Posted in Academic Issues

The Last Supper, the Iranians and the Perfect Dissertation: A Maundy Thursday Reflection

In 2015 the PhD program I was going through nearly collapsed. We lost fifteen faculty members and key staff people in as many months. Needless to say, that produced consternation among the students, most of whom came from outside the United States. They did not understand our system (and honestly until I consulted with some officials of another university I didn’t either) required the University to support the program until the current students had graduated.

The exodus of faculty members created a great deal of empty office space. Like nature, bureaucracies abhor a vacuum, and my program director knew that, if he didn’t fill the office space, he would lose it. Since I was a faculty member (being faculty and student at the same time is as weird as it sounds) I got an office, the best one I ever had at UTC.

My office at UTC, where my Iranian colleagues admired the Last Supper sculpture on the top shelf.

One day one of my Iranian colleagues came to see me. She was going through the program with her husband. The two of them exuded the charm and sophistication that the Iranians are famous for. But she was drawn to the ceramic sculpture based on Leonardo da Vinci’s The Last Supper. It had been given to me when I was working for my church a decade earlier. You can see it in detail at the top of the post.

Not too long after that her husband came to see me. He too was drawn to the sculpture. I was amazed; the Iranians tended to be secular and this couple was from Isfahan, known for its own architecture.

We all eventually graduated and I retained the office for while. Eventually I was evicted; another Iranian colleague allowed me to split an office with him in another building, for which I was grateful because I was given no alternative. By then this person had become a Christian and had been baptized. In spite of the fact that yet another Iranian faculty colleague had assured me that this new building had “bad spirits” in it, we went forward.

But going back, to prepare for our dissertation defense, I attended a seminar where the Assistant Dean of the Graduate School, Dr. Randy Walker, assured us that he reviewed every dissertation and had never found one without a mistake. But our program director sent an email to all of us about my first office visitor:

I want to congratulate ________ for a first !!!!   I received word from Dr. Randy Walker that __________’s dissertation was the first and only dissertation/thesis that he has reviewed that did not require any revisions.

Dr. Walker retired after this.

Results of the shallow water equation, the subject of the perfect dissertation.

A perfect dissertation at the end of the long effort a PhD is not common. But a perfect work is not unique. Maundy Thursday is the day in the Christian calendar when the Last Supper of Jesus Christ and his disciples is commemorated. Shortly after that, he was arrested by the authorities and crucified the following day. But on the following Sunday he rose from the dead.

Perfection was part of his being: “We have, then , in Jesus, the Son of God, a great High Priest who has passed into the highest Heaven; let us, therefore, hold fast to the Faith which we have professed. Our High Priest is not one unable to sympathize with our weaknesses, but one who has in every way been tempted, exactly as we have been, but without sinning.” (Hebrews 4:14-15 TCNT) His action on the cross was likewise complete: “…for then Christ would have had to undergo death many times since the creation of the world. But now, once and for all, at the close of the age, he has appeared, in order to abolish sin by the sacrifice of himself.” (Hebrews 9:26 TCNT)

Perfection and completeness are hard to obtain in this life. But if we make Jesus Christ’s work on the cross our own, we too can have them in this life and the next.

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Posted in Academic Issues, Geotechnical Engineering, STADYN

Presentation of “Estimating Load-Deflection Characteristics for the Shaft Resistance of Piles Using Hyperbolic Strain Softening”

Last year we posted the paper Estimating Load-Deflection Characteristics for the Shaft Resistance of Piles Using Hyperbolic Strain Softening. Today it’s presented at the University of Tennessee at Chattanooga’s Research Dialogues, and a slide show of the presentation is below.

Posted in Academic Issues, Geotechnical Engineering

The Invertibility of the p-q Diagram System

We know that we can transform the traditional Mohr-Coulomb \sigma-\tau system to the p-q system by using the equations

p=1/2\,\sigma_{{1}}+1/2\,\sigma_{{3}}

and

q=1/2\,\sigma_{{1}}-1/2\,\sigma_{{3}}

Stated formally, this means that, for every set of principal stresses, there is a unique pair of p and q values.

