Pavement Stress Analysis Software University of Florida.docx

Pavement Stress Analysis Software
University of Florida
Topic 2b – Pavement Stress Analysis Software
1. Multilayer Elastic Theory
E1, ν1
E2, ν2
E3, ν3
∞
h1
h2
a = radius
q = pressure
Point A
Point B
Assumptions (p. 60):
• Each Layer

– Continuous
– Homogeneous
– Isotropic
– Linearly Elastic
– Material is weightless & infinite in areal extent
– Finite thickness (except last layer)
Properties @ A = Properties @ B
Same properties in all directions
Hooke’s Law
�� =
1
�
�� − ν �� + ��
1. Multilayer Elastic Theory (cont.)
Assumptions (cont.):
• Load
– Circular
– Vertical
– Uniformly distributed
• Full friction between layers
–
• Each layer continuously supported
Point A

Point B
E1, ν1
E2, ν2
E3, ν3
∞
h1
h2
a = radius
q = pressure
Why do we want full
friction between layers?
2. Computer Program KENPAVE
Program should be on a CD at the back of your textbook
2.1 System
• Multilayer elastic analysis system

• Elastic theory assumptions apply
2.2 Loads
Circular, uniform pressure
PARAMETER ACTUAL LOAD
LOAD=0 Single wheel
LOAD=1 Dual wheel
X
Y X – Longitudinal (direction of traffic)
Y – Transverse
LOAD=2 Dual tandem
X
Y
YW
YW
XW

2.3 Material Properties
• Material types
– 1 = Linear elastic
– 2 = Nonlinear elastic
– 3 = Linear viscoelastic
– 4 = Combination of 2 & 3
t
ε
ε
σ
1
2
3
2.4 Procedure
• Create input file
– Use LAYERINP to define type of analysis, material,
thickness, load,
points of interest
• Perform the analysis
– Use KENLAYER to run the analysis

• Retrieve the output
– Output is stored in a .TXT file
– Spreadsheets are useful for post-processing and plotting
Sign convention:
– Positive (+) = Compression
– Negative (-) = Tension
Is there a way to find out?
2.5 KENLAYER Example 1
a = 5”
q = 100 psi
E3=10,000 psi ; ν3=0.45
E1=500,000 psi ; ν1=0.35
E2=50,000 psi ; ν2=0.40
∞
h1= 6”
h2= 12”
Given:
• Three-layer system
• Uniform circular load
• Linear elastic materials

Calculate:
• Maximum deflection
• Critical tensile strain
• Critical compressive strain
Where would the critical/maximum values occur?
– Maximum deflection δmax @ z=0
– Critical tensile strain εt @ bottom of AC layer
– Critical compressive strain εc @ top of subgrade
2.5 KENLAYER Example 1 (cont.)

• Single wheel load is analyzed in axisymmetric space
Output format:
Given:
• Dual wheel load
• Elastic material

∞
8”
4”
14” 4”
q=100 psi
a=4 in
E1=200,000 psi
ν1 =0.35
E2=15,000 psi
ν2 =0.45
E3=5,000 psi
ν3 =0.45
Plane of
Symmetry
x
xx
x
x
xx
x
x x x

x
Check output
2.6 KENLAYER Example 2
Calculate:
1. δmax
2. εt
3. εc
Where would the
critical/maximum
values occur?
• Dual wheel load is analyzed in spatial coordinates
Output format:

Which strain is considered critical for:
- Cracking?
- Rutting?
- At which location?
Output format:
• Results for each point (x,y) at each requested depth (z)
(x,y) z δ σz σ1 σ3 σ2 εh εz ε1 ε3 ε2
Point
No.
Vertical
Coord.
Vertical
Displ.
Vertical
Stress
Major
Principal
Stress
Minor
Principal
Stress
Interm.

Principal
Stress
Horizontal
‘Principal’
Strain
Vertical
Strain
Major
Principal
Strain
Minor
Principal
Strain
Interm.
Principal
Strain
Output format:
• Results for each point (x,y) at each requested depth (z)
τ
σσ1σ3 σ2
Principal stresses act on
planes where τ = 0

τmax
(x,y) z δ σz σ1 σ3 σ2 εh εz ε1 ε3 ε2
Point
No.
Vertical
Coord.
Vertical
Displ.
Vertical
Stress
Major
Principal
Stress
Minor
Principal
Stress
Interm.
Principal
Stress
Horizontal
‘Principal’
Strain
Vertical
Strain

