howladar, m. farhad; hayashi, daigoro 琉球大学理学部紀要 = … · m. farhad howladar and...

Title Fault analysis around Himalaya by means of 2 dimensionalfinite element method.

Author(s) Howladar, M. Farhad; Hayashi, Daigoro

Citation 琉球大学理学部紀要 = Bulletin of the College of Science.University of the Ryukyus(75): 19-53

Issue Date 2003-03

URL http://hdl.handle.net/20.500.12000/2619

Rights

Bull. Fac. Sci., Univ. Ryukyus, No. 75 : 19-53 (2003) 19

Fault analysis around Himalaya by means of2 dimensional finite element method.

M. Farhad Howladar and Daigoro Hayashi

Department of Physics and Earth Sciences, University of the Ryukyus, Nishihara,

Okinawa, 903-0213, Japan.

ABSTRACT

We examined the nature of stress around the Himalaya via numerical simulation using

the 2 dimensional plane strain finite element models with elastic rheology. Mohr-Coulomb

failure criterion also adopted to analyze the relationship between stress distribution and its

influence on forming faults around the Himalaya. From this point of view, we presented

three finite element elastic models and considered convergence displacement that is subjected

along the SW-NE horizontal direction. Results point out that the convergence displacement

boundary conditions and elastic properties of rock control the distribution, orientation,

magnitudes and intensity of stress during the experiments.

Some interesting features of our models are: (l) principle stresses are mainly compressive;

(2) a, directs vertically in deeper part and horizontally in the upper part of all layer; (3)

a2 exhibits horizontal direction in the deeper part and vertical in the upper part; (4) magnitudes

of both stresses are relatively high in the deeper part compared with the shallower part; (5)

some tensional stresses are displayed in the upper part of Higher Himalayan region; (6)

most of the elements are failed in layer 2 (Sub-Himalaya) and in the upper part of layers.

1 (Pre-Cambrian Basement), 4 (Higher Himalaya) and 5 (Tethys Himalaya).

These features allow us to infer that the nature and direction of compressive and tensional

principle stresses are responsible for forming thrust and normal faults in these layers,

respectively and they are intensely concentrated along Sub-Himalaya and upper part of other

layers. The results from our numerical experiments are in agreement with the seismicity and

focal mechanism solutions of earthquakes in the study area.

Key words: Geological cross-section, finite element method, Mohr-Coulomb failure envelop, elastic

rheology, convergence displacement, fault.

1. Introduction

The concepts of finite element method have wide variety of applications in all branches

of sciences as well as in the geological sciences. In the geological Sciences, these includes

the development of igneous, sedimentary and metamorphic rock fabric, the formation of

geological structures, the flow of glaciers, the movements of tectonic plate, the nature of

seismic waves, the origin of earthquakes and the earth's materials. In spite of these great

20 M. Farhad Howladar and Daigoro Hayashi

applicability, we have endeavored to condense the facts into a more regional and comprehensive

fault related structural pictures around Himalayas by means of 2D finite element method.

Since the geological processes are certainly slow phenomena and are also the abstruse

geological annals, it is required in the finite element analysis carefully to take account of

these phenomena and annals of the geologic structures in the study area.

The Himalayan mountain (Pig.l) is too long and wide world standard mountain belt

accredited by the collision of two supreme continents (Dezes, 1999). For this reason,

Himalayan mountain belt has been investigated by many Earth scientists, including geologist

(Gansser, 1964; Hashimoto et al., 1973; Le Fort, 1975; Stocklin, 1980; Sakai, 1983, 1985;

Colchen et al., 1986; Searle et al., 1987; Burchfile et al., 1992), geophysist, geochemist,

climatologist and so on.

IS&ijfesjife&ji Higjn Himalayan 'DSHBiOBlBI Crystalline Sequence

^^*n^ MCT

E-—-*-j Lesser Himalaya

N

A H- B1 S

cz

^^ XIBEX

NEPAL

^"^v^ MBT INDIA ~*~

%W& Trans-Himalaya -{- 3S°

ii n Indus Yarlung

^tJ Suture

i *'-'\ Tethyan Himalaya

-b -+-2SO9CT 5OO lcm.

Fig. 1. Generalized geologic map of Himalayan extremity showing the main litho-tectonic units of theorogen. Slightly modified after Le Fort (1975) and Dezes (1999).

The active steep faults close to the MBT are geometrically normal faults in a dynamically

compressional wedge (Mugnier et al., 1994). The active faults within the Himalaya are the

MBT (Joshi and Patel, 1997). The major active fault along the Himalaya is the Main

Frontal Thrust that marks the southern edge of the Himalayan foothills (Nakata, 1989).

Steeply dipping faults transverse to Himalaya are distributed in the Sub-Himalaya and the

Lesser Himalaya. Many of these faults in the lesser Himalaya are conjugate wrench faults

striking approximately NNE and NNW (Kumar and Mahajan, 2001). Convergence between

the India and Eurasia is taking place north of Tibet on the great strike-slip faults of

China (Molnar and Tapponier, 1975). Thrust faulting with strike-slip motion along gently

dipping planes towards north, southwest and southeast direction (Molnar, 1990; Kumar

Fault analysis around Himalaya by means of 2 dimensional finite element method. 21

and Mahajan, 1991). The Greater Himalayan crystallines are thrust over Middle Proterozoic

phyllites, metaquartzites, and mylonitic augen gneisses of the Lesser Himalaya along the

MCT (Pecher, 1989). Active tectonics in southern Tibet is characterized by normal faulting

along N-S grabens (Armijo et al., 1986). At places, the oblique strike-slip faults displaced

the Main Boundary Thrust by 4-12 km and entered into the Siwalik foothills (Rajal et al.,

1986). Thrust faulting began south of the suture in the Himalaya in the Oligocene

(Gansser, 1964). Fault plane solutions in the Himalayan region give the same general

pattern of thrust faulting, with one plane gently dipping beneath the Himalaya (Banghar,

1974).

The northern boundary of the Higher Himalayan Sequence is marked by the low-angle

normal fault that separates the high-grade sequence from the virtually unmetamorphosed

Tibetan Tethys series (Herren, 1987). This normal fault system, named the STDS has been

traced across much of the length of the Himalayan orogen (Burchfile et al., 1992). Molnar

et al. (1977) analyzed the structure and tectonics of the Himalaya and noted about thrust

faulting and that are consistent with the Indian subcontinent underthrusting the Himalaya

at shallow angles. Cattin and Avouac (2000) analyzed the two-dimensional mechanical

model and they explain that over geological timescale (5 Ma) the ~20mm/yr estimated

shortening rate across the range is accommodated by localized thrust faulting along the

Main Himalayan Thrust Fault.

Alam and Hayashi (2002) proposed a 2D finite element model for simulating the stress

and fault types around the Himalaya and they interpreted that most of the maximum

principal stress is horizontally distributed and all of the analyzed faults are thrust types

fault. Chandra (1975) performed the focal mechanism solutions in the Himalayas and showed

that the continued convergence of the Indian plate with Eurasian plate is accommodated

partly by the crustal shortening, as indicated by thrust focal mechanism solutions throughout

the entire Himalayas and Burmese ranges.

To understand the nature of fault, we choose three geological cross sections (Figs. 2 A,

B and C) from different parts of Himalaya to produce the finite element model grids and

stress field which have modified from (Pandey et al., 1999; Kaneko, 1997 and Dezes, 1999),

respectively. We adopted the Mohr-Coulomb failure criterion and also reviewed the seismic

nature and focal mechanism solutions from previously published studies around Himalayas. In

the present research, firstly we focus the attention to apply 2D finite element method for

simulating the behavior of stress on forming faults in the Himalaya when Indian subplate

subducted beneath the Eurasian Plate. Secondly, to apply the Mohr-Coulomb failure criterion

to find out the possible failed elements (area). Thirdly to present focal mechanism solutions for

providing information concerning the orientation of regional stress, nature of faulting and

sense of motion on faults.


