NNOVATIVE ECHNOLOGY AND REATIVE NGINEERING V ...ia800305.us.archive.org/34/items/IJITCE/vol3no102.pdfINTERNATIONAL J OURNAL OF INNOVATIVE T ECHNOLOGY AND C REATIVE E NGINEERING (ISSN:2045-8711)

INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.3 NO.1 JANUARY 2013

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STATIC DEFORMATION OF TWO HALF SPACES IN SMOOTH CONTACT DUE TO

VERTICAL TENSILE FAULT Mahabir Singh#1, Meenal Malik#2 and Jagdish Singh#3

#1 Deenbandhu Chhotu Ram University of Science and Technology, Murthal, Sonepat-139031 #3 Department of Mathematics, Maharshi Dayanand University, Rohtak-124001

#2Department of Applied Sciences, Matu Ram Institute of Engineering and Management, Rohtak-124001 [email protected]

[email protected]@gmail.com

I. ABSTRACT

Closed-form analytic expressions for the Airy stress function, stresses and displacements for half-spaces in smooth contact by applying suitable boundary conditions at the interface are first obtained. These expressions are then integrated analytically to derive the Airy stress function for a vertical tensile fault of arbitrary dip and finite width. Closed-form analytical expressions for the displacements and stresses follow immediately from the Airy stress function. The variation of the stresses with the horizontal distance from the fault and with the depth studied numerically. The results obtained in smooth contact are compared with that of welded contact.

KEYWORDS Deformation, Dyke injection, Vertical tensile fault, Smooth contact, Welded contact

II. INTRODUCTION Rongved (1955) obtained closed-form algebraic

expressions for the Neuber-Papkovich displacement potentials for an arbitrary point force acting in an infinite medium consisting of two elastic half-spaces in welded contact. Dundurs and Hetenyi (1965) obtained these functions when the half-spaces are in smooth contact and also obtained the corresponding displacement field. Moreover, they compared the traction for a smooth interface with that for a perfect bond between the two semi-infinite solids. Heaton and Heaton (1989) used the expressions for the Neuber-Papkovich functions derived by Rongved (1955) to obtain analytical expressions for

the static deformation field produced by point forces and point force couples embedded in two Poissonian half-spaces in welded contact. Kumari et al. (1992) generalized the results of Heaton and Heaton (1989) and they obtained the expressions for the displacements for arbitrary Poisson’s ratio. Furthermore, they obtained closed-form analytical expression for the stresses as well. Sharma et al. (1991) obtained closed-form analytical expressions for the displacement and stresses at any point of either of the two homogeneous, isotropic, perfectly elastic half-spaces in welded contact due to very long strike-slip dislocations.

Singh and Garg (1986) obtained the integral expression for the Airy stress function in an unbounded medium due to various two-dimensional seismic sources. Beginning with these expressions, Rani et al. (1991) obtained the integral expressions and hence closed form analytical expressions for the Airy stress function, displacements and stresses in a homogeneous, isotropic, perfectly elastic half-space due to various two-dimensional sources by applying the traction-free boundary conditions at the surface of the half-space. Singh and Rani (1991) obtained closed-form analytical expressions for the displacements and stresses at any point of a two-phase medium consisting of a homogeneous, isotropic, perfectly elastic half-space in welded contact with a homogeneous, orthotropic, perfectly elastic half-space caused by two-dimensional seismic sources located in the isotropic half-space.Singh et al. (1992) followed a similar procedure to obtain the closed-form analytical expression for the displacements and stresses at any point of either of two homogeneous, isotropic, perfectly elastic half-spaces in welded contact due to two-dimensional sources.


