Geotechnics for Natural Disaster Mitigation and Management (A Murali Krishna, Takeshi Katsumi) (z-lib org)

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Developments in Geotechnical Engineering
A. Murali Krishna
Takeshi Katsumi Editors
Geotechnics for 
Natural Disaster 
Mitigation and 
Management
Developments in Geotechnical Engineering
Series Editors
Braja M. Das, California State University, Henderson, CA, USA
Nagaratnam Sivakugan, James Cook University, Townsville, QLD, Australia
More information about this series at http://www.springer.com/series/13410
http://www.springer.com/series/13410
A. Murali Krishna • Takeshi Katsumi
Editors
Geotechnics for Natural
Disaster Mitigation
and Management
123
Editors
A. Murali Krishna
Department of Civil Engineering
Indian Institute of Technology Tirupati
Tirupati, AP, India
Takeshi Katsumi
Graduate School of Global
Environmental Studies
Kyoto University
Kyoto, Japan
ISSN 2364-5156 ISSN 2364-5164 (electronic)
Developments in Geotechnical Engineering
ISBN 978-981-13-8827-9 ISBN 978-981-13-8828-6 (eBook)
https://doi.org/10.1007/978-981-13-8828-6
© Springer Nature Singapore Pte Ltd. 2020
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https://doi.org/10.1007/978-981-13-8828-6
Preface
Indian Geotechnical Society (IGS) and Japanese Geotechnical Society (JGS) made
an agreement of cooperation to promote and enlarge the exchange of technical,
scientific and professional knowledge related to geotechnical engineering. In this
context, a series of workshops are being conducted with collaboration between the
two societies (IGS and JGS) for the growth of geotechnical engineering and fruitful
interaction between researchers in both the countries. The first workshop was held
in 2011 at Kochi, India, on ‘Earthquake Geotechnical Engineering’ theme, and the
second workshop was held in 2015 at Fukuoka, Japan, on ‘Geotechnics for
Resilient Infrastructure’ theme. The third workshop was held in conjunction with
‘Indian Geotechnical Conference 2017’ in December 2017, Guwahati, India, on
‘Geotechnics for Natural Disaster Mitigation and Management’ theme. The
workshop focussed on the recent advances and the developments that are taking
place in geotechnical aspects of natural disaster mitigation and management.
Speakers from Japan and India presented some of the salient aspects of natural
disasters and their mitigation strategies. A total of about 30 eminent researchers and
practitioners from both the countries participated in the workshop deliberations.
This book titled Geotechnics for Natural Disaster Mitigation and Management is
the compilation of the some of the expert deliberations made at the third Indo-Japan
workshop held on 13 December 2017 at IIT Guwahati, India. This book is organized
into 13 chapters covering the landslides and earthquake natural disasters for effective
mitigation and management. Chapter 1 discusses the geotechnical and geological
perspectives of The 2017 July Northern Kyushu Torrential Rainfall Disaster.
Chapter 2 outlines disaster management strategies that are being adopted in India
and typical geotechnical characterization aspects for earthquake disaster. Chapter 3
presents details of shear strength characterization gravel–tyre chips mixtures for
sustainable geotechnical engineering through the usage and recycled waste tyres for
various disaster mitigation techniques. At times, back analysis-based approaches are
to be adopted to the characterization of soils through numerical simulations and
analyses. Chapter 4 explains an example of the application of such an approach for
determination of elastic modulus of soil. It is also essential to account for a special
variation of the properties of soils for realistic analyses. Chapter 5 provides the
v
details of the evaluation of the spatial distribution of strength of few embankments in
Japan and India through field investigation. Various aspects of landslides like
integrating rainfall load in landslide warning system (Chap. 6); application of
physically based models for landslide hazard evaluation (Chap. 7); and debris
flow-related aspects in the case of rock fall (Chap. 8) are also included in this book.
Chapter 9 describes the significance of surface and sub-surface drainage measures
for efficient landslide mitigation strategies. Waterfront retaining structures including
breakwater systems are being affected by earthquake and tsunami. Design aspects
(Chap. 10) and countermeasures (Chap. 11) against disaster-induced instabilities are
also included herein. For efficient disaster mitigation strategies, ground improvement
methods play a vital role. Ground modification techniques using vibro methods
(Chap. 12) and cement-based grouting are briefly discussed.
We sincerely thank and appreciate the efforts of all the expert contributors in
formulating the book chapter contributions. We also thank Springer team for giving
inputs for finalizing the manuscripts and publishing the contributions to spread the
conglomerated ideas through this book. It is believed that this book will be a good
resource for academicians, researchers, practising professionals and, especially,
students of the geotechnical fraternity related to the natural disaster mitigation and
management.
Tirupati, India A. Murali Krishna
Kyoto, Japan Takeshi Katsumi
vi Preface
Contents
1 The 2017 July Northern Kyushu Torrential Rainfall
Disaster—Geotechnical and Geological Perspectives . . . . . . . . . . . . 1
H. Hazarika, S. Yamamoto, T. Ishizawa, T. Danjo, Y. Kochi,
T. Fujishiro, K. Okamoto, D. Matsumoto and S. Ishibashi
2 Disaster Management in India and Characterization
for Geohazards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
B. K. Maheshwari
3 Shear Strength Behaviour of Gravel–Tire Chips Mixture . . . . . . . . 33
S. M. K. Pasha, H. Hazarika and N. Yoshimoto
4 Elastic Modulus Estimation Using a Scaled State Parameter
in the Extended Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
M. C. Koch, A. Murakami and K. Fujisawa
5 Spatial Distribution of Strength—Comparison Between Indian
and Japanese Embankments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
S. Nishimura, K. Imaide, T. Ueta, T. Hayashi, K. Inoue, T. Shibata
and B. Chaudhary
6 Integrating Rainfall Load into Remedial Design of Slopes
Affected by Landslides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
G. L. Sivakumar Babu and Pinom Ering
7 Investigation of Rainfall-Induced Landslides at the Hillslopes
of Guwahati Region, Assam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Chiranjib Prasad Sarma, Arindam Dey and A. Murali Krishna
8 Evaluation of the Risk Distribution of the Debris Flow Occurred
Using Numerical SimulationSubjected to Rockfall . . . . . . . . . . . . . 89
Y. Isobe, H. Inagaki and H. Ohno
vii
9 Significance of Drainage Measures on Landslide Mitigation
Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Minimol Korulla
10 Design of Waterfront-Retaining Walls Subjected to Waves
and Earthquakes: A Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
D. Choudhury and B. G. Rajesh
11 Instability of Composite Breakwater Subjected to Earthquake
and Tsunami and Its Countermeasures . . . . . . . . . . . . . . . . . . . . . . 119
B. Chaudhary, H. Hazarika, A. Murakami and K. Fujisawa
12 Ground Modification Techniques to Improve Liquefaction
Resistance in Indo-Gangetic Soils . . . . . . . . . . . . . . . . . . . . . . . . . . 127
J. T. Shahu and Mamata Mohanty
13 Extended Application of Cement-Based Grouting
to Gravel/Boulder Ground Improvement . . . . . . . . . . . . . . . . . . . . 135
H. Ishii
viii Contents
About the Editors
Dr. A. Murali Krishna joined the Department of Civil
Engineering, Indian Institute of Technology (IIT)
Tirupati as an Associate Professor (Geotechnical
Engineering) inMay 2019.He has been a facultymember
in Department of Civil Engineering at IIT Guwahati,
since 2008. He obtained doctoral degree from Indian
Institute of Science Bangalore, M.Tech degree from IIT
Kanpur and B.Tech degree from Sri Venkateswara
University, Tirupati. His research interests include:
Earthquake Geotechnics, Geosynthetics and Ground
Improvement, Site characterization and Numerical
and Physical modelling of geotechnical structures.
Dr. Murali Krishna supervised 7 Doctoral students and
24 Masters students. He co-authored nearly 170 publi-
cations of technical papers in international/national
Journals and conference/seminar proceedings, includ-
ing book chapters. He is a recipient of BRNS Young
Scientist Research award, BOYSCAST fellowship and
HERTAGE fellowship. Dr. Murali Krishna is an exec-
utive member of ISRM (India) and ISET. He is also a
Member of TC 203 of ISSMGE, since 2011. He served
Indian Geotechnical Society as an ‘Executive Member’
for four terms (2011–2018). Dr. Murali Krishna organ-
ised several national and international workshops and
short courses. He is a reviewer for several national and
international journals.
ix
Dr. Takeshi Katsumi is a Professor at the Graduate
School of Global Environmental Studies (GSGES),
Kyoto University, Japan. He served as Assistant to the
Executive Vice-President of Kyoto University for two
years from 2012 October, and is currently Vice Dean of
GSGES. He graduated from the Department of Civil
Engineering, Kyoto University, and obtained his doc-
toral degree from the same university in 1997. He has
research interests in a variety of topics of environmental
geotechnics, including waste landfills, remediation of
contaminated sites, and re-use of by-products in
geotechnical applications. He has received several
awards including the “JSPS Prize” by the Japan Society
for the Promotion of Science. He has been a member of
ISSMGE Technical Committee No. 215 on
Environmental Geotechnics for more than 15 years, and
has been the International Secretary of the Japanese
Geotechnical Society (JGS) since 2014. He has deliv-
ered keynote lectures at several international confer-
ences such. He has been involved in several projects
regarding the recovery works from the 2011 East Japan
earthquake and tsunami, and has been a contributing
member to the Central Environment Council of Japan
for the last two years.