Fig. 2 A. Geologic cross section across the central Himalaya of Nepal. Slightly modified after Brunei

(1986) and Pandey et al. (1999).

NE Teiin

Fig. 2 B. Geologic cross section along the Himalayan Metamorphic belt in Central Nepal. Slightly

modified after Kaneko (1997).

Crystalline sequence of

Higher Himalaya

Fig. 2 C. Geologic cross section of the north-western Himalaya modified after Dezes (1999).


2. Geological Setting

The Himalayan arc extends -2400 km from Nanga Parbat (8138 m) in the west to

Namche Barwa (7756 m) in the east (e.g. Le Fort, 1996). This region includes the

independent kingdoms of Nepal and Bhutan as well as parts of Pakistan, India, and

China. The orogen forms a sharp transition between the average ~5 km-high, arid Tibetan

, plateau and the warmer, wetter Indian lowlands and is comprised of roughly parallel,

crustal-scale fault systems that bound distinctive lithologic units (Catlos, et al., 2000).

The Himalayan territory begins from the sudden rise of topography from the Ganges

plain. The first step of topography corresponds to the position of Main Boundary Thrust.

The second step appears in the southern front of the Great Himalayas as a steep wall of

the southern slope. The base of the topographic step corresponds to the position of the

Main Central Thrust. The area between these two steps is the Midland zone where relatively

gentle topography met. The Great Himalayan range runs almost straight from Sikim to

western Nepal, including most of high peak above 8,000 m above the sea level.

Physically, the Himalayas forms three parallel zones: the Great Himalayas, the Middle

Himalayas (also known as the Inner or Lesser Himalayas), and the Sub-Himalayas, which

includes the Siwalik Range and foothills and the Tarai and Duars piedmont (an area of

land formed or lying at the foot of a mountain or mountain range). Each of these lateral

division exhibits certain similar topographic features. The Great Himalayas, the highest

zone consists of a huge line of snowy peaks with an average height exceeding 6100 m

(20,000 ft). The width of this zone, composed largely but not entirely of gneiss and granite,

is about 24 km. The Nepal and Sikkim (a state of northern India) portion of the Great

Himalayas contains the greatest number of high peaks. The snow line on the southern

slopes of the Great Himalayas varies from 4480 m (14,700 ft) in the eastern and central

Himalayas of Nepal and Sikkim to 5180 m (17,000 ft) in the western Himalayas (Kizaki,

1984). To the north of the Great Himalayas are several ranges such as the Zanskar,

Ladakh, and the Kailas. The Karakoram Range lies on the Tibetan side of the Great

Himalayas.

Nepal Himalayas are geologically divided into three regions from east to west: eastern,

central and western Nepal Himalaya (Fig 3). The east Nepal Himalayas are characterized

by the development of nappe structure, widespread augen gneiss and well exposed

migmatitic gneiss and tourmaline granite in the root zone. The nappe structure developed

in the region where the augen gneiss and tourmaline granite or migmatitic gneiss are

widely activated. The west Nepal Himalayas are recognized by the extreme displacement

of Himalayan gneiss producing a large klippe, wide distribution of augen gneiss and vast

intrusive body of tourmaline granite in the root zone. On the other hand central Nepal

Himalayas are geologically distinguish by simple homoclinal structure, narrow Himalayan

gneiss zone and less amount of the augen gneiss and granitoid (Kano, 1984).

24 M. Farhiid [lowladar and Daigoro Iliiyashi

Granite

ffiftj Siwalik Group

il>e<:m Tethys

|^.v-| Himalayan Gneiss

E ■ | Injection Gneiss

inmnts ^ J Maliabhnmt zone

Midland Meta Sediments I R Augen Gneiss

Thakmar Oroup ^j p^^^ Centra, xhrust

U-^l IVIiiin Boundary Thrust

WEST NEPAL

HIMALAYA

CENTRAL NEPAL

HIMALAYAEAST NEPAL HIMALAYA

Fig. 3. Geological sketch Map of the Nepal Himalayas. Slightly modified after Kano (1984).

3. Geological Cross Sections around the Study Area

We choose three geologic cross sections from different areas around Himalaya (Fig. 2)

to analyze the characteristics of stress by using the finite element method (FEM). The

cross section A (Model A) from the Central Himalaya of Nepal after (Brunei, 1986 and

Pandy et al., 1999); cross section B (Model B) from the Himalayan metamorphic belt in

Central Nepal after Kaneko (1997) and cross section C (Model C) has collected from the

north-western Himalaya after Dezes (1999) which have shown by the line A—A, B—B and

C~C in figures 1, 3 and 12, respectively. These are distinguished and typical by their own

characteristics. The stratigraphic zones and structural elements of these section maps

along the Himalaya can be presented by the following ways (Table 1).

3.1. Tectonic Zones:

3.1.1. Pre-Cambrian Basement Zone: The basement rocks are distributed many places over

the Himalaya as exposed or unexposed formation. Tethyan Himalayas are found mixed

with the granitic rocks. The oldest, recognized unit in Spiti is the Vaikrita Group which is

overlain by the Haimanta Group. They consist of mica schist, phyllite and quartzite. The

oldest rocks in the Kashmir Tethyan basin belong to the Salkhala Group. The rocks are

slate, phyllite, schist, marble and quartzite. The lower part of this group is often mixed

with granitic rocks. The Salkhala Group is overlain by Dogra Slate of Late Pre-Cambrian

age. The Upper Pre-Cambrian, of an elongated and narrow intracontinental sea between

the Indian continent and the Cimmerian Superterrane is documented by the sedimentary

series of the Phe Formation. The sediments of this 5000 to 10,000 metres thick formation

are mainly derived from the erosion of the relief fringing this trough to the north (Fuchs

and Linner, 1995; Wyss, 1999).


Table l: Stratigraphic zones and Tectonic lines of the Nepal Himalaya after Kano (1984) and Kaneko(1997).

Tethys Himalaya

Higher Himalaya

Lesser Himalaya

Sub-Himalaya

Indus-Tsangpo suture zone

Tibetan Tethys Group

Himalayan Gneiss Group

Mainly lower Paleozoic to

Mesozoic clastic and

calcareous sediments

Rejuvenated Pre-Cambrian

basement, mostly

polymetmorphosed and

migmatized at the Alpine

stage by the intrusion of

tourmaline granites.

Main Central Thrust Zone

Midland Group Mainly Eocambrian clastic

Sediments with limestone and

quartzite, mostly altered to

phyllite and metasandstone.

Main Boundary Thrust

Churia (Siwalik) Group Tertiary to Quarternary

molasses sediments

3.1.2. Sub-Himalayan Zone: This foreland zone consists of clastic sediments that were

produced by the uplift and subsequent erosion of the Himalayas and deposited by rivers.

These rocks have been folded and faulted to produce the Siwalik Hills that are at the foot

of the great mountains. According to Hagen (1969), the Lower, Middle and Upper Siwalik

is available in this region. The Middle Siwalik is prominent in the Nepalese Sub-Himalayas.

Lower part of this group consists of brick colored fine to medium grained sandstone and

contains some intercalations of muscovite bearing coarse-grained sandstone. The middle

part is made up of fine to medium grained calcareous sandstone and of fine to medium

grained brick colored sandstone in the upper portion. The Upper part is largely composed

of conglomerate. Predominantly pale schistose quartzites, purple and white quartzites, dark

hyalites, arkoses, purple and dark pebbly quartzites, salty brown sandstones and tourmaline

(Gasser et al., 1964 and Arita et al., 1984). Siwalik in the Karnali-Bheri region contains

sandstone, mudstone, conglomerate and limestone (Fuchs and frank, 1970; Hayashi et al.,

1984; Bashyal, 1986).

Sub-Himalayan rocks have been overthrust by the Lesser Himalayas along the Main

Boundary Thrust. This steep thrust flattens with depth, developed during the Pliocene

time and has been shown as active through the Pliestocene (Ni, et al., 1984). In turn, the


Sub-Himalayas are bounded by a thrust fault to the south and are forced over sediments

on the Indian plate. This fault system is called the Himalayan Frontal Thrust (Sorkhabi,

1999).