Major
Principal
Strain
Minor
Principal
Strain
Interm.
Principal
Strain
�� =
�� − ��
2
Homework Assignment
a = 5”
q = 100 psi
E3=10,000 psi ; ν3=0.45
E1=1,000,000 psi ; ν1=0.35
E2=20,000 psi ; ν2=0.40
∞
h1= 6”

h2= 12”
Given:
• Uniform circular load
• Linear elastic materials
Calculate:
• Plot deflection basin
• Critical tensile strain
• Critical compressive strain
• Estimate the number of cycles to failure (Nf & Nd)
• Identify the dominant failure mode
• Compare results to Example 1
Response one-pol-07
Bureaucratic governance in the governance of a country is
largely assumed to cut across policy making and
implementation. While this is the basis of bureaucratic
functions, the role that bureaucracy plays in governance is of
greater significance. In the context of the mechanism within
which bureaucracy operates, the guiding rules on state
operations and citizen engagement are assessed. Basically,
bureaucracies have rules of how citizens’ requests are delivered
and attended to. In third world countries however, it is more
than evident that bureaucracy is responsible for huge economic
growth. This kind of success results from the structural
organization of bureaucracies that enables effective
implementation of policies and keen observance of the rules of
a bureaucracy. This is the ultimate mechanism through which
bureaucracies add value to governance (Atkinson & Coleman,
2012).
First of all, bureaucracies are small sections of governance, they

are not as big as the cabinets. Bureaucratic agencies in
themselves are independent but answerable to the president’s
office for all the operations. These agencies are justified by the
Congress acts and are entirely meant to disintegrate government
functions. As part of the executive branch, government parties
regulate the agencies. As an example, the Central Intelligence
Agency (CIA) is a ground breaking body in matters internal
security. Far from dealing with crime investigations, the CIA
helps in law enforcement, it executes diplomatic intelligence,
defense actions. It also tackles infrastructural development
(Atkinson & Coleman, 2012). This body acts under the defense
arm of the government and operates within the limits of this
arm. The heads of the CIA are appointed by the President
himself meaning that they report to him and execute the office’s
commands. This way, the CIA is run with the intent of
actualizing the ambitions set for national defense.
Unlike the large cabinets of the government, the CIA and other
bureaucratic agencies have specific tasks that are strategically
broken down. The CIA is mandated to use intelligence to collect
information of national interest. There are rules and guidelines
on how this is done so as to accommodate for the privacy of the
citizens. The CIA in Australia for instance operates so
dynamically to help in dealing with emerging security
challenges. This agency integrates a whole-some approach to
the issues of security. The inclusion of society, the government
and private bodies in implementation of pertinent policies
ensures higher levels of security within the nation. It is easy for
the bureau to coordinate distinct cultures, traverse business
practices and break prejudices so as to perform. The more
complicates tasks undertakes by the bureaucratic agencies is
paid off by higher performance in assuring state security.
The government constantly revises the laws guiding the defense
strategies just to keep up with the defense issues that arise. This
implies that the government is actually on the same level with
the agency. Both complimenting each other in the achievement

of state security. The operations of the CIA and other
bureaucratic agencies therefore stem from the government
objectives. The policy making process is monitored by the
government to ensure all is in accordance with the needs of the
citizenry and for the sake of realization of the cabinet goals. In
essence, bureaucratic agencies add significant value to
governance (Markusen, 2003). The focus on specific objectives
enables better focus on issues giving their specifics the
attention they deserve. In addition to this, the ability to merge
efforts from various groups also draws the support needed for
the government to serve its people.
References
Atkinson, M. M., & Coleman, W. D. (2012). Policy networks,
policy communities and the problems of
governance. Governance, 5(2), 154-180.
Markusen, A. R. (2003). The case against privatizing national
security. Governance, 16(4), 471-501.
Response two-pol-07
The Department of Education is one federal agency that plays a
vital role in the bureaucratic governance of our nation's
schools. It is an organization that is currently vital and vibrant,
and it is representative of what works with bureaucracies.
Even though the federal role in education is limited, the
complexity and size of the American Education system, over
66.2 million students, is such that it requires a civil service
organization to oversee its mission and its workings (U.S.
Department of Education, National Center for Education
Statistics 2016). The Department of Education provides the
hierarchical structure needed to provide accountability to the
state departments of education so that across our nation there is
both equity and equality in the education of our young people.
It provides the manpower to give the support "necessary to
implement and enforce federal law" (Grulke 2018). ESSA, the
2015 "bipartisan measure that reauthorizes the 50-year-old
Elementary and Secondary Education Act (ESEA), the nation’s
national education law and longstanding commitment to equal

