Posted in Academic Issues, Geotechnical Engineering

Derivation of Boussinesq’s Stress and Strain Equations for a Point Load on a Semi-Infinte Space (like soil)

Most Soil Mechanics and Foundations text and reference books (such as NAVFAC DM 7.01 and Verruijt) state the equations for Boussinesq’s point load problem without proof. For those who are interested in how these equations are developed, below is the derivation, taken from Manual of the Theory of Elasticity, by V.G. Rekach, where more detail is given along with the notation, which is different from what we have in the U.S.. The derivation from Rekach is given below.

Posted in Geotechnical Engineering

Manual of the Theory of Elasticity, by V.G. Rekach

An introduction to problems in the theory of elasticity. You can download the book by clicking here. Contents are as follows: Notation Chapter I Theory of Stress I. Static and Dynamic Equilibrium Equations II. Surface Conditions III. State of Stress at a Point Problems Chapter 2 Theory of Strain I. Strain Equations in Orthogonal Co-ordinates […]

Manual of the Theory of Elasticity, by V.G. Rekach
Posted in Geotechnical Engineering, Soil Mechanics

Mexico City’s surprising crisis: the city is sinking

The city with a metropolitan population of over 20 million is sinking at a rate of almost 50 centimeters (20 inches) per year — and this isn’t stopping anytime soon.

At first glance, you’d be inclined to attribute this to the strong earthquakes that sometimes strike Mexico City. But while earthquakes can cause their own damage, they’re not the main culprit here. Instead, it’s something much more inconspicuous: subsidence.

You can read it all here. Put into geotechnical terms, the bed of old Lake Texcoco has some very high void ratio soils, and as a large city puts pressure on them the void ratio decreases as the voids between the soil grains shrink. Thus the entire city has severe settlement, total and differential.

A diagram, from the Swedish geotechnical engineer and academic Bengt Broms, showing how we consider the volume and mass/weight relationships in soil. The particulate matter of the soil means that the soil mass has three components: solid (particles,) water (in the voids) and gas/air (also in the voids.) That simplification is shown above, along with the definition of void ratio.
A diagram, again from Bengt Broms, illustrating the problem in Mexico City and whenever what we call consolidation settlement takes place. The soil particles have been combined into one mass (hatched area.) As pressure is applied, the particles come closer to each other and the volume of the voids decreases, thus we have settlement.
A photo from Mexico City showing the effects of subsidence many years ago. The top of the pole was originally the ground surface before structures were built on it and subsidence started. The photo and an explanation can be found in the textbook Soils in Construction. Needless to say, it’s only gotten worse in the intervening years. Photo courtesy of J.R. Bell.

My own lecture on the subject of settlement and consolidation is here.

Posted in Geotechnical Engineering

Retaining Wall Collapse on I-295 Project in Bellmawr, New Jersey

An MSE Retaining Wall suffered a dramatic failure last week closing the right northbound lanes of I-295 indefinitely. The wall is part of the Direct Connection Project to reduce congestion on I-295/I-76/Route 42 in Bellmawr, […]

Retaining Wall Collapse on I-295 Project in Bellmawr, New Jersey
Posted in Deep Foundations, Geotechnical Engineering, Pile Driving Equipment

Reconstructing a Soviet-Era Plastic Model to Predict Vibratory Pile Driving Performance —

The latest in our series of monographs on vibratory pile drivers, this one takes us back to the beginnings of vibratory pile driving in the Soviet Union. It was prepared for the ReSEARCH Dialogues at the University of Tennessee at Chattanooga in April 2021. The vibratory driver that started it all: the Soviet BT-5, used […]

Reconstructing a Soviet-Era Plastic Model to Predict Vibratory Pile Driving Performance —