Page at Parker Executive Search to submit application. Using a search firm is standard practice at UTC for Dean and higher positions. My experience with other academic searches in this state tells me that one reason they do this is to deal with applicants confidentially, something that is tricky to do with Tennessee’s open records laws.

There is one requirement that merits some comment:

A demonstrated record of intentional and successful actions to foster and enhance inclusion, equity, and diversity…

And this:

UTC takes its commitment to inclusion, equity, and diversity seriously. Letters of interest and other application materials should specifically address the candidate’s intentional and systematic initiatives and accomplishments related to that commitment.

The College of Engineering and Computer Science (including the current Dean) has the most ethnically diverse faculty on campus. This is something the administration does little to publicize.

You can link to Parker’s website to submit an application. If you would like to ask me questions about this, you can go to the Contact page to reach me.

In our very popular post Analytical Boussinesq Solutions for Strip, Square and Rectangular Loads we discuss the use of the theory of elasticity (as originally formulated by Boussinesq) to estimate the stresses and settlements under foundations. We start by giving methods of estimating the stresses under various configurations of rectangular foundations (the circular ones are discussed in the post Going Around in Circles for Rigid and Flexible Foundations.) We then show the use of superposition to expand the use of these results for complex foundations (with further discussion in our post Superposition, and Using Point Loads in Place of Distributed Ones.) We then show the estimation of deflections for simple rigid and flexible foundations. But when it comes to deflections for more complex situations…crickets.

This post is an attempt to solve the “crickets” problem through the use of a method shown in Tsytovich (1976). It’s doubtless useful for preliminary calculations and to enhance our understanding of how settlements of foundations in one place can affect adjacent structures. It also uses some of the linkage between elastic and consolidation settlement theory which is discussed in From Elasticity to Consolidation Settlement: Resolving the Issue of Jean-Louis Briaud’s “Pet Peeve”.

Let us start with Equation (4) of the last linked post, namely

(1)

where we swap p for as the vertical pressure.

Now let us define an equivalent height h_{eq}. Keep in mind that we are assuming that the soil’s reaction to vertical pressure is that of a laterally confined specimen; the equivalent height is the height of that equivalent specimen. Multiplying both sides of Equation (1) by this equivalent height,

(2)

Since by definition

(3)

where s is the settlement, Equation (1) becomes

(4)

Equation (7) of the last linked post tells us that

The value of is discussed in that post for squares and rectangles and for circles in Going Around in Circles for Rigid and Flexible Foundations. These are very complex (and in the case of circles have no closed form solution.) For convenience the table for these is reproduced below.

If we equate the right hand sides of Equations (8) and (9) and solve for h_{eq}, we have at last

(10a)

We can also substitute Equation (7) into Equation (10a) and obtain

(10b)

If we define

(10*)

we can also write the equation thus

(10c)

It should be evident that there are several computational routes to obtain the equivalent height, which is then substituted into Equation (8) to obtain the settlement. Let us consider these options:

We could tabulate values of for various foundation configurations and then use these to compute the equivalent height using Equation (10c). This is given in Tsytovich (1976).

We could determine values for (it is simply a function of Poisson’s Ratio ), obtain using the table above and then compute the equivalent height using the width of the foundation . Values for both and are shown in graphical form as a check for computations.

We could perform direct substitution into Equations (10a) or (10b.) Equation (10a) is probably the best as it will be necessary to compute using Equation (7).

The complete solution is given in the same spreadsheet as the solution for the stress problem, which you can access here. The geometry is the same and the loading is the same: 5 kPa on the yellow (2 m x 10 m foundation) and 15 kPa on the brown foundation (2 m x 6 m.) Keep in mind that, for this method, the value b is always the smaller of the two, and that goes for the “void” foundations as well.

We do not need the depth from the surface; we are only interested in surface deflections. We do need the elastic modulus and Poisson’s Ratio of the soil, which are E = 10,000 kPa and ν = 0.25.

The superposition is exactly the same as before, using the following diagram as before:

The superposition scheme is as follows:

Yellow Foundation Positive, corners ABFG, pressure +5 kPa

Yellow Foundation Negative, corners ABJH, pressure – 5kPa

Brown Foundation Positive, corners ACEG, pressure +15 kPa

Brown Foundation Negative, corners ABFG, pressure – 15 kPa

We will only go through the calculations for the first one; you can view the spreadsheet for the rest. We proceed as follows:

We compute A and β as follows:

From Equation (10*), A = (1-0.25)^{2}/(1-(2)(0.25)) = 1.125

From Equation (7), β = 1-(2)(0.25)^{2}/(1-0.25) = 0.833

You can verify these using the plot of these parameters.