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Singh and Singh (2000) derived closed–form analytical expressions for the displacements and stresses at an arbitrary point of the half-space caused by a long vertical tensile fault of finite width. Singh et al. (2002) extended the results of Singh (2000) and obtained the closed-form analytical expression for the subsurface stresses and displacements caused by a long inclined tensile fault buried in a homogeneous isotropic half-space. The effect of depth of the upper edge of the fault and the dip angle on the deformation field has been examined. Kumar et al. (2005) derived analytical expressions for the displacements and stress fields at any point of the two homogeneous, isotropic elastic half-spaces in welded contact caused by a long tensile fault of arbitrary dip and finite width.

In this paper, we obtain closed-form analytical expressions for the displacements and the stresses at any point of either of the two homogeneous, isotropic, perfectly elastic half-spaces in smooth contact caused by various two-dimensional sources embedded in one of the half-spaces. The results are valid for arbitrary Poisson’s ratio. Only plane strain case is considered. The stresses for the smooth interface case are compared with the corresponding stresses for the welded interface.

We begin with the integral expressions for the Airy stress function in an unbounded medium given by Singh and Garg (1986) to obtain the integral expressions for the Airy stress functions stresses and displacements for the two half-spaces in smooth contact by applying suitable boundary conditions at the interface. The integrals are then evaluated analytically, obtaining closed-form expressions for the stresses at any point of either of the two half-spaces caused by vertical tensile fault. For numerical calculations, half spaces are assumed Poissionian.

III. THEORY Let the Cartesian coordinates be denoted by

� � �� x x x with

��x axis vertically downwards. Consider

a two-dimensional approximation in which the displacement components

� � �� u u u are independent of

�x so that

��x∂ ∂ ≡ .Under this assumption, the plain

strain problem �

� ��u = can be solved in terms of the Airy stress function U such that

� � �

��

� � � �

� ��

U U U

x x x x

τ τ τ∂ ∂ ∂

= = = −∂ ∂ ∂ ∂

(1)

� �� U∇ ∇ = (2)

where i j

τ are the components of stress and � �

�

� �

� �

U

x x

∂ ∂∇ ≡ +

∂ ∂.

We have (Sokolnikoff,1956,Sec.71) �

� �

�

�

� �

�

��

�

��

�

U

u U x

x

U

u U x

x

µα

µα

∂− ∇∫∂∂− ∇∫∂

(3)

where � � � ��

λ µα

λ µ σ−.

We consider two homogeneous, isotropic, perfectly elastic half-spaces which are in smooth contact along the plane

��x = . The upper half-space

�� x 〈 is called

medium I and the lower half-space �

� ��x 〉 , medium II, with elastic constants

� �� λ µ and

� �� λ µ respectively

(Figure 1). The superscript (1) denotes the quantities related to medium I and the superscript (2) denotes those related to medium II.

Let there be line source parallel to �x ��As

shown by Singh and Garg (1986), the Airy stress function

�U for a line source parallel to the

�x axis

passing through the point �� h in an infinite medium can be expressed in the form

( )

( )

� � ��

� ��

� ��

��

U L M k x h k x

k x hP Q k x h k x k e k

−

∞= + −∫

− −+ + −

��(4)

where the source coefficients� � �� L M P and

�� are

independent of the variable k .For a line source parallel to the

�x axis passing through the point �� h of

medium II, the expression for the Airy stress functions in the two half-spaces are of the form

( )

( )

��

�

� ��

� �

��

�� k x

U L M k x

P Q k x k e k

k x

k x

∞

−

= +

+

∫ ��(5)


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( )

( )

��

�

� ��

�

� �

��

�� k x

U U L M k x

P Q k x k e k

k x

k x

∞

−−

= +

+

+ ∫ ��(6)

where �U is given in equation (4) and the

unknowns� � � �� L M P Q and

� � � �� L M P Q are to be

determined from the boundary conditions.

