1
A Framework for Structural Geology

1.1 Introduction

Structural geology is the branch of earth sciences that focuses on understanding the processes by which geological materials deform. Structural geologists use the rock record to study naturally deformed rocks, an endeavor that relies upon both fieldwork and, to an increasing degree, the use of microstructural observations to characterize deformed rocks. Other academic disciplines - such as branches of geophysics, engineering, materials science, and physics - share the goal of characterizing and understanding how natural materials deform. Those fields focus on laboratory deformation experiments or theoretical models of material behavior.

1.1.1 Deformation

The term deformation encompasses changes of position (movement) and changes of shape (distortion). Natural deformation of rock produces a variety of rock structures that include fractures, faults, folds, deformation fabrics (e.g. foliations and lineations), shear zones, and microstructures. Structural geologists are interested in how to interpret rock structures and microstructures in terms of geometry, kinematics (the motion associated with deformation), dynamics (the forces involved in deformation), and the material behavior of rocks undergoing deformation.

1.1.2 Empirical vs. Theoretical Approaches

Three critical components compose the framework for structural geology: (1) The three-dimensional geometry of all geological structures and microstructures in the region; (2) the exact path that each part of the material followed as the individual structures formed and microstructures developed (the kinematic evolution); and (3) how the rock structures and microstructures evolved in terms of the absolute rates at which component parts moved, the forces that operated on the rocks, and the deformation-related physical properties of the rocks during deformation (the deformation dynamics).

The terms kinematics and dynamics will be familiar to students of physics. For those unfamiliar with the terms, kinematics refers to descriptions of the motion of parts of a system, whereas dynamics considers how systems respond to forces and boundary conditions. Kinematics and dynamics carry no connotation of what sort of entities are moving or what type of system is under consideration. In the physical sciences, the term mechanics refers to the field of study that examines how materials respond, i.e. move or change, in response to forces or displacements imposed on them. Combining these concepts, we see that a branch of science that is highly appropriate to structural geology is the mechanics of continuous media (e.g. continuum mechanics). We need to introduce one final term - rheology, which is often used as shorthand for the mechanics of continuous media. Rheology refers to the study of the relations between the displacements or velocities observed within a deforming material and the forces or stresses that act upon that material. We recommend reading a short recounting of an after-dinner speech by Marcus Reiner, in which he outlined his role in coining the term "rheology" (Reiner 1964).

The Deborah Number

(Physics Today, January 1964, p. 62/with permission from AIP Publishing)

From an after-dinner talk at the 4th Int. Congress on Rheology by Marcus Reiner, Israel Institute of Technology

In 1928 I came from Palestine to Easton, PA, to assist Eugene Cook Bingham at the birth of Rheology. I felt strangely at home. There was Bethlehem quite near, there was a river Jordan, and a village called Little Egypt. The situation was, however, also slightly confusing. To go from Bethlehem to Egypt, one had to cross the river Jordan, a topographic feature which did not conform to the original. Then there were, here, places such as Allentown, to which there was no analogy. And this could lead to strange situations, such as when a girl at school was asked where Christ was born and replied, "In Allentown." When corrected by, "No, in Bethlehem," she remarked, "Well I knew it was somewhere around here."

In Palestine I was working as a civil engineer doing science as a hobby. In 1920 a chemist had asked my help in the problem of the flow of a plastic material through a tube. I solved the problem and derived what is now known as the Buckingham-Reiner equation, Buckingham at the US National Bureau of Standards having derived the equation before. When Bingham learned of my work, he invited me to Lafayette College.

When I arrived, Bingham said to me, "Here you, a civil engineer, and I, a chemist, are working together at joint problems. With the development of colloid chemistry, such a situation will be more and more common. We therefore must establish a branch of physics where such problems will be dealt with."

I said, "This branch of physics already exists; it is called the mechanics of continuous media, or mechanics of continua."

"No, this will not do," Bingham replied. "Such a designation will frighten away the chemists."

So he consulted a professor of classical languages and arrived at the designation of Rheology, taking as the motto of the subject Heraclitus' pa?ta ?e? or "everything flows."

Rheology has become a well-known branch of physics, but most typists think it is a misprint for theology. I constantly receive mail addressed to the Theological Laboratory of the Israeli Institute of Technology and, on the occasion of the Second International Congress at Oxford 10?years ago, there was a special coach in the train at Paddington Station reserved for members of the Theological Congress. This seems ridiculous, but there is some relation between rheology and theology and on this, I want to say a few words.

Heraclitus' "everything flows" was not entirely satisfactory. Were we to disregard the solid and deal with fluids only? There are solids in rheology, even if they show relaxation of stress and consequently creep. The way out of this difficulty had been shown by the Prophetess Deborah even before Heraclitus. In her famous song after the victory over the Philistines, she sang, "The mountains flowed before the Lord." When, over 300 years ago, the Bible was translated into English, the translators, who had never heard of Heraclitus, translated the passage as "The mountains melted before the Lord" - and so it stands in the authorized version. But Deborah knew two things. First, that the mountains flow, as everything flows. But, secondly, that they flowed before the Lord, and not before man, for the simple reason that man in his short lifetime cannot see them flowing, while the time of observation of God is infinite. We may therefore define the non-dimensional Deborah Number:

The difference between solids and fluids is then defined by the magnitude of D. If your time of observation is very large, or conversely if the time of relaxation of the material under observation is very small, you see the material flowing. On the other hand, if the time of relaxation of the material is larger than your time of observation, the material, for all practical purposes is a solid. In problems of industrial design, you may substitute the time of service for the time of observation. When designing a concrete bridge you make up your mind to decide how long you expect it to serve, and then compare this time interval with the relaxation time for concrete.

It therefore appears that the Deborah Number is destined to become the fundamental number of rheology, bringing solids and fluids under a common concept, and leaving Heraclitus' pa?ta ?e? as a special case for infinite time of observation, or infinitely small time of relaxation. The greater the Deborah Number, the more solid the material; the smaller the Deborah Number, the more fluid it is.

There is a story they tell about two students of theology, who were praising the Almighty God. Said one, "For God, 1000 years are like a minute. And as he is the Creator of all, 1000 dollars are for Him like a cent." Said the other, "Wonderful, next time I pray to God, I shall pray, 'God, give me a cent'." Said the first: "What will it help you? He will say, 'Wait a minute.'"

The man did not take care of the difference between God's and his own time scale. This then is the connection between Theology and Rheology. In every problem of rheology, make sure you use the right Deborah Number.

Structural geologists, like all scientists, use the scientific method of developing ideas into testable hypotheses, which contribute to the construction of theories. Theories comprise hypotheses tested against data, but they also include deductions from tested hypotheses, mathematical and numerical analyses that extrapolate or interpolate data, predictions derived from models, etc. From plate tectonics theory, we infer that mountain belts may result from continent-continent collisions. Kinematic evidence supports the deduction that the Alpine mountain chain of Eurasia formed when continental landmasses on the European plate, on several small microplates, and on the African plate collided. Models...