opportunity for all students," is just one provision that the
Department of Education will help to oversee to ensure success
for students and schools ("Laws & Guidance”).
Another benefit of the bureaucratic governance of the
Department of Education is seen in its substantive rationality
(Thompson 2005). It represents positive values and ethics. The
mission of the DOE is "to promote student achievement and
preparation for global competitiveness by fostering educational
excellence and ensuring equal access" ("About ED”). It does
this by establishing policies for distributing federal aid for
education with a $68 billion dollar budget, collecting data on
America's schools, and focusing national attention on education,
and prohibiting discrimination (Ibid). All of these missions
show the socially embedded character of this agency.
The particular bureaucracy of the Department of Education is
also a benefit to the 3.6 million educational employees of our
nation us (U.S. Department of Education, National Center for
Education Statistics 2016). It provides workplace organization
models and structure for our nation's schools that holds to
conventional employment rules and career hierarchies. This is
one advantage of a bureaucracy when it come to their formal
emphasis on employees' education and work expertise. These
qualities are central for employment and promotion and "reduce
the risk of personal preferences and prejudices in recruitment,
rewards, and promotion"(Thompson 2005).
Finally, the bureaucracy of the Department of Education helps
to provide valuable resources to our nation with variety
information about grants, to financial aid, to research and
statistics, to policy and guidance, to programs and policies
("About ED"). It also "collects data and oversees research on
America's schools and disseminates this information to
Congress, educators and the general public" (ibid). Its
centralized location of information and its structure is
functional.
In short, the Department of Education is a valuable bureaucracy
that it is a working mechanism for governance.

"About ED.” U.S. Department of Education,
http://www.ed.gov.
Grulke, Eric, “Week 7: Bureaucracy: Open Systems Model."
American Military University,
https://edge.apus.edu/portal/site/366584/tool/ac046166-37b2-
492d-8e6e-b208146732e9
"Laws & Guidance." U.S. Department of Education,
http://www.ed.gov.
Thompson, Paul and Mats Alvesson (2005). "Bureaucracy at
Work." The Values of Bureaucracy. Paul Du Gay ed. chapter 4.
http://ezproxy.apus.edu/login?url=http://library.books24x7.com/
toc.aspx?bookid=12879
U.S. Department of Education, National Center for Education
Statistics. (2016). Digest of Education Statistics, 2015 (NCES
2016-014), Chapter 1 and 2.
Response three -pol-07
According to the American Heritage Dictionary defines
bureaucracy as, “an administrative system is one in which the
need or inclination to follow rigid or complex procedures
impedes effective action: innovative ideas that get bogged
down in red tape and bureaucracy, as well as, Administration of
a government chiefly through bureaus or departments that
are staffed with nonelected officials.”[1]
Heskett in his treatise on “How Much Bureaucracy is a Good
Thing in Government and Business?” quoted Hare and
Wittenberg: “(Bureaucracies) are far too often about themselves
and expanding their power and influence of the people who head
them.”[2] Those were my sentiments exactly. Quoting others,
he goes on to say that bureaucracies result in think groups who
disagree about how to get something done or what results that
they are looking for. Then that goes up the ladder to someone
who is a paper pusher and then the final decision goes to
someone who was not in the loop and is clueless about any of
the “roundtable discussions” (my words).[3]
One thing that Heskett points out is that voters like to hear the

new administration say that they are going to change the way
the last administration did things. Then the other thing voters
like to hear is that the new administration is going to shrink the
size of government and eliminate some departments. When
politicians talk about shrinking the size of government and
balancing the budget, voters will vote for the most likely
candidate to get that done. Heskett posits that is shy Donald
Trump was elected. Further, Heskett points to history which
shows us that when business men get elected, they are used to
getting things done and don’t have the quagmire of bureaucracy
in their business dealings. So when they are faced with each
bureaucratic quagmire, they cannot understand all of the layers
of bureaucracy and why they are necessary. Example of these
impediments would enormous amounts of meetings discussing
the same thing, “delays, decision screens, and minority vetoes.”
In our reading for this week, under the heading of “Defending
and Attacking Bureaucracy,”[4] there are two schools of
thought. One is that bureaucracies are the greatest things since
sliced bread and the opposing view, they are the worst thing
that can happen to an organization. Which is it? du Gay’s
research comes from old and outdated information. Let me
delineate the authors and years he is using to do his
research: Merton (1949), Blau (1955), Pugh et al (1969),
Mintzberg (1961), Burns and Stalker (1961), and Heydebrand
(1989) to name a few. In his “Concluding Comments,”[5] for
Chapter 4, du Gay says that to gain appreciation for
bureaucracies, more research is necessary.
Let me answer that with the Veterans Administration Health
Care system. That is a bureaucracy that is an example of
how not to run a health care system, that is a bureaucracy that
does not work, and that he government should not be in the
business of health care. Here is some information from the
Washington Post:
“Behind the door of Army Spec. Jeremy Duncan's room, part of
the wall is torn and hangs in the air, weighted down with black
mold. When the wounded combat engineer stands in his shower