Fig. 1. Two half-spaces in smooth contact with a line source in the lower half-space at (0, 0, h)

Since the interface is��x = , then smooth contact implies

that �u and

��τ are continuous but

��τ vanishes at the

interface. Since the half-spaces are assumed to be in smooth contact along the plane

��x = , the boundary

conditions at the interface ��x = are

��

��

��

� � ��

��

� ��

τ τ τ

τ =

=

(7)

Due to discontinuity in horizontal displacement �u

at�

��x = there may be a slip between the two media. From equations (1) – (6), we get the following integral expressions for the stresses and the displacements for the two media:

( )

( ) ]

��

��

� ��

��

L M M k x k x

k xP Q Q k x k x e k

τ ∞

= + +∫

+ +

(8)

( )

( ) ] �

��

��

� � � � �

��

�� k x

k x

k x

L M M k x

P Q Q k x e k k

τ∞

= + +∫

+ +

−

+��

( )

( ) ] �

��

��

� � � �

��

�� k x

k x

k x

L M k x

P Q k x e k k

τ∞

= − +∫

+

+�

(10)

( )

( )

( )

( )

�

�

�

�

��

� � � � �

��

� � � � �

� ��

��

��

��

k x h

k x

k x h

k x

k

k

k

k

L M M x h e

L M M x e k x k k

P Q Q x h e

P Q Q x e k x k k

τ − −

−

− −

−

−

−

−

−

∞= + −∫

+

∞+ + −∫

+

+

+

(11)

( )

( )

�

�

��

� � � � �

�

�

��

k x h

k x

k

k

L M M x h e

L M M x e k x k k

τ − −

−

−

−

∞= ± + −∫

+

+

�

�� ( ) ��

k x h

kP Q Q x h e− −

−∞

− ± + −∫ �

( ) �� k xkP Q Q x e k x k k−− + + ��12)

( )

( )

( )

( )

�

�

�

�

��

� � � �

��

� � � �

��

��

��

��

k x h

k x

k x h

k x

k

k

k

k

L M x h e

L M x e k x k k

P Q x h e

P Q x e k x k k

τ − −

−

− −

−

∞= − + −∫

+

∞− + −∫

+

+

+

(13)

( )( ) ] �

��

�

��

�

� ��

��

��

k x

Mu k

Qk

L M x k x

P Q x k x e k

µα

α

+

+

∞= +∫

+

−

+ (14)

( )( ) �

��

�

��

�

� ��

�� k x

Mu k

Qk

L M M x k x

P Q Q x k x e k

µα

α

− +

− +

∞= − +∫

+

+

(15)

( )( )

�

�

��

�

��

�

� �

�

��

k x h

k x

M

u k

M

k

L M x h e

L M x e k x k

µα

α

− −

−

− +

− +

∞= − −∫

+

( )( )

�

�

��

�

�

� � � ��

��

��

k x h

k x

Qk

Qk

P Q x h e

P Q x e k x k

α

α

− −

−

− +

− +

∞+ −∫

+

(16)


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( )( )

( )( )

�

�

�

�

��

�

��

�

��

�

��

�

� ��

��

��

��

k x h

k x

k x h

k x

Mu M k

MM k

QQ k

QQ k

L M x h e

L M x e k x k

P Q x h e

P Q x e k x k

µα

α

α

α

− −

−

− −

−

− + +

− + +

− + +

− + +

∞= ± −∫

∞± −∫

+

+

(17)

It is noticed from appendix that the coefficients

� � �� L M P and

�� have different values

for�x h

>< ; let � � PL M− − − and Q − be the values of

� � �� L M P and

�� respectively, valid for

�x h< . Then

from equations (9) to (17) and the boundary conditions (7), we obtain

( )

} ( )

( )

��

�

� � ��

� �

��

� �

��

��

��

��

x h x

R

R

h

x x xU C L P

R h x

h x x h xx hM

R R

h x xhQ

R R

− −=

+

−

− −− +−

−−+ − +

−+ − +

�(18)

( ) ( )

( )( )

( )

�

��

��

� �

� �

�

� � �

� ��

� � �

� ��

� �

x h x x x h x

C L

R R

h x h x

P

R R

x h x x h

M

R R

τ +− −−=

− −−+ − +

− −+ + −

�

( )( ) ( )��

� � ��

h x h x h x h x x h x

R R

− − −+ +

�

�

��

( ) ( )( )