But did you know you can go the other way, if you need to? Let’s start by putting these equations into matrix format, which yields

\left[\begin{array}{cc} 1/2 & 1/2\\ {\medskip}1/2 & -1/2 \end{array}\right]\left[\begin{array}{c} \sigma_{{1}}\\ {\medskip}\sigma_{{3}} \end{array}\right]=\left[\begin{array}{c} p\\ {\medskip}q \end{array}\right]

Inverting the matrix and premultiplying the right hand side yields

\left[\begin{array}{c} \sigma_{{1}}\\ {\medskip}\sigma_{{3}} \end{array}\right]=\left[\begin{array}{cc} 1 & 1\\ {\medskip}1 & -1 \end{array}\right]\left[\begin{array}{c} p\\ {\medskip}q \end{array}\right]

The inversion is the key step. The fact that the matrix is invertible, square and of the same rank as the vectors means that the transformation is linear, one-to-one and onto. We can also say that, for every set of p and q values, there is a unique set of principal stresses.

Those principal stresses are

\left[\begin{array}{c} \sigma_{{1}}\\ {\medskip}\sigma_{{3}} \end{array}\right]=\left[\begin{array}{c} p+q\\ {\medskip}p-q \end{array}\right]

As an example, consider the first set of p and q values computed in my original post on the subject. Substituting those into the last equation yields

\left[\begin{array}{c} \sigma_{{1}}\\ {\medskip}\sigma_{{3}} \end{array}\right]=\left[\begin{array}{c} 200\\ {\medskip}70 \end{array}\right]

which of course are the original values given.

Posted in Geotechnical Engineering

A Geotechnical View of the Effect of Explosions in the Earth

Certainly relevant with events in the Ukraine, from Tsytovich’s Soil Mechanics text:


Explosions may cause a whole series of rapid mechanical processes in soils: appearance of an explosion gas chamber within a rather short interval of time (sometimes a few thousandths of a second), which exerts an enormous pressure (of the order of a few hundred thousand atmospheres), causes the formation and propagation of explosion waves which change the stressed state of a soil mass and cause its particles to move with velocities varying from a few thousand metres per second to zero.

Explosion impulses are characterized by the maximum pressure p_{max} the rise time t_1 during which this pressure is formed, the fall time t_2 during which the pressure drops from the maximum to zero, and the total time of explosion action t_{\sigma} .

As seen from experiments of Prof. G. M. Lyakhov*, the gas chambers formed in soil through explosion of deep concentrated charges of explosives are almost spherical in shape. With time, a gas chamber (the cavity in soil) is destroyed, but the time period of its destruction may be very different , from a few minutes (in sands) to several months (in dense clays).

As has been shown by the experiments, the radius of an explosion gas chamber R_{ch} , after it has been formed completely, is determined by the following relationship:

R_{ch} = \aleph \sqrt{C}

where

  • C = weight of explosive charge, kg
  • \aleph  = proportionality factor depending on the properties of the soil

According to G. M. Lyakhov, numerical values of this factor are:

for saturated sands\aleph = 0.4-0.7
for loams (according to G. I. Pokrovsky)\aleph = 0.45
for loess soils\aleph = 0.35
for clayey soils\aleph = 0.6-0.7

Explosion of a concentrated charge in a soil results in the formation of normal (radial) pressures p , lateral (tangential) pressures p_{\tau} , and the motion of particles with a velocity u .

For non-saturated soils and rocks, all these three parameters are determined in calculations as functions of time, i.e.,

p = p(t);\,p_{\tau} = p_{\tau}(t);\,\dot u=\dot u(t)

For saturated soils and liquid media, it is sufficient to investigate only two of these parameters, for instance,

p = p(t);\,\dot u=\dot u(t)

The parameters of stress waves in soils caused by explosions and the parameters of velocities of their propagation are determined by special field tests. Using the results of such tests, empirical formulae are established for determination of the design parameters of explosion, waves in soils depending on the weight of charge, the distance from explosion centre, etc.

* Lyakhov G. M. Osnovy dinamiki vzryva v gruntakh i zhidkikh sredakh (Fundamentals of Dynamics of Explosion in Soils and Liquid Media), Moscow, Nedra Publishers, 1964.


Although geotechnical engineering has always had a military application (witness the prominence of documents such as NAVFAC DM 7 and the many others offered on this site,) this is the only elementary level soil mechanics text where I can recall seeing such a presentation.

Posted in Geotechnical Engineering

Free Gravity and MSE Wall Design Software – RRWall+ — GeoPrac.net

Designing gravity or MSE retaining walls with the attractive Redi-Rock precast modular block (PMB) facing just got a lot easier! The latest version of RRWall+ design software was created by Fine Software, GeoPrac.net sponsors, and […]

Free Gravity and MSE Wall Design Software – RRWall+ — GeoPrac.net