Adapting Graphical Coulomb Methods to Numerical Solutions p.10-1 Chapter 10: Adapting Graphical Coulomb Methods to Numerical Solutions By Karl Hanson, S.E., P.E.* August 2012 10.1 Introduction: Many of the design approaches that we use today to design walls, foundations and excavation bracing originated from Coulomb’s stability methods developed in 1796. One of the earliest known physicists, Coulomb is also famously responsible for his discoveries in the field of electricity. Today, we understand that Coulomb’s soil pressure theories are based on energy principles. In Coulomb’s day and age, the concept of energy was not quite articulated as well as today. Charles Coulomb (1736-1806) What became known as “Coulomb’s Theory” was soon adapted into graphically based methods. Using a pencil and paper and drafting board, a solution for either active or passive wall force can be determined. The “answer” for a force against a wall is measured from the drawing. These methods are tedious, yet they clearly demonstrate failure planes. The appeal of these methods has been lost, since the accuracy of the answer literally depends on how well one draws and how sharp a pencil is used! Notably, the father of soil mechanics, Karl Terzaghi, routinely used these graphical methods to develop his geotechnical theories on many subjects. In Terzaghi’s 1943 book, “Theoretical Soil Mechanics” (Ref 1), he derived a theory for soil bearing failure, by treating the soil mass under a footing as similar to the problem of passive pressure against a wall. In connection with the bearing capacity problem, Terzaghi wrote: “…the computation of the critical load…requires the determination of the component of… the passive earth pressure which requires several hours of work.” (meaning hours of drawing and re-drawing failure planes) Karl Terzaghi (1883-1963) To expedite the use of his theories, Terzaghi opted for a “simplified” bearing pressure equation, which did not require graphical methods. This trend has continued, perpetuating various forms of bearing pressure equations developed by researchers, typically derived from the Theory of Plasticity (Ref 4). Why not “dust off” these old methods, and use our computers to construct the graphics? Today, we have an opportunity to resurrect these old graphical methods, adapting them to numerically based solutions. Perhaps, with these methods, engineers can better visualize soil failure mechanisms for the structures which we design. (* DesignCalcs, Inc., http://www.designcalcs.com)
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Adapting Graphical Coulomb Methods to Numerical Solutions
p.10-1
Chapter 10: Adapting Graphical Coulomb Methods to Numerical Solutions By Karl Hanson, S.E., P.E.*
August 2012
10.1 Introduction:
Many of the design approaches that we use today to design walls,
foundations and excavation bracing originated from Coulomb’s
stability methods developed in 1796. One of the earliest known
physicists, Coulomb is also famously responsible for his discoveries
in the field of electricity.
Today, we understand that Coulomb’s soil pressure theories are
based on energy principles. In Coulomb’s day and age, the concept
of energy was not quite articulated as well as today.
Charles Coulomb
(1736-1806)
What became known as “Coulomb’s Theory” was soon adapted into graphically based
methods. Using a pencil and paper and drafting board, a solution for either active or
passive wall force can be determined. The “answer” for a force against a wall is measured
from the drawing. These methods are tedious, yet they clearly demonstrate failure planes.
The appeal of these methods has been lost, since the accuracy of the answer literally
depends on how well one draws and how sharp a pencil is used!
Notably, the father of soil mechanics, Karl Terzaghi, routinely used
these graphical methods to develop his geotechnical theories on many
subjects. In Terzaghi’s 1943 book, “Theoretical Soil Mechanics” (Ref
1), he derived a theory for soil bearing failure, by treating the soil mass
under a footing as similar to the problem of passive pressure against a
wall. In connection with the bearing capacity problem, Terzaghi wrote:
“…the computation of the critical load…requires the determination of
the component of… the passive earth pressure which requires several
hours of work.” (meaning hours of drawing and re-drawing failure
planes)
Karl Terzaghi
(1883-1963)
To expedite the use of his theories, Terzaghi opted for a “simplified” bearing pressure
equation, which did not require graphical methods. This trend has continued, perpetuating
various forms of bearing pressure equations developed by researchers, typically derived
from the Theory of Plasticity (Ref 4).
Why not “dust off” these old methods, and use our computers to construct the
graphics? Today, we have an opportunity to resurrect these old graphical methods,
adapting them to numerically based solutions. Perhaps, with these methods, engineers can
better visualize soil failure mechanisms for the structures which we design.
(* DesignCalcs, Inc., http://www.designcalcs.com)
Adapting Graphical Coulomb Methods to Numerical Solutions
p.10-2
10.2 The Physics Behind Energy Principles:
We begin this discussion by asking, “What is energy?” The term “energy” is now so
common place in our language, it’s something that we take for granted. Putting aside
modern day concepts represented in advertising, we need to define energy using the
language of physics.
Leibniz was the first to note the importance of the kinetic
energy term, “mv2”. Also, about the same time, Newton, in his
“Third Law of Motion”, implicitly stated the whole doctrine of
energy. It wasn’t until 1807 that the term “energy” was first
coined by Thomas Young.
Maxwell explained energy principles as follows:
“(Energy)..has no individual existence…The transactions of
the material universe appear to be conducted, as it were, on a
system of credit. Each transaction consists of the transfer of so
much credit or energy from one body to another. This act of
transfer or payment is called work.” (Ref 2)
James Clerk Maxwell
(1831-1879)
Various Forms of Energy
Kinetic Energy The most obvious type of energy is
kinetic energy:
A mass, “m”, moving at a velocity, “v”,
has kinetic energy,
K.E. = ½*mv2
Potential
Energy
A more complex form of energy is the
potential energy stored in a spring:
A spring with force, “F”, compressed
“D” has potential energy,
P.E.=1/2*F*D
Other Energies Even less obvious forms of potential energy are chemical energies,