Frontiers in Geotechnical Engineering (FGE), Volume 4, 2016 www.seipub.org/fge doi: 10.14355/fge.2016.04.001
Modelling of Reverse Dip‐Slip Faults Using 3D Applied Element Method Mohammad Ahmed Hussain1, Ramancharla Pradeep Kumar 2 Department of Civil Engineering, Alhabeeb college of Engineering and Technology, Damergidda(v), Chevella, R. R District ‐ 501503, Telangana State, India 1
Earthquake Engineering Research Center, International Institute of Information Technology Hyderabad, Gachibowli, Hyderabad, India 2
ahmediiithyd@gmail.com; 2ramancharla@research.iiit.ac.in
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Abstract It has been observed that near fault ground motion consists of different characteristics compared with the far fault ground motions. In this paper, the near fault ground motion due to dip‐slip surface faults using 3D Applied element method is studied. Using AEM, the crack initiation and propagation can be modelled in reasonable time by using the available parallel computing power. The main advantage of this method of modelling is the ability of crack initiation based on the material failure and propagation of crack till the collapse. This method is used for studying the spatial variation of ground motion due to seismic bedrock displacement at the bedrock level. The influence of dip angle and the presence of lower velocity layer on the near fault ground motion is also studied. It has been noted that in all cases with different fault dip angle, there is greater ground motion on the hanging wall side compared with the ground motion of foot wall side. This effect is due to two important reasons. First, the points on the hanging wall are closer to the fault plane and secondly, the trapped seismic energy in the wedge shape hanging wall leads to multiple reflections. The results from different dip angles indicate that the near fault ground motion is sensitive to the dip angle. Variation of peak ground acceleration with site natural period has also been studied. Systematic decrease in the response is seen with the increase in the site natural period. Keywords Applied Element Method, Near‐Fault Ground Motion, Fault Motion, Dip‐Angle
Introduction The most seismological research on the investigation of ground motion due to fault dynamics has been limited to faults with a high degree of symmetry, such as faults in homogeneous whole spaces and vertical strike‐slip faults due to computational and theoretical constraints. Much can be learned from such studies. However, there are both observational and theoretical arguments that the dynamics of faults with asymmetrical geometry are both qualitatively and quantitatively different from those of symmetrical faults. In particular, there is observational evidence that symmetry of ground motion with respect to fault‐slip direction is lost when a fault does not have a vertical dip. The M7.6 1999 Chi‐Chi (Taiwan) earthquake will undoubtedly be recognized as one of the most significant earthquakes for the science of seismology, due to the unprecedented amount of high‐quality near‐ source data that it generated (Lee et al., 1999). This wealth of data not only allows more precise determination of faulting models of this event, but also addresses new questions concerning faulting and dynamics. In particular, this event allows the verification of many pre‐dictions of ground‐motion behaviour in the near source area of dip‐ slip faults, where data have been especially scarce to date. In this paper, it is shown that many of the observations of the near‐source displacements and peak accelerations can be explained as simple consequences of the asymmetry of the dipping fault geometry. Closer to the subject of the Chi‐Chi earthquake, it has been previously argued that the dynamics of dip‐slip faults (especially those that intersect the free surface of the earth) are strongly affected by their fault geometry (Brune, 1996; Oglesby et al., 2000; Shi et al., 1998; Oʹ Connel et al., 2007). In particular, these studies showed that in comparison with vertical strike‐slip faults, dip‐slip faults exhibit many unique features associated with their asymmetrical geometry. These effects include reflections from the free surface that cause a feedback between the rupture and radiation processes, leading to thrust faults having greater dynamic