x About the Editors
Chapter 1
The 2017 July Northern Kyushu
Torrential Rainfall
Disaster—Geotechnical and Geological
Perspectives
H. Hazarika, S. Yamamoto, T. Ishizawa, T. Danjo, Y. Kochi, T. Fujishiro,
K. Okamoto, D. Matsumoto and S. Ishibashi
1.1 Introduction
Record-breaking localized and torrential rainfall on July 5, 2017, caused many land-
slides, debris flows, and flooding of rivers in several areas of the Fukuoka and Oita
prefectures of Kyushu, Japan. The disaster, officially known as “The 2017 July
Northern Kyushu Torrential Rainfall Disaster”, is one of the unprecedented in
disaster histories of Japan in many decades. The record-breaking magnitude of the
heavy and localized rains triggered landslides and debris flow that swept massive
volumes of driftwood and soils into cities, towns, and villages located at the bases
of mountains, leaving 34 dead including 4 still missing. It also resulted in 1,428
H. Hazarika (B)
Department of Civil Engineering, Kyushu University, Fukuoka, Japan
e-mail: hazarika@civil.kyushu-u.ac.jp
S. Yamamoto
Chuo Kaihatsu Corporation, Fukuoka, Japan
T. Ishizawa · T. Danjo
NIED, Tsukuba, Japan
Y. Kochi
K’s Lab Inc., Yamaguchi, Japan
T. Fujishiro · K. Okamoto
Fukuyama Consultants Co. Ltd., Kitakyushu, Japan
D. Matsumoto
Japan Foundation Engineering Co. Ltd., Fukuoka, Japan
S. Ishibashi
Nihon Chiken Co. Ltd., Fukuoka, Japan
© Springer Nature Singapore Pte Ltd. 2020
A. M Krishna and T. Katsumi (eds.), Geotechnics for Natural Disaster Mitigation
and Management, Developments in Geotechnical Engineering,
https://doi.org/10.1007/978-981-13-8828-6_1
1
http://crossmark.crossref.org/dialog/?doi=10.1007/978-981-13-8828-6_1&domain=pdf
mailto:hazarika@civil.kyushu-u.ac.jp
https://doi.org/10.1007/978-981-13-8828-6_1
2 H. Hazarika et al.
completely, half and partially destroyed houses. The large amount of driftwood that
got caught on bridges and other structures blocked the flow of the rivers, thereby
spreading the damage even further.
According to data analysis by the Japan Meteorological Agency (JMA), in
Asakura city, Fukuoka prefecture recorded some 1,000 mm of rain in the 24-h period
ending onmidnight of July 5, 2017. The city of Hita, Oita Prefecture and Toho village
of Fukuoka Prefecture each had some 600 mm of rain; and the city of Nakatsu, Oita
Prefecture, and Soeda town of Fukuoka Prefecture each had around 500 mm of rain,
according to an analysis by the JMA’s Fukuoka Regional Headquarters [1].
Figure 1.1 shows the extent of the flooded area and the landslide disaster areas.
In the figure, blue areas represent the flooded rivers and their tributaries, and the
red areas represent the extent of damage due to landslides, debris flows, and flood-
related damage. The authors conducted an extensive investigation of the damage
covering several cities, towns, and villages of the Fukuoka and Oita Prefectures. The
investigation team consisted of people from the industry, government, and academia.
Figure 1.2 shows the survey routes and locations of the surveyed areas (Location 1
to Location 6).
Flooding, numerous slope failures and debris flows caused serious damage to
many infrastructures, and they can be broadly classified into the following categories:
(1) Landslides and debris flow related damage, (2) Formation of landslide dam, (3)
River erosion, (4) Agricultural dam damage, (5) Roads and railways damage, and 6)
Environmental damage due to disaster debris (including driftwood). A preliminary
investigation report by the Japanese Geotechnical Society has covered many aspects
of the abovementioned damage [2].
Asakura City Toho Village
Hita City
Haki IC
Asakura IC
Chikugo River
Fig. 1.1 Distribution of the flooded and damaged area [6]
1 The 2017 July Northern Kyushu Torrential Rainfall Disaster … 3
Loc.1
Hita-City
Ono-District Nagio
Loc.3
Asakura-City 
Hakiakatani 
Loc.2
Kazurahae 
Toho-Village Asakura-
Gun
Loc.4
Choan-temple 
 Asakura-City 
Sugawa 
Loc.5
Asakura-City 
Miyano
Loc.6
Pond around 
Asakura-City 
Sugawa 
Survey area of 
slope failure 
along Otoishi River
Fig. 1.2 Location map of the investigation area (modified from the [6])
Many professional societies and research institutions of Japan have carried out
disaster survey and submitted their reports. However, in most of the reports, they
focused only on the shallow landslides, and none provide an in-depth analysis of the
failure form. The authors have felt that the damage causedby this disaster cannot be
analyzed solely from the geotechnical engineering perspectives, as the areas covered
by the disaster have many complicated geologies and geomorphologies, which made
the damage devastating with far-reaching economic implications [3]. Therefore, the
authors conducted a special investigation of the slope failure areas in and around
Otoishi River basin, located approximately 3 km upstream from Matsusue Elemen-
tary School (see Fig. 1.2). It was found that the slope failures that occurred in this
basin were not only shallow landslides of strongly weathered granite (decomposed
granite) but also included failures that reflected the geological structure (fault fracture
zone) and large-scale (deep-seated) landslides in the areas with crystalline schist. In
this paper, the characteristics of the slope failures that occurred in the Otoishi River
basin are summarized, and the classification of failure focusing on the geological
structure are described based on the slope failure mechanism.
1.2 Topographical and Geological Features of the Otoishi
River Basin
As shown in Fig. 1.3, the Otoishi River is located in the southern area of the Sangun
Mountains where themain peaks extend in the northwest–southeast direction. It joins
the Akatani River, the right branch of the Chikugo River, near Matsusue Elementary
School, which was badly affected due to accumulation of disaster debris in the school
compound leading to the closure of the school for months.
4 H. Hazarika et al.
Loc. 3: Landslide of crystalline schistLoc. 4: Failure of crystalline schist
Loc. 2: Failure 
around the fault 
fracture zone 
Loc. 1: Failure of 
Strongly weathered 
granite 
Matsusue Elementary 
Fig. 1.3 Location map of the detailed investigation (modified from [6])
The geological map of the investigated areas (Fig. 1.4) suggests that a valley plain
lies in the Otoishi River basin in the northwest–southeast direction. The geological
formations of the entire basin are indicated in the figure. On the left side of the
bank, valleys lay vertically in the northeast–southwest direction, while on the right
bank side, valleys lay horizontally in the northeast–southwest direction. In addition,
several topographic elements such as saddles, knick lines, and straight valleys can
also be observed in the same direction. These directions are in line with the direction
of the fault fracture zone in northern Kyushu. This suggests that the topography of
this basin is vulnerable to discriminate erosion due to the geological structure (faults).
Moreover, Asakura granodiorite is distributed in the middle-to-downstream basin of
the Otoishi River, and Sangun metamorphic rocks are distributed in the upstream
area. Mount Hiko volcanic rocks from the Pliocene epoch in the neo-tertiary period
are distributed in the ridge, which is the drainage basin of the uppermost basin.
1.3 Characteristics of the Slope Failures
1.3.1 Granite Failure
The most common failure form found along the basin occurred in the so-called
strongly weathered “decomposed granite,” which transformed into soil (Location 1
of Fig. 1.3), as shown in Fig. 1.5a. The failure was roughly 1 m deep, and many
traces of springs are thought to be due to piping. Gully erosions had formed on the
failure surface. Since there was little colluvial deposit at the toe of the slope, it had
likely been eroded by the debris flow and been washed downstream. The probable
failure mechanism of the slope is described schematically in Fig. 1.5b.
1 The 2017 July Northern Kyushu Torrential Rainfall Disaster … 5
Akatani 
River 
Akatani 
River 
Otoishi 
River
Chikugo 
River 
Fig. 1.4 Geologicalmap of the investigated area (tl: Low terrace deposit, A4:Aso 4 pyroclastic flow
deposit, tm: Medium terrace deposit, H: Mount Hiko volcanic rocks, K: Kita-Sakamoto formation,
E: Paleogene period formations (Hoshuyama, Kawamagari, and Haji), Ku: Asakura granodiorite,
m2: Muddy schist, s2: Sandy schist, g2: Hard-iron schist)
(a) Slope failure with many gully erosions (b) Schematic profile
Fig. 1.5 Failure in highly weathered granite
InLocation 2,which is in the riverbank side slope in themiddle basin of theOtoishi
River (Refer toFig. 1.3), a 10mwide fault fracture zonewas found (Fig. 1.6).Multiple
such formations were observed in the northwest–southeast direction, as well as the
north-northeast–south-southwest and northeast–southwest directions. In some, fault
fracture zones strongly crushed by fault gouge could be observed. In this location,
at the end of the slope failure zone, a 1 m-wide gouge zone and a fault fracture zone
with a crack zone with a large opening of around 5 m wide were verified (Fig. 1.7).
6 H. Hazarika et al.
The direction of the fault was N54°W, 70°SE, and it worked as a receiving board to
the slope. Furthermore, a substantial volume of groundwater was flowing from the
crack zone on the slope side (around 50 L/min).