3.1.3. Lesser Himalayan Zone: The Lesser Himalayan zone is bounded by the Main

Central Thrust (MCT) in the north and Main Boundary Thrust (MBT) to the south. Unlike

the Higher Himalayas, the Lesser Himalaya only experienced up to greenschist facies

metamorphism. The rock types present here are also different and they are belonging to

the Midland metasediments group. Midland metasediments sequence presents two types of

lithofacies that are observed separately in the north and south part of the Nepal. Southern

facies is composed of limestone, slate and phyllite and northern facies consists of slate,

limestone and siliceous sandstone and with some schist (Hayashi et al., 1984). This group

in the Jajarkot area comprises mainly of garnet-mica, chlorite phyllite schist, black

phyllite, crystalline limestone, blastomylonitic augen gneiss, limestone, dolomite and

calcareous sandstone (Arita et al., 1984). Rock units here also show a series of anticlines

and synclines. Fossils have been documented in this zone, but they do not occur at the

same frequency as Tehtyan zone fossils.

3.1.4. Higher Himalayan Zone: The Higher Himalayas are also known as the Central

Crystalline zone, comprised of deformed metamorphic rocks and mark the axis of orogenic

uplift. Mica schist, quartzite, paragneiss, migmatite, and leucogranite bodies characterize

this uppermost Himalayan zone. They represent a multiphase deformation event, the first

being Barrovian type, or normal geothermal gradient conditions. There was then a shift to

Buchan-type metamorphism, low pressure and high temperature conditions, with temperatures

greatly exceeding normal gradient temperatures (Sorkhabi, 1999). Corresponding minerals

assemblages are dominated by biotite to sillimanite, representing greenschist to amphibolite

facies deformation. Deformation seems to have occurred in a north to south direction and

is associated with the Main Central Thrust (MCT), which brings the Higher Himalayas on

top of the Lesser Himalayas (Sorkhabi, 1999). Initially, it was thought that approximately

350 km of shortening had occurred in the Greater Himalayan sequence of rocks.

3.1.5. Tethys Himalayan Zone: The Tethyan Himalayas are located to the south of the

ITSZ. The belt has been extending from Kashmir to Nepal. Spiti valley in Himachal

Pradesh and Kashmir where have seen a continuous succession from Pre-Cambrian to

Mesozoic ages. They consist of thick, 10-17 km, marine sediments that were deposited on

the continental shelf and slope of the Indian continent. This occurred as India was drifting

but still in the southern hemisphere (Verma, 1997). Sediments are largely unmetamorphosed,

which has made for excellent preservation of fossils and occur in synclinorium-type basins.

Some however, have experienced greenschist facies deformation (Windley, 1995). Fossils

occur in this east-west zone within strata that are very clearly known. The large variety

of size and distribution of fauna suggests that life was flourishing in this area before the

orogen. Such success in biological diversity is accounted for by the relatively stationary


position of the Tehthyan Zone between mid-Proterozoic and Eocene time. Episodic formation

of land barriers enabled life to grow and diversify (Sorkhabi, 1999).

3.2. Major Tectonic Lines:

3.2.1. The Main Frontal Thrust (MFT): The Sub-Himalayas are bounded by a thrust fault

to the south and are forced over sediments on the Indian plate. This type of fault is

known as the Himalayan Frontal Thrust (Dezes, 1999). The MFT is along this still active

structure that the Sub-Himalaya is thrust towards the SW over the Quaternary fluvial

deposits of the Indian plains.

3.2.2. The Main Boundary Thrust (MBT): This structure separates the metapsammitic

schists and phyllites of the Lesser Himalaya from the conglomerates and sandstones of the

Sub-Himalaya (Arita et al., 1984). The SW-directed movements associated with this structure

are characterized by brittle deformation.

3.2.3. Main Central Thrust (MCT): This thrust was first described by Heim and Gansser

(1939) when they noted a contact between terrigenous carbonate rocks and thick overlying

metamorphic rocks, mica schists and gneiss (Sinha, 1987). The Main Central Thrust marks

the boundary between the Higher and Lesser Himalayan mountain. It is a longitudinal

thrust fault, and in many places is marked by a several kilometer thick zone of deformed

rocks with varying degrees of shearing and imbrication (Sorkhabi, 1999). Mylonitization

and retrograde metamorphic assemblages also occur here. The MCT is the actual suture

between Gondwanaland (India) and the Proto-Tehtys microcontinent to the north

(Spikantia, 1987). Movement along the fault has brought crystalline rock from the Higher

Himalayan zone on top of Lesser Paleozoic sediments in the form of klippen in synclines

(Windley, 1995). These units are called the outer crystallines. Outer crystalline rocks, garnet

and kyanite-bearing, were exposed by slip along the MCT followed by uplift and erosion of

10 km of overlying rock (Molnar, 1986).

3.2.4. The Indus Tsangpo Suture (ITS): This structure marks the limit between the Indian

Plate and the Eurasian plate. It is along the Indus Suture zone that the Indian plate was

subducted below Eurasia. Remains of oceanic crust and island arc, mixed with flysch and

molasse deposits, can be found within the ITS as well as in the Spontang Klippe (Dezes,

1999).

3.2.5. The South Tibetan Detachment System (STDS): The South Tibetan Detachment

System also called North Himalayan Shear Zone (NHSZ), (Dezes, 1999) represents a major

system of north-dipping structural detachments at the boundary between the High Himalayan

Crystalline Sequence and the Tethys Himalaya. This structure was first identified by Burg

(1984). A detailed analysis of the STDS was made by Burchfiel et al. (1992). Deformation

along this structure was accommodated either by dextral strike-slip or by extensional

shearing. Unlike the MCT, the STDS is not a continuous structure along the entire

Himalayan belt.


4. Finite Element Method

Finite Element Method (FEM) was first developed approximately in 1943. Shortly

thereafter, a paper published in established a broader definition of numerical analysis

(Turner et al., 1956). The paper centered on the "stiffness and deflection of complex

structures".

Finite element method widely used by the engineer, geologist, and physicist to model the

behavior of a wide variety of complex system such as fluid flow, heat flow, and electromagnetic

problems. The finite element method enables to analyze the static and dynamic behavior

of a real and continuous structure that is simulated by an equivalent model written in a

matrix form. In performing the FEM analysis, it is assumed that the geological materials

involving in the analysis are homogeneous and perfectly elastic, although it is certain that

the geological rock body must be regarded as visco-elastic body as already mentioned by

Uemura (1971). This may make the results differ from the true on certain points but this

study would be considered an approach to better understanding of the nature. This section

illustrates the use of the method for mapping out of distributions of displacement, stress,

strain in geological bodies with known mechanical properties and subjected to given

external stress.

4.1. Modeling

To construct the finite element model, we selected three geological cross sections

around Himalaya. Model A collected from the central Himalaya of Nepal after (Brunei,

1986 and Pandey et al., 1999); model B from the Himalayan metamorphic belt in Central

Nepal after Kaneko (1997) and model C from the north-western Himalaya after Dezes

(1999). These models are shown in Figures 2 A, B and C. In order to determine the stress

field in these models by using FEM, we assumed the linear elastic behavior of material

and also plane strain situation.

4.2. Geometrical Configuration

The geometry of model A, model B, and model C are represented by a simple triangular

element (Figs. 6 A, B and C) and which covers the total area of all the models. The

approximate length and depth of models A, B, and C are about 140x32, 330x58 and

290x46 km, respectively. Model A contains 479 elements and 285 nodal points. Model B

and C are composed of 459 and 593 elements with 271 and 358 nodal points, respectively

which are shown in Figures 6 A, B and C.

The grid of all models have been designed and modified to permit assignments of different

rigidities for numerous tectonic units. Each model represented five major structural units

as their regional tectonic setting and they are divided as follows: Pre-Cambrian Basement

is named as Layer 1, The Sub-Himalaya, Lesser Himalaya, Higher Himalaya and Tethys

Himalaya are named as Layer 2, 3, 4 and 5, respectively in all models (Table 2 and Figs.