and looks up, he can see the bathtub on the floor above through
a rotted hole. The entire building, constructed between the
world wars, often smells like greasy carry-out. Signs of neglect
are everywhere: mouse droppings, belly-up cockroaches, stained
carpets, cheap mattresses… This is the world of Building
18… The wounded manage other wounded. Soldiers dealing
with psychological disorders of their own have been put in
charge of others at risk of suicide. Disengaged clerks,
unqualified platoon sergeants and overworked case managers
fumble with simple needs… They do the paperwork, they lose
the paperwork. Then they have to redo the paperwork…Even the
stuff they've fixed has only been patched… many soldiers with
impaired memory from brain injuries sat for weeks with no
appointments and no help from the staff to arrange them… The
typical soldier is required to file 22 documents with eight
different commands -- most of them off-post -- to enter and exit
the medical processing world, according to government
investigators. Sixteen different information systems are used to
process the forms, but few of them can communicate with one
another. The Army's three personnel databases cannot read each
other's files and can't interact with the separate pay system or
the medical recordkeeping databases. The disappearance of
necessary forms and records is the most common reason soldiers
languish at Walter Reed longer than they should… Lost
paperwork for new uniforms has forced some soldiers to attend
their own Purple Heart ceremonies and the official birthday
party for the Army in gym clothes, only to be chewed out by
superiors.”[6]
Before President Trump, you could not fire anyone. There was
no accountability and as you can see, veterans were not getting
the care they needed, had to wait months to get an appointment
to see a doctor, or even get the medicine they needed.
Meanwhile, Walter Reed Hospital, as an example, was
crumbling. Doctors were earning $175,000 a year (How do I
know that? I took a call when I was working in a student loan
consolidation company and I had to obtain the prospect’s

current income) and there were roach and rat infestations. That
is bureaucracy in all its glory that has run amok.
Response four-pol-07
This is an interesting topic to consider given the current status
of bureaucracies under the Trump Administration. It is easy to
see that whatever the current President’s agenda or opinion is
on a topic can translate into more or less funding for those
specific bureaucracies. For an example, President Trump’s
opinion on climate change is reflected in the fact that his budget
proposal slashes the Environmental Protection Agency’s (EPA)
budget by nearly 23%(). Now I do not wish to debate the merits
of climate change, all I am saying is President Trump does not
value the EPA’s mission as others did and so he cutting that
particular regulatory bureaucracy by nearly a quarter of its
funding, resulting in less programs and responsibilities; or the
ability to successfully carry out their responsibilities. In
contrast, President Trump values the military and the United
States Department of Defense arguably the most. In last week’s
budget proposal, President Trump is asking for a nearly 74
billion dollar raise to the Department of Defense’s budget ();
bringing the total to almost 700 billion dollars. Again, I do not
wish to debate whether or not this is a good or bad thing, just to
show how that bureaucracy is alive and well.
As covered in our weekly lesson, bureaucracies are a very
important and powerful tool at the disposal of the President.
The President appoints individuals (confirmed by Senate) to
lead the numerous Cabinet positions, appoints chairpersons for
the regulatory boards (confirmed by the Senate), appoints
people to lead the “Government Corporations, and chooses who
serves in the White House (). This is a lot of power to have at
one’s disposal. Due to the nature of each Bureaucracy’s
responsibilities, the rules and regulations they pass and adopt
carry the weight of law (). These “laws” can be changed with
the swift stroke of a pen, but none the less, they have meaning
and can effectively assist in carry out the President’s agenda.

Just to further show how bureaucracies are still heavily valued
and play an important role in Washington, nearly 98% of all
Federal Government employees work within the Executive
Branch (). Again, looking at the Department of Defense’s
budget proposal, the money increase is attached to some goals
and tasks to be completed. As our lesson pointed out, measuring
the accomplishments of each bureaucracy can be very difficult
at times and lead to the negative connotations we have all heard
been given to bureaucracies. This vagueness and ambiguity can
be used by the President to either exploit the bureaucracy and
show why they is budget cuts or the President can exploit how
the bureaucracy has had great success using “hard to get
statistics”. This is why bureaucracies are still big players in
politics. They are still the main “vehicles” in which the
President uses at their sole discretion to carry out their agenda.
While Congress and the Courts still have oversight, it can be
very difficult to “police” all of the bureaucracies in existence;
remember, those other two branches only have 2% of all the
Federal Government employees to oversee the 98%....
References
Dennis, Brady. "Trump budget seeks 23 percent cut at EPA,
eliminating dozens of programs."
Washington Post. February 12, 2018. Accessed February 13,
2018. https://www.washingtonpost.com/news/energy-
environment/wp/2018/02/12/trump-budget-seeks-23-percent-
cut-at-epa-would-eliminate-dozens-of-
programs/?utm_term=.775f294ac5d3.
Grulke, Eric, “Week 7: Bureaucracy: Open Systems Model”,
American Military
University, accessed February 13,
2018, https://edge.apus.edu/portal/site/366584/tool/ac046166-
37b2-492d-8e6e-b208146732e9
Stone, Mike. "Trump proposes bigger budget for Pentagon,
nuclear arsenal." Reuters. February
12, 2018. Accessed February 13,
2018. https://www.reuters.com/article/us-usa-budget-

