SEISMIC RESPONSE OF TEHRI DAM

Dr.STGRaghu Kanth &MaheshreddyIndianInstituteofTechnologyMadras

It is quite apparent that the structural layout (particularly related to faults andthrusts in the areas chosen) and the seismicity of the region were not taken intoconsideration.

Overtopping of dam due to waves generated in the impounded water of reservoirsbehind dams, besides slope failures and attendant mass movements.

It would be safer to design dams that can withstand PGA as high as 1.0g.

Current science June 2014

WCEProf. R.N. Iyengar, (Chairman)Prof. D.K. Paul, Dr. R.K. Bhandari, Prof. Ravi Sinha, Dr. R.K. ChadhaDr. Prabhas Pande, Prof. CVR Murthy, Dr. A.K. Shukla (Member-Secretary)

Project Team

Dr.STG Raghukanth

CSIR SERC

http://www.ndma.gov.in/en/study-reports-of-mitigation-division.html

Advances in Engineering Seismology

SeismicHazardofIndia Installationdetails

1. NavigatetoGooglePlayorPlayStore2. SearchSeismicHazardofIndia3. TheapplicationisavailableforFreeongoogle play.4. ReaddescriptionandInstallapplicationonyourandroiddevices.5. Compatibleforandroid3.0andabove(MobileandTablets).

TEHRIDAM

Tehri dam is an earth and rock-fill dam located in the CSG region of Himalaya andconstructed across the Bhagirathi River.

The height of the dam at the deepest point is 260.5m.

The width of the crest is 20m with a 9.5 m of freeboard and spans 574m across the valley.

The base width of the dam in upstreamdownstream direction is nearly 1 km.

The Tehri Hydro Development Corporation Ltd (THDC) reported the first six natural time periodsfor the central section of the dam as 2.272, 1.672, 1.476, 1.256, 1.087, and 1.104 seconds.

These time periods are calculated by two dimensional finite element analysis.

The shear wave velocity (Vs) for the dam material has been estimated to be 300-320 m/s(Iyengar 1993).

The dam has been designed for an effective peak ground acceleration (EPGA) as 0.25g.

At present no clear-cut information aboutthe last great earthquake in the centralseismic gap.

The recent GPS measurements indicatethat the strain in CSG is increasing.

The strains in this region has the capabilityof generating one or more greatearthquakes (Bilham and Gaur 2000,Bilham et al 2001).

Bilham (2001) has estimated slip potentialof 4m for the central seismic gap byassuming convergence rate of the plate as20 mm/yr.

The 100 year probability of a greatearthquake in central seismic gap is 0.52(Khattri 1999).

8

Seismic gap is the sections of the plateboundary that have not ruptured in the past 100years.

Three seismic gaps are identified byresearchers in Himalayan region

o Kashmir Gapo Central Seismic Gap (CSG)o Assam Gap

Hypothetical Earthquake

The size of the chunk is 35o 35o. The number of spectral elements are 68.9 million. The number of degrees of freedom are 12.7 billion. The average distance between grid points is 2 km Simulate ground displacements accurately

NGRI

SRTM DATA

HIGH PERFORMACE COMPUTING ENVIRONMENT

292 Compute Nodes

Total Compute Power 97 TFlops

IBM System x iDataPlex dx360 M4

A total of 64 GB RAM per node

Layers of Earth

Simulation of ground motion at global level

2

2

( , ) ( , )( ) 2 ( , ) ( , )t t t tt t

u r u rr u r f rH

2

2

( , ) ( , ) 1( ) 2 ( )t tt t

u r u rr u u g

22

( , ) ( , )( ) 2 ( , ) ( , )t t t tt t

u r u rr u r f rH

( , )tu r( ) r

( , )tf r

H

The governing equation for the Earth medium in spherical domain subjected to a unitimpulsive double couple applied at location (Crust and Inner core)

Material density,

is the Earth's angular rotation vector and

denotes the body force.,

displacement field,

elasto-gravity operator

( , ) ( ) ( ) ( )t u r u u g u gH( ,t) ( ) ( )s S t f r M r r KomatitschandTromp(2002).