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stress drops, greater fault motion, and greater near‐source ground motion than normal faults. Also the smaller size of the hanging wall (coupled with the possibility of trapped waves between the fault and the free surface) leads to an asymmetry between hanging‐wall and footwall motion near the free surface. It should be emphasized that all these effects are strongly dependent on the fault either intersecting or closely approaching the free surface, and that most of these predictions are for the near‐source area. Numerical modelling allows us to investigate a number of aspects of the fault rupture propagation, which are difficult to study from the examination of case histories or the conduct of physical model tests. Numerical simulations of earthquake fault rupture have the advantage of being much more flexible to investigate a number of aspects of the fault rupture propagation phenomenon than analytical solutions. Since our problem is related to the fault rupture propagation, a method is needed which can handle the discontinuities. The Applied element method which was used to study fault rupture phenomenon by Pradeep et al. (2001) has many advantages with respect to the above problems. Using AEM, the crack initiation and propagation can be modeled in reasonable time by using the available parallel computing power. The main advantage of this method of modeling is that it has the ability of crack initiation based on the material failure and propagation of crack till the collapse.In this paper the near fault ground motion due to dip‐slip surface fault studied using Applied element method. In the coming section, the numerical method will be described briefly and numerical results will be discussed. 3D Applied Element Method Applied Element Method is an efficient numerical tool based on discrete modeling (Hatem, 1998). The two elements shown in Fig. 1 are assumed to be connected by the set of one normal and two shear springs. Each set is representing the volume of elements connected. These springs totally represents stress and deformation of that volume of the studied elements. Six degrees of freedom are assumed for each element. These degrees of freedom represent the rigid body motion of the element. Although the element motion is considered as a rigid body, its internal de‐formations are represented by spring deformation around each element. This means that the element shape doesn’t change during analysis, which means that the element is rigid, but the behaviour of element collections is deformable. To have a general stiffness matrix, the element and contact spring’s locations are assumed in a general position. The stiffness matrix components corresponding to each degree of freedom are determined by assuming a unit displacement in the studied degree of freedom direction and by determining forces at the centroid of each element. The element stiffness matrix size is (12 X 12). Fig. 2 shows the components of the upper left quarter of the stiffness matrix. It is clear that the stiffness matrix depends on the contact spring stiffness and the spring location. The stiffness matrix given is for only one pair of contact springs. However, the global stiffness matrix is determined by summing up the stiffness matrices of individual pair of springs around each element.
FIG. 1 ELEMENT FORMULATIONS IN 3D AEM
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(1) (2) KnNx2 NxKnNy (1) +K1sS1x2 +S1xK1sS1y +K2sS2x2 +S2xK2sS2y KnNy2 (2) S(1,2) +K1sS1y2 +K2sS2y2
(3) NxKnNz +S1xK1sS1z +S2xK2sS2z NyKnNz +S1yK1sS1z +S2yK2sS2z KnNz2 +K1sS1z2 +K2sS2z2
(4) KnNx(RyNz-RzNy) +K1sS1x (RyS1z-RzS1y) +K2sS2x (RyS2z-RzS2y) KnNy(RyNz-RzNy) +K1sS1y(RyS1z-RzS1y) +K2sS2y(RyS2z-RzS2y) KnNz(RyNz-RzNy) +K1sS1z(RyS1z-RzS1y) +K2sS2z(RyS2z-RzS2y)
(5) KnNx(RzNx-RxNz) +K1sS1x(RzS1x-RxS1z) +K2sS2x(RzS2x-RxS2z) KnNy(RzNx-RxNz) +K1sS1y(RzS1x-RxS1z) +K2sS2y(RzS2x-RxS2z) KnNz(RzNx-RxNz) +K1sS1z(RzS1x-RxS1z) +K2sS2z(RzS2x-RxS2z) KnNz(RyNz-RzNy) (RzNx-RxNz) +K1sS1z(RyS1z-RzS1y) (RzS1x-RxS1z) +K2sS2z(RyS2z-RzS2y) (RzS2x-RxS2z)
(3)
S(1,3)
S(2,3)
(4)
S(1,4)
S(2,4)
S(3,4)
Kn(RyNz-RzNy)2 +K1s(RyS1z-RzS1y)2 +K2s(RyS2z-RzS2y)2
(5)
S(1,5)
S(2,5)
S(3,5)
S(4,5)
Kn(RzNx-RxNz)2 +K1s(RzS1x-RxS1z)2 +K2s(RzS2x-RxS2z)2
(6)
S(1,6)
S(2,6)
S(3,6)
S(4,6)
S(5,6)