defense/trump-proposes-bigger-budget-for-pentagon-nuclear-
arsenal-idUSKBN1FW1YL.
President Trump signed the Veterans Accountability Act giving
veterans choice in their healthcare and the government the
ability to fire employees that can’t or won’t do their job.[7]
Why did it take an act of congress to provide the veterans what
they should have had all along? Because, and this bears
repeating, that is bureaucracy in all its glory that has run amok.
Trish
Sources:
American Heritage Dictionary
online, https://ahdictionary.com/word/search.html?q=bureaucrac
y&submit.x=37&submit.y=30, (accessed February 11, 2018).
Gay, Paul du. "Chapter 4 - Bureaucracy at Work:
Misunderstandings and Mixed Blessings," The Values of
Bureaucracy. Oxford University Press. (2005):
npn, Books24x7, http://common.books24x7.com.ezproxy1.apus.
edu/toc.aspx?bookid=12879, (accessed February 11, 2018).
Heskett, James L., “How Much Bureaucracy is a Good Thing in
Government Business?” Harvard Business School, Business
Research for Business Leaders, (January 4,
2017), https://hbswk.hbs.edu/item/how-much-bureaucracy-is-a-
good-thing-in-government-and-business, (accessed February 12,
2018).
Priest, Dana and Hull, Anne, “Soldiers Face Neglect,
Frustration at Army’s Top Medical Facility,” Washington
Post, February 18, 2007, http://www.washingtonpost.com/wp-
dyn/content/article/2007/02/17/AR2007021701172_5.html,
(accessed February 14, 2018).
Shane, III, Leo , “VA Backs Trump’s State of the Union
Comments About Accountability Law’s Impact”, Army Times,
(January 30,
2018), https://www.armytimes.com/news/2018/01/31/trump-
exaggerates-va-accountability-laws-impact-in-state-of-the-

union-address/, (accessed February 14, 2018).
Material Characterization
Topic 3 – Material Characterization – Soils and Granular Bases
Classification provides some insights on soil characteristics
and expected response in terms of:
• Modulus
• Strength
• Bearing capacity
• Particle structure (gradation)
• Moisture susceptibility
• Drainage
• Erosion potential
1 Soils
Why is it important to classify soils?
1.1 Soil Classification
Subgrade performance generally depends on:

• Load bearing capacity; subgrade must be able to support loads
passed on from the pavement structure
• Moisture content; it tends to affect a number of subgrade
properties including load bearing capacity
• Shrinkage and/or swelling; some soils shrink or swell
depending
upon their moisture content
1.1 Soil Classification (cont.)
Remedies for poor subgrade conditions:
• Remove and replace; subgrade soil can be removed and
replaced with higher quality fill
• Stabilization; adding an appropriate binder – such as lime,
Portland cement or emulsified asphalt – can increase subgrade
stiffness and/or reduce water susceptibility
• Additional base layers; include a subbase, or increase
thickness
of base

No pavement construction should proceed without a soil report
which should include the following:
• Soil boring logs of the subgrade material along the roadway
alignment at designated intervals with a specified maximum
depth of testing (usually 5 feet below the surface)
• Sieve analysis and Atterberg’s limit test to facilitate soil
classification
• Determination of the modulus of the subgrade and base
material
• Analysis of the water table fluctuations
Sieve Analysis
Atterberg’s Limits
AASHTO or USCS Classification System
USCS Soil Classification
Unified Soil Classification System (USCS) (ASTM D 2487)

Major Divisions Typical Names
Course-Grained Soils
≥50% retained on 0.075
mm (No. 200) sieve
Gravels
≥50% of course
fraction retained
on 4.75 mm
(No. 4) sieve
Clean Gravels
GW Well-graded gravels and gravel-sand mixtures, little or no
fines
GP Poorly-graded gravels and gravel-sand mixtures, little or no
fines
Gravels with
Fines
GM Silty gravels, gravel-sand-silt mixtures
GC Clayey gravels, gravel-sand-clay mixtures
Sands
≥50% of course
fraction passes
4.75 mm
(No. 4) sieve