An analysis of this failuremechanism (Fig. 1.7b) based on the characteristics of the
crush zone and flowing water suggests that the gouge zone, which normally indicates
low permeability, became a cut-off wall, and the groundwater flowed from the crack
zone. However, during the torrential rainfall event, a large volume of groundwater
that accumulated in a short period of time likely raised the groundwater level inside
the slope resulting in the increase of pore water pressure, and eventually led to a
bedrock failure that included the crack zone.
Fig. 1.6 Whole view of the failure
(a) Enlarged view (b) Schematic profile 
Gouge
zone
Crack zone
(Large opening)
Sound rock
(Decomposed
granite)
Crack
zone
Topsoil
Fig. 1.7 Fault fracture zone and flowing water
1 The 2017 July Northern Kyushu Torrential Rainfall Disaster … 7
Fig. 1.8 Large-scale
landslide in the crystalline
schist-distributed area
(Source GIJ)
1.3.2 Failure of Crystalline Schist
1.3.2.1 Landslide on the Left Side of the Upstream Bank
In the upstream area of the Otoishi River with crystalline schist (Location 3 in
Fig. 1.3), a landslide with a length of approximately 300 m (landslide scarp to clod
end), width of 110 m, and an average depth of 15–20 m occurred (Fig. 1.8). This
landslide formed two landslide scarps, and a landslide clod that still remains in the
slope. The frontal part of the landslide clod traversed the road below, reached the
Otoishi riverbed and stopped, blocking most of the river channel (Fig. 1.9). However,
there was no evidence that this moving clod turned into a debris flow.
The slope was inclined to the south-southwest, and the landslide occurred near
the ridge. The topography of this area before the landslide had typical characteristics,
such as a steep slope in the end and a gentle slope at the halfway point (Fig. 1.10).
There was a layer of debris with rock fragments over 5 m thick near the left end
(Fig. 1.11), indicating that the same activity may have occurred several times in the
past.
8 H. Hazarika et al.
Fig. 1.9 Frontal section of the landslide clod blocking most of the Otoishi River
Fig. 1.10 Landslide scarp seen from halfway up the slope (gentle gradient)
Fig. 1.11 Layer of debris with rock fragments on the left end
1 The 2017 July Northern Kyushu Torrential Rainfall Disaster … 9
The geology of this slope was crystalline schists consisting of muddy and basic
schist penetratedwith fine-grain granite. Xenolith, crystalline schist, was found in the
fine-grain granite near the landslide scarp (Fig. 1.12). The crystalline schists, which
dominated the landslide scarp and side, were more evident on the upper areas. Also,
this area was thought to be the bedrock, which showed many cracks, with evidence
of fractioning and loosening. Since there was no regularity in the direction of cracks
(Fig. 1.13), the landslide may have caused high deformation and crushing. This was
because the strike and inclination measured in the area were N48°E and 36°NW,
which did not match the measurements outside the landslide range of N86°W and
32°N. Furthermore,the entire geological structure of the original slope presumably
formed an opposite slope. In addition to the fine-grain granite (aplite), a small-scale
fault fracture zone (a fault breccia zone less than 1 m wide) from the north-northeast
to south-southwest direction was found in some places with the intense formation of
clay. Heavily transformed fine-grain granite boulders were also observed. The rela-
tionship between these observations and the mechanism of the landslide is unknown,
but there may be a geological predisposition involving faults and alterations.
Except for the clod immediately below the landslide scarp, the landslide mass of
this slope did not preserve its original form. The status of the landslide scarp and
the side indicated that the landslide mass was composed of a sediment layer with
rock fragments and crystalline schists that had turned into soil and crumbled (rock
classification: D ~ CL).
The thickness of this landslide mass was estimated to be 15–20 m on average,
with a maximum of 25 m. The relatively firm crystalline schist (rock classification:
mainly CM) with few cracks on the lowermost part of the mass strongly suggests
Fig. 1.12 Fine-grain granite and crystalline schist
10 H. Hazarika et al.
Fig. 1.13 Left landslide scarp
that it was composed ofD ~ CL class crystalline schist (Fig. 1.14). However, because
landslide clods remained on the failure surface, there was no geological weak line
that could act as a sliding surface.
Multiple points of outflowing water were observed in the area from the land-
slide scarp to its end, where the flow increased (Fig. 1.15). However, since most of
these gushed out after the landslide clod yielded, the detailed status of groundwa-
ter is unknown. Since it has been estimated that the landslide occurred at a depth
of approximately 20 m, the deep groundwater likely contributed to the landslide
movement. Schematic diagram of the mechanism of failure is shown in Fig. 1.16.
1.3.2.2 Group of Failures on the Right Side of the Upstream Bank
In Location 4, multiple slope failures occurred (Fig. 1.17) opposite to the landslide in
Location 3 of the Otoishi Riverbank. The failures were smaller than the landslide of
the opposite bank (left side of the bank) and around 5 m deep, but different types of
failure forms were found, including failure of colluvial deposit that filled the valley,
failure of schist that weathered and transformed into soil, and failure dominated
by a fault fracture zone. Since there were fault fracture zones of almost the same
formation as in the granite-distributed areas, as well as schists full of cracks and
aplite formations in some parts of the failure surface, the primary cause of the failure
was likely controlled by these complicated geological structures.
The failure mechanism in this location can be classified into two groups. The first
failuremechanism (Fig. 1.18) is caused by fault fracture zones, as shown in Figs. 1.19
and 1.20, where the bedrock around the fault fracture zone weakened, likely resulting
in the failure in this part. The second failure mechanism (Fig. 1.21) is caused by a
highly weathered rock, as seen in Figs. 1.22 and 1.23. Soft sedimentation of bedrock
1 The 2017 July Northern Kyushu Torrential Rainfall Disaster … 11
Fig. 1.14 Geologic stratigraphy found at the landslide scarp
from aging due to weathering likely caused the failure of highly weathered rock due
to the heavy rainfalls. Regardless of the failure mechanism, both bedrock failures
undoubtedly involved the weathered rock.
1.3.3 Classification of Failure Patterns in Otoishi River Basin
Table 1.1 shows the various failure forms found in this investigation. The classifica-
tion in the Table summarizes the failure forms according to the geology and geolog-
ical structure. The granite group (Group I) can be subdivided as shallow landslides
of decomposed granite (Ia) and bedrock failures (Ib) dominated by the presence of
several fa fracture zones. On the other hand, the crystalline schist group (Group II)
12 H. Hazarika et al.
Fig. 1.15 Alteration and flowing water
Fig. 1.16 Schematic profile (failure and landslide of crystalline schist)
can be subdivided as failures of strongly weathered rocks distributed at the surface
(surface failure, IIa), bedrock failures (IIb) controlled by the geological structure,
and failures caused by large-scale (deep-seated) landslides (IIc).
1 The 2017 July Northern Kyushu Torrential Rainfall Disaster … 13
Colluvial deposit
Fault fracture
zone
Highly
weathered
rock
Schist and granite
Fault fracture
zone
Highly
weathered
rock
Fig. 1.17 Group of slope failures on the right side of the upstream bank (Source GIJ)
Fig. 1.18 Illustrative diagram of the failure form involving the crush zone
14 H. Hazarika et al.
Fig. 1.19 Low-angle fault distributed on the failure surface
Fig. 1.20 Failure controlled by the fault fracture zone (whole view)
Fig. 1.21 Illustrative diagram of the failure form due to highly weathered rock
1 The 2017 July Northern Kyushu Torrential Rainfall Disaster … 15
Fig. 1.22 Whole view of the landslide scarp
Fig. 1.23 State of the collapsed surface
1.4 Conclusions and Future Challenges
Below are the few important findings from this study:
(1) Fault fracture zones of multiple formations, such as NW, NS, and EW types,
are distributed along the Otoishi River.
(2) These zones are the primary cause of the slope failures and landslides that
occurred in this basin.
(3) The slope failures in the granite-distributed areas can be classified into two
groups: shallow landslides of highly weathered granite (decomposed granite)
16 H. Hazarika et al.
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1 The 2017 July Northern Kyushu Torrential Rainfall Disaster … 17
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18 H. Hazarika et al.
and bedrock failures (a type of failure around the fault fracture zones driven by
the geological structure and groundwater).
(4) The failure form of the crystalline schist-distributed area on the left side of
the upstream bank suggests that it was a landslide failure. Judging from the
topographic form before the failure, this area had likely suffered repeatedly
from gravity transformation.
(5) In the crystalline schist-distributed area on the right side of the upstream bank,
multiple failures of strongly weathered areas were found. In addition, a bedrock
failure near the fault fracture zone was observed.
Many aspects of the torrential rainfall disaster this time remain unclear. For exam-
ple, it is still not clearly known how the geological structure and groundwater charac-
teristics in the upstream,where crystalline schist is distributed, are related to the slope
failures. It is necessary to understand the topography of a wider area and perform
surface geological and hydrogeological surveys to examine the failure mechanism
in greater detail. Hydrological phenomena are closely related to the geology that
forms aquifers and the formation process of its structure [4, 5]. The five failure
forms proposed in this paper can be validated from the hydrogeologicalperspective
by measuring simple water quality parameters and the specific flow rate.
To prepare for the risk of landslide disasters caused by torrential rains, it is first
necessary to understand the evolution of the topography of the entire basin, as well as
the geological composition and structure in addition to the geotechnical engineering
knowledge. This enables a better understanding of the classification of failure forms
and failure mechanism to adopt both the hard-type and soft-type countermeasures
according to the types of disasters. Therefore, validating the classification of the slope
failure forms proposed in this paper from the geotechnical engineering perspective
is another important task of the future.