2

2

( , ) ( , ) 1( ) 2 ( )t tt t

u r u rr u u g

(Outer core)

( )sr

Sample of slip field (cm) on the rupture plane. Mai and Beroza (2001) Raghukanth and Sangeetha (2014)

STOCHASTIC SLIP MODELS

STRONGGROUNDMOTIONDATAANDSOURCEPARAMETERSOFHYPOTHETICALEVENT

Recorded acceleration time histories for Uttarkashi-2012 event

IIT Roorkee, DST, Govt. of India, 2004 294 strong motion accelerographs in the

Himalayan region of India. Recorded ground motion data for these

events is available in www.pesmos.com. The recorded small events data can be

used as IRF to simulate ground motionsfor future great events.

Since 2005, more than 24 small events whosemagnitudes vary from 3.2 to 5.7 are happenedwithin the CSG region.

The recorded ground motion data containsinformation about the source mechanismand the medium properties.

Five small events recorded data isavailable at Tehri station.

The small events magnitude (Mw) varyfrom 3.5 to 5.7.

The magnitude of the hypothetical earthquake(Mw= 8.5) and its fault properties like length(303 km), width (113 km) and epicenter aretaken from Raghukanth et al. (2012).

Strike (300oN), dip (20o), epicenter (30oN,79.2oE) and the depth to the top of the fault(Z0 = 15 km).

rupture velocity 2.5 km/s.

Small events epicenter, the location of the station and rupture plane of the hypothetical event (Black rectangle).

SIMULATIONOFGROUNDMOTIONSFORHYPOTHETICALEARTHQUAKE

The empirical method proposed by Frankel (1995) is used to simulate the accelerationtime histories for hypothetical earthquake.

The main fault is divided into square subfaults. Each subfault time histories can be taken as recorded small event time histories,

multiplied by a correction factor. Sum all these subfaults time histories with appropriate time delay. The correction factor is a function of corner frequency of the small event and slip

distribution of the main event. The stress drop () for these small events has taken from Raghukanth et al. (2014).

The corresponding corner frequencies for small events are estimated by

25 random samples of slip distributions are generated for hypothetical event. A total of 25 acceleration time histories are simulated from each slip distribution. The corresponding response spectra is estimated from time histories. The mean response spectra (from different events and 25 slip distributions) and its

standard deviation values are estimated.

SIMULATIONOFGROUNDMOTIONSFORHYPOTHETICALEARTHQUAKE

Simulated acceleration time histories at Tehri from Uttarkashi-2012 events.

Comparison of horizontal PGA simulated in thepresent study and other studies in the region

Station

Presentstudy

Dineshetal.(1999)

SumerChopraetal.(2012)

Babitasharma etal.(2013)

Tehri (0.50.3)g

(0.970.33)g

0.65g 0.22g

SEISMICANALYSISOFTEHRIDAM

Modeled the dam as 1D and 2D shear beam.

The shear wave velocity (Vs = 310 m/s) of thedam is taken from Iyengar (1993).

Two different acceleration time histories whosePGA values are 0.3g and 0.5g are used foranalysis.

Parameters like crest acceleration and shearstrains at different levels are estimated fromseismic analysis.

one-dimensional shear beam theory (infinitelength)

2 2

2 2

1u G u ut y y y

The equation of motion governing free vibration ofan elastic wedge considered as a shear beam

where u(y,t) is the displacement at depth y in the xdirection, and is the mass density of the dammaterials and G is shear modulus.

The natural frequencies and modes of vibrationcan be given by

0,

,

nn

n n

Gh

yY y Jh

n=1,2,3,...,

where n, n = 1, 2, 3, ..., are the roots of the Besselfunction of zero order of the first kind, J0(n). Themodal participation factor is given by

12

nn n

PJ

1

, n nn

u y t Y y T t

2n n n n gT t T t P u t

n=1,2,3,...,

x

y

u

h

One-dimensional shear-wedge model representing long earth dams

SEISMICANALYSISOFTEHRIDAMThe twodimensional shear beam theory (finitelength)The dam is assumed to be a triangular wedge in arectangular canyon with finite length (l)

2 2 2

2 2 2

1u G u u ut y z y y

Thenaturalfrequenciesandmodesofvibrationaregivenby

12 2

2

0

sin

snr n

nr n

V r hh l

y r zJh l

The modal participation factor is given by

, 18

n rn n

Pr J

n,r=1,2,3,...,

The first six natural time periods from 1Danalysis in seconds are 2.195, 0.9565, 0.6101,0.4478, 0.3536 and 0.2922.

From 2D analysis in seconds are 1.886,1.4155, 1.076, 0.9261, 0.8531 and 0.8498.

The first six natural time periods for thecentral section of the dam reported byTHDC are 2.272, 1.672, 1.476, 1.256,1.087, and 1.104 seconds.