(6) KnNx(RxNy-RyNx) +K1sS1x(RxS1y-RyS1x) +K2sS2x(RxS2y-RyS2x) KnNy(RxNy-RyNx) +K1sS1y(RxS1y-RyS1x) +K2sS2y(RxS2y-RyS2x) KnNz(RxNy-RyNx) +K1sS1z(RxS1y-RyS1x) +K2sS2z(RxS2y-RyS2x) Kn(RyNz-RzNy) (RxNy-RyNx) +K1s(RyS1z-RzS1y) (RxS1y-RyS1x) +K2s(RyS2z-RzS2y) (RxS2y-RyS2x) Kn(RzNx-RxNz) (RxNy-RyNx) +K1s(RzS1x-RxS1z) (RxS1y-RyS1x) +K2s(RzS2x-RxS2z) (RxS2y-RyS2x) Kn(RxNy-RyNx)2 +K1s(RxS1y-RyS1x)2 +K2s(RxS2y-RyS2x)2
Kn: Stiffness of normal spring K1s, K2s: Stiffness of shear springs N: Normal spring vector S1, S2: Shear springs Vector R: Vector connecting the center of the element FIG. 2 ONE QUARTER OF STIFFNESS MATRIX
The displacement time histories is computed by the three‐dimensional dynamic elasticity equation given by Eq. 1
M U C U K U P(t) (1) where [M], [C] and [K] are the mass, damping and global stiffness, respectively; U the displacement vector and P(t) the applied load vector. Here mass proportional damping matrix is used with 10% damping coefficient. The above differential equation is solved numerically by Newmark’s method. The material model adopted in AEM is the two‐ parameter model called hyperbolic model. It is logical to assume that any stress‐strain curve of soils is bounded by two straight lines that are tangential to it at small strains and at large strains as shown in Fig. 3. The tangent at small strains denoted by Go, represents the elastic modulus at small strains and the horizontal asymptotic at large strain indicates the upper limit of the stress f, namely the strength of soils. The stress‐strain curve for the hyperbolic model can be obtained directly from Eq. 2.
FIG. 3 NON‐LINEAR BEHAVIOR OF SOIL ‐ SKELETON CURVE
Go (2) 1
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The above equation has been extensively used for representing the stress‐strain relations of a variety of soils. Since the target of this study is to show the application of AEM, the material model adopted is based on only two parameters, namely, initial modulus, Go and reference strain, =f / Go, where f is the upper limit of the stress. However, any type of material model can be adopted in AEM. To define the failure criteria, it is needed to find the three‐dimensional state of stress at each point where the spring is defined. The three‐dimensional state of stress is defined at each spring location point. After obtaining all the components of stress tensor the failure criteria is to be defined. A Mohr Coulomb failure criterion has been adopted here. Mohr Coulomb invariants I1, J2 and θ (smith et al., 2004) has been calculated using three dimensional stress components. After defining the Mohr Coulomb invariants, soilʹs internal friction angle ‘ ’ and cohesion ʹcʹ is calculated using uni‐axial tension capacity yt and uni‐axial compression capacity yc and from Eq. 3 & Eq. 4. (Boresi et al. 2002).
2 tan 1 2
c
yt 2
yc yt
yt yc
(3)
(4)
Using the above invariants, the Mohr‐Coulomb failure envelops is defined by Eq. 5 (Smith et. al. 2004). In principal stress space, this criterion takes the form of an irregular hexagonal cone, as shown in Fig. 4. F
1 sin sin c cos (5) I1 sin J 2 cos 3 3
Failure if F ≥ 0
FIG. 4 MOHR COULOMB FAILURE ENVELOP IN THREE DIMENSION
The failure envelop F depends on the invariants discussed above and the cohesion c and the friction angle ‘ ’ which depends on the soil uniaxial tension (yt) and uniaxial compression (yc). If the F value is greater or equal to zero, the spring is said to be failed. The normal and shear forces in the failed springs are redistributed in the next increment by applying the forces in the reverse direction. These redistributed forces are transferred to the element centre as a force and moment, and then these redistributed forces are applied to the structure in the next increment. The redistribution of spring forces at the crack location is very important for following the proper crack propagation. For the normal spring, the whole force value is redistributed to have zero tension stress at the crack faces. Although shear springs at the location of tension cracking might have some resistance after cracking due to the effect of friction and interlocking between the crack faces, the shear stiffness is assumed zero after crack occurrence. Having zero value of shear stress indicates that the crack direction is coincident with the element edge direction. In shear dominant zones, the crack direction is mainly dominant by shear stress value. This technique is simple and has the advantage that no special treatment is required for representing the cracking.