4 A, B and C).


Table 2. Structural units, considering layers and their respective major and most common rock

properties.

Structural Units

Pre-Cambrian Basement

Sub-Himalaya

Lesser Himalaya

Higher Himalaya

Tethys Himalaya

Considering Layers

Layer 1

Layer 2

Layer 3

Layer 4

Layer 5

Major and most common

rocks

Granite and gneiss

Sandstone

Metasediments

Gneiss and granite

Limestone and sandstone

Pre-Cambrian Basement (layer 1)

Sub-Himalaya (Layer 2)

Lesser Himalaya (Layer 3)

Higher Himalaya (Layer 4)

Tethys Himalaya (Layer 5)

NESTDS

cd •"

KathmanduMCT

MBT

MFT

SW

14 28 42 56 70 84

x-axis (km)

112 126 140

(a)

STUS MCT

33 66 132 165 198

x-axis (km)

231 264 297 330

(b)


ISZSTD

MCT MBT

58 87 116 145 174

x-axis (km)

203 232 261 ::<« i

(c)

Fig. 4. Simplified geometrical configuration of finite element clastic models A, B and C. All models

represented five major structural units as to their regional tectonic setting and each unit

appeared here as a layer like Pre-Cambrian basement is layerl, Sub-Himalaya is Layer2,

Lesser Himalaya is Iayer3, Higher Himalaya is Iayer4 and Tethys Himalaya is layero. MFT

= Main Frontal Thrust, MBT = Main Boundary Thrust, MCT = Main Central Thrust, STDS

= South Tibetan Detachment System, ISZ = Indus Suture Zone, MDT = Main Detachment

Thrust.

4.3. Rock Property

All the models are divided into five layers as shown in Figures 4 A, B and C with different

rock properties that are listed on Table 3. We choose the most dominant rocks for each

layer to find out the more homogeneous pictures concerning the stress trajectories. The

distribution of major and most common rocks in layer 1, 2, 3, 4 and 5 are gneiss and

granite, sandstone, metasediments, granite and gneiss and limestone and sandstone,

respectively that are listed in Table 2. The physical properties of rocks have been defined

Table 3. Number of layers and their respective physical Parameters that have used in the finite

element elastic models A, B and C (Source: The value; of five parameters listed within the

table have collected and modified from the Handbook of Physical Constant in 1966).

Finite element elastic modelsA, B and C

Number of

layers in

the Models

Layer 1

Layer 4

Layer 3

Layer 5

Layer 2

Young1 s

Modulus

(GPa)

80

72

64

58

40

Poisson's

Ratio

0.30

0.27

0.25

0.23

0.20

Density

Ckg/m3)

2800

2740

2680

2650

2500

Friction

angle

(degree)

45

42

39

37

30

Cohesion

(MPa)

30.00

25.00

20.00

17.50

10.00


by five parameters such as Young's modulus, Poisson's ratio, density, cohesion and friction

angle. The values of these parameters are listed in Table 3 and presented by Figure 5.

The order of strength of the layers are, layer 1 (Pre-Cambrian Basement), layer 4 (Higher

Himalaya), layer 3 (Lesser Himalaya), layer 6 (Tethys Himalaya) and layer 2 (Sub-Himafaya).

1

8

I

II

1

.. 80 m

" 72

40

Young's

modulus (GPa)

.30

.27

25

.23

.20■ 1

Poisson's

ratio

2800

2740

2680

2650

2500

Density

<Kg/m3)

Physical constants of rock

45

42

39

37

30

Friction angle

(degree)

30

25

—■ i ..«

20

17.5

10

Cohesion

(MPa)

■ Layer 1

■ Layer 2

a Layer 3

Layer 4

■ Layer 5

i

Fig, 5. Abundance ratio of physical constants of rock in different layers of Himalaya.

We used models with variety of values in order to explore the effect of changes in

these parameters and found that the patterns of stress states are little sensitive to the

absolute value and they are moderately influenced by the ratios of these parameters. This

indicates that the geometry and boundary conditions play important roles in all models.

4.4. Boundary Condition

The magnitudes of stress are directly related to the elastic properties of rocks and the

imposed displacement boundary conditions. We imposed velocity (or displacement) boundary

conditions instead of forces because the velocity of plate movement between the Indian

subplate and Eurasian plate is known.

Many authors deduced the convergence rate of Himalayan region and among them;

Chugh (1974) explained that the uplift of the mountains is about 4 to 5 mm/yr with

respect to the level in the Ganga Basin. Agrawal and Gaur (1972) measured vertical and

horizontal displacement across the Himalayan region for a six months period and found

out the convergence rate is approximately 9 mm/yr. Hayashi (1980 and 1987) reported that

the northerly migration of the Indian plate deformed the overlying Asian continental crust


and which was deformed by a 60 km deep ramp dipping 45 degrees northwards on a rigid

mantle moving at 100 mm/yr.

We have performed a number of experiments with different combinations of reasonable

convergence displacement boundary conditions (e. g. 2.5 cm/yr, 3 cm/yr, 5 cm/ yr, 7.5 cm/yr

and 10 cm/yr) along the South-West to North-East direction. The amount of displacement

boundary conditions have proportionally distributed to the horizontal length (x-axis) of all

models that have shown by the length of line with arrow in Figures 6 A, B and C and the

estimated boundary conditions of all models are shown in Table 4.

Tablt; 4. Imposed convergence displacement boundary conditions in the finite element elastic models.

Name of models

Model A

Model B

Model C

Convergence displacement (m)

100 and 500

100 and 500

100 and 500

The boundary conditions of finite element models A, B and C are as follows; The base

of all models are constrained to move vertically but are free to move horizontally whereas

the right and left wall side of all models are free to move vertical direction and constrained to

move horizontally. The upper surface of all models are free to move in all direction and

the corner nodes (origin) are fixed to move in all direction (Figs. 6 A, B and C).

NE

I"

STDS

Triangular finite elements

Nodal points MCT

MBT

40 m60 m

Mill!

100 m

14 28 70 84

x-axis (kni)

112 126 140

Fig. 6 A. Number of triangular finite elements, Nodal points and Imposed boundary condition of finite

element clastic model A (ace text for details). Used rheology in the model has listed inTable 3. Horizontal convergence displacement up to 500 m is imposed in an incremental

Steps of 100 m. The length of line with arrow prescribed the rate of displacement along SW-NE horizontal length (x-axis) of this experiments.

Fault analysis around Himalaya bv means of 2 dimensional finite element method. 33

Triangular finite elementsNodal Points

NE

sw

40 m60 m

"i

132

1 1—

165 198

x-axIs (km)

330

Pig. 6 li. Number of triangular finite elements, Nodal points and Imposed boundary condition of finite

element elastic model B (see text for details). Used rheology in the model has listed in

Table 3. Horizontal convergence displacement up to 500 m is imposed in an incremental

steps of 100 m. The length of line with arrow prescribed the rate of displacement, along BW"

NE horizontal length (x-axis) of this experiments.

Triangular finile elements

40 m60 m

80 m100 m

116 145

x-axls (km)

174 290

Fig. 6 C. Number of triangular finite elements, Nodal points and Imposed boundary condition of finite

element elastic model C (see text for details), Used rheology in the model has listed in

Table 3- Horizontal convergence displacement up to BOO m is imposed in an incremental

steps of 100 m. The length of line with arrow prescribed the rate of displacement along SW-

NE horizontal length (x-axis) of all Experiments.

The boundary condition of model A : At node 281, 282, 283, 284 and 285 displacement

along the horizontal direction are imposed. The nodal point 1 is restricted to move in all

directions. The nodes 1, 2, 3, 4, 5, 6, 7, 8, and 9 are free to move vertically (Fig. 6 A).

The boundary condition of model B : The nodal point 1 is fixed and nodes 1, 2, 3, 4,

5, 6, 7, 8 and 9 are free to move vertically but constraint to move horizontally. At nodes

270, 269, 268, and 267 displacements along horizontal direction are imposed (Fig. 6 B).