The estimated time periods from 2Danalysis are comparable with the valuesreported by THDC.

Crest acceleration of dam for simulated ground motionwith 0.3g

Crest acceleration of dam for simulated ground motionwith 0.5g

Earthquake-induced dynamic shear strain (at 0.25h) for two different acceleration time histories.

SEISMICANALYSISOFTEHRIDAM(PreliminaryResults)

Since, the representation of a nonlinear material such as the earthen dam by the linear modelused in this study may not represent the real behavior of the dam

CONCLUSIONS PGRDhastobeconsideredinselectingsites.Overtoppingofdamduetowavesgeneratedintheimpoundedwaterof

reservoirsbehinddamsduetoPGRD The maximum crest acceleration values for Tehri dam obtained in thepresent study varies from 1 to 1.6g obtained using sitespecific groundmotions.

Thesevaluesarehigherthanthemaximumcrestaccelerationvaluesof0.62to0.96greportedbySengupta (2010).

Themaximumshearstrainsobtainedinthisstudyareintherangeof1.2103 to1.7103.

Anonlinearanalysisusingthesimulatedsitespecificgroundaccelerationtimehistorieshastoperformedtounderstandtherealbehaviorofdam(InProgress)

THANK YOU

The first step in SPECFEM is to create the mesh files. Single chunk whose center is 25oN and 82oE is used in this study. The size of the chunk is 35o 35o. The number of spectral elements are 68.9 million. The number of degrees of freedom are 12.7 billion. The average distance between grid points is 4.88 km.

At the top surface the average size of a spectral element is 19.54 km.

The 3D velocity model for the mantle and crust are taken from the work of Kustowskietal.(2008) and Bassinet al. (2000).

The viscoelastic constants of the crust, mantle and inner core are taken from Komatitsch andTromp (2002).

The topography and bathymetry model available at 5min interval grid (ETOPO5) is from the USNational Oceanic and Atmospheric Administration (http://www.ngdc.noaa.gov/).

Strong motion data

(Chi-Chi earthquake)

Trackwithabout2mofverticaluplift

Near FieldGroundMotion

Awaterfall7mhighformedduringChiChiearthquake

c( , ) ( ) 0t r r n r2

OCB2

( , )( , ) ( ) ( )wtt h r

t

u r r n r n r

| ( ) | 0 ICB,CMBrt

u n r

| ( , ) ( ) | 0 ICB,CMBt r r n r

BoundaryConditions

20

0

0

20

0

M M sin( ) cos( ) sin(2 ) sin(2 ) sin( ) sin ( )

M M sin( ) cos( ) cos(2 ) 0.5sin(2 ) sin( ) sin(2 )

M M cos( ) cos( ) cos( ) cos(2 ) sin( ) sin( )

M M sin( ) cos( ) sin(2 ) sin(2 ) sin( ) cos ( )

M M cos( )

r

r

0cos( ) sin( ) cos(2 ) sin( ) cos( )

M M sin(2 ) sin( )rr

The Earth is divided into a number of hexahedral non-overlapping volume as shown in Figure 2. Each element is mapped to a reference cube by the classical Jacobian matrix. In SPECFEM high-degree Lagrange interpolant is used to represent functions on the element. The nodes needed to define the Lagrange polynomials of degree n are chosen to be the classical n+1 socalled Gauss-Lobatto-Legendre (GLL) quadrature points.

M u W u + Ku + Bu = F M andK aretheglobalmassmatrixandstiffnessmatrix.W containstermsrelatedtoangularrotationvectorandB isrelatedtotheboundaryinteractionsatCMBandICBandFisthesourceterm.

KomatitschandTromp(2002).

Cubed Sphere Mapping

The Earth is divided into 6 chunks based on the cubed sphere mapping. These chunks are further subdivided into 25 mesh slices for a total of 150 slices. Each slice is handled by separate processor. The total number of processors needed to handle the mesh would be 150. Each slice is further subdivided into 64 x 64 spectral elements at the earth's surface.

Thetotalnumberofspectralelementsinthemeshshownis8.3968millionandthetotalnumberofdegreesoffreedomis1.55billion. Sincegridpointsaresharedamongtheelements,theentireglobeisrepresentedby553.4milliongridpoints.Thetotalnumberofdegreesoffreedominentiremeshis1.55billion.TheaveragegridspacingattheEarth'ssurfaceisabout7.8km

Bassinetal.(2000).