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Model Description In this paper, the influence of fault dip angle is studied on the ground motion. For this purpose, a 3D model of length 3 km, width 500m and depth 200m is constructed. The seismic bed rock motion in the form of displacement is applied at the base of the structure. Since the crack does not propagate in the direction in which the displacement is given at the base, a predefined fault plane with a specified angle reaching the surface is defined in the model. The failure of the material takes place only in the predefined fault plane. This has been assumed only to see the influence of dip angle reaching the surface on the ground motion. The dynamics of faulting is simulated for the dip angles 20°, 30°, 40° and 50°. The numerical models used for the study are shown in Fig. 5. The boundary at the left side and the bottom side of the footwall is kept fixed in all the direction. The displacement is applied at the bottom side and right side of the hanging wall. The location of the base fault is assumed to lie exactly at the centre of the model. Generally, soil strata and bedrock extend upto longer distances in horizontal direction. Before starting the analysis, the stability analysis must be carried out in order to bring the model to initial condition. There are two ways for preparing the model for performing dynamic analysis. One is dynamic way and the other is static way. For stability analysis, bottom of the model is considered as fixed boundary and two side boundaries are fixed in horizontal direction. In dynamic way, the model is set with no loading except the self‐weight, which is applied as gravity load in the first increment, the model exhibits free vibrations across the equilibrium position. If there is no damping, these vibrations will not subside till the infinite time. Hence, it is difficult to carry out the studies of dynamic fault rupture propagation till these vibrations subside. In static way, the self‐weight is applied in increments without considering inertia forces. In this method, it is important to decide the number increments in which the gravity load is applied. This number of increments will depend on the material properties. It is important to check the failure of the material, i.e., the connecting springs of the material should not fail during the application of self‐weight. The static method of applying gravity load takes less CPU time compared with the dynamic method. Hence, while performing the dynamic analysis, the model is brought into equilibrium in the static way, and then the dynamic analysis is performed. Applying the bedrock displacement value in the form of Pulse‐like displacement time history that represents the base motion is considered referring to Malden (2000). As an approximation, the corresponding displacement pulse can be assumed as Gaussian‐type function (Eq. 6) where Vsp is the amplitude of static velocity pulse, Tp Velocity pulse duration, tc time instant at which the pulse is centered, n constant equal to 6 and t time. The term Tp / n has the meaning of standard deviation and controls the actual spread of the pulse with respect to the given pulse duration and Φ is the normal probability function. d sp ( t )
t t 2 C V sp T p T p / n n
(6)
FIG. 5 3D NUMERICAL MODEL’S CONSIDERED FOR THE ANALYSIS WITH 50°, 40°, 30° AND 20° OF FAULT DIP ANGLE
For all the dip angles, a vertical slip of 3 m as shown in Fig. 6 is applied and the horizontal slip depends on the dip angle. The shear wave velocity of the material has been taken as 500m/sec.