Acknowledgements The authors would like to express their sincere gratitude to the following
individuals for their assistance and cooperation during the field survey: Mr. Yokou (Chuo Kaihatsu
Corporation, Kyushu branch), Mr. Kariya (K’s Lab Inc., Yamaguchi), Mr. Ide (Nihon Chiken Co.
Ltd., Fukuoka). The tremendous help during the survey from the graduate students (Messrs Manafi,
Ali, Ogo, Zawad and Makimoto) of Geodisaster Prevention Laboratory of Kyushu University,
Fukuoka are also gratefully acknowledged.
References
1. Japan Meteorological Agency (JMA). http://www.jma.go.jp/jma/menu/H29kyusyu_hokubu.
html (2017)
2. Japanese Geotechnical Society (JGS): Report of the 2017 July Northern Kyushu Tor-
rential Rainfall Disaster. https://www.jiban.or.jp/wp-content/uploads/2017/07/saigai_
kyusyuhokubugoukinkyuhoukoku20170713.pdf (2017) (In Japanese )
3. Yamamoto, S., Yata, J., Yano, K.: Classification of slope failure along the Otoishi River: distri-
bution and features. In: Proceedings of the Annual Conference of Japan Society of Engineering
Geology, pp. 65–74 (2017) (In Japanese)
http://www.jma.go.jp/jma/menu/H29kyusyu_hokubu.html
https://www.jiban.or.jp/wp-content/uploads/2017/07/saigai_kyusyuhokubugoukinkyuhoukoku20170713.pdf
1 The 2017 July Northern Kyushu Torrential Rainfall Disaster … 19
4. Miyazaki, S.: Hydrogeological survey method. In: Booklet Hydrogeology Series 4. Senjōchi
Suikankyō Kenkyū Kikō, Japan (2017) (In Japanese)
5. Kashiwagi, T.: Hydrology: research and measurement method (flow survey and hydrogeologi-
cal properties of mountainous areas). In: Booklet Hydrogeology Series 3. Senjōchi Suikankyō
Kenkyū Kikō, Japan (2017) (In Japanese)
6. Geospatial InformationAuthority of Japan (GIJ). https://saigai.gsi.go.jp/3/20170726handokuzu/
handokuzu.pdf (2017)
https://saigai.gsi.go.jp/3/20170726handokuzu/handokuzu.pdf
Chapter 2
Disaster Management in India
and Characterization for Geohazards
B. K. Maheshwari
2.1 Introduction
Thedisastersmaydamage the public infrastructure of billions of dollars. Thedisasters
have occurred from millions of years and may continue in the future. However,
to mitigate the effects of disasters, it is necessary to understand how a hazard is
converted into a disaster. The primary objective is to prevent from turning a hazard
into a disaster. India, particularly the Himalayan region, is vulnerable to various
disasters including earthquakes, landslides and floods. As a follow up to Disaster
Management Act [1], in 2006, the Govt. of India established “National Disaster
Management Authority (NDMA)” headed by the Prime Minister. Later guidelines
on “National Policy on Disaster Management” was published [10]. Accordingly,
there is a paradigm shift, from relief-centric response to a proactive prevention,
mitigation and preparedness approach towards disasters.
Disasters disrupt the progress of nations particularly, pushbackdevelopingnations
by several decades. In recent times, efficient management of disasters, rather than a
mere response to their occurrence, has received increased attention worldwide. This
is the result of the recognition of the increasing frequency and intensity of disasters
and acknowledgement by the government that good governance in a caring and
civilized society, needs to deal effectively with the devastating impact of disasters.
India is vulnerable to a large number of various types of natural and man-made
disasters. The approximate proportions are 58.6% of the landmass is prone to
earthquakes of moderate to very high intensity; over 12% of land (40 million
hectare) is prone to floods and river erosion; about 76% of coastline (5,700 km
out of 7,516 km) is prone to cyclones and tsunamis; 68% of the cultivable area is
vulnerable to drought and hilly areas are at risk from landslides and avalanches.
B. K. Maheshwari (B)
Department of Earthquake Engineering and Former Head, Centre of Excellence in Disaster
Mitigation & Management, IIT Roorkee, Roorkee, India
e-mail: bkmahfeq@iitr.ac.in
© Springer Nature Singapore Pte Ltd. 2020
A. M Krishna and T. Katsumi (eds.), Geotechnics for Natural Disaster Mitigation
and Management, Developments in Geotechnical Engineering,
https://doi.org/10.1007/978-981-13-8828-6_2
21
http://crossmark.crossref.org/dialog/?doi=10.1007/978-981-13-8828-6_2&domain=pdf
mailto:bkmahfeq@iitr.ac.in
https://doi.org/10.1007/978-981-13-8828-6_2
22 B. K. Maheshwari
Vulnerability to Chemical, Biological, Radiological and Nuclear (CBRN) origin
disasters/emergencies also exists. Heightened vulnerabilities to disaster risks can
be related to population expansion, urbanization, and industrialization development
within high-risk zones, environmental degradation and climate change.
Disaster Management Act [1] led to the creation of the NDMA headed by the
Prime Minister, State Disaster Management Authorities (SDMAs) headed by the
Chief Ministers, and District Disaster Management Authorities (DDMAs) headed
by the District Collector/Magistrate or Deputy Commissioner to adopt a holistic and
integrated approach to disaster management (DM). The vision of NDMA is to build
a safe and disaster resilient India by developing a holistic, proactive, multi-disaster
oriented and technology-driven strategy through a culture of prevention, mitigation,
preparedness and response. The process, objective and elements of disaster manage-
ment as per the government’s policy on disaster management [10] are discussed.
One of the strategies for disaster mitigation is “seismic microzonation”, which
involves ground motion, liquefaction hazard and slope stability analysis (ISSMG
Manual). For seismic microzonation, the geotechnical site characterization is must
and the same is discussed here in detail. This characterization has been carried out
based on the in situ and laboratory test data. The data of tests conducted by the
author and his research group in Roorkee region are presented. The Roorkee is a
town in north India and located at about 200 km north of New Delhi in Uttarakhand
state. According to IS:1893 [2], Roorkee falls in seismic zone IV. The data indicate
that how geotechnical engineering plays a crucial role in the characterization of sites
which has been also indicated by Eurocode-8 and NEHRP.
2.2 Process and Objectives of Disaster Management
A disaster refers to a catastrophe or mishap from natural or man-made causes,
which is beyond the coping capacity of the affected community. Disaster manage-
ment involves following integrated process of planning, organizing, coordinating and
implementing measures [10]:
(i) Prevention of danger or threat.
(ii) Mitigation or reduction of risk.
(iii) Preparedness to deal with.
(iv) Prompt response to disaster threatening situation.
(v) Assessing the severity or magnitude of effect.
(vi) Evacuation, rescue and relief.
(vii) Rehabilitation and reconstruction.
(viii) Capacity building including research.
Objectives of the National Policy on Disaster Management [10] are
(i) Promoting a culture of prevention, preparedness and resilience at all levels
through knowledge, innovation and education.
2 Disaster Management in India and Characterization for Geohazards 23
(ii) Encouraging mitigation measures based on technology, traditional wisdom
and environmental sustainability.
(iii)Mainstreaming disaster management into the developmental planning
process.
(iv) Establishing institutional and techno-legal frameworks to create an enabling
regulatory environment and a compliance regime.
(v) Ensuring efficient mechanism for identification, assessment and monitoring
of disaster risks.
(vi) Developing contemporary forecasting and early warning systems backed by
responsive and fail-safe communicationwith information technology support.
(vii) Ensuring efficient response and relief with a caring approach towards the
needs of the vulnerable sections of the society.
(viii) Undertaking construction as an opportunity to build disaster resilient struc-
tures and habitat for ensuring safer living.
(ix) Promoting a productive and proactive partnership with the media for disaster
management.
Institutional framework under DM act consists of NDMA, SDMAs, DDMAs and
local authorities. Besides these, two important organizations are NIDM (National
Institute of Disaster Management) and NDRF (National Disaster Response Force).
2.3 Elements of Disaster Management
In general, disaster management can be broadly categorized into two groups, i.e.
actions before the disaster which include prevention, mitigation and preparedness
and actions after the disaster which includes response, relief, rehabilitation, recovery
and reconstruction. These are further discussed in detail [10].
2.3.1 Prevention, Mitigation and Preparedness
As the natural hazards like floods, earthquakes and cyclones cannot be avoided, with
mitigation measures along with proper planning of developmental work in the risk-
prone area, these hazards can be prevented from turning into disasters. To undertake
mitigation measures a multi-pronged approach needs to be adopted:
• Building mitigation measures into all development projects.
• Initiating of national level mitigation projects, in high priority areas.
• Encouraging and assisting state level mitigation projects.
• Indigenous knowledge of disaster and coping mechanisms.
24 B. K. Maheshwari
Further, mitigation measures include risk assessment and vulnerability mapping,
climate change adaption. Preparedness for disasters includes forecasting and early
warning systems, strengthening emergency centres, medical preparedness, corporate
social partnerships, mock drills, communication, IT support and media partnerships.
2.3.2 Response, Relief and Rehabilitation
and Reconstruction and Recovery
The existing and new institutional arrangements need to ensure proactive and inte-
grated approaches in dealing with any disaster. Prompt and effective response min-
imizes loss of life and property. This is possible through contemporary forecasting
and early warning systems, fail-safe communication and anticipatory deployment of
specialised response forces. A well-informed and prepared community can mitigate
the impact of disasters. The NEC (National Executive Committee) coordinates the
overall response in the disaster. Further state governments and SDMAare responsible
to monitor the situation and informNDMA. All stakeholders need to follow standard
operating procedures (SOPs). Incident Command System andMedical response need
to be strengthened.