The boundary condition of model C ; At the nodes 355, 356, 357 and 358 displacement

along horizontal direction are permitted. The nodal point 1 is restricted to move in all

directions. Nodes 1, 2, 3, 4, 5, 6, 7, 8 and 9 are free to move vertically (Fig. 6 C).

4.5. Results of Simulation

We have numerically simulated three models A, B and C that permit to infer the

characteristics of stress field and its related tectonic events in the study area. Stress fields

of the models are shown in Figures 7 A, B and C. In these models ff, indicates the


maximum compressive stress and a2 minimum compressive stress. During the experiment,

we have imposed various convergence displacement boundary conditions and all of them

present nearly the same stress pattern in all models. The Convergence displacements 100

m and 500 m experiments have been explained for all models herein.

4.6. Stress Field of Model A

4.6.1. Stress field under convergence displacement 100 m (Model Al): We determined the

stress field throughout the model using the boundary conditions that are shown in Figure

6 A. oy and er3 are compressive. a, in the deeper part of Pre-Cambrian basement, Higher

Himalaya and Lesser Himalayan layer directs vertically and it's magnitude is strong in

this region (Fig. 7 Al). The direction of principal stresses in the Sub-Himalayan and

Tethys Himalayan layer are complicated to determine because of their low magnitude. The

value of ox is comparatively higher than a2 all over the model. Few numbers of principal

stresses show inclined orientation in the right part of layer 1, upper-middle part of layer

3 and left upper part of layer 4. Principal stresses display hydrostatic condition in upper

middle part of layer 1, 3 and 4. The values of compressive o, are from 34 MPa to 853 MPa

and ct, from 13 MPa to 375 MPa.

Layer-5STDS Scale: 100 MPa

MBT

MFT

14 42 70

x-axis (km)

112 126 140

Fig. 7 A (1). Distribution, orientation and magnitudes of stress trajectories of model A (l) under 100

m convergence displacement. Black color with straight line reflects compressionai stress and

red color with straight line represents the tensional stress. (Note : The rate of considered

convergence displacement: boundary conditions have listed in Table 4).

4.6.2. Stress field under convergence displacement 500 m (Model A2): o{ and oz are

compressive everywhere (Fig. 7 A2). The intensity of a, and a2 is relatively high in the

deeper part in all layers. Magnitude of principal stresses are approximately the same in

layer 1 and middle part of layer 3 and layer 4 which indicate the hydrostatic condition

prevail over these area, ct, directs horizontally in the upper part on the other hand o2

directs vertically. The magnitude of o2 is low in the upper part especially in layer 2 and

5. Direction of a, is inclined within some elements in deeper part of the Pre-Cambrian

basement layer, The values of a, and a2 are from 164 MPa to 885 MPa and 11 MPa to 564

MPa, respectively.


E —

STDSLayer-5 .^ Scale: lOOMPa •

MCTMBT

MFT

*+*-&V•* ■2V**.-* *•"- — *-.

*-*■■

14 28 42 56—I

70

x-axis (km)

-r-

8'J 9BT112 126

"I140

Fig. 7 A (2). Distribution, orientation and magnitudes of stress trajectories of model A (2) under 500m convergence displacement. Black color with straight line reflects compressional stress and

red color with straight line represents the tensional stress. (Note : The rate of consideredconvergence displacement boundary conditions have listed in Table 4).

4.7. Stress Field of Model B

4.7.1. Stress field under convergence displacement 100 m (Model Bl): a, and a, shows the

compressive pattern of stress (Fig. 7 Bl). Direction of ax is vertical whereas o2 directs

horizontally all over the area. The magnitude of a, and a2 are low in the Sub-Himalayan

region and upper part of the layer 1, 3, 4 and 5. The Maximum and minimum compressive

stresses are strong in deeper part of the Pre-Cambrian basement layer than the shallower

region of other layers. The absolute value of a, may be two times larger than that of the

a., in the deeper part in layer 1. The value of ot is from 24 to 1381 MPa and the value

of a, 13 to 624 MPa.

Seals: 100 MPa

Indus Suture ,

Layer-5STDS

MCT MBTLayer-2

I—33

"1132

T—

165T—198

1—Z64

1—297

"13300 33 66 99 132 165 198 231

x-axis (km)

Fig. 7 B (1). Distribution, orientation and magnitudes of stress trajectories of model B (l) under 100

m convergence displacement. Black color with straight line reflects compressional stress and


convergence displacement boundary conditions have listed in Table 4).

4.7.2. Stress field under convergence displacement 500 m (Model B2): Direction of compressive

<7j is vertical and it's intensity is nearly the constant in deeper region of layer 1. Layers

3 and 4 show the intermediate magnitude and most parts of layers 2 and 5 exhibit weak


magnitude. o] and a2 show angular direction near the MCT and below the Sub-Himalayan

layer. Minimum Principal stress (aK) is also compressive in character and directs nearly

horizontal (Fig. 7 B2j. The value of ox in deeper part of layer 1 is same as model Bl.

Several finite elements are belong to hydrostatic environment in upper middle part of

layer 1 and middle part of 3, 4 and 5. The value of <7, and a, ranges from 66 to 1389 MPa

and 14 to 763 MPa, respectively.

Scale: 100 MPa

Tarim

Indus Suture

1*

1 T*™- S STDS— J_ jr MCT MBT■* "» *' '»'- *■* "* 5%*t* '* -J^-^^-^t^r—r~-»^_a^' ^ Layer-2

33 66 132 165

x-axis (km)

198 231 264 297 330

Fig. 7 B (2). Distribution, orientation and magnitudes of stress trajectories of model B (2) under 500




4.8. Stress Field of Model C

4.8.1. Stress field under convergence displacement 100 m (Model Cl): Calculated stress

exhibits compressive in all layers except few parts of layer 4 (Fig. 7 Cl) when 100 m

convergence displacement is imposed along SW-NE direction. Most of maximum compressive

principal stress (cr,) is vertically distributed all over the models. The magnitude of a, is

strong in the deeper part of the layer 1 and 4 also few places in the layers 3 and 2 than

s s

12

Scale: 100 MPa

Indus Suture STDS

MCTMBT

29 58 B7 116 145

x-axis (km)

174 203 232 261 290

Fig. 7 C (1). Distribution, orientation and magnitudes of stress trajectories of model C (l) under 100





the upper region of all the layers. Both stresses reflects comparatively low magnitude in

layer 5. at is also compressive and direct horizontally in most of regions and it's magnitude

low with compared to that of ax. The values of a, and o2 are from 3 to 1334 MPa and 1

to 1272 MPa, respectively. Some tensional stress observed in the upper part of the Higher

Himalayan region. On average the intensity of these stresses are low than that of the

compressive stress.

'1.8.2. Stress field under convergence displacement 500 m (Model C2): Hydrostatic condition

occurs in upper middle area of layers 1, 2, 3 and 4 and the deeper part of layer 5.

Directions of o1 and o2 and their magnitudes exhibit more obvious when convergence

displacement is gradually increasing from 100 m to 500 m. The magnitude of ol and o, is

very small in the upper part. o] directs vertical in the deeper region whereas it shows

reverse direction in the upper region all over the models (Fig. 7 C2). Magnitude of a] is

strong and nearly the same in bottom part of all the layers. oz directs horizontally and

shows higher magnitude in the deeper part of layers 1 and 4 compared with other layers,

a, and o., show inclined orientation in shallow depth of all layers. This model also shows

several tensional stresses in the same position as model Cl. The value of a, and o2 ranges

from 35 to 1343 MPa and 10 to 1157 MPa, respectively.

