Dynamic Analysis of Matatila Earthen Dam – A Case Study

Chhatre, M.V. Muralidhar, B.Senior Research Officer Senior Research Officer

e-mail: cmegha2003@yahoo.com e-mail: muralibhageerath@yahoo.com

Central Water and Power Research Station, Pune

ABSTRACT

Matatila dam, constructed across river Betwa, near Jhansi in Uttar Pradesh is a multipurpose dam and located in

the zone II of seismicity map of Inda. The dam is a composite dam having central spillway flanked on either sides

by earthen dams and the maximum height of zoned earthen dam is 24.38 m. Shear strength properties and dynamic

properties of soil samples were determined in laboratory and paper presents details of dynamic studies carried

out and its findings . Dynamic response analysis of earthen dam with earthquake having peak ground acceleration

of 0.062g indicated maximum crest acceleration as 0.107g. The Factor of Safety for the pseudo-static slope

stability analysis ranged from 0.74 to 0.88 for upstream and 1.28 to 1.83 for downstream slopes. Earthquake

induced permanent deformation was evaluated by the method of Prof. Seed and F.Makdisi and found to be in the

range of 0.3 to 5.0 cm. The studies revealed that Matatila earthen dam was safe against the site specific design

basis earthquake.

Indian Geotechnical Conference – 2010, GEOtrendz

December 16–18, 2010IGS Mumbai Chapter & IIT Bombay

1. INTRODUCTION

Matatila dam was constructed in 1964 across river Betwa,50 Km from Jhansi in U.P. Its water is used for irrigation,power generation and drinking purposes. Matatila dam iscomposite dam having 737.42 m long 23 gated, centralspillway flanked on either sides by earthen dams of 3657.6m long on left side and 1905.0 m long on right side. Theheight of the earthen dam from Ground Level is 24.38 m.

In 1983, a spillway discharge of 8.26 lakh cusecs hadoccurred as against the design capacity of 5.26 lakh cusecs.Many people working on the dam felt the vibration of thedam during this flood. A Committee constituted under thechairmanship of Chief Engineer (Betwa) , opined thatMatatila dam be checked for its dynamic stability accordingto new seismology of the area. This paper gives the detailsof the dynamic studies carried out on Matatila earthen dam.The cross section of Matatila earth dam considered for thedynamic analysis is shown in Figure 1.

Fig. 1: Cross Section of Matatila Earth Dam

2. FIELD INVESTIGATIONS

To enable us to evaluate the soil properties of dam aswell as foundation material, undisturbed and disturbedsoil samples were collected from the pits of 1.2 m x1.5 m x 2.0 m deep. Core soil ( clay ) was collectedfrom a pit formed by removing the casing soil ofabout 2.0 m deep at the top of the dam. Foundationsoil were collected from two pits on either sides of thedam on the downstream located at 50 m from the toeof the dam.

3. LABORATORY TESTS

Casing soils were classified as poorly graded sand(SP), Core soil (black soil), were classified