Relief is not a provision of emergency relief supplies in time but also facilitating
an overarching system of assistance to the disaster victims for their rehabilitation and
ensuring their social safety and security. The relief should be prompt, adequate and of
approved standards. This includes setting up of temporary relief camps, management
of relief supplies, temporary rehabilitation and socio-economic rehabilitation.
Incorporating disaster resilient features to “build back better” is the guiding princi-
ple of reconstruction. Essential services and intermediate shelters need to be provided
at earliest. The capacity development can be addressed effectively with the active
and enthusiastic participation of the stakeholders. This process comprises awareness
generation, education, training, Research and Development (R&D), etc. It further
addresses putting in place appropriate institutional framework, management sys-
tems and allocation of resources for efficient prevention and handling of disasters.
Thus, a roadmap for disaster management is laid by NDMA.
2.4 Characterization for Earthquake Geohazard
Assessment of damage during past earthquakes indicated that the degree of damage
due to an earthquake is controlled mainly by three important factors [10]:
(a) Earthquake source and path characteristics.
(b) Local geological and geotechnical characteristics.
(c) Structural design and construction features.
2 Disaster Management in India and Characterization for Geohazards 25
Thus, the seismic ground response at a site is strongly influenced by local soil and
geological conditions.Hence, the details of the local geological and geotechnical data
along with the background of regional seismotectonic and seismicity are needed for
effective evaluation of ground response and site effects.
The damage patterns during an earthquake depend on the soil characteristics at
a site which will have a major effect on the level of ground shaking. This high-
lights the importance of site characterization, particularly, in microzonation studies.
The regional tectonic maps as well as surface geology maps and vertical geologi-
cal profiles are the essential ingredients for the seismic microzonation study. The
geological, geomorphological and geotechnical databases including the thickness of
site’s soil conditions are needed for assessing the local site effects for site amplifi-
cation as well as for liquefaction and landslide susceptibility. To obtain these data
either in situ geophysical and geotechnical explorations and/or laboratory tests are
conducted. The results of some of the tests conducted by the author and his research
group are discussed.
2.5 In Situ Field Tests for Site Characterization
The most common field tests are the Standard Penetration Test (SPT), Cone Pene-
tration Test (CPT) and Multichannel Analysis of Surface Wave (MASW) which are
discussed in following subsections.
2.5.1 Standard Penetration Test (SPT)
The standard penetration test (SPT) is done in a borehole using a split-spoon sampler.
The sampler consists of a driving shoe, a split-barrel of circular cross-section. The
procedure is discussed in detail in IS: 2131 [3]. In this test, the soil sample is also
obtained which can be further examined in the laboratory for index and dynamic
properties. The measured N value from field is denoted as Nm and this is equal to the
number of blows required to penetrate the sampler into the soil for 300 mm beyond
seating drive of 150 mm. To find the liquefaction resistance of soil, this N value is
corrected as follows [11]:
(N1)60 = NmCnCeCbCrCs
where values of various correction factors are given in Table 2.1.
Figure 2.1 shows soil profiles obtained from SPT conducted at four sites near
Roorkee [4, 6]. These SPT data are used either to evaluate liquefaction resistance of
the site or shear wave velocity (using correlations as discussed later). For liquefaction
26 B. K. Maheshwari
Table 2.1 Various correction factors applied to SPT values (after [11])
Factor Equipment variable Term Correction
Overburden pressure Cn See Fig. 4.3
Energy ratio Safety hammer Ce 0.60–1.17
Donut hammer 0.45–1.00
Automatic trip 0.9–1.6
Hammer See Table 4.2 for
details
Borehole diameter 65–115 mm Cb 1.0
150 mm 1.05
200 mm 1.15
Rod length 3–4 m Cr 0.75
4–6 m 0.85
6–10 m 0.95
10–30 m 1.0
>30 m <1.0
Sampling method Standard sampler Cs 1.0
Sampler without liners 1.2
resistance, first (N1)60 is found and then corresponding Cyclic Resistance Ratio
(CRR) is evaluated using empirical charts [11]. The liquefaction potential of these
sites was found as presented by Muley [8] and Muley et al. [9].
2.5.2 Cone Penetration Test (CPT)
Cone Penetration Test (CPT) is an in situ test done to determine the soil properties
and to get the soil stratigraphy. The cone havingan apex angle of 60° and an end
contact area of 10 cm2 will be pushed through the ground at 2 cm/sec. However,
like SPT no soil sample is collected in case of CPT. During the penetration of cone
penetrometer through the ground surface, the forces on the cone tip (qc) and sleeve
friction (f s) are measured. The Friction Ratio (f r = f s/qc), will vary with soil type
and it is also an important parameter. CPT with Piezocone termed as CPTu can also
measure the porewater pressure with the depth. Muley [8] examined the liquefaction
potential of few sites in Roorkee region using both CPT and CPTu data. Also, the
CPT and CPTu profiles can be used for determining soil behaviour type (Ic) and fines
content. One such profile for Solani Riverbed site is shown in Fig. 2.2.
2 Disaster Management in India and Characterization for Geohazards 27
(a) Solani Riverbed Site (b) Bhagwanpur Site 
(c) Bahadrabad Site (d) Haridwar Site
Fig. 2.1 Variation of penetration resistance (N) with depth for four sites near Roorkee (after [6])
28 B. K. Maheshwari
Fig. 2.2 Soil profile at Solani riverbed site, CPT; a normalized tip resistance (qc1N); b normalized
friction ratio (F); c soil behaviour type (Ic) and d fines content (after [8])
2.5.3 Multichannel Analysis of Surface Waves (MASW)
The most widely used geophysical technique is MASW (Multichannel Analysis
of Surface Waves) based on the seismic method that can be used for geotechnical
characterization of near-surface materials. The MASW has been found to be an
efficient method for unravelling the shallow subsurface properties. In particular,
the MASW is used in geotechnical engineering for the measurement of shear
wave velocity (V s) and dynamic properties, identification of subsurface material
boundaries and spatial variations of V s. MASW generates a shear wave velocity (V s)
profile (i.e. V s vs. depth) by analysing surface waves obtained from multichannel
records for active or passive seismic sources. Figure 2.3 shows two-dimensional soil
profiles at Bahadrabad and Haridwar site [9].
Based on MASW and SPT data in Roorkee region, Kirar et al. [5] proposed the
following relationship.
Vs = 99.5N 0.345 (2.1)
For site classification, Eurocode-8 andNEHRP usedweighted average shear wave
velocity for 30 m depth
(
V 30s
)
, for n number of layers of thickness di with shear wave
velocity Vi. This is defined as:
V 30s =
30
n∑
i=1
(
di
/
Vi
) (2.2)
2 Disaster Management in India and Characterization for Geohazards 29
Fig. 2.3 2D shear wave velocity (V s) profiles obtained from MASW tests (after [9])
2.6 Laboratory Tests for Site Characterization
Besides the index property tests, the most common laboratory tests for dynamic
analysis are Cyclic Triaxial for High-Strain testing and Resonant Column for Low-
Strain testing. Both are described in detail in the following subsections.
2.6.1 Cyclic Triaxial Tests
Cyclic triaxial test is the most commonly used laboratory test for the evaluation of
cyclic strength and strain-dependent dynamic properties of soils at high strain levels.
In this test [6], the deviator stress is applied cyclically on soil specimens under stress-
controlled condition. An automated triaxial testing system with five sensors (a load
cell to monitor the axial load; an LVDT to measure the vertical displacements; and
three transducers to detect the cell pressure, pore water pressure and volume change)
was used in this study.Kirar andMaheshwari [6] presented cyclic triaxial tests carried
out on Solani riverbed sand specimens of 50 mm diameter and 100 mm height, at
the in situ relative density and tested at effective confining pressure equivalent to
overburden pressure. Figure 2.4 shows modulus reduction and damping ratio curves
for Solani riverbed site. It can be observed that there is an effect of depth on these
curves and good agreement with literature.
30 B. K. Maheshwari
Fig. 2.4 a Modulus reduction curves. b Damping ratio curves of Solani riverbed sand (after [6])
2.6.2 Resonant Column Tests
The resonant column test is another laboratory test used for measuring the low-strain
dynamic properties of soils. The basic principle of the resonant column test is to
vibrate a cylindrical soil specimen in a fundamental mode of vibration, in torsion
or flexure. Once the fundamental mode is established, measurements of resonant
frequency and amplitude of vibration are obtained. In the present research, a com-
puterized resonant column apparatus was used. To evaluate dynamic soil properties
2 Disaster Management in India and Characterization for Geohazards 31
Fig. 2.5 aModulus reduction curves. bDamping ratio curves in low-strain range of Solani riverbed
sand (after [7])
in low-strain range (0.000–0.07%), resonant column tests were carried out on the
soil samples obtained from SPT [7]. Each sample was prepared with 50mm diameter
and 100 mm height. All the samples were prepared at the in situ relative density and
tested at an effective confining pressure equivalent to overburden pressure at that
depth. Figure 2.5 shows modulus reduction and damping ratio curves for the Solani
riverbed site in low-strain range. It can be observed that there is an effect of depth
on these curves and good agreement with literature.
32 B. K. Maheshwari
2.7 Summary and Conclusions
In this article, the policy of the Government of India for disaster management is
presented. The “National Disaster Management Authority (NDMA)” looks after the
disaster management in the country. One of its wing “National Disaster Response
Force (NDRF)” takes care of relief and rescue operations during the disasters.