Scale; 100 MPa

Indus Suture

1STDS

MCTMBT

29 58 87 116 145 174 203 232 2G1 290

x-axis (km)

Fig. 7 C (2). Distribution, orientation and magnitudes of stress trajectories of model C (2) under 500




5. Mohr-Coulomb Failure Criterion and Possible Location of Faults

Stress of rock in nature is interest because it controls many processes in the earth's

crust including: fracturing, faulting, folding, earthquakes, landslides, subduction of continental

crust and strike-slip motion of the earth's major plate as they slide past eachother. In

order to interpret these phenomena, Mohr-Coulomb Failure envelope (Fig. 8) is applied to

predict which elements and parts of the study area are more possible to fail or form faults.


Fig. 8. Construction of Mohr-Coulomb failure envelop demonstrating the concept of proximity to failureafter Melosh and Williams (1989). Where C is the cohesive strength and <f> is the angle ofinternal friction.

5.1. Mohr-Coulomb Failure Criterion

Deformations of rocks are simulated using the rock properties that have shown in

Table 3 and the convergence displacement boundary conditions in Table 4. As the value of

gtj and ct2 is known, the third principal stress a' which acts perpendicularly to the section

plane, calculated as:

a = v (a,+<72) (11)

Where, v is Poisson's ratio (Timoshenko & Goodier, 1970, Hayashi and Kizaki, 1972).

Since the values of ax, a2 and a' for every elements have been calculated, calculation can

define which is the maximum, intermediate and minimum compressive stress among them.

The 2D stress field of each model is envisaged with the newly calculated principal stresses

au a2 and a3. After the stress field of each model is calculated, it is possible to describe in

which finite element, fault will develop according to the Mohr-Coulomb failure criterion.

The criterion is expressed on the basis of the linear relation between the shear stress

(t) and the normal stress (an):

t = c+<v tan^ (12)

Where c is the cohesion of rock and <p is the angle of internal friction (Melosh and

Williams, 1989). As the rule, failure occurs when the Mohr circle first touches the failure

envelope. This takes place when the radius of the Mohr circle, ——— is equal to the

perpendicular distance from the center of the circle at to the failure envelope. It is

possible to calculate the proximity to failure (P7) for each element by using the following

equations (Melosh and Williams, 1989).


■(13)

■(14)

Using the equation, the value of Pf is calculated. Whenever the value of P, is less than 1.0

the1 Mohr circle is inside the failure envelope and it indicates that no fault occur, on the

other hand faulting occurs if the P} value is over 1.0.

5.2. Possible location of Faults

The ct, and a2 within the failed elements are shown in Figures 9 A, B and C. Faults

are assumed on the basis of the proximity to failure. Formation of fault mainly depends

on the physical properties of rock especially cohesion and internal .friction angle and also

the imposed convergence displacement. The required physical properties of rock in our

simulation are listed in Table 3. Thirty experiments have performed for the models A, B

and C with different combinations of convergence displacement (e. g. 25 m, 30 m, 50 m,

STDS Scale:i 00 MPa

MBT

&

S -

MFT

70 80

x-axis (km)

100 110 120 130 140

Fig. 9 A (1). Failure resulting from the stress of finite element elastic model A 1 after applied the conceptof proximity to failure with 100 m convergence displacement.

Layer 5 STDSScalen oo MPa

MBT

MFT

70 80

x-axis (km)

90 100 110 120 130 140

Fig. 9 A (2). Failure resulting from the stress of finite element elastic model A 2 alter applied the

concept of proximity to failure with 250 m convergence displacement.

40 M. Farhad Ilowladar and Daigoro Hayashi

Scale: 100 MPa —

Tarim

Indus Suture

£ 2 Trmt

STDS

MCT

33 G6 99 132 165 198

x-axis (km)

Z31 264 297 330

Fig. 9 B. Failure resulting from the stress of finite element elastic model B after applied the concept

of proximity to failure with only gravity. (Note: no element failed in the model in other

cases).

Scale: 100 MPa _

Indus Suture

I SiMCT

MBT

58 07

I

116 145

x-axis (km)

1/4 203 232 261 290

Fig. 9 C (1). Failure resulting from the stress of finite element elastic model C 1 after applied the


Scale: TOO MPa _

Indus Suture

MCTMBT

29 58 87 116 145 174

x-axis (km)

203 232 261 290

Fig. 9 C (2). Failure resulting from the stress of finite element elastic model C 2 after applied the



75 m, 100 m, 125 m, 250 m, 300m, 375 m and 500 m) to examine faults under the Mohr-

Coulomb failure criterion. All experiments did not include here, but under displacement

100 and 250 m experiments are shown in Figure 9 A, B and C. Depending on the mentioned

above convergence displacement: In model A, when convergence displacement 250 m, 300

m, 375 m, and 500 m experiments are considered, some failure occurred in the upper part

of the Sub-Himalaya, Tethys Himalaya and in the left-bottom boundary partition of Higher

Himalayan region besides the experiments under convergence displacement 25 m, 50 m, 75

m and 125 m cases did show any failed elements in layers 1, 2, 3 and 5 except the layer

4. In model B, few failed elements exhibited in the upper part of layer 1 when only gravitational

force is considered and other experiments did not display any failed elements. In model C,

failure occurred for all experiments in the Sub-Himalayan layer, upper part of Higher

Himalayan, and also in the lesser Himalayan layer.

6. Seismo-Tectonics and Focal mechanism

6.1. Seismotectonics

Geological structure, topography and seismicity are quite uniform along the Himalayan

front. The most prominent seismic feature is a narrow earthquakes belt where all available

fault-plane solutions indicate thrusting and this belt can easily identify along the entire

Himalaya (Seeber et al., 1981). Himalayan mountain range and its adjoining area constitutes

one of the most seismically active regions of the world. Four earthquakes with magnitudes

greater than 8 occurred since 1897 and all appear to be related to mountain building processes

in the Himalaya. Although earthquakes occur in neighboring regions, figure 10 shows the

selected epicenters for the period 1961-1970. Most of the epicenters fall near the trace of

the Main Central Thrust and not near the Main Boundary Thrust. From this observation

it is tempting to conclude that the MCT is active but not the MBT. However, one considers

that the MBT dips gently to the north or northeast (Gansser, 1964), and that earthquakes

occur at finite depth, it seems more reasonable to conclude that along most of the

Himalaya, the activity is associated with the MBF and the zone surrounding it. The

seismicity at the both ends of the Himalaya appear to be more complicated with diffuse

zone south of the main ranges.

The southward migration of thrust faults may result in part from the buoyancy of

continental crust. In the east, seismicity is distributed over the Shillong plateau and it's

margins (Fig. 10). Arambruster et al. (1978) and Jacob et al. (1976) considered both the Main

Central Thrust and the Main Boundary Fault to be active in the northwest meanwhile the

tectonics of this part of the Himalaya is possibly too abstruse than to the southeast. From

these pictures, Arambruster et al. (1978) and Jacob et al. (1976) assumed that the

seismicity along the entire range is not restricted to a single narrow fault zone. The level

of seismic activity along the Indus-Tsangpo suture zone is very low. The lack of seismicity

along the suture zone indicates that this region is relatively rigid, it does not keep stress


35'

30*

25

* / 1905 £?k K^ 4>

/ E

•

•

• *••

Z2_ -Suture

1934

1897

• * U i95°

75' 80 85" 90' 951

Fig. 10. The Shallow focus seismicity map of the Himalayan region. Selected wells located epicenters

from the ISC or NOAA from 1961-1970 and majors shocks, since 1897 modified after Molnar

et al. (1977).

and transmit them to the neighboring regions.

6.2. Focal Mechanism Solutions

Focal mechanism solutions of the study area have been undertaken by many authors

over the past two decades. The major structural trends are approximately at the western

extremity, the mountain ranges of the Himalayas curve around into a semicircular arc towards

the west and then bend towards the south, forming the Sulaiman and Kithar ranges while

eastern extremity, the Arakan Yoma Range, which forms a part of the Indonesian arc,

convergence into it. South of the Himalayas lies a major platform depression of the Ganga

Basin (Sastri et al., 1971). Towards the north lies the Tibetan Plateau.

