Rock Dynamics

Omer Aydan

• Publisher: CRC Press
• Year: 2017
• ISBN:
  9781315391281
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Geology & Earth Sciences

Rock dynamics has become one of the most important topics in the field of rock mechanics and rock engineering. The spectrum of rock dynamics is very wide and it includes the failure of rocks, rock masses and rock engineering structures such as rockbursting, spalling, popping, collapse, toppling, sliding, blasting, non-destructive testing, geophysical explorations, science and engineering of rocks and impacts. The book specifically covers fundamentals of rock dynamics, constitutive models, numerical analysis techniques, dynamic testing procedures, the multi-parameter responses and motions of rocks during fracturing or slippage in laboratory experiments, earthquakes and their strong motion characteristics and their effect on various rock structures such as foundations, underground structures, slopes, dynamic simulation of loading and excavation, blasting and its positive utilization in rock engineering, the phenomenon of rockburst in rock excavations, non-destructive testing of rockbolts and rock anchors and impacts by meteors or projectiles. The main goal of this book is to present a unified and complete treatise on Rock Dynamics and to represent a milestone in advancing the knowledge in this field and in leading to new techniques for experiments, analytical and numerical modelling as well as monitoring of dynamics of rocks and rock engineering structures.

Chapter 1

Introduction

Rock dynamics has become one of the most important topics in the field of rock mechanics and rock engineering (e.g. Aydan et al., 2011; Aydan, 2016; Zhou and Jiao, 2011). The spectrum of rock dynamics is very wide and it includes, the failure of rocks, rock masses and rock engineering structures such as rockbursting, spalling, popping, collapse, toppling, sliding, blasting, non-destructive testing, geophysical explorations, and, impacts (see Figure 1.1).

The fundamental governing equation used in the dynamics of materials and structures is presented in Chapter 2. As rock mass in nature has discontinuities in the form of tiny cracks in small scale to fault zones in large scale, such discontinuities must be taken into account in any type of analysis involving rock masses. Constitutive models for rocks, discontinuities and rock masses are explained and some fundamental features of the numerical methods used in the rock dynamics problem are outlined.

Figure 1.1 Examples of dynamic issues in rock mechanics and rock engineering.

The experimental techniques and monitoring equipment are quite important for evaluating the dynamic characteristics of rocks, discontinuities and rock masses. Chapter 3 describes current available techniques for measuring the dynamic properties in rock mechanics and points out also some new directions how to deal with actual issues in this field.

The dynamic responses such as acceleration, velocity and displacement of geo-materials during fracturing and slippage have not been studied in the fields of geo-engineering and geo-science as measurement, monitoring and logging technologies were not so advanced in the past. By virtue of the recent advances in measurement, monitoring and logging technologies, it is now possible to carry out such experiments on geo-materials ranging from very soft materials such as clay to hard rocks such as siliceous sandstone by using different loading schemes and loading frames as well as rock discontinuities with different surface roughness characteristics. These experiments and experimental results concerned with the acceleration, velocity and displacement responses of geo-materials during fracturing and slippage under laboratory conditions are given in Chapter 4. The velocity and displacement responses are obtained through the Erratic Pattern Screening (EPS) integration technique proposed by Aydan and Ohta (2011).

Earthquakes are known to be one of the natural disasters resulting in huge losses of human life and properties as experienced in the recent earthquakes. Since there is no way to prevent the occurrence of earthquakes in earthquake-prone countries such as Turkey, Japan, USA and Taiwan, the design of structures and residential and industrial developments must be done according to possible types and magnitude of earthquakes. It is well known that ground motion characteristics, deformation and surface breaks of earthquakes depend upon the causative faults. While many large earthquakes occur along the subduction zones, which are far from the land and their effects appear as severe shaking, the large in-land earthquakes may occur just beneath or nearby urban and industrial zones as observed in the recent great earthquakes. The seismic design of engineering structures is generally carried out by considering the possible shaking characteristics of the ground during earthquakes in a given region. It is a fact that the residual (permanent) relative displacement of the ground is not considered in any seismic code all over the world, except for very long linear structures such as pipelines. This problem is currently considered to be beyond the capability of seismic design concept for structures in earthquake engineering, although it must be dealt with somewhat. The fundamental aspects and features of current methods for estimating strong motions and permanent ground deformations are described in Chapter 5.