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FIG. 6 TIME HISTORY OF INPUT VERTICAL DISPLACE MENT APPLIED AT THE BEDROCK LEVEL
The uni‐axial tension capacity yt and uni‐axial compression capacity yc has been taken as 1,500 kN/m2 and 15,000 kN/m2. Numerical Results In this section, attention is focused on the phenomenalistic description of the dynamic effects of the reverse faulting. The rupture nucleation process is not in focus but geometric effects on the ground motion is, when the rupture reaches the surface due to seismic base fault movement. Initially, as the slip is applied at the base of the hanging wall after the self‐weight is applied in a static way as stated in the previous section, the stress resultants in the material of the fault plane builds up, and the two blocks undergo a small deformation to store strain energy. When the stress resultant of the elements at the base along the fault plane reaches the failure strength, the local element connection springs of the elements of the fault plane are considered to be failed. This allows the rupture to propagate along the fault. In general, the rupture initiated at the deepest part of the fault and propagated to the free surface. Variation of PGA with Fault Dip Angle Fig. 7 (a), (b) shows the peak ground acceleration from the time histories of the surface elements for the fault dip angle 20°, 30°, 40° and 50° respectively. The asymmetry of the ground motion between the hanging wall and the foot wall can be seen in all the cases of dip angle. The vertical line in each figure represents the surface fault rupture. The model to the left side of the vertical line represents the foot wall and to the right side of the vertical line the hanging wall. In all cases, there is greater ground motion on the hanging wall side compared to the ground motion of foot wall side. In all the figures, solid line is indicating the vertical component and dotted line is showing the horizontal component. An asymmetry between footwall and hanging wall motion is being noted. This effect is interpreted as being due to two important reasons. First, the points on the hanging wall are closer to the fault plane as compared with the points of foot wall. The second reason for this asymmetry is due to the trapped seismic energy in the wedge shape hanging wall which leads to multiple reflections. The energy does not enter into the foot wall as the stiffness of the fault plane is considered to be a minimum value after the process of rupture takes place. Therefore, the energy stays in the hanging wall. Additionally, there is the mass and volume difference between the two sides of the fault near the free surface i.e. the hanging wall wedge is much smaller than the footwall wedge. From this Figure, it can also be said that the peak responses are not maximum near the place where rupture is occurring on the ground surface. Instead, they are maximum little away from it and this is because of the reduction in the response of the soil deposit as it has become highly non‐linear at the place of surface rupture. Note that while the difference between hanging wall and footwall motion decreases rapidly with distance away from the fault plane. This consistently higher ground motion is largely caused by the increased fault motion near the surface due to the reason’s explained above. The influence of the dip angle on the ground motion can also be seen, the response on the ground surface is increasing with the decrease in the dip angle. The response for the smallest dip angle of 20° is very large compared with the other dip angle which is approximately of 1g. The main reason here is due to the multiple reflections in the wedge shape hanging wall and the points on the hanging wall are closer to the fault plane. This reflection is more for lower dip angle. Moreover, as fault dip decreases a greater
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proportion of a surface‐rupturing fault’s subsurface area becomes closer to the free surface. The proportion of up going P and S waves (i.e. body waves) released during the process of fault rupture with lower dip angle interacts with the free surface with sufficiently large incident angles to induce significant surface‐wave excitation near the fault, producing a stronger ground motion on the hanging wall farther from the surface trace of the fault than a fault with a steeper dip. Additionally, the lower dip angle mass and volume of the hanging wall is less for the lower dip angles.
(A)
(B) FIG. 7 COMPARISON OF PEAK GROUND ACCELERATION ON THE SURFACE FOR ALL DIP ANGLES: A) HORIZONTAL; B) VERTICAL
FIG. 8 HORIZONTAL TIME HISTORIES OF MAX PGA FOR ALL DIP ANGLES
FIG. 9 FOURIER SPECTRA FOR THE ACCELERATION TIME HISTORIES
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FIG. 10 SNAPSHOTS OF THE KINETIC ENERGY RADIATION PATTERNS RELATED TO THE RUPTURE PROCESS FOR THE 20° DIP ANGLE CASE.