Clean Sands
SW Well-graded sands and gravelly sands, little or no fines
SP Poorly-graded sands and gravelly sands, little or no fines
Sands with
Fines
SM Silty sands, sand-silt mixtures
SC Clayey sands, sand-clay mixtures
Fine-Grained Soils
≥50% passes 0.075 mm
(No. 200) sieve
Silts and Clays
LL ≤ 50%
ML Inorganic silts, very fine sands, rock four, silty or clayey
fine sands
CL
Inorganic clays of low to medium plasticity,
gravelly/sandy/silty/lean clays
OL Organic silts and organic silty clays of low plasticity
Silts and Clays
LL > 50%
MH
Inorganic silts, micaceous or diatomaceous fine sands or silts,
elastic silts

CH Inorganic clays or high plasticity, fat clays
OH Organic clays of medium to high plasticity
Highly Organic Soils PT Peat, muck, and other highly organic
soils
USCS Soil Classification (cont.)
Casagrande’s chart:
AASHTO Soil Classification
General Classification
Granular Materials (35% or less passing the 0.075 mm
sieve)
Silt-Clay Materials (>35%
passing the 0.075 mm sieve)
Group Classification
A-1
A-3
A-2

A-4 A-5 A-6
A-7
A-1-a A-1-b A-2-4 A-2-5 A-2-6 A-2-7
A-7-5
A-7-6
Sieve Analysis, % passing
2.00 mm (No. 10) 50 max … … … … … … … … … …
0.425 (No. 40) 30 max 50 max 51 min … … … … … … … …
0.075 (No. 200) 15 max 25 max 10 max 35 max 35 max 35 max
35 max 36 min 36 min 36 min 36 min
Characteristics of fraction passing 0.425 mm (No. 40)
Liquid Limit … … 40 max 41 min 40 max 41 min 40 max 41
min 40 max 41 min
Plasticity Index 6 max N.P. 10 max 10 max 11 min 11 min 10
max 10 max 11 min 11 min
1
Usual types of significant
constituent materials
stone fragments,
gravel and sand
fine
sand

silty or clayey gravel and sand silty soils clayey soils
General rating as a subgrade excellent to good fair to poor
• Penetration test (strength)
• Used for granular and fine-grained soils
• Load (pressure) is recorded
• Take the ratio to the bearing capacity of a standard rock
• Range: 0 (worst) – 100 (best)
1.2 California Bearing Ratio (CBR)
�� =
��0.1"��ℎ��
��
��0.1"��
��
1.2.1 California Bearing Ratio (CBR) Laboratory
Piston
Deflection dial (loading)

Deflection dial
(swelling)
Proctor
Ø = 6”
Sample 4.5”
Surcharge
(confinement)
• ASTM D 1883: Performed in the laboratory
• ASTM D 4429: Performed in the field
1.2.2 California Bearing Ratio (CBR) Field
Load
Deflection
measurement
Loading Plate
(Φ=10”)
• Determination of the bearing capacity (strength)

• Laboratory test @ different moisture contents
• Used for limestone, stabilized soils and materials encountered
in Florida
• Load (pressure) is recorded
• Take the ratio to the bearing capacity of a standard rock
1.3 Limestone Bearing Ratio (LBR)
�� =
��0.1"��ℎ��
��
800��(��)
�� ≈ 0.8 � ��
1.4 Stabilometer (R-value)
Pressure Gauge Testing
Head
Bottom
Plunger
Sample

Fluid under
pressure
(ph)
Apply a vertical pressure
and then measure the
resulting horizontal
pressure (reaction)
pv
• Resistance (internal friction) value determined by stabilometer
• Laboratory test for granular materials and asphalt mixtures
• Apply vertical pressure
• Measure horizontal pressure induced in the fluid
1.4 Stabilometer (R-value)
pv & ph = Vertical and horizontal pressure respectively
D2 = displacement of stabilometer fluid to increase ph from 5 to
100 psi, measured in revolutions of a calibrated pump handle
� = 100 −
100

2.5
��
�
��
��
− 1 + 1
1.5 Triaxial Test
Sample
= Confining Pressure (σ2, σ3)
= Deviator Stress (σd)
σ1
σ2
σ3
In Triaxial cell
(cylinder): σ2=σ3
Deviator Stress:
Axial stress in excess of the
confining pressure in Triaxial cell
σ3

σd
σ1
�� = �� − ��
• Laboratory test for granular materials (including asphalt
mixtures) and fine-grained soils
1.5 Triaxial Test (AASHTO 307-ASTM D5311)
εp,2
1.5.1 Triaxial Test on Granular Soils
• Effect of confinement on modulus
Triaxial test #1 (σ3,1)
D
e
v
ia
to
r
st
re

ss
(
σ
d
)
ε
Triaxial test #2 (σ3,2)
σ3,2 > σ3,1
MR,1
MR,2
εp,1 εr,1
εr,2
εr,2 < εr,1
��,� =
σ�
��,�
��,� =
σ�
��,�
MR,2 > MR,1