Recent earthquakes showed that the foundations of large structures on rock masses may be damaged by permanent ground deformation resulting from faulting or slope failure. Chapter 6 describes some model experiments, case histories on various foundation types of bridges, buildings, highways, railways, dams, pylons, pipelines. Possible methods for evaluating the effects of permanent ground deformation of foundations and associated structures are summarized and several examples of applications are described.

Underground structures are well known as earthquake-resistant structures. However, the recent earthquakes showed that underground structures are also vulnerable to seismic damage. There may be several reasons such as high ground motions and permanent ground movements. Various forms of damage to underground structures such as tunnels, caverns, natural caves and abandoned mines during major earthquakes are presented in Chapter 7. Results of various model tests on underground opening using shaking tables are also presented to show the effect of ground shaking on the response and collapse of underground structures in continuum and discontinuum. Furthermore, some empirical equations are proposed to assess the damage to underground structures, which may be useful for quick assessments of possible damage. Applications of numerical methods on the dynamic responses and stability are also presented in this chapter.

Large inland earthquakes caused many large scale rock slope failures in recent years. The slope failures induced tremendous damage to infrastructures as well as to residential areas, and they involved not only cut slopes but also natural rock slopes. Compared to the scale of soil slope failures, the scale and the impact of rock slope failures are very large and the form of failure differs depending upon the geological structures of rock mass of slopes. Furthermore, the failure of the rock slope failures may involve both active and passive modes. However, the passive modes are generally observed when the ground shaking is quite large. Some model experiments, case histories on slope failures are described in Chapter 8. Possible methods for evaluating the dynamic stability of rock slopes are summarized and several examples of applications are described.

Historical structures are mainly masonry structures, which are composed of blocks made of natural stones, bricks or both, and they are assembled in different patterns with or without mortar. Furthermore, masonry houses presently constitute more than 60 percent of the residential buildings all over the world and they have a very long building history. Despite widespread utilization of masonry structures in building history all over the world, there are a few studies on their seismic response and stability. The observations of damage to actual masonry and historical structures and monuments, the shaking table experiments, available limiting equilibrium and numerical methods for estimating their responses are presented in Chapter 9. Furthermore, a recent example of monitoring multi-parameter response of rock foundations of Nakagusuku Castle during earthquakes and in the long-term is described and its implications are discussed.

It is very rare to see discussion or experimental results on the load-displacement-time or stress-strain-time responses during experiments and loading or excavation of rock engineering structures. The author has found that the responses might be quite different during the transient process from those under static assumptions. It is concluded that the loading of samples and structures as well as excavation of rock engineering structures should be treated as a dynamic phenomenon. Chapter 10 describes some experiments and theoretical and numerical solutions for modeling the loading excavation of rock engineering structures as a dynamic phenomenon.

Blasting is the most commonly used excavation technique in mining and civil engineering applications. Blasting induces strong ground motions and fracturing of rock mass in rock excavations. The characteristics of blasting agents, vibration monitoring in open-pit mines, quarries and underground openings are presented in Chapter 11. Furthermore, negative and positive effects of blasting are also presented and discussed in this chapter. It is also shown how to evaluate and use p-wave explorations to assess the average equivalent mechanical properties of rock masses.

The rockburst phenomenon is one of most dangerous forms of instability in rock engineering. First some available studies on this topic are presented and some effective monitoring and analysis methods for predicting rockburst are explained in Chapter 12. First, the fundamentals of various possible methods such as empirical techniques, analytical approaches and various finite element methods based on conventional elasto-plasticity, energy methods and extension strain method for predicting rockburst are briefly described. Then, some laboratory tests were carried out on the circular openings excavated in sandstone from Tarutoge Tunnel and Third Shizuoka Tunnel intercalated sandstone and shale samples and multi-parameter measurements were done in order to develop some observational and monitoring techniques for predicting rockburst. It is experimentally demonstrated that the combined utilization of monitoring AE, rock temperature, infrared imaging and electric potential may be a quite effective in-situ monitoring tool for predicting rockburst.

