obtain solutions for the spatial
variation of excess pore water pressure with time and depth.
ï¶ Various distributions of pore water pressures within a soil layer are
possible.
ï± For Example
ï¶ Uniform distribution of initial excess pore water pressure with depth
ï¶ Triangular distribution of initial excess pore water pressure with depth
ï¶ The boundary conditions for a uniform distribution of initial excess pore
water pressure in which double drainage occurs are
4. Terzaghi's One-dimensional Consolidation Theory
33. ï¶ The boundary conditions for a uniform distribution of initial excess
pore water pressure in which double drainage occurs are
ï¶when ð¡ = 0, âð¢ = âð¢ð = âð¢ð§
ï¶At top boundary ð = 0, âð¢ = 0.
ï¶At bottom boundary, ð§ = 2ð»ðð, âð¢ = 0,
ð€âððð ð»ðð ðð ðððððððð ððð¡â ððððð¡â.
ï¶ A solution for the governing consolidation equation, which satisfies
these boundary conditions, is obtained using the Fourier series,
âð¢ ð§, ð¡ =
2âð¢ð
ð
ð ðð
ðð§
ð»ðð
â
ð=0 ðð¥ð âð2ðð£
where ð =
ð
2
2ð + 1 and ð is a positive integer with values from
0 ð¡ð â ððð
ðð£=
ð¶ð£ð¡
ð»ðð
2 where ðð£ is known as the time factor; it is a dimensionless
term.
4. Terzaghi's One-dimensional Consolidation Theory
34. 3. Degree of consolidation or consolidation ratio (ðŒð) - gives us
the amount of consolidation completed at a particular time and
depth.
ïThis parameter can be expressed mathematically as:
ðŒð = ð â
âðð
âðð
= ð â
ðâðð
ðŽ
ððð
ðŽð
ð¯ð ð
â
ð=ð
ððð âðŽðð»ð
4. Terzaghi's One-dimensional Consolidation Theory
An isochrones illustrating
the theoretical excess
pore water pressure
distribution with depth.
35. ï¶ ðð§ = 0 everywhere at the beginning of the consolidation(âð¢ð§ =
âð¢ð) but increases to unity as the initial excess pore water pressure
dissipates.
ï¶ A geotechnical engineer is often concerned with the average degree
of consolidation(U) of a whole layer at a particular time rather than
the consolidation at a particular depth(ðð§).
⢠The shaded area in Figure represents the amount of consolidation of
a soil layer at any given time.
4. The average degree of consolidation(U)
ïŒ U expressed mathematically from the solution of the one
dimensional consolidation equation as:
ð = 1 â
2
ð2
exp âð2ðð£
ð
ð=ð
ï¶ Consider the figure below shows the variation of the average degree
of consolidation with time factor ðð£ for a uniform and triangular
distribution of excess pore water pressure.
4. Terzaghi's One-dimensional Consolidation Theory
37. ⢠A convenient set of equations for double drainage, found by curve
fitting from above figure is
ð»ð =
ð
ð
ðŒ
ððð
ð
ððšð« ð < ðð%
ð»ð = ð. ððð â ð. ððð ð¥ðšð ððð â ðŒ , ðŒ ⥠ðð%
ðð£ = 0.197 corresponding to 50% and ðð£ = 0.848 corresponding to
90% consolidation are often used in interpreting consolidation test
results.
Example
4. Terzaghi's One-dimensional Consolidation Theory
38. 5. Secondary Compression Settlement
ï±consolidation settlement consists of two parts.
ï±The first part is primary consolidation, which occurs at early
times
ï±The second part is secondary compression, or creep, which
takes place under a constant vertical effective stress.
ï± Primary consolidation is assumed to end at the intersection of the
projection of the two straight parts of the curve as shown in Figure
Fig. Secondary
compression
39. ï§ The secondary compression index is
ðªð¶ = â
ðð â ðð
ððð
ð
ðð
=
âð
ððð
ð
ðð
; ð > ðð
ï§ Overconsolidated soils do not creep significantly but creep settlements
in normally consolidated soils can be very significant.