• For granular soils:
– MR = function of confinement
• Triaxial tests are performed at certain levels of confining
pressure and vary the deviator stress (σd)
– k1 & k2 experimentally determined values
log θ or s3
lo
g
M
R
k2
xk1
MR = k1 · s3
k2
MR = k1 · q
k2
State of confinement defined by
the first stress invariant:
θ = σ1 + σ2 + σ3
20

MR = k1 · θ
k2
MR =3960 · θ
0.35
AI suggests:
• σ3=σ2=2 psi
• σd=σ1-σ3=6 psi
θ=12 psi
• Example:
k1 = 3960
k2 = 0.35
MR =9450 psi
• Effect of deviator stress on modulus
D
e
v
ia
to

r
st
re
ss
(
σ
d
)
ε
MR,1 MR,2 < MR,1
1.5.2 Triaxial Test on Fine-grained Soils
MR,2
k2
k1
k3
k4
• For fine-grained (cohesive) soils:
– MR = function of deviator stress (σd)

• Run triaxial tests at certain values of deviator stress and vary
the confining pressure
– k1, k2, k3 & k4 experimentally determined values
�� = �� + �� − ��
�� = �� − �� − ��
∀ �� ≤ ��
∀ �� > ��
σd
M
R
• Example:
�� = �� − �� − �� = 5600 − 388 � 6 − 5.2 =
5290��
AI suggests:
• σ3=σ2=2 psi
• σd=σ1-σ3=6 psi
σd > k2

1.6 Design Resilient Modulus (Soils)
1.6.1 Correlations
Maybe there is information
already available
Asphalt Institute Conversions:
• MR=1500·(CBR)
• MR=1155+555·(R)
Obtaining MR from a series
of different test types
Source:
Guide for Mechanistic Empirical
Design of New and Rehabilitated
Pavement Structures
Appendix CC-1 (ARA, 2001)
1.6.1 Correlations (cont.)
1.7 Plate Loading Test
Reaction (Steel Beam)

Δ
Pressure Gauge
Deflection Dial @ 1/3 Points Hydraulic Jack
� =
�
∆
• Deflection measurements are used to estimate modulus
• Field test
• Used for granular and fine-grained soils
• Best way to obtained a single value for design
• Modulus of subgrade reaction:
Plate (Φ=30”)
1.7 Plate Loading Test (cont.)
Modulus of subgrade reaction: � =
�
∆
Resilient modulus (rigid plate): �� =

�
2
1 − ν� ��
∆
Substituting Δ from MR into k: � =
2
�
��
1 − ν� �
For a 30-in plate (ν=0.45): � ��/�� =
�� /��
�
18.8
1.7.1 Modulus of subgrade reaction-resilient modulus
relationship
• Penetration test (strength)
• Field test
• Used for sands and fine-grained soils
• Drop a hammer and record penetration vs. #blows

1.8. Dynamic Cone Penetrometer
1.8.1 DCP Index conversion to CBR
Source:
Predicting California Bearing Ratio
from Trafficability Cone Index Values
(Shoop et al., 2008)
1.9 Water Table Elevation
Installation of a piezometer in the soil with a perforated pipe
after a continuous flight auger drills a hole into the ground
1.10 Subgrade Seasonal Variations
Normal MR
50,000 psi
Frozen MR
Thaw MR

Freeze
Time
Thaw
Time
Recovery
Time
Normal
Time
Total Time = 12 Months
MR
Time
2 Asphalt mixtures
2.1 Components
Topic 3 – Material Characterization – Asphalt mixtures
2.2 Superpave Performance Grade System for Asphalt Binders
• Asphalt binder: black sticky substance composed of high-
molecular-weight hydrocarbons; results from distillation of
crude oil
• Rheological characterization tests:

2.2 Superpave Performance Grade System for Asphalt Binders
• Grading is based on climate:
PG 64—22Performance Grade
Average 7-day maximum
pavement temperature
(@20 mm below surface)
Minimum pavement
temperature
(@ surface)
2.3 Purpose of Asphalt Mixtures
• Riding surface:
- Smooth
- Safe (friction)
• Distribute stresses (protect subgrade)
• Resist loads without excessive permanent deformation

• Remove water
- Impermeability
- Specialty mixtures (OGFC)
2.4 Resilient Modulus (MR)
Time
S
tr
e
ss
(
σ
)
Time
S
tr
a
in
(
ε
)

