Back Analysis in Rock Engineering: 1st Edition (Hardback) book cover

Back Analysis in Rock Engineering

1st Edition

By Shunsuke Sakurai

CRC Press

226 pages

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Hardback: 9781138028623
pub: 2017-08-17
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pub: 2017-09-01
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This book provides practicing engineers working in the field of design, construction and monitoring of rock structures such as tunnels and slopes with technical information on how to design, how to excavate and how to monitor the structures during their construction. Based on the long-term engineering experiences of the author, field measurements together with back analyses are presented as the most powerful tools in rock engineering practice. One of the purposes of field measurements is to assess the stability of the rock structures during their construction. However, field measurement results are only numbers unless they are quantitatively interpreted, a process in which back analyses play an important role.

The author has developed both the concepts of “critical strain” and of the “anisotropic parameter” of rocks, which can make it possible not only to assess the stability of the structures during their construction, but also to verify the validity of design parameters by the back analysis of field measurement results during the constructions. Based on the back analysis results, the design parameters used at a design stage could be modified if necessary. This procedure is called an “Observational method”, a concept that is entirely different from that of other structures such as bridges and buildings. It is noted that in general, technical books written for practicing engineers mainly focus on empirical approaches which are based on engineers’ experiences. In this book, however, no empirical approaches will be described, instead, all the approaches are based on simple rock mechanics theory. This book is the first to describe an observational method in rock engineering practice, which implies that the potential readers of this book must be practicing engineers working on rock engineering projects.


"Critical Strain, defined as the ratio of the uniaxial compressive strength of the rock to its deformation modulus, is a topic on which Professor Sakurai has published many papers since the early 1980s. This book presents a detailed summary of the basic principles of critical strain and its application to the assessment of the stability of tunnels, underground caverns, excavated slopes and landslides. Many practical examples, based on the author’s practical experience, are presented to demonstrate the uses, advantages and limitations of the method.

The uses of Critical Strain and Critical Shear Strain, a close relative, in back analysis of measured displacements in rock masses and of forward analysis of slopes and underground excavations are described in detail in the 23 chapters of this book. It is shown that the parameters required for the derivations of these criteria can be obtained from laboratory tests on intact rock samples and that the criterion can be scaled for applications in large rock masses. It is shown that confining pressure, moisture content and temperature have an almost negligible influence on Critical Strain and that it is applicable to a wide range of rock and soil masses.

A particularly useful practical tool is a chart in which Hazard Warning Levels are presented for use during tunnel construction. Measured displacements of tunnel closure are divided by the tunnel diameter to estimate the Critical Strain. These Critical Strains are then compared with the Hazard Warning Levels for the uniaxial compressive strength of the rock in which the tunnel is being excavated. Critical Strains below Hazard Warning Level I indicate that the tunnel behaviour is essentially elastic and that no design changes or additional support measures are required. Warning Level II coincides with the onset of plastic deformation in the rock mass surrounding the tunnel and suggests the need for caution. Warning Level III indicates that the stability of the tunnel is at risk and that urgent remedial measures, design changes or even stopping tunnel excavation may be required.

Since the failure of slopes generally involves shear failure, Critical Shear Strain criterion is more useful than Critical Strain for the back analysis of measured slope displacements and the estimation of factors of safety. The application of this criterion to excavated slopes and landslides is discussed in the final seven chapters of the book. Several practical examples are included to assist the reader in understanding the methods used.

An important limitation to the use of the Critical Strain concept is that it is only applicable to rock and soil masses that can be considered as homogeneous and isotropic. In other words, rock masses in which a few discontinuities such as joints, shear zones and faults occur and where the spacing of these features is large compared to the scale of the problem under consideration, cannot be analysed directly using Critical Strain.

This is not an easy book to read and hard work is required to understand some of the terminology, concepts and examples. However, for someone already familiar with the use of back analysis in geotechnical engineering, there are many useful ideas, discussions and practical examples that make this hard work well worth while."

Evert Hoek, Professor Emeritus in Geotechnical Engineering, review published in November 2017

"The back analysis techniques nowadays applicable in geotechnical engineering derive from the original concept known as Observational Design Method proposed by Karl Terzaghi. That method requires a proper plan for carrying out in situ measurements during the various stages of the construction. The experimental data (e.g. displacements, strains, stresses, etc.) are then compared with the corresponding quantities evaluated during design. If a significant discrepancy is observed between predicted and actual quantities, the in situ measurements are used not only to "refine" the mechanical parameters of the soil/rock mass adopted during design but, if necessary, to choose a different and more adequate material model for describing the behaviour of the geotechnical medium. Consequently, on the basis of the refined parameters and material model, the design can be modified or tuned in order to comply with the actual conditions met in the field.