We compute the coefficient of volume compressibility by using Equation (5), m_{v} = 0.833/10000 = 0.0000833 1/kPa

We then use Equation (10c) to compute the equivalent height, thus h_{eq} = (1.125)(0.71)(6) = 4.8 m. This value will be different for each corner point considered.

Using Equation (8), the settlement for this portion of the analysis is s = (4.8)(5)(0.000083333) = 0.002 m = 1.998 mm.

You repeat this process for all four “foundations.” Keep in mind that the negative foundations will result in negative settlements. A summary of the results is as follows:

Every now and then something comes up that you really didn’t expect. That took place with a paper published this year cited “W.J. Lu, B. Li, J.F. Hou, X.W. Xu, H.F. Zou, L.M. Zhang, “Drivability of large diameter steel cylinders during hammer-group vibratory installation for the hong kong–zhuhai–macao bridge,” Engineering (2022), doi: https://doi.org/10.1016/j.eng.2021.07.028.” (You can […]

It’s happened again: the paper “Vibratory and Impact-Vibration Pile Driving Equipment” has been cited by Mohammed Al-Amrani and M Ikhsan Setiawan in their paper “Prefabricated and Prestressed Bio-Concrete Piles: Case Study in North Jakarta.” The abstract of their paper is here: In this research, we will talk about Prefabricated and Prestressed Concrete piles in general and […]

This is the last (hopefully) post in a series on consolidation settlement. We need to start by a brief summary of what has gone before. Note: the material for this derivation and those that preceded it have come from Tsytovich with some assistance from Verruijt.

where E is the modulus of elasticity and is a factor based on Poisson’s Ratio and includes the effects of confinement, be that in an odeometer or in a semi-infinite soil mass. We also showed that, for a homogeneous layer,

(2)

where is the settlement of the layer, is the thickness of the layer and is the uniaxial stress on the layer. The problem is that is not constant, and the settlement more accurately obeys the law

(3)

where is the compression index, is the initial void ratio of the layer, is the change in pressure induced from the surface, and is the average effective stress in the layer.

Turning to the post Deriving and Solving the Equations of Consolidation, we first determined that the change in porosity could, for small deflections, be equated to the change in strain . From this we could say that

(4)

The change in porosity, for a saturated soil whose voids are filled with an incompressible fluid (hopefully water) induces water flow,

(5)

where is the flow of water out of the pores and is the porosity as a function of position and time. The flow of water is regulated by the overall permeability of the soil, and all of this can be combined to yield

(6)

where is the permeability of the soil and is the unit weight of water. Defining

(7)

and making some assumptions about the physics, we can determine the equation for consolidation as

(8)

where $latex u(x,t) is the pore water pressure. If we invoke the effective stress equation and solve this for the boundary and initial conditions described, we have a solution

(9)

The Degree of Consolidation

One thing that our theory presentation demonstrated was the interrelationship between pore pressure, stress and deflection. We know what the ultimate deflection will be based on Equation (3) above (or more complicated equations when preconsolidation is taken into consideration.) But how does the settlement progress in time?

We start by defining the degree of consolidation thus:

(10)

where is the settlement at any time before complete settlement. For the specific case (governing equations, initial equations and boundary conditions) at hand, the degree of consolidation–the ratio of settlement at a given point in time to total settlement–can be determined as follows:

(11)

In this case the result is divided by the uniform pressure p and the height h. Let us further define the dimensionless time constant

(12)

That being the case, if we integration Equation (9) with Equation (11), we obtain

(13)

otherwise put

(14)

As was the case with Equation (9), only the odd values of n are considered; the even ones result in zero terms.

It is regrettable that, in defining , the value was not included, as using Equation (14) would be much simpler. For certain cases, it is possible to use the first two or three terms. In any case the usual method for determining –and by extension the degree of consolidation–is generally done either using a graph or a table, as is shown in the graph at the start of the post (repeated below:)

The notation is a little different. We use the variable to emphasise that we are dealing with the “standard” case. The above graph also gives approximating equations; it is easy to see that, for , the equation given is simply the first two terms of Equation (14). The distinction between the drainage length h ( in the graph above) and the layer thickness H is clear.