εr = resilient
(recoverable)
εp = permanent
Type and duration of loading
is supposed to simulate that
occurring in the field
• Typical response of materials under repeated loading:
�� =
σ
��
2.5 Dynamic Modulus (|E*|)
Time
σ
Time
ε
• Specimens subjected to cyclic (sinusoidal) loading:
�∗ =
σ�

��
σ0
ε0
Δt
� =
∆�
�
� 2�
T
2.6 Fatigue testing
εt
Why 3rd-point loading?
To have an even distribution
of M; we know the value of
M, no matter where the
specimen fails
V
M
�� = �
1

��
�� 1
��
��
2.6 Fatigue testing (cont.)
2.6.1 Constant Stress (Load) Fatigue Test
• Apply constant stress (load)
• Failure occurs when the material fractures
σ0
S
tr
e
ss
,
σ
Number of Cycles, N
S
tr

a
in
,
ε
Number of Cycles, N
ε0
• More representative of pavements with thick asphalt layer
2.6.2 Constant Strain (Deformation) Fatigue Test
• Apply constant strain (rate of deformation)
• Failure occurs when E=½E0
S
tr
e
ss
,
σ
Number of Cycles, N
S
tr

a
in
,
ε
Number of Cycles, N
ε0
σ0
• More representative of pavements with thin asphalt layers
2.6.3 Fatigue Test Analysis
• Plot the strain VS number of repetitions to failure on log
scales
• C1 & C2 curves for different material/temperature
S
tr
a
in
,
L
o
g
ε

t
Number of Cycles, Log Nf
Which curve has the highest stiffness?
Check:
• Select a strain level
• Find the corresponding Nf
• Higher stiffness will have less
number of cycles to failure
C1
C2
Nf1Nf2
Low
High
From the graph:
• Stiffness of the material will depend on time of the year
(temperature)
• εt depends on the material properties (E)
• So, the cycles to failure Nf will also depend on the
temperature
Must use cumulative damage approach to evaluate failure

What material properties do we used for design?
• Most paving materials are non-linear and experience some
permanent deformation (not elastic) after each load
application
• If the load is small compared to the strength of the
material and is repeated for a large number of cycles, the
deformation is almost fully recoverable and the response
can be considered elastic
Topic 3 – Material Characterization – Summary
3 Summary
Flexible Pavement Stress Analysis
Topic 2 – Flexible Pavement Stress Analysis
Need to predict & understand stress/strain distribution within
the pavement structure as they (σ & ε) relate to failure (mainly
cracking & rutting)
Numerical Models
• Need model to compute deflections (δ) and strains (ε)
• Numerous models available with different:
– Capabilities
– Underlying assumptions

– Complexity
– Material information requirements
IDEAL MODEL
What would be an
ideal model?
Predicts Input Parameters
• Stresses
• Strains
• Static & dynamic loads
• Material properties
• Traffic
• Environment
No current model meets these requirements!
However, can obtain
reasonable estimates!
1. Available Models
Most widely used
• Reasonable Results
• Properties Relatively Simple to Obtain
• Multilayer Elastic Theory (MLET)
• Finite Element Methods
• Viscoelastic Theory (time and temp.-dependent behavior)

• Dynamic Analysis (inertial effects)
• Thermal Models (temperature change)
How do we get E? Before
& after construction
E &
Before: lab testing (MR)
After: field testing (FWD)
Units Guidelines
• Stress:
– Reported in psi:
• Strain:
– Reported in με:
• Deflections:
– Reported in mils:
For homework, exams, and projects, you are expected to
convert all of your answers to these units.
�� =
��
��
�� = 10�

�
��
�� = �� = 10��
�� =
��
1000
��
10
2. One-layer System
2.1 Based on Boussinesq (1885)
Half-space: infinite
area & depth
Z
σz
σz
X
P
r

zσz
Point load on an elastic half-space
• Examine σ distribution along Z & X
Where:
– σz = Vertical stress
– r = Radial distance from load
– z = Depth
– P = Point load
Notice that the stress distribution is
independent of material stiffness (E)
�� =
3
2�
�
1
1 +
�
�
�
�
�
�
�
��

What does a load from a tire look like?
Contact area
What shape do we use for stress analysis in MLET?
Why a circle?
What shape do we use for stress analysis in MLET?
a
q
• Where:
– q = intensity or
uniform pressure
– a = radius

2.2 One-layer
Solution
s (Foster & Ahlvin)
Figures 2.2 – 2.6
• Axisymmetric loading:
– σz = Vertical stress
– σr = Radial stress
– σt = Tangential stress
– τrz = Shear stress
– w = Deflection
• Pre-solved @ radial distances
a

q
02a 1a3a
0
2a
1a
Offset
D
e
p
th
2a
q
z
r

σz
σr σt
τrz
2.2 One-layer

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