In this context, the back analysis consists in finding the material model of the geotechnical medium and/or the values of its parameters that, when adopted for the stress analysis of the problem under examination, lead to results (e.g. displacements, stresses, etc.) as close as possible to the corresponding in situ measurements. In general terms, two "ingredients" are necessary to perform a back analysis. The first one is a stress analysis procedure for determining the stress, strain and displacement distributions for the problem at hand. The second one is a suitable optimisation algorithm which minimises a non-linear function representing the discrepancy between the quantities measured in the field and the corresponding data obtained by the stress analysis. The free variables in this process consist of the mechanical parameters of the soil/rock mass,

The book of Professor Shunsuke Sakurai provides an extensive and consistent overview of the recent methods for back analysis, and of their application to rock engineering, with particular reference to underground excavations and rock slope stability. After outlining the link between back analysis and forward analysis, observational design method and system identification, the book describes in detail the methodology of observational design. Subsequently, the concept of critical strain is discussed as a practical approach for the design of tunnels and slopes. This is a concept not yet widely used in geotechnical engineering which perhaps needs some further investigation and comparative evaluation with more traditional design approaches. The book covers also other valuable topics, in the framework of back analysis, such as rock anisotropy, influence of the initial stress state, laboratory tests, constitutive modelling of rocks. A number of case histories and applications are presented mainly concerning tunnels and slope stability. With respect to this later subject, the use of displacement measurements through the GPS technology is presented and discussed upon.

This book is of interest for engineers, researchers and PhD students involved in the design of rock works and in developments of geotechnical engineering."

Giancarlo Gioda, Professor at the Department of Architecture, Construction Engineering and Built Environment at the Politecnico di Milano, December 2017.