Focal mechanism solutions for earthquakes around the Himalayan extremity have been

shown in (Fig. 11). Focal mechanism solutions that are the trends 0 and plunge 0, of the

mechanism axes P, T, B, and the dip direction and dip of two nodal planes, are presented

in Table 5. The mechanism solutions of events 8 and 9, which occurred in this region,

show thrust faulting. The near vertical orientation of the T-axis in these solutions suggests

that the earthquakes are caused by the tension within the sinking slab. In the NW

extremity of the Himalaya, the geological formations bend sharply towards the south, then

SW and curve towards the west to form the Kashmir syntaxis. The event occurred at the

NW alignment of epicenter and shows the thrust focal mechanism solutions with NE


Fig. 11. Focal mechanism solutions of earthquakes in the Himalayas and surrounding regions modified

after Chandra (1978).

Table 5. Focal mechanism solutions after Chandra (1978).

$'\ trend measured clockwise from the north.6', plunge measured from the horizontal.

Ref3, a = Chandra (1970); b = Chandra (1971); c = Chandra (1975a);d = Chandra (1975b); e = Chandra (1977a).

N

1

2

3

4

5

6

7

8

9

10

11

11

Date

1 Aug. 1966

24 Jan. 1966

7 Feb. 1966

7 Feb. 1966

28 Dec. 1972

15 May 1969

13 Oct. 1964

14 Mar. 1965

6 Jun. 1966

28 Dec. 1974

3 Sep. 1972

3 Sep. 1972

hr.

21

7

4

23

61

20

23

15

7

12

23

23

P

0" e"1

322

155

147

163

48

160

123

196

175

151

38

153

1

24

0

6

42

30

0

17

7

23

15

6

T

</> e

53

19

237

58

328

353

214

62

322

345

218

271

11

58

90

68

48

60

54

66

82

67

75

77

B

0 e

229

254

57

256

58

254

33

291

84

243

308

62

79

20

0

21

0

5

36

16

4

5

0

11

Nodal planes

X Y

Dip Dip Dip Dip

Direction Direction

187

300

327

182

328

324

334

209

0

320

218

346

82

27

45

55

3

16

55

64

38

23

30

40

278

171

147

321

148

165

93

352

271

155

38

143

83

72

45

43

87

75

55

31

52

68

60

52

Ref'3

(a)

(b)

(c)

(e)

(e)


Table

12

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

35

36

37

38

39

40

41

42

43

44

45

46

47

48

5 (continued)

4 Sep. 1972

4 Sep. 1972

3 Sep. 1972

29 Jan. 1965

2 Sep. 1963

20 Feb. 1967

16 Jan. 1973

2 Feb. 1965

12 Jan. 1972

22 Jun. 1965

15 Aug. 1966

6 Mar. 1966

6 Mar. 1966

26 Sep. 1964

16 Dec. 1966

27 Jun. 1966

12 Jun. 1965

27 Mar. 1964

18 Feb. 1964

15 Sep. 1967

1 Sep. 1964

26 Sep. 1966

21 Oct. 1964

14 Mar. 1967

9 Feb. 1970

9 Feb. 1970

15 Jun. 1965

21 Jun. 1963

25 Jun. 1963

18 Jun. 1965

28 Sep. 1966

29 Jul. 1970

30 May. 1971

29 Dec. 1971

12 Jul. 1964

13 Jul. 1964

17 Oct. 1969

22 Jun. 1964

27 Feb. 1964

13

13

16

20

1

15

21

15

18

5

2

2

2

0

20

10

13

23

3

10

13

5

23

6

7

7

7

15

10

8

14

10

15

22

20

10

1

15

15

37

323

40

253

235

52

25

161

200

219

191

225

135

207

190

212

181

346

212

173

134

163

174

186

145

77

88

163

171

180

50

265

261

214

211

272

354

266

265

10

0

16

56

25

0

3

2

11

48

75

90

80

28

6

18

33

26

5

15

25

25

42

39

5

10

14

33

20

32

85

39

11

26

24

14

31

63

26

217

53

228

19

55

145

290

70

292

39

11

135

315

19

10

9

1

166

32

353

314

343

354

6

239

337

354

5

351

53

230

135

352

337

340

71

197

120

95

80

90

74

22

65

83

59

11

11

42

15

0

10

62

84

71

57

64

85

75

65

65

48

51

40

46

14

55

70

44

5

38

3

48

55

75

57

23

63

307

233

131

120

325

322

117

261

66

129

101

45

45

115

280

120

271

256

302

83

44

253

84

96

49

176

221

262

81

290

320

20

97

107

110

181

91

24

357

0

0

2

25

0

7

31

79

75

0

0

0

0

3

0

7

0

0

0

0

0

0

0

0

49

42

70

8

0

30

0

28

78

30

24

5

10

14

4

217

323

217

162

235

239

177

205

336

219

191

315

315

204

190

206

181

346

21

353

314

343

354

6

4

219

221

316

351

204

230

19

36

190

192

268

145

326

268

35

45

29

32

70

45

50

84

90

3

30

45

55

73

51

63

78

71

50

30

20

20

3

6

59

51

70

14

25

83

50

28

84

78

73

60

17

25

71

37

143

42

39

55

45

51

296

66

39

11

135

135

35

10

43

1

166

32

173

134

163

174

186

109

109

131

174

171

306

50

110

127

81

70

100

3

109

75

55

45

61

71

20

46

55

81

75

87

60

45

35

17

39

28

12

19

40

60

70

70

87

64

67

67

90

79

65

31

40

189

80

33

30

31

76

70

19

(e)

(e)

(e)

(e)

(e)

(e)

(e)

(b)

(e)

(e)

(e)

(e)

(e)

(e)

(e)

(e)

(e)

(e)

(e)

(e)

(e)

(d)

(d)

(d)

(d)

(d)

(d)

(d)


striking nodal planes. The events 11-13 occurred near the Indus suture zone and also produce

the thrusting along the NW striking nodal planes. Event 14, which occurred at about 50

km SE of events 11-13, has a normal fault plane solution (Chandra, 1978; Molnar et al.,

1977 and Satuder, 1968). The axis of tension is nearly horizontal and dips towards NNE.

Events 15-17 occurred further SE along the NE flank of Kashmir syntaxis. These are spatially

correlated with the MCT-MBT system. Fault plane solutions are of thrust type and the

strike of one of the nodal planes in each of these solutions is NW, conforming with the

local strike of the MCT-MBT.

In the Karakoram and Pamir ranges the events 18, 19 and 20 occurred and their

solutions produced the strike-slip faulting with right lateral motion along with the nodal

planes striking in the SE direction. These solutions indicates that the northward movement of

Indian plate, subsequent to the continental collision, besides being absorbed by crustal

shortening is transformed into a major mass movement towards SE along the dextral

Pamir-Karakoram fault separating these ranges from the Tibetan Plateau on the east

(Peive et al., 1964; Desio, 1973; Chandra, 1975).

Events 22 and 23 occurred near Gartok, Tibet. Both events are characterized by normal

fault-plane solution with nodal planes striking in the NE direction. The earthquakes resulted

from NW-SE extension. Molnar and Tapponnier (1975) and Banghar (1976) noted that normal

faulting with E-W T-axes in Tibet may reflect EW flow of material in the lower crust and

upper mantle beneath Tibet to compensate for the pressure imposed by the plate motion.

Events 21 and 24-34 occurred along the central and eastern Himalayas. Focal mechanism

solutions of these earthquakes are of thrust type (Chandra, 1978). The strikes of the

northward-dipping nodal planes in these solutions are generally parallel to the local structural

trend. The solutions indicate underthrusting of Indian plate towards the north along the

Himalayan Arc.

