Modelling the Effects of Blasting on Rock Breakage

V.A. Borovikov, I.F. Vanyagin

• Publisher: CRC Press
• Year: 2020
• eBook ISBN:
  9781000150421
• Topic: Physical Sciences
• Subtopic: Civil Engineering

This work provides a translation of "Modelirovanie deistviya vzriva pri razruzhenii gornikh porod" (Moscow, 1990). Presenting theories of simulating blast effects in elastic and elastoplastic media, it covers topics such as the classical and modern methods for modelling rock breakage by blasting.

1

Theoretical Concepts of Modelling the Effects of Blasting in Different Media

1.1 Elements of Dimensional Analysis

The physical quantities commonly dealt with in scientific investigations and production processes are usually quantified. They are measured in some or the other unit. Further, the quantity is expressed as a numerical value, which characterises the quantity irrespective of whether it has been measured by experimental methods (viz., measurement of length, time, mass) or mathematical expressions (viz., measurement of velocity, acceleration, area, volume etc.).

It is conventional in the dimension theory to classify all physical values into fundamental, derived, non-dimensional or dimensional. The fundamental are those that possess independent dimensions. In other words, the numerical value of a fundamental physical quantity does not change while changing the unit of measurement of another fundamental physical quantity (viz., length, time, mass). Derived physical quantities are those whose numerical values depend on measurement units of fundamental physical quantities (viz., velocity, acceleration, force etc.). Such a distinction between fundamental and derived physical quantities depends entirely on the selection of units of measurement and not on their nature. Hence this classification is a conditional one. In practice, the number of fundamental physical quantities is limited. In mechanics three fundamental quantities are taken into consideration (length, time and mass or force) whereas four fundamental units are considered in electrical technology, heat technology and optics by adding one more to the fundamental three mechanical units, depending on the area of science. For the sake of convenience, the fundamental units have been defined and accepted in all countries and continents, in fact, throughout the whole world. It is known as the system of units for measuring fundamental quantities.

In the former USSR the so-called technical and physical systems of units were long used in mechanics. The fundamental units in technical sciences are length (I), force (F) and time (t), which are measured in metre, kilogramme-force and second respectively (MKS). The fundamental units in physical sciences are length (I), mass (m) and time (t), which are measured in centimetre, gramme and second respectively (CGS).

On 1 January 1968 an international system of units (SI) was introduced by the State Standards. In this system the fundamental unit for length I is metre, for mass m kilogramme, time t second, electric current I ampere, temperature degree Kelvin and intensity of light, candle.

Those quantities whose numerical values depend on the adopted scale and unit of measurement are called dimensional. On the other hand, those quantities whose numerical values do not depend on a unit of measurement are called non-dimensional. Examples of dimensional quantities are length, mass, time, velocity, acceleration, force, energy, moment of a force etc. Examples of non-dimensional quantities are ratio of two lengths, ratio between energy and moment of a force, angles etc.

However, this classification is somewhat conditional. Let us consider the case of an angle. We have labelled it non-dimensional. Nevertheless an angle is measured in units such as radian, degree or percentage of a right angle. Hence the numerical value of an angle depends on a unit of measurement and thus an angle may be termed dimensional. But if an angle is measured as a ratio between the length of an arc and a radius, then whatever the unit of measurement of the values may be, the numerical value of an angle shall be invariant. Hence an angle may be termed non-dimensional. Length can similarly be made non-dimensional by measuring it as a ratio to a fixed unit length. However, it is convenient to measure an angle by a fixed unit since its value does not change with change in scale of the object. But to measure a length the unit of measurement may be varied as the value changes significantly with change in scale. This change may be of the order of hundreds.

The concepts of dimensional and non-dimensional quantities are relative in nature and were formulated by L.I. Sedov: ‘These quantities, whose numerical values depend on the selection of a specific unit system from a possible set of unit systems, are called dimensional. Quantities for which the numerical values remain the same in all unit systems of the whole set, are called non-dimensional.’

It may also be noted that the number of fundamental quantities can be either increased or decreased along with the respe...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Preface
• Table of Contents
• 1. Theoretical Concepts of Modelling the Effects of Blasting in Different Media
• 2. Application of Theories of Similarity and Dimension to Investigations into Blast Effects in Various Media
• 3. Physical Modelling of Blast Effects in Rock Breakage
• 4. Mathematical Fundamentals of Modelling Blast Effects in Rocks
• Literature Cited