Table of Contents

1 Introduction

1.1 Aims and scope

1.2 Field measurements and back analyses

2 Back analysis and forward analysis

2.1 What is back analysis?

2.2 Difference between back analysis and forward analysis

2.3 Back analysis procedures

2.4 Brief review of back analysis

3 Modelling of rock masses in back analysis

3.1 Modelling of rock masses

3.2 Back analysis and modelling

3.3 Difference between parameter identification and back analysis

4 Observational method

4.1 What is observational method?

4.2 Design parameters for different types of structures

4.3 Difference between stress-based approach and strain-based approach

4.4 Strain-based approach for assessing the stability of tunnels

4.5 Displacement measurements in observational method

4.6 Back analysis in observational method

4.7 Flowchart of observational methods

4.8 Hazard warning levels

5 Critical strains of rocks and soils

5.1 Definition of critical strain of geomaterials

5.2 Scale effect of critical strains

5.3 Simple approach for assessing tunnel stability

5.4 Hazard warning level for assessing crown settlements and convergence

5.5 Uniaxial compressive strength and Young’s modulus of rock masses

6 Environmental effects on critical strain of rocks

6.1 Critical strain in triaxial condition

6.2 Effects of confining pressure

6.3 Effects of moisture content

6.4 Effects of temperature

7 General approach for assessing tunnel stability

7.1 Critical shear strain of geomaterials

7.2 Hazard warning levels in terms of maximum shear strain

7.3 How to determine the maximum shear strain distribution around a tunnel

8 Back analyses used in tunnel engineering practice

8.1 Introduction

8.2 Mathematical formulation of the proposed back analyses

8.3 Case study I (Washuzan tunnels)

8.4 Case study II (two-lane road tunnel in shallow depth)

9 Universal back analysis method

9.1 Introduction

9.2 Mathematical formulation considering non-elastic strain

9.3 Case study (tunnel excavated in shallow depth)

9.4 Modelling of support structures

10 Initial stress of rock masses determined by boundary element method

10.1 Introduction

10.2 Three-dimensional back analysis method

10.3 Case study

11 Back analysis for the plastic zone occurring around underground openings

11.1 Introduction

11.2 Assumptions

11.3 Fundamental equations

11.4 The method for determining the elasto-plastic boundary

11.5 Computer simulation

12 Back analysis considering anisotropy of rocks

12.1 Introduction

12.2 Constitutive equations

12.3 Different modes of deformation

12.4 Computer simulations

12.5 Case study (underground hydropower plant)

13 Laboratory experiments

13.1 Absolute triaxial tests (true triaxial tests)

13.2 Conventional triaxial compression tests

13.3 Simple shear tests

14 Constitutive equations for use in back analyses

14.1 Fundamental theory of constitutive equations for geomaterials

14.2 Failure criteria

14.3 Anisotropic parameter and anisotropic damage parameter

14.4 Proposed constitutive equation for geomaterials

14.5 Applicability of the proposed constitutive equation

14.6 Conclusions on the results of the numerical simulation

14.7 Forward analysis vs. back analysis

15 Cylindrical specimen for the determination of material properties

15.1 Introduction

15.2 Constitutive equation for cylindrical coordinate systems

15.3 Numerical simulation

16 Applicability of anisotropic parameter for back analysis

16.1 Physical model tests in laboratory

16.2 Excavation of the tunnels and strain distributions around them

16.3 Back analysis for simulating the maximum shear strain distributions

16.4 Results and discussion

17 Assessing the stability of slopes

17.1 Factor of safety of slopes

17.2 Paradox in the design and monitoring of slopes

17.3 Difference between the factor of safety of tunnels and slopes

17.4 Factor of safety for toppling of slopes

18 Back analysis of slopes based on the anisotropic parameter

18.1 Mechanical model of rock masses

18.2 Laboratory experiments for toppling

18.3 Numerical analysis of toppling behaviours

18.4 Applicability of the anisotropic parameter to simulation of various deformational modes

18.5 Factor of safety back-calculated from measured displacements

19 Back analysis method for predicting a sliding plane

19.1 Introduction

19.2 Procedure of the method

19.3 Accuracy of the method

20 Back analysis of landslides

20.1 Introduction

20.2 Finite element formulation

20.3 Applicability of the proposed method (forward analysis)

20.4 Case study of landslide due to heavy rainfall (back analysis)

21 Back analysis for determining the strength parameters

21.1 Introduction

21.2 Back analysis procedure

22 Application of back analysis for assessing the stability of slopes

22.1 Cut slope

22.2 Slope of open-pit coal mine

23 Monitoring of slope stability using GPS in geotechnical engineering

23.1 Introduction

23.2 Displacement monitoring using GPS

23.3 Practical application of GPS displacement monitoring

23.4 Back analysis in GPS displacement monitoring

About the Author

Prof. Sakurai studied Civil Engineering at Kobe University (B.E) and at Kyoto University (M.E), and finally at Michigan State University USA (Ph.D). He also received his Dr Eng. degree from Nagoya University, Japan.

Prof. Sakurai worked at Kobe University as Professor of rock mechanics, and of structural mechanics, and then worked at the Hiroshima Institute of Technology as President. He is now Professor Emeritus of Kobe University, and also Professor Emeritus of Hiroshima Institute of Technology.

Professionally, Prof. Sakurai has been involved in various types of Rock Mechanics projects (hydropower, nuclear power, pumped storage, compressed air energy storage schemes, highway and railway tunnels, slopes etc.) in Japan and abroad.

His research interests have been connected to numerical analysis particularly back analysis and field measurements. The aim of these research activities is mainly concerned with building a bridge between theory and practice.

About the Series

ISRM Book Series

The ISRM Book Series comprises significant scientific publications in rock mechanics and related disciplines. The aim of the Series is to promote the scientific output of ISRM (International Society for Rock Mechanics).

The Series will be published on a regular basis, according to the emergence of noteworthy scientific developments. Each volume in the Series is prepared independently and focuses on a topical theme. Volumes are published on an occasional basis, and include high quality scientific contributions that have not been published elsewhere before. Contributions will be rigorously peer-reviewed by experts in the field, ensuring strong scientific standards, and are expected to be leading in rock mechanics and related disciplines. The Series may include edited volumes, textbooks, reference works and books on advanced scientific topics. ISRM members benefit from a 40% discount on ISRM Book Series volume purchases.

- Rock and rock mass characterization
- Field and Laboratory testing methods in rock mechanics and rock engineering
- Crustal stresses and earthquakes
- Rock dynamics
- Rock mechanics modelling
- Rock engineering design of foundations, slopes, open pit and underground excavations, tunnels and caverns, and other types of works
- Coupling thermo-hydro-mechanical-chemical processes in rocks, etc.
- Petroleum Geomechanics
- Preservation of ancient stone monuments

The expected readers of the book are all those involved in rock mechanics and rock engineering activities, in the fields of civil, mining and petroleum engineering, and engineering geology. This includes professionals working in field and laboratory testing, modelling of rock structures, rock engineering design or petroleum geomechanics. The ISRM book series will also be of interest to scientists, researchers and post-graduate students carrying out their investigations in rock mechanics.

The Initial Editorial Board during the establishment of the ISRM Book Series (i.e. the current ISRM Board—which will change for the period 2015–2019):

Prof. Xia-Ting Feng, China
Dr. Eda Freitas de Quadros, Brazil
Mr. Jacques Lucas, South Africa
Dr. Yingxin Zhou, Singapore
Dr. David Beck, Australia
Prof. Frederic Pellet, France
Dr. John Tinucci, USA
Dr. Antonio Samaniego, Peru
Prof. Yuzo Ohnishi, Japan
Prof. Ivan Vrkljan, Croatia
Dr. Manoj Verman, India
Dr. Luís Lamas, Portugal

Learn more…

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