Events 37 and 38 occurred near the Dauki Fault at the southern edge of the Shillong

Plateau. Focal mechanism solutions show thrusting along EW striking nodal planes. The

axes of pressure trend on the NS direction and suggests that both events are caused by

the stress system related to the collision of northward moving Indian continent with the

Eurasia. Event 39 has a thrust solution with small component of strike-slip faulting. The

NS trend of the axes of pressure implies that the distribution of stress pattern in the

region is greatly influenced by the continental collision. Events 45 and 48 have thrust focal

mechanism solutions with NS striking nodal planes. The axes of pressure are nearly horizontal

and approximately perpendicular to the trend of Burmese Arc in this region. The solution

of these events suggests that the earthquakes occurred in the intermediate depth and

underthrusting of the lithosphere plate along the nodal plane dipping gently towards the

east. Event 47 has a normal faulting solution. Nodal plane strikes in the NS direction and

dips steeply towards the east. The event 46 has a thrust focal mechanism solution having

EW striking nodal planes.


Events 36, 41, 42, 43, 44 reflect the underthrusting of the lithospheric plate along the

nodal planes dipping gently towards the NE to SE. Focal mechanism solutions for the

events 27-34, 45, 56 and 48 indicate that the Indian plate is underthrusting the

Himalayan Arc in a northerly direction and Burmese Arc in the easterly direction. Event

40 shows the normal faulting solution with both nodal planes striking in the NW direction

and the earthquakes is caused by the NE-SW tension. The region is a zone of recent extension

(Molnar and Tapponnier, 1978).

6.3. Results

Seismic data and focal mechanism solutions for 48 most prominent earthquakes have

been adopted to observe the tectonics around the Himalayan mountain. The seismicity map

shows the large earthquake (magnitude 7.0 and above) from the earliest time through

1976. Eleven of these earthquakes are of magnitude 8.0 and above. The epicenters of

earthquake generally follow the trend of mountain with greatest concentration of seismic

activity occurring along the Hindu Kush and near the Kashmir and Assam syntaxes.

Throughout Tibet, however, the distribution of epicenters is rather irregular and no clear

trends are apparent. Most of the earthquakes in the region occur along the Himalaya,

Hindukush, Pamir and Arakan Yoma ranges and large-magnitude earthquakes have

occurred as far south of the Himalaya. It is not clear whether these earthquakes represent

tensional foci caused by the flexure of the lithospheric plate, or are related to a new thrust

zone such as one speculated by Le Fort (1975), or to some other cause. Focal mechanism

solution of earthquakes around the Himalaya indicates that the thrust faulting is predominant

tectonic features though some solutions show the normal and strike-slip faulting (Chandra,

1978).

7. Discussions

The studies have been produced three models (Figs. 2 A, B and C) from different areas

of Himalaya, among them two from Central Nepal Himalaya and other one from north

western Himalaya (Figs. 1 and 3) to understand the characteristics of stress field and its

influences on occurring faults around the Himalaya with numerical simulation. We simplify all

models and divide them into five layers according their regional tectonic divisions and

specify the major rock types for each layers to neglect the complexity of calculations and

to get the stress field for each models. Within the general simplifications of all the models,

the choice of elastic properties of rocks offers a good approximation. The elastic constants

include the Young's modulus (E), Poisson's ratio (v). The actual values of these parameters are

not well constrained; as a consequence, we tested all models with a variety of values in

order to explore the effects of changes in parameters and sensitivity of our results to various

choices. The values finally retained (Table 3) should be regarded somewhat arbitrary, and

have been chosen in order to be compatible with a better fit of the models calculated.

Five parameters (Young's modulus, Poisson's ratio, density, cohesion and internal


friction angle) for each layer are shown in Table 3. Because several major structural units

have quite different rheological properties, Young's modulus thus ranges from 40-80 GPa.

The comparison of these parameters of rock in each layers are presented in Figure 5. The

order of value of Young's modulus is layer 1, layer 4, layer 3, layer 5, and layer 2 from

high to low. The values of other four parameters are taken as nearly similar way as

Young's modulus in all layers.

Secondly, imposed the velocity (or displacement) boundary conditions instead of forces

(Figs. 6 A, B and C). The displacement boundary condition simply corresponds to the

convergence of the Eurasian plate relative to the Indian subplate. The Indian craton moves

north-northeast at a rate of 44-61 mm/yr relative to Eurasia/Siberia (Minster and Jordan,

1978; Armijo et al., 1986; De Mets et al., 1990; Bilham et al., 1997). The GPS geodesy has

established the rate of India-Asia convergence at 54 ± 4 mm/yr. Only about 30 percent

(e.g. 18 ± 2mm/yr.) of India-Asia convergence is absorbed across the Himalaya, the average

rate of accommodation derived on the basis of slip rates of great earthquakes being -17

mm/yr. Recent GPS measurements along the Delhi-Malari and Delhi-Milam sections across

the Kumaun Himalaya shows that the Tethyan domain beyond the Great Himalaya is

advancing southwards at the rate of 18 to 20 mm/yr.

On the basis of the convergence concept between India and Eurasia, we applied 25, 30,

50, 75, 100, 125, 250, 375, and 500 m displacements. Obtained stress field for example 100

m and 500 m displacements illustrated in Figures 7 A, B and C. As the distribution of

stress in every model, which are presented by principal stresses ( ax and a2) in the triangular

domain. The nature of principal stresses are mostly compressive but in the upper part of

Higher Himalaya exhibit some tensional stresses. at is named as the maximum compressive

stress and a2 is the minimum compressive stress. In every figures (Figs. 7 Al, A2; Bl, B2;

and Cl, C2), each pair of lines which are perpendicular each other and whose lengths

indicate the absolute values, represents the maximum compressive stress (a,) and the

other one is the minimum compressive stress (<72) of the respective triangle.

Thirdly, we use Mohr-Coulomb failure criterion and observe that convergence displacement

and physical constants of rocks regulate the failure phenomena of the study area. For the

proposed convergence displacements, some elements failed in the upper part of layers 2,

and 5 of model A. Also two elements failed near the left lower boundaries of this model,

this may be due to the disturbance of boundary effect. Few elements failed in layer 1 and

4 for model C whereas no element failed in model B for any imposed displacement boundary

condition but few elements failed in the upper area of layer 1 with 0 m displacement

boundary condition (Figs. 9 A, B and C). In general no failure observed in the middle part

of all layers and also deeper part of layers 1, 3, 4 and 5 for all types boundary conditions.

Axes of CTj horizontally distributed within failed elements in the upper part of layer 2 and

5 which indicates that thrust fault should take place along these layer. Besides it oriented

vertically in the deeper part of layer 2, indicates normal fault occur in this region. Normal


faults also expect in the upper part of layer 1 and 4, due to tensional character and

vertical distribution of Axes of a,. Focal mechanism solutions also show nearly the same

types of fault in the study area. So the results of the present studies are agreement with

the previously performed focal mechanism solutions of earthquakes around the study area

(Chandra, 1978).

8. Conclusions

Three models are performed to analyze stress and its relation to develop faults around

the Himalaya by using the 2D FEM and the Mohr-Coulomb failure criterion. On the basis

of overall results of these models an attempt has been made to conclude the followings:

1. Stress states depend on the applied convergence displacement and physical properties of

rocks.

2. Compressive stresses are dominant over the study area but a few areas in the upper

part of Higher Himalaya are covered by the tensional stresses.

3. Magnitude of ax and a2 are high in the deeper part than the upper part in all models.

4. Direction of principal stresses varies from layer to layer. In general a{ directs vertically

and a2 horizontally in deeper region. On the other hand they reflect reverse direction in

upper part of all layers, respectively.

5. Mohr-Coulomb failure criterion suggests that thrust faults might be expected to develop

along the upper part of layers 2 and 5 (Sub-Himalaya and Tethys Himalaya) and

normal faults along layers 1 and 4 (Pre-Cambrian Basement and Higher Himalaya) and

deeper region of layers 2 and 5 due to nature and direction of principal stresses (Figs.

9 A, B and C).

6. The focal mechanism solutions of earthquakes refer that the thrust faults and also few

number of normal and strike-slip faults occur around the Himalaya. Therefore, the

present research is consistent with the focal mechanism solutions.

Acknowledgement

M.F.H. is highly grateful to the Ministry of Education, Culture, Sports, Science and

Technology, Japan for financial support that made this study possible.

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