However, the government’s policy is to increase capacity for prevention, mitigation
and preparedness before the occurrence of disaster rather than simply react after it.
The paper also highlighted the important methods of geotechnical site character-
ization for disaster mitigation. This includes both field and laboratory tests. Some of
the results from the author and his research group are presented.
References
1. DMAct: The DisasterManagement Act, the Gazette of India (Extraordinary), No. 53. Ministry
of Law and Justice, Government of India, New Delhi (2005)
2. IS: 1893 (Part 1): Criteria for earthquake resistant design of structures: general provisions and
buildings. Bureau of Indian Standards, New Delhi, India (2016)
3. IS: 2131: Method for standard penetration test for soils. Bureau of Indian Standards, New
Delhi, India (1981)
4. Kirar, B.: Dynamic Stiffness Characteristics of Unreinforced and Reinforced Sands. Ph.D.
thesis, Department of Earthquake Engineering, IIT Roorkee, India (2016)
5. Kirar, B., Maheshwari, B.K., Muley P.: Correlation between shear wave velocity (Vs) and
SPT resistance (N) for Roorkee region. Int. J. Geosynth. Ground Eng. 2(1), Article 9 (2016)
6. Kirar, B., Maheshwari, B.K: Dynamic properties of soils at large strains in Roorkee region
using field and laboratory tests. Indian Geotech. J. 48(1), 125–141 (2018)
7. Maheshwari, B.K., Kirar, B.: Dynamic properties of soils at low strains in Roorkee region
using resonant column tests. Int. J. Geotech. Eng. 13(5), 399–410 (2019)
8. Muley, P.: Assessment of liquefaction potential using in-situ and laboratory tests. Ph.D. thesis,
Department of Earthquake Engineering, IIT Roorkee, India (2016)
9. Muley, P., Maheshwari, B.K., Paul, D.K.: Liquefaction potential of Roorkee region using field
and laboratory Tests. Int. J. Geosynth. Ground Eng. 1(4), Article 37 (2015)
10. NDMA: National Policy on Disaster Management. National Disaster Management Authority
(NDMA), Ministry of Home Affairs, Government of India, New Delhi (2009)
11. Youd, L., Idriss, I.M.: Summary Report, Proceedings of the NCEER Workshop on Evaluation
of Liquefaction Resistance of Soils. Technical Report NCEER-97-0022, pp. 1–40 (1997)
Chapter 3
Shear Strength Behaviour of Gravel–Tire
Chips Mixture
S. M. K. Pasha, H. Hazarika and N. Yoshimoto
3.1 Introduction
It has been estimated that more than 1.5 billionscrap tires are generated in all over
the world annually. In 2016, over 95 million scrap tires in quantity and 1 million
tones in weight are generated and disposed in Japan. One common disposal practice
around the world is to dump scrap tires in very large mono-fill stockpiles. This can
pose serious threat to environment and public health such as increased breeding
ground for disease carrying pests, insidious animal’s activity and combustion.
Recycling is a definite option to reduce the amount of stockpiled scrap tires in
landfills. Over 63% of total scrap tires are being used as fuel for energy production
purposes in industries, while only 16% are reused as Tire-Derived Materials (TDM).
Due to unique physical and mechanical properties of Scrap Tire Derived Materials
(STDM) like low unit weight, low bulk density, high hydraulic conductivity, and
high elastic deformability, this has recently found it is way into the civil engineering
application with an advance growing interest each year. Retaining wall and bridge
abutment backfills, fills for lightweight embankment and landfill liners are just
examples of using STDM in civil engineering applications [3, 5]. The use of STDM
only may undermine the serviceability of civil and geotechnical structures, because
they are highly compressible. Researches in recent years focused on the use of sand
and STDM mixtures. Outcome of some researches have shown addition of STDM
(mostly tire shreds) leads to slightly improvement in shear strength of sand [7],
however referring to others, it was found to reduce the shear strength of sand [6].
On the other hand, most of studies unanimously have reported that sand and STDM
S. M. K. Pasha (B) · H. Hazarika
Department of Civil Engineering, Kyushu University, Fukuoka 819-0395, Japan
e-mail: manafi.siavash@gmail.com
N. Yoshimoto
Department of Civil and Environmental Engineering, Yamaguchi University, Ube-shi, Yamaguchi
755-8611, Japan
© Springer Nature Singapore Pte Ltd. 2020
A. M Krishna and T. Katsumi (eds.), Geotechnics for Natural Disaster Mitigation
and Management, Developments in Geotechnical Engineering,
https://doi.org/10.1007/978-981-13-8828-6_3
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34 S. M. Khajeh Pasha et al.
Fig. 3.1 Particle size
distribution of Gravel and
tire chips
Gravel
Tire chips
mixtures experienced high deformation resulted in non-explicit peak point or failure
at stress–deformation curves. STDM and sand–STDM mixture are often being used
as protective layer due to low liquefaction potential and interesting damping property
[1]. However, high compressibility and low elastic modulus of tire chips and tire
chips and STDM mixture could result in high differential settlement and inadequate
bearing capacity of foundation. So in order to overcome aforementioned issues,
gravel–tire chips mixture (GTCM) as an alternative geomaterial has been introduced
by Hazarika et al. [4], Hazarika and Abdullah [2]. Unfortunately, there is a lack of
study on the physical and mechanical properties of GTCM. Therefore, this study
aims to identify influential parameters affecting the shear strength and dilatancy
behaviour of gravel tire chips mixture. This paper presents results of the study on
the effect of confining pressure, relative density, and gravel fraction (VGravel/VT) on
the mechanical behaviour and deformation characteristic of gravel and GTCM.
3.2 Material Properties and Testing Program
Stress-controlled drained triaxial compression testswere conducted on the specimens
of 100 mm in diameter by 200 mm in height. The particle size distribution of the
gravel and tire chips used in this research is plotted in Fig. 3.1. The maximum grains
size of TC and gravel were limited to less than 1/6 of specimen diameter to avoid
the effect of sample size on the results of experiments. According to JGS 0131 (JIS
A1204), gravel is classified as poorly graded (SP). Regarding to shape andmaximum
grain size of STDM, they are classified as tire chips (TC). Specific gravity (Gs) of
gravel and TCwere obtained 2.81 and 1.17 respectively (Fig. 3.2). In order to proceed
with the preparation of specimens for CD triaxial tests at desired relative density, a
series of vibratory test were conducted on Gravel and GTCM mixtures according to
JGS-0161 standard .
The following empirical expression has been proposed to estimate the maximum
and minimum void ratio of GTCM:
3 Shear Strength Behaviour of Gravel–Tire Chips Mixture 35
Fig. 3.2 Specific gravity of
GTCM particles
Tire chips content ratio by weight (%)
Sp
ec
ifi
c 
Gr
av
ity
 o
f G
TC
M
Table 3.1 Fitting parameters
for max. and min. void ratio
Parameters A B C D
Maximum void ratio 0.83 0.35 41.39 −0.05
Minimum void ratio 0.56 0.42 43.26 −0.03
Fig. 3.3 Maximum and
minimum void ratio of
GTCM Max Void ratio
Min Void ratio
emin,GTCM, emax,GTCM = A + B
/(
1 + 10(C−(Gf%)×D
)
, D50,Tc
/
D50,G ≈ 1.2, D50,Tc = 6mm
(3.1)
where emin,GTCM, emax,GTCM are minimum and maximum void ratio of GTCM for
a given gravel fraction (Gf) in mixture. Where A, B, C,D are fitting parameters listed
in Table 3.1. As it can be seen in Fig. 3.3, the value of void ratio decreases as the
gravel fraction increases. Considering theory of packing of binary mixture, if large
particles are of the same size as small particles, large particles will be replaced by
small ones and gradual transition in void ratio without exhibiting any minimal value
can be observed Reid et al. [8, 9].
Under-compaction method was used for the preparation of specimens. Gravel
and tire chips were measured by mass corresponds to the desired volume of gravel
in the mixture and afterward mixed carefully by hand and placed into the mould
and sequentially compacted into 10 layers. The sample was saturated by allowing
36 S. M. Khajeh Pasha et al.
de-aired water flow through from the bottom of the sample. 200 kPa back pressure
was applied to the specimen in order to increase the degree of saturation (B > 0.95).
An isotropic consolidation pressure was applied to the sample while maintain-
ing initial backpressure constant. Specimen was undergone shearing with a constant
axial strain rate of 0.1%/min until the axial strain of 20% was achieved. The effect
of relative density, confining pressure and gravel fraction (Gf) in a mixture on shear
strength and deformation characteristics of gravel and GTCM was investigated in
this study. To this end, Gravel fraction by volume (Gf) in GTCM mixtures varies
between 0 (pure tire chips) and 100% (pure gravel). Confining pressures are con-
sidered to vary in the range of 50 and 200 kPa and three different relative density
Dr = 35, 50 and 75% are taken into account for this study.