( )

�

� � �

� �

�

� �

�

�

��

� � � ��

��

��

�

h h x h h x h x

Q

R R

h x h x

R

+

− − −−+ − +

−

(19)

( ) ( )

( )

( ) ( )

( ) ( )

�

��

��

�

��

� � �

� �

� �

� �

�

� � �

� ��

� ��

��

� ��

��

h x h x

C x L

R R

h xx hP M

R R R

h x h x

R R

h x h x h x

Q

R R

τ− −−= − −

−− −+ − −

− −− +

− −−+ −

(20)

( )

( )( ) ( )

( )( )

( )

�

��

�

� � � �

� � �

� � ��

� �

��

� � �

� �

��

��

��

� �

� � ��

� ��

��

� �

h

R

x x h x x hC L

R R

h x h x x h x

P

R R R

h x h x h xx hM

R R

h x x h x

Q

R

h h

τ −

−

−

−

−−= −

− + −− +

− +−+

− −+ +

+

( )( ) ( )� ��

��

x h x h x h x

R R

+− −

(21)

( )��

� �

��

�ux x hC x

h L

RR

µα α

−− − + −= −

�

��( )� � �

� �

�

��

x x h x

x P

Rα

− −− +

( ) ( )��

h h x

h h x x

Rα α

− − + − − −

�

( ) ( )�

� � ��

�

� ��

�x h

R

h x h x

M h x

R α

+ −

− − −

�

} ( )�

� � �

� ��

��

h x x x h

x Q

R

−+ −

(22)


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( )

( ) ( )

( ) ( ) ( )

��

� ��

�

� � � ��

�

�

� � � � ��

�

�

��

� ��

��

�

��

u

h x h x h

x

R

x x x hC x hL x

RR

x x h h x xP h x

RR

h x x x h

M

R

µ

α

α αα

α

− +

− −− −

−= + − +

− −−− +

− −−

( )��

�

��

h x h xhQ

Rα

−+ −−

(23)

( ) ( ) ( )

( ) ( ) {

( )( )

��

�

�

��

�

� � � ��

� � � ��

��

��

��

�� x h

M x x hxU L P R

x h R

Q x h C x x xL C

R S x h

C x x h x MP C S x h

S S

C h x x h

h C

S S

−

−

+

−= − +

−

− −+ + + ++

−+−− + − +

−++

{

( )

��

�

� � �

�

��

h C

C h x x h

S

+

++

(24)

( )

( )

��

��

� �

� ��

� ��

L x x h P x h

RR R

M x x h x h

RR

τ

− −= + − +

− −+ − +

��( ) ( )� ��

� � �

� � ��

Q x h x h

R RR

− −+ − + �

( ){��

��

�� x h C h x

x L

S

+ − +−

+

( )( )

( ) ( )

( ) ( )} ( )

( ) ( ){ }

�

� � � �

��

��

� � �

�

� � �

� � � � �

� � � �

� �

�

��

�

� ��

��

� ��

��

C x x h x Mx h

S S

x h h x x hh C

SS

P C x x hx h h C h x

SS

x h x h C h x

C

S

Q

S

−++ + − +

+ ++ − −

−+

+ − +

+ + − +− +

−−

+ +

( ) ( )

( ) ( ) ( ){ }

( )

�

� � �

�

� �

� � � �

�

�

� � �

�

� � �

� ��

��

x h h C h x

S

x h x h h C h x

S

C h x x h

S

+ + +

+ + − +

++

(25)

( ) ( )

( ) ( )

( ) ( )

��

��

� �

� �

� ��

� � �

��

� ��

� ��

� ��

P x x h L x h

RR R

Q x x h x h

RR

x h x hM

R R R

τ

− −= − ± − +

− −+ −

− −± − +

��

( ) ( )