ï§ The secondary consolidation settlement is ðð ð =
ð»ð
1+ðð
ð¶ðŒ log
ð¡
ð¡ð
5. Secondary Compression Settlement
40. 6. One-dimensional Consolidation Laboratory Test
1. Oedometer Test- It is the 1D consolidation test, is used to find
ð¶ð, ð¶ð, ð¶ðŒ, ð¶ð£, ðð£ ððð ðð§ð
â²
ï¶Read the procedures in laboratory
2. Determination of the Coefficient of Consolidation
ï There are two popular methods to calculate ð¶ð£
a. Root time method: proposed by Taylor
ðªð =
ð. ðððð¯ð ð
ð
ððð
b. Log time method: proposed by Casagrande's and Fadum.
ïŒRead the procedure how we can determine ð¶ð£ using
these methods
ðªð =
ð. ðððð¯ð ð
ð
ððð
41. 3. Determination of Void Ratio at the End of a Loading Step.
To calculate the void ratio for each loading step as follows:
1. Calculate the final void ratio, ðððð = ð€ðºð
2. Calculate the total consolidation settlement of the soil sample
during the test, âð§ ððð = ðððððð â di where ðððð is the final
displacement gage reading and ðð is the displacement gage
reading at the start of the test.
3. Back-calculate the initial void ratio, ðð =
ðððð+
âðððð
ð¯ð
ðâ
âðððð
ð¯ð
4. Calculate e for each loading step
6. One-dimensional Consolidation Laboratory Test
42. 4. Determination of the Past Maximum Vertical Effective Stress
ï§ From e versus log ðð§ð
â² curve determine the preconsolidation stress
using a method proposed by Casagrande's.
ï§ The procedure, with reference to Figs. below, is as follows:
1. Identify the point of maximum curvature, point D, on the initial
part of the curve.
2. Draw a horizontal line through D
3. Draw a tangent to the curve at D.
4. Bisect the angle formed by the tangent and the horizontal line at D
5. Extend backward the straight portion of the curve (the normal
consolidation line), BA, to intersect the bisector line at F.
6. The abscissa of F is the past maximum vertical effective
stress= ðð§ð
â²
6. One-dimensional Consolidation Laboratory Test
43. Fig. Determination of the past maximum vertical effective stress using
(a) Casagrandeâs method.(b) simplified method
6. One-dimensional Consolidation Laboratory Test
44. 5. Determination of Compression and Recompression Indices
6. One-dimensional Consolidation Laboratory Test
6. Determination of the Secondary Compression Index
45. 7. Evaluation of Total Soil Settlement
⢠In general, the total settlement ðð¡ðð¡ðð total of a foundation can be
given as:ðð¡ðð¡ðð = ðð + ððð + ðð ð
where ðð = ðððð ð¡ðð ðð ðððððððð¡ð ð ðð¡ð¡ðððððð¡
ððð = primary consolidation settlement
Ïð ð = secondary consolidation settlement
ïŒ The immediate settlement is sometimes referred to as the elastic
settlement.
ïŒ In granular soils this is the predominant part of the settlement,
whereas in saturated inorganic silts and clays the primary
consolidation settlement predominates.
ïŒ The secondary compression settlement forms the major part of
the total settlement in highly organic soils and peats.
46. 8. Relationship Between Laboratory and Field Consolidation
ïŒ The time factor (TV) provides a useful expression to estimate the
settlement in the field from the results of a laboratory consolidation
test.
ïŒ If two layers of the same clay have the same degree of consolidation,
then their time factors and coefficients of consolidation are the same.
Hence,ðð£ =
ð¶ð£ð¡ ððð
ð»ðð
2
ððð
=
ð¶ð£ð¡ ððððð
ð»ðð
2
ððððð