3.3 Results and Discussion
3.3.1 Effect of the Gravel Fraction in GTCM (Gf)
As can be seen in Fig. 3.4 peak deviatoric stress decreases and the corresponding
value of axial strain increases with a decrease in the percentage of gravel fraction (Gf)
in GTCM. Three different behavioural zones of GTCM are clearly distinguishable
in the figure. Gravel-like behaviour was observed for Gf > 83%, where essentially
gravel particles forms GTCM soil matrix and stresses are mainly transmitted by
gravel to gravel contact forces.Well defined peak deviatoric stress and highly dilative
behaviour can be observed. Tire chips like behavior is evident for the specimens with
Gf < 55%. Tire chips particles are dominant in GTCM, as a results force chains are
mainly formed between tire chips particles. Therefore, mixture shows significant
reduction in the shear strength and demonstrates properties which can be found
in tire chips. For GTCM samples with 55% < Gf < 83%, very ductile behaviour
was observed when the peak of the deviatoric stress–strain curve is reached. Slightly
dilative behaviourwhich follows clear contractive behaviour can be seen in the figure.
Except in the case of GTCM with Gf = 83%, no distinct peakshear strength has
been observed for the GTCM samples with Gf < 83%.
3.3.2 Effect of the confining pressure
(
σ́3
)
Test results demonstrated that the shear strength of GTCM with Gf = 83% has
been remarkably enhanced by the effective confining pressure (see Fig. 3.5). GTCM
exhibits completely contractive behaviour at high confining pressure (σ́3 = 200 kPa).
At lower confining pressures, majority of gravel particles are still in contact and
as a result, stresses transmitted mainly by gravel particle and is found to carry its
properties that could be the reason for the observed phenomena.
3 Shear Strength Behaviour of Gravel–Tire Chips Mixture 37
Fig. 3.4 a Deviatoric
stress–axial strain.
b Volumetric strain–axial
strain relation of GTCM at
different GFs
(Dr = 50%, σ́3 = 100 kPa)
3.3.3 Effect of the Relative Density (Dr)
The rise in the degree of relative density (Dr) has almost no influence on the initial
slope of stress–strain curve but slightly increases peak shear strength and intensifies
dilatancy of GTCM specimens with Gf = 55% (see Fig. 3.6). Similar results have
been reported by other researchers.
3.3.4 Tangent Modulus of GTCM
The tangent modulus (Et) can be determined from stress–strain curve of the type
shown in Fig. 3.7. As can be seen in Fig. 3.8, for the GTCM samples with GF >
83% tangent modulus (Et) decreases (to 25% of its initial value for axial strains
over 6%) drastically with increasing axial strain and becomes negative beyond the
peak deviator stress (softening) and eventually increases again to around zero as the
residual strength is achieved (Gravel like behaviour).
38 S. M. Khajeh Pasha et al.
Fig. 3.5 a Deviatoric
stress–axial strain.
b Volumetric strain–axial
strain relation of GTCM at
different confining pressures
(Dr = 50%,Gf = 88%)
50 kN/
100 kN/
200 kN/
50 kN/
100 kN/
200 kN/
GTCM like behavior
(a)
(b)
For GTCM samples with 55% < Gf < 83%, Et decreases with axial strain until it
reaches to an almost positive threshold value. However, for samples with Gf <=55%,
no significant change in Et values has been observed (tire chips like behaviour).
Another remark that can be concluded from the figure is that no softening was
observed for samples with Gf < 70%. A slightly decreasing trend can be seen for the
first few percentages of axial strain, in the case of pure tire chips (Gf = 0%).
3.4 Conclusion
This paper presents the results of a series of triaxial test conducted on Gravel–Tire
Chips Mixture (GTCM). A new relationship has been proposed to predict the maxi-
mum andminimum void ratio of GTCM as a function of gravel fraction by volume in
the mixture. The behaviour of GTCM has been found to be significantly influenced
by the percentage of tire chips in mixture.
3 Shear Strength Behaviour of Gravel–Tire Chips Mixture 39
Fig. 3.6 a Deviatoric
stress–axial strain.
b Volumetric strain–axial
strain relation of GTCM at
different relative densities(
Gf = 55%, σ́3 = 100 kPa
)
Fig. 3.7 Definition of
tangent modulus
40 S. M. Khajeh Pasha et al.
Fig. 3.8 Variation of
tangent modulus with axial
strain. a 78% < Gf < 100% ,
b 0 < Gf < 70%
(
(
Dr = 50%, σ́3 = 100 kPa
)
Gf=100%
Gf=87%
Gf=83%
Gf=78%
Gf=70%
Gf=55%
Gf=44%
Gf=0%
(a)
(b)
Peak shear strength and tangent modulus of GTCM decreases as gravel fraction
decrease in the mixture because tire chips particles have relatively low stiffness
in comparison to that of gravel and do not contribute remarkably to improve shear
stiffness ofmixture. Three different behavioural zones, gravel-like, gravel–tire chips-
like and tire chips like behaviours have been observed.
In the first zone, gravel particles form GTCM material matrix and in third zone
tire chips form GTCM matrix and the second zone is established by a binary matrix
where gravel and tire chips have contributed in forming GTCM material matrix.
The effect of confining pressure on stress–strain and dilatancy behaviour of GTCM
was also investigated. Shear strength increases with increasing confining pressure
and contraction behaviour has been found to be intensified by the confining pressure.
Shear strength ofGTCMhas been found to be enhanced by increasing relative density
of GTCM up to a limited extent in comparison to that of the confining pressure.
Acknowledgements The authors would like to express their sincere gratitude to the Bridgestone
Corporation, Tokyo, Japan for their partial financial support. We would like to express our deep
gratitude to Prof. Yukio Nakata of the geotechnical engineering laboratory of Yamaguchi University
3 Shear Strength Behaviour of Gravel–Tire Chips Mixture 41
for his support. A special thanks go to Mr. Kanta Matsui of the geotechnical engineering laboratory
of Yamaguchi University for his help and support while conducting experiments.
References
1. Bahadori, H., Manafi, S.: Effect of tyre chips on dynamic properties of saturated sands. Int. J.
Phys. Model. Geotech. 15(3), 116–128 (2015)
2. Hazarika, H., Abdullah, A.: Improvement effects of two and three dimensional geosynthetics
used in liquefaction countermeasures. Jpn. Geotech. Soc. Spec. Publ. 2(68), 2336–2341 (2016)
3. Hazarika, H., Kohama, E., Sugano, T.: Underwater shake table tests on waterfront structures
protected with tire chips cushion. J. Geotech. Geoenviron. Eng. 134(12), 1706–1719 (2008)
4. Hazarika, H., Yasuhara, K., Kikuchi, Y., Karmokar, A.K., Mitarai, Y.: Multifaceted potentials of
tire-derived three dimensional geosynthetics in geotechnical applications and their evaluation.
Geotext. Geomembr. 28(3), 303–315 (2010)
5. Kaushik, M.K., Kumar, A., Bansal, A.: Performance of tire chips–gravel combinations with
nonwoven geotextile and encapsulated tire chips layers used as filter/separator under incremental
stress levels. Eur. J. Environ. Civ. Eng., 1–34 (2017)
6. Kawata, S., Hyodo, M., Orense, P., Yamada, S., Hazarika, H.: Undrained and drained shear
behavior of sand and tire chips composite material. In: Proceedings of the International Work-
shop on Scrap tire Derived Geomaterials—Opportunities and Challenges, Yokosuka, Japan,
pp. 277–283 (2007)
7. Mashiri, M.S., Vinod, J.S., Sheikh, M.N., Tsang, H.-H.: Shear strength and dilatancy behaviour
of sand–tyre chip mixtures. Soils Found. 55(3), 517–528 (2015)
8. Reid, R.A., Soupir, S.P., Schaefer, V.R.: Mitigation of void development under bridge approach
slabs using rubber tire chips. Recycl. Mater. Geotech. Appl. ASCE, 37–50 (1998)
9. Pasha, S.M.K., Hazarika, H., Yoshimoto, N.: Dynamic properties and liquefaction potential of
gravel-tire chips mixture (GTCM), J. Jpn. Soc. Civ Eng, Ser. A1 Struct Eng & Earthq Eng
(SE/EE), 74(4), I_649-I_655 (2018)
Chapter 4
Elastic Modulus Estimation Using
a Scaled State Parameter in the Extended
Kalman Filter
M. C. Koch, A. Murakami and K. Fujisawa
4.1 Introduction
Kalman Filtering is a Bayesian approach and one of the most popular methods
for state estimation in linear systems [1]. It is a powerful tool that combines the
information in the presence of uncertainty. The Kalman Filter can be applied to the
State-Space Model, that contains a system equation and an observation equation.
The state covariance and observation noise (0, R) are input parameters to the Kalman
Filter. Initially, the Kalman Filter makes an “apriori” estimate to the next step based
on the system equation. Then the state is updated (“aposteriori” estimate) using the
Gain that is calculated based on a weighting of the state covariance and observation
noise variance. The Extended Kalman Filter is a natural extension of the Kalman
Filter for nonlinear systems. It is based on a linearization along the state estimates
resulting from the observations. TheKalman Filter and associated techniques like the
Extended Kalman Filter (EKF) and Particle Filter have been vastly used to estimate
a wide range of geotechnical parameters [2, 3].