Since the mass and volume is less near the free surface, it will have greater motion for the same forces. The decrease in the ground motion with increase in the dip angle can be seen upto 50°. Fast Fourier Transform analysis is carried out for the horizontal time histories of the points on the surface having maximum acceleration values. Time histories of the ground acceleration can be seen in Fig. 8 for the fault dip angle 20°, 30°, 40° and 50° respectively. From the time history plots, the duration of strong ground motion and the peak ground accelerateon value is seen to be maximum for lower dip angle. Fourier spectra can be seen for these time histories in Fig. 9. The frequency content is also seen to be maximum for lower dip angle, because of multiple reflections. Fig. 10 shows the snapshots of the kinetic energy (proportional to velocity squared) propagation pattern related to the rupture process for the reverse fault model with 20° dip angle. The resultant radiated energy shown in these snapshots have been normalized to the maximum kinetic energy. This figure also shows the seismic energy distributions around the fault as the ruptures approach or reaches the free surface. Energy released from the process of rupture and hitting the free surface of hanging wall can be seen from the snapshots. The asymmetrical particle motion patterns imply that the dynamic process near the free surface is more complicated than commonly assumed from kinematic dislocation modelling. The energy concentration on the hanging wall side from the snapshots. Therefore, a stronger shaking on the hanging wall side of the fault than on the footwall side is expected because of the multiple reflecting stress waves trapped in the wedge‐shaped hanging wall of the fault. Variation of PGA with Site Natural Period In this section, the variation of PGA on the ground surface for different value of site natural period is studied. If the ground consists of a single soil layer and bedrock, the natural time period of the ground, Tg, is exactly obtained by Eq. 7 (Kramer12) S., 2007),
Tg
4H Vs (7)
where H is the depth of the overburden and VS is the shear wave velocity. Here the natural time period of the model is dependent on two parameters, i.e., depth of the overburden (H) and the shear wave velocity (VS). In the first case, the shear wave velocity (VS) is varied keeping the overburden depth (H) constant (Table 1) and in the second case the overburden depth (H) of the model is varied keeping the shear wave velocity constant (Table 2). Fig. 11 (A‐B) show the distribution of horizontal and vertical PGA along the surface for different site natural period. In this case as shown in Table 2, only shear wave velocity is varied in order o change the natural period of the site, in other words only the stiffness of the deposit is varied. Systematic decrease in the response is seen with the increase in the site natural period. The reason for this is, in stiff soils the energy released during the process of rupture is more comparet to that of soft soils and this leads to amplification of high frequency waves. Fig.12 (A‐B) show the distribution of horizontal and vertical PGA along the surface for different site natural period varied with respect to the depth of the overburden.From this figure, it can be said that the trend of the result of attenuation of PGA and the value of PGA is the same as in the previous case. Increase in the site natural period with depth of overburden leads to decrease in natural frequency of the model and hence, the response in reduced.
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(A)
(B) FIG. 11 DISTRIBUTION OF PGA ALONG THE SURFACE FOR DIFFERENT SITE NATURAL PERIOD WITH VARYING SHEAR WAVE VELOCITY; A) HORIZONTAL ACCELERATION, B) VERTICAL ACCELERATION
(A)
(B) FIG. 12 DISTRIBUTION OF PGA ALONG THE SURFACE FOR DIFFERENT SITE NATURAL PERIOD WITH VARYING DEPTH; A) HORIZONTAL, B) VERTICAL ACCELERATION TABLE 1 VARIATION OF TIME PERIOD (TG) WITH SHEAR WAVE VELOCITY (VS)
Sl. No.
Shear Wave Velocity ‐ Vs (m/s)
Depth of the Overburden H (m)
1
615
200
1.3
2
500
200
1.6
3
421
200
1.9
4
363
200
2.2
5
320
200
2.5
Time Period Tg
4H (s) Vs
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TABLE 2: VARIATION OF TIME PERIOD (T g ) WITH DEPTH OF THE OVERBURDEN (H)
Time Period Sl. No.
Shear Wave Velocity ‐ Vs (m/s)
Depth of the overburden H (m)
1
500
162
1.3
2
500
200
1.6
3
500
237
1.9
4
500
275
2.2
5
500
312
2.5
Tg
4H (s) Vs
Conclusions The results of the numerical simulation have explained many dynamic and geometric aspects of the reverse faulting. In all cases of different fault dip angle, there is greater ground motion on the hanging wall side compared with the ground motion of foot wall side. This effect can be interpreted as being due to two important reasons. Firstly, the points on the hanging wall are closer to the fault plane, and secondly, the trapped seismic energy in the wedge shape hanging wall leads to multiple reflections. The results from different dip angles indicate that the near fault ground motion is sensitive to the dip angle. Systematic decrease in the response is seen with the increase in the site natural period REFERENCES
[1]
Japan Society of Civil Engineers, The 1999 Ji‐Ji earthquake, Taiwan, Investigation into damage to civil engineering structures, Earthquake Engineering Committee, Japan Society of Civil En‐gineers, 1999.
[2]
Lee, T., Cheng C., and Hsu S. : Fault rupture associated with the September 21, 1999 Chichi earthquake, West Central Taiwan, AGU , 14. 1999.