( ){ }

�

� � � �

� � ��

� � � �

� ��

� �

� ��

x P C x x h

x h C x

SS

x h x h C xL

S S

−

−

+− + − +

+ + −− +

�

��( ) { ( )

��

� � �

��

� ��

�x h

S

C x x h M

S S

−− ++

+ + +

��( ) ( ){ }� ��

� �

�� x h C h xx hC h x

S S

+ −+

++ �

��( ) ( )��

��

C h x x h x x h Q

S S

−+ +−

( ){ } ( )��

� �

��

�x h C h x

S

C h x x h

S

+ −− +

++

(26)


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( )

( )

( ) ( )

( ) ( )

��

��

��

��

� � �

� �

� � ��

��

�

�

�

��

� ��

� �

� ��

��

��

C

L x x h P x h

RR R

M x x h x h

RR

Q x h x h

RR

C x x hx Lx h

S S

x Mx

S

τ

−

−

− +

−

−

− +

− −= − −

− −+

− −+

++ +

− −

( ) ( )�� x h

h h C

S

++ + +

�

( ) ( ){ }� � � ��

� ��

x h x h C h xP

C

S S

− + + + −− − − +

�

( ) ( ){ }{� �� C x x h x h h CS

Q

S

+ + − − + +

−�

( ) ( ) ( ){ }( )

�

��

� � ��

�

� � �

��

��

��

x h

x h h C h x

S

C h x x h

S

++ + −

++

(27)

( )

��

�

�

�

�

�

��

u

L x h M x hP x

R R R

x h

R

µ

α

+ +

−+ −

− −= −

��( )��

� �

�

��

x hQ x

R Rα

−− +

�

( ) ( )�

��

�

��

x hC

x h D x C

S

L

Sα

− + − + − − − �

( )� � ��

�

��

S

x x hx P C

D

S

C

α+ +

− +−

�

( ) ( (

( ) ( )

( ) ( )

� �

� ��

� �

�

� � � �

� �

�

� � �

� � ��

� ��

� �

�

��

��

� ��

��

��

�

Q x h

S

x h CM

x h D

S

x h h x C x h

S S

x h x

S S

h x CC

x h D

S

α

α α

α

+−

− +− − + + −

+ +− +

−+− +

+ −

( )��

��

x h

S

+−

��28)

( )��

�P x hL x M x

u

R R R

µ−

= ± + ±�

��( ) ( )��

� �

�

��

x h Q x h

R Rα

− −− + + +

�

( )

( ) ( )

�

� � �

� ��

�

� � � �

��

�

��

� � �

��

x h x L C

R S

x C x h C

P x h

S

αα

α

+

−−− + + +

+ −+ + +

��

( )

( )

�

� �

� � � �

� � ��

� �

��

��

��

h C

x h

x h x M

x C

S S

x h h x C

S Sα α

− + + +

−++ − +

+

��( ) ( )

�

�

��

�

� ��

x h Qx h

S S α+

−+− + −

�

��( )��

� �

�

��

x hh C

x h

Sα

++ + + −

�

( ) ( )��

� ��

h x C x h x h

S S

+ ++ −

��(29) �

where ( )z h≠ , ( ) ( )

� ��

� � � �� R x x h S x x h= + − = + +

The expressions given in equations (18)-(29) are in terms of the source coefficients L0, M0, P0 and Q0. The results for the Airy stress functions and the stresses in the two half-spaces for a vertical tensile source on putting the values of the source coefficients from given appendix are as follows:


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��

� �

�

� �

��

� ��

� ��

� � ��

x h xC b d s h

U R

R R

h x x h

R

µ

π σ

−= + +

−

−−

(30)

{ }

( ) { } ( )

��

� ��

� ��

� ��

� ��

� ��

C b d s

h h x x

R R

h x h x h x

h x h x

R R

µτ

π σ= − + − +

−

− −+ − − −

�

(31)

( )( )��

��

��

C x x b d s h x h x

RR

µτ

π σ

− −= − +

−

�

��( )��

�

��

h h x

R

−−

� � ��(32)

{ } ( )

{ } ( )

��

� ��

��

� � �

�

�

� ��

� ��

��

R

C b d s h x

h h x x

RR

h x h x

h x h x

R

µτ

π σ

− +

−

−= − − +

−

−+ −

��(33)

( ){�

��

� ��

� ��

x hb d s

U R C S

R

µ

π σ−

−= − − +

−

�

��( ) {� � � ��

��

C x x h

x h

SS

−+

− +

( )��

��

C h x x h

h C

S

++

(34)

( )( ){

( )

( )( ) ( ){ }

� ��

� ��

�

��

� ��

��

�

��

��

� �

��

��

x h x hb d s

R R R

C

C x h

S S

x h

h x C

S

C x h h x C

µτ

π σ

−

− −−= + −

−

−+ + − +

++ −

+ + −

�

� � �

��

� � ��

C h x x h

S

+−

��(35)

{ }

{ }

��

��

�

� � ��

��

��

��

��

� � �� x h

x h x hx b d s

R R

x h

x h C x

S S

C h x x h

C x x h

S

µτ

π σ−

+

+ −

− −−=

−

++ −

+− +

(36)

( ) ( )}{

� ��

� � � ��

�

��

��

S

x h x hb d s

R R R

C

x h C h x h x

S

µτπ σ

− + −

+− +

− −−= −

+ + − −

�

( ){ }�

� � ��

� � � ��

�

� � �

��

��

��

x h

C x h h x x h

S

C h x x h

S

+− − − +

+−

(37)

IV. NUMERICAL RESULTS

We want to compare the stresses for the smooth interface case with the corresponding stresses for the welded interface. For the numerical computations, we assume that the half-spaces are Poissonian ( )

i iλ µ= so

that � � ��

α α= =

�

� �

� ��

� �C C

β ββ β

− −= =

+ +�

�

� �

� ��

� � �C C

ββ β

− −= =

+ +�

( )� ��

� � � �

��

� �

C D

D D C D

ββ

− +−= = + =

+We define the following dimensionless quantities �� xxY

h h

= = , where h is the distance of the line source from the interface. Let the dimensionless stresses for the welded interface(Kumar et.al 2005) be denoted by ��

i j i jP P and the dimensionless stresses

for the smooth interface be denoted by �� i j i jP P . Then,

�

��

� �

�� i j i j i j i j

L L

P P

b d s b

π πτ τ

µ µ= = (38)

From equations (31)-(33) and (35)-(37),we get the following expressions for the dimensionless stresses for the two cases for a vertical tensile line source:


�

24 www.ijitce.co.uk

( )

( ) ( ) ( )

��

� �

�

� ��

� ��

��

� � ��

C

P Z Z

A A

Z Z Z

Z Z

A A

σ

− −

= − + − +−

− −+ −

��

(39)

��

� ��

��

C Y Z Z Z Z

P

A A Aσ−

− − −= + −

−

(40)

( )

( ) ( ) ( )

��

� ��

� ��

� ��

��

� � � � ��

C

P Z Z

A A

Z Z Z Z Z

A A

σ+

−

−= − + −

−

− + − −

(41)

�

( )( ) ( ) }{

( ) ( ){ }

� ��

��

� ��

�

��

�

�

�

��

� ��

��

� � ��

� ��

��

� � ��

C Z C Z

C Z Z C

B

B

Z Z

P

A A A

C

B B

Z

C Z Z

σ

+ − + + −

− + + −

−

− − −= + −

−

−+

+

+

(42)

( ){ } {

( ) } ( )

��

��

��

�

�

�

��

��

��

��

��

��

�

Z Z

Z Z

P

A A B

Z

Z C

B

C Z Z

Z

B

Y

C

σ− +

− − +

− +

− −−

−

++

++

(43)

( ) ( )}{( ) ( ){ }

� ��

��

��

��

��

�

�

�

��

��

� ��

��

� ��

��

��

� Z ZP

A A A

C

Z C Z Z

B B

Z

C Z Z Z

B

C Z Z

B

σ− + −

− +

−

−

− −= −

−

++ + − −

+− − +

+

��(44)

Following are the expressions for welded contact (Kumar et.al 2005) for the dimensionless stresses for the two cases for a vertical tensile line source:

{

}

��

�

� ��

� ��

��

��

��

��

�

�

Z

Z

C D

P D C

A A

Z C Z D

C D

A

σ

−= −

+

−

−

− +−

+

(45)

{ }� � � ��

��

��

Z D C C DY

P

Aσ

− −+=

−

�

� �

�

��

Z C Z D

A

− +

(46)

��

�

� � � �

� ��

� � � � � ��

��

��

�

��Z Z

C D Y C D

P

A A

Z C D Y Z C D

A A

σ

+ +

+ += − −

−

− −− +

��(47)

( )

( )

��

��

��

� �

�

�

��

� � ��

��

��

D CZ

P

A A B

Z D CZ

A B

σ

+= +

+− −

− −+

−

+−

�

��( ) �

� �

� �

� � �� ZC Z Z C Z

B B

− ++ +− +

� �

�

�

��

� �

��

� ��

� � ��

��

Z

C Z Z Z

B

C Z ZC Z

B B

+−

+ + +

++ ��

(48)

��

��

�

� �

� �

�

� �

� �

� �

� �

� �

��

��

��

� ��

��

Y Z Z

P

A A

Z D CZ

A B

C Z C Z Z Z

B B

C Z C Z Z

B B

σ

− −= +

−

+ +−− −

+ + + −− +

+ ++ −

��

(49)

� ��

��

��

� ��

� � ��

� ��

��

� � ��

� Z YP

A A A

Y D CD CY Z

A B B

σ− − +

− −

−=

−

−−−+

�

��

�

� �

��

� � � � �� Z ZY C Z C

BB

− ++− − �


�

25 www.ijitce.co.uk

�

�

�

� �� ZC Z Z Y

B

+ ++�

� �

�

�

� � � � �Z ZC Y

B

− ++ �

� �

�

�

��

C Z Y Z

B

−+

� � � (50) �

V. DISCUSSION

Figures 2(a)-2(d), 3(a)-3(d) and 4(a)-4(d) show the variation of the dimensionless stresses P22, P23 and P33 at the interface with the horizontal distance from the fault and the figures 5(a)-5(d), 6(a)-6(d) and 7(a)-7(d) show the variation of the dimensionless stresses P22, P23 and P33 at the interface with the depth from the fault for the rigidity contrast �

�

� ��

� �

µµ

= , respectively for the two

cases. In all the figures (from 2(a)-7(d)), and are dimensionless stresses in the case when contact of half-space is smooth, whereas and denote stresses when contact of half-space is welded. The superscript denotes the medium. Figure 2(a) shows variation of normal stress P22 for smooth contact and in case of welded contact with distance from the fault for

�

�

�

�

µµ

= . In the succeeding figures i.e. 2(b) to 2(d), we

increase the rigidity ratio to ��

respectively. It is noticed that near the origin, the values of stress components and lies between and . As we move away from the fault, this difference becomes less and approaches to zero for infinitely large distances from the fault. Figures 3(a) to 3(d) show variation of stress and with distance from the fault for the rigidity contrast �

�

� ��

� �

µµ

= ��

��

�� and decreases in welded contact. It is also observed in figures from 2(a) to 4(d) that initially, the value of stress is larger in medium I as compared to medium II for smooth contact. components

, and . Variation of stresses with depth from the fault is

shown in figures 5(a) to 7(d). Here, too, variation is examined for same rigidity ratios as explained above. It

is observed that initially the values of stresses and are nearly zero.

VI. CONCLUSION In both cases i.e in welded contact and

smooth contact, stresses tend to zero as x2 and x3approaches to infinity respectively. We notice that the magnitude of stresses for smooth contact model are greater than the magnitude of stresses for welded contact model up to some epicentral distances and then decreases rapidly. Also, in case of smooth contact, the behavior of stresses at the interface for the two half-spaces is opposite to each other i.e., when it is increasing in medium I, it is decreasing for medium II and vice versa. We observe that a change in value of

�

�

µµ

��

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-100

-80

-60

-40

-20

0

20

40

DIMENSIONLESS DISTANCE FROM THE FAULT

P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)P22(µ1/µ2=1/5)

P(1)22P(2)22P*(1)22P*(2)22

Fig. 2(a) Variation of the dimensionless normal stress P22 with distance from the fault for � � ��µ µ = for smooth contact and welded contact.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-100

-50

0

50

100

150


P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)P22(µ1/µ2=1)

P(1)22P(2)22P*(1)22P*(2)22

Fig. 2(b) Variation of the dimensionless normal stress P22 with distance from the fault for

� ��µ µ = for smooth contact and

welded contact.


�

26 www.ijitce.co.uk

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-100

-50

0

50

100

150

200


P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P22(µ1/µ2=3/2)P(1)22P(2)22P*(1)22P*(2)22

Fig. 2(c) Variation of the dimensionless normal stress P22 with distance from the fault for

� ��µ µ = for smooth contact and

welded contact.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-100

-50

0

50

100

150

200

250

300


P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P22(µ1/µ2=5)P(1)22P(2)22P*(1)22P*(2)22

Fig. 2(d) Variation of the dimensionless normal stress P22 with distance from the fault for

� ��µ µ = for smooth contact and welded contact.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-2

-1

0

1

2

3

4

5

6

7

8



P(1)23P(2)23P*(1)23P*(2)23

Fig. 3(a) Variation of the dimensionless shear stress P23 with distance from the fault for � � ��µ µ = for smooth contact and welded contact.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-5

0

5

10

15

20

25



Fig. 3(b) Variation of the dimensionless shear stress P23 with distance from the fault for

� � �µ µ = for smooth contact and welded contact.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-5

0

5

10

15

20

25

30


P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P23(µ1/µ2=3/2)P(1)23P(2)23P*(1)23P*(2)23

Fig. 3(c) Variation of the dimensionless shear stress P23 with distance from the fault for

� � ��µ µ = for smooth contact and welded contact.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-5

0

5

10

15

20

25

30

35

40



Fig. 3(d) Variation of the dimensionless shear stress P23 with distance from the fault for � � �µ µ = for smooth contact and

welded contact.


�

27 www.ijitce.co.uk

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-20

-15

-10

-5

0

5

10



P(1)33P(2)33P*(1)33P*(2)33

Fig. 4(a) Variation of the dimensionless normal stress P33 with distance from the fault for � � ��µ µ = for smooth contact and welded

contact.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-50

-40

-30

-20

-10

0

10

20

30


P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)P33(µ1/µ2=1)

P(1)33P(2)33P*(1)33P*(2)33

Fig. 4(b Variation of the dimensionless normal stress P33 with distance from the fault for � � �µ µ = for smooth contact and welded contact.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-60

-50

-40

-30

-20

-10

0

10

20

30



P(1)33P(2)33P*(1)33P*(2)33

Fig. 4(c) Variation of the dimensionless normal stress P33 with distance from the fault for � � ��µ µ = for smooth contact and welded contact.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-100

-80

-60

-40

-20

0

20

40


P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2=5)P33(µ1/µ2

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NNOVATIVE ECHNOLOGY AND REATIVE NGINEERING V ...ia800305.us.archive.org/34/items/IJITCE/vol3no102.pdfINTERNATIONAL J OURNAL OF INNOVATIVE T ECHNOLOGY AND C REATIVE E NGINEERING (ISSN:2045-8711)