In this paper, an attempt is made to estimate the Elastic Modulus (E) of soil in the
presence of heterogeneities. The heterogeneous element in thesoil may be a cavity
or a material of different Elastic Modulus embedded in the otherwise homogenous
soil. The elastic wave propagation is simulated using the Finite ElementMethod. The
unconditionally stable Newmark β method is used for evaluating the Finite Element
equations in the time domain. The accelerations recorded at predetermined points are
used as observation data. As the observation equation is nonlinear, hence, the EKF
is used for state estimation. A simple case is considered wherein the location of the
heterogeneity is known but the Elastic Modulus (E) is unknown. The EKF is then
used to try and estimate the Elastic Modulus of the homogenous soil as well as the
heterogeneity. The EKF is known to perform poorly in the caseswhere the initial state
M. C. Koch (B) · A. Murakami · K. Fujisawa
Graduate School of Agriculture, Kyoto University, Sakyo-ku, Kyoto, Japan
e-mail: michaelkoch044@gmail.com
© Springer Nature Singapore Pte Ltd. 2020
A. M Krishna and T. Katsumi (eds.), Geotechnics for Natural Disaster Mitigation
and Management, Developments in Geotechnical Engineering,
https://doi.org/10.1007/978-981-13-8828-6_4
43
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44 M. C. Koch et al.
covariance is very large with respect to observation noise covariance [4, 5]. The large
difference in covariance’s, makes the filter pay too much attention to the observation
data which can cause numerical divergence. In practice the Elastic Modulus of soil
could range between 106 and 109 Pa, hence the initial state covariance would be in
this range. The accelerations recorded would typically be magnitudes lower and so
would the associated noise. Citing the above problem, a simple scaled formulation is
proposed that considers a scaled parameter as the state rather than the actual Elastic
Modulus. The formulation is presented and the effectiveness of this formulation is
investigated in relation to the given problem.
4.2 Extended Kalman Filter
4.2.1 Linearization of the System and Observation Equations
A state-space description for a nonlinear system would be of the form shown below
[6]. The system equation is given as
xt+1 = ft(xt) + ξt (4.1)
and the observation equation is
zt = gt(xt) + ηt (4.2)
where xt , zt are the true state vector and observation vector at time t, respectively. ft
and gt are nonlinear functions of the state vector. ξt is the white noise contribution to
the state vector while ηt is the error in the observation vector which is also assumed
to be a Gaussian white noise.
The covariance associated with ξt and ηt are given by
E
(
ξtξ
T
p
)
=
{
Qt, t = p
0, t �= p (4.3)
E
(
ηtη
T
p
)
=
{
Rt, t = p
0, t �= p (4.4)
E
(
ξkη
T
l
) = 0 for all t and p (4.5)
Let the state estimate at time t be x
∧
t then the predicted state at t + 1 is given as
x
∧
t+1|t = f t
(
x
∧
t
)
(4.6)
The covariance associated with states x
∧
t|t−1 and x
∧
t|t are shown in Eq. (4.7) and
Eq. (4.8), respectively:
4 Elastic Modulus Estimation Using a Scaled State Parameter … 45
Pt,t−1 = E
[(
xt − x
∧
t|t−1
)(
xt − x
∧
t|t−1
)T]
(4.7)
Pt,t = E
[(
xt − x
∧
t
)(
xt − x
∧
t
)T]
(4.8)
The state and observation functions ft and gt are linearized by considering a linear
Taylor series approximation. While the function ft is linearized at time x
∧
t|t , gt is
linearized at x
∧
t|t−1 .
f t(xt) � f t
(
x
∧
t
) + �t
(
xt − x
∧
t
)
(4.9)
gt(xt) � gt
(
x
∧
t|t−1
) + Ht
(
xt − x
∧
t|t−1
)
(4.10)
where
�t = ∂f t
∂xt
(
x
∧
t
)
and Ht = ∂gt
∂xt
(
x
∧
t|t−1
)
(4.11)
Equations (4.9) and (4.10) can be substituted back into Eqs. (4.1) and (4.2) to get
xt+1 = �txt + ξ t + f t
(
x
∧
t
) − �tx
∧
t (4.12)
zt = Htxt + ηt + gt
(
x
∧
t|t−1
) − Htx
∧
t|t−1 (4.13)
Setting
ut = ft
(
x
∧
t
) − Φtx∧t
yt = zt − gt
(
x
∧
t|t−1
) + Htx
∧
t|t−1
(4.14)
we get the linearized state and observation equations as shown in (4.15) and (4.16)
xt+1 = �txt + ut + ξ t (4.15)
yt = Htxt + ηt (4.16)
Using the usual formula for the Kalman filter on this linearized system, to obtain
the corrected state from the predicted state (x
∧
t|t−1 ), we get
x
∧
t = x
∧
t|t−1 + Gt
(
yt − Htx
∧
t|t−1
)
(4.17)
where Gt is the Gain calculated at time t.
On substituting wt from (4.14) in (4.17), we get
x
∧
t = x
∧
t|t−1 + Gt
(
zt − gt
(
x
∧
t|t−1
))
(4.18)
46 M. C. Koch et al.
4.2.2 Algorithm
The complete EKF algorithm is as follows:
1. Pt,t−1 = Var(x0), x
∧
0 = E(x0)
2. For = 1, 2, . . .
3. Pt,t−1 = [�t−1
(
x
∧
t−1
)]Pt−1,t−1
[
�t−1
(
x
∧
t−1
)]T + Qt
4. x
∧
t|t−1 = ft−1
(
x
∧
t−1
)
5. Gt = Pt,t−1
[
Ht
(
x
∧
t|t−1
)]T[[
Ht
(
x
∧
t|t−1
)]
Pt,t−1
[
Ht
(
x
∧
t|t−1
)]T + Rt
]−1
6. Pt,t =
[
I − Gt
[
Ht
(
x
∧
t|t−1
)]]
Pt,t−1
7. x
∧
t = x
∧
t|t−1 + Gt
(
zt − gt
(
x
∧
t|t−1
))
(4.19)
4.3 Formulation
4.3.1 Finite Element Method
The Galerkin Finite Element Method was used to simulate the wave propagation
based on the following discretized equation:
Müt + K
(
Ei
)
ut = Ft (4.20)
whereM is the Mass Matrix, K
(
Ei
)
is the stiffness matrix. Ei is the Elastic Modulus
of all the elements in the domain and F(t) is the Force applied at time t. u(t) and
ü(t) are the displacement and acceleration vector for all the nodes. No damping was
considered.
4.3.2 Derivation of the H Matrix
The dynamic analysis of the system was done using the Newmark β Method (γ =
0.5, β = 0.25) Newmark [7]. The equations of the Newmark Beta Method are as
follows:
ut+1 = ut + �tu̇t +
[(
1
2
− β
)
�t2
]
üt + β�t2üt+1 (4.21)
u̇t+1 = u̇t +
[(
1
2
− γ
)
�t
]
üt + γ�t2üt+1 (4.22)
4 Elastic Modulus Estimation Using a Scaled State Parameter … 47
Substituting Eqs. (4.21) and (4.22) in (4.20) and rearranging the terms, we get
üt+1
(
Ei
) = S(Ei)−1[Ft+1 − T
(
Ei
)
üt − V
(
Ei
)
u̇t − K
(
Ei
)
ut
]
(4.23)
where,
S
(
Ei
) = M + K(Ei)�t
2
4
,T
(
Ei
) = K(Ei)�t
2
4
and V
(
Ei
) = K(Ei)�t (4.24)
As it can be clearly seen S, V, and T are all functions of the Elastic Modulus. More
specifically, it can be seen that the dependence of üt+�t on E is nonlinear. In order
to use the EKF, it is necessary to linearize this equation. This is done as follows [8]:
Hit+1 =
∂üt+1
∂Ei
= −S−1 ∂S
∂Ei
S−1Ft+1 −
[
−S−1 ∂S
∂Ei
S−1Tüt + S−1 ∂T
∂Ei
üt
]
−
[
−S−1 ∂S
∂Ei
S−1Vu̇t + S−1 ∂V
∂Ei
u̇t
]
−
[
−S−1 ∂S
∂Ei
S−1Kut + S−1 ∂K
∂Ei
ut
]
(4.25)
Hit+1 =
∂üt+1
∂Ei
= −S−1 ∂S
∂Ei
S−1
[
Ft+1 − Tüt − Vu̇t − Ku̇t
] − S−1
[
∂T
∂Ei
üt + ∂V
∂Ei
u̇t + ∂K
∂Ei
ut
]
(4.26)
H = Hit+1 =
∂üt+1
∂Ei
= −S−1
[
∂S
∂Ei
üt+1 + ∂T
∂Ei
üt + ∂V
∂Ei
u̇t + ∂K
∂Ei
ut
]
(4.27)
4.3.3 Setting Blocks and Scaling the State Vector
The domain is set up in such a way that a finite number of elements are grouped
together to form a block, i.e., all the elements in the same block are forced to have
the same Elastic Modulus. If the domain discretized with n elements is divided into
N blocks (N ≤ n) then the new state vector has only N dimensions. Let this vector
be called W.
A simple scaling operation is executed by simply considering the state vector
E = [E1,E2,E3, · · · ,En]T = E′[w1,w1,w2, · · · ,wN]T
i.e. Ei = E′wj ∀i ∈ block j (4.28)
where wj is the scaled state vector representing the Elastic Modulus of block j to
which element i belongs.
The scaling parameter E′ is kept constant during the filtering process. The lin-
earization of the observation equation now needs to be done with respect to the new
variable. This is done as follows:
48 M. C. Koch et al.
ht+1 = ∂üt+1
∂W
= ∂üt+1
∂E
∂E
∂W
= HJ (4.29)
where,
J = ∂E
i
∂wj
=
{
E′ if i ∈ blockj
0 otherwise
(4.30)
4.3.4 The EKF Formulation
The system equation is given as
Wt+1 = IWt (4.31)
while the Observation Equation is given as
yt = htW t + ηt (4.32)
where based on Eq. (4.14)
yt = üt − üt|t−1 + htw
∧
t|t−1 (4.33)
The Extended Kalman filtering process can then be started by substituted by
placing