Rockbolts and rock anchors are commonly used as principal support members in underground and surface excavations. These support members may be subjected to earthquake loading, vibrations induced by turbines, vehicle traffic and long-term corrosion. Chapter 13 is concerned with rockbolts and rock anchors and some theoretical, numerical and experimental studies on rockbolts and rock anchors under shaking are presented in the first part of this chapter. In the remaining part, the fundamentals of non-destructive techniques for the evaluation of the soundness of rockbolts and rockanchors are described and several practical applications of non-destructive technique utilizing impact waves are given and discussed.

Chapter 14 is concerned with impact phenomena observed in various fields such as collision of vehicles in transportation engineering, collision of adjacent structures during earthquakes, standard penetration tests in soil mechanics, and impact craters due to meteorites, anchoring of ships or platforms in marine engineering and bullets and missiles destroying targets. The state of art on the impacts of meteorites and their effects are presented. It is shown that the impacts by projectiles such as bullets and missiles and their effects are quite similar to those of the meteorites except their size. Drop tests, which are used in various fields, are explained and several laboratory tests and empirical and analytical formulations for practical applications are presented. In the last part, the impact induced tsunami issue is discussed and some experimental and analytical formulations are presented in relation to water level variations in closed water bodies such as lakes and reservoirs.

The main purpose of the author is to present a treatise on Rock Dynamics. It is hoped that this publication will be a mile-stone in advancing the knowledge in this field and leading to the techniques for experiments, analytical and numerical modelling as well as monitoring in dynamics of rocks and rock engineering structures.

Chapter 2

Fundamental equations, constitutive laws and numerical methods

2.1 FUNDAMENTAL EQUATIONS

Momentum conservation law for rock mass can be given as (e.g. Eringen, 1980) (Figure 2.1):

$\rho \frac{\partial \mathbf{\text{v}}}{\partial t}=-\nabla .\mathbf{\sigma }+\mathbf{\text{b}}$

(2.1)

where ρ, v, σ and b are density, velocity, stress tensor and body force, respectively. This governing equation is valid whether rock mass is treated as continuum or discontinuum.

Figure 2.1 Illustration of momentum conservation law.

2.2 CONSTITUTIVE LAWS FOR ROCKS

2.2.1 Linear constitutive laws

When rock or rock mass behaves linearly without any rate dependency, the simplest constitutive law is Hooke’s law. This law is written in the following form:

${\sigma }_{ij}=D_{ijkl}{\epsilon }_{kl}$

(2.2)

where σ_ij, ε_kl and D_ijkl are stress, strain and elasticity tensors, respectively.

If material is homogenous and isotropic, Eq. (2.2) may be written as

${\sigma }_{ij}=2\mu {\epsilon }_{ij}+\lambda {\delta }_{ij}{\epsilon }_{kk}$

(2.3)

where δ_ij is Kronecker delta tensor. λ and µ are Lame coefficients, which are given in terms of elasticity (Young’s) modulus (E) and Poisson’s ratio (υ) as

$\text{λ =}\frac{Ev}{\left(1+v\right)\left(1-2v\right)};\mu =\frac{E}{2(1+...}$

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• About the author
• Acknowledgements
• 1 Introduction
• 2 Fundamental equations, constitutive laws and numerical methods
• 3 Tests on dynamic responses of rocks and rock masses
• 4 Multi-parameter responses and strong motions induced by fracturing of geomaterials and slippage of discontinuities and faulting model tests
• 5 Ground motions due to earthquakes and estimation procedures
• 6 Dynamic responses and stability of rock foundations
• 7 Dynamic responses and stability of underground excavations in rock
• 8 Dynamic responses and stability of rock slopes
• 9 Dynamic responses and stability of historical structures and monuments
• 10 Dynamics of loading and excavation in rocks
• 11 Blasting
• 12 Dynamics of rockburst and possible countermeasures
• 13 Dynamics of rockbolts and rock anchors and their non-destructive testing
• 14 Dynamics of impacts
• 15 Conclusions
• References
• Subject index