[3]
Brune, J. (1996). Particle motions in a physical model of shallow angle thrust faulting, Proc. Indian Acad. Sci. (Earth Planet Sci.) 105, L197‐L206.1996.
[4]
Oglesby, D. D., R. J. Archuleta, and S. B. Nielsen: Dynamics of dip‐slip faulting: exploration in two dimensions, J. Geophys. Res. 105, 13,643 ‐653, 2000.
[5]
Shi, B., A. Anooshehpoor, J. N. Brune, and Y. Zeng : Dy‐namics of thrust faulting: 2‐D lattice model, Bull. Seismol. Soc. Am.. 88, 1484 ‐1494, 1998.
[6]
OʹConnell. D.R .H, Shuo Ma, and Ralph J. Archuleta : Influence of Dip and Velocity Heterogeneity on Reverse‐ and Normal‐Faulting Rupture Dynamics and Near‐Fault Ground Motions, Bull. Seismol. Soc. Am., Vol. 97, No. 6, pp. 1970‐ 1989, 2007.
[7]
Pradeep R.K.: Numerical analysis of the effects on the ground surface due to seismic base fault movement, PhD thesis, University of Tokyo, Japan, 2001.
[8]
Hatem. Tagel‐Din: A new efficient method for nonlinear, large deformation and collapse analysis of Structures, Ph.D. thesis, The University of Tokyo, 1998.
[9]
Smith,I M, D.V Griffiths : Programming the finite element method. John Wiley and Sons publications, 2004.
[10] Boresi. Arthur, Richard J. Schmidt : Advanced Mechanics of Materials, John Wiley and Sons publications, 2002. [11] Mladen V. K.: Utilization of strong motion parameters for earthquake damage assessment of grounds and structures, Ph.D. Thesis, University of Tokyo,2000. [12] Kramer S.L.: Geotechnical Earthquake Engineering, Pear‐son Education. 2007.
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Pradeep K. Ramancharla worked in L&T‐ECC for about a year (1997‐98) and went to Tokyo, Japan for pursuing Ph.D. After receiving degree, he worked as a post‐doctoral research fellow for one year (2001‐02). He joined IIIT Hyderabad in September 2002 and started Earthquake Engineering Research Centre (EERC). He was also instrumental in initiating graduate program on Computer Aided Structural Engineering (CASE) at IIIT Hyderabad. Dr. Ramancharla research interests are; i) macro seismotectonics of Indian plate, ii) large deformation analysis of faults, iii) Non‐linear structural response & damage estimation, iv) Health diagnosis of historical and critical structures, v) Sustainable construction technologies (with local & natural materials) and v) Capacity building on disaster safety. In addition to the above, Dr. Ramancharla has keen interest in research on humanities and human values. Dr. Ramancharla is a member of a few committees at both state and national level. He is a member of Post Earthquake Reconnaissance Team (PERT) of NDMA, GoI. As a member of expert committee of NDMA; in addition, he has contributed to the preparation of National Disaster Management Policy and Guidelines for Earthquakes and Tsunamis as well as to the preparation of policy for restructuring of Fire and Emergency Services Department, Govt of AP. He is also a member of expert committees on Disaster Mitigation of Cyclones and Urban Floods. He is currently a BIS panel member of IS 456 & IS 1343 (CED2) and also a member of National Building Code of India (CED 46:P16). Mohammad Ahmed Hussain has completed his PhD in Civil Engineering from Earthquake Engineering Research Centre, IIIT Hyderabad in 2012. He is presently working in Alhabeeb College of Engineering and Technology as Associate Professor in the Civil Engineering Department. Dr. Mohammad Ahmed Hussain is currently involved in numerical simulations of fault motion & wave propagation in 2D and 3D using Applied Element Method. Research in this area contributes to the understanding of near fault ground motion, phenomenon of surface faulting and fault rupture propagation by preparing a numerical model with actual field conditions on the existing faults. His main research Areas of Interests are 1. Numerical simulation of structural analysis, 2. Earthquake engineering and Structural Dynamics, 3. Wave propagation in the soil media, 4. Collapse Analysis of structureʹs and 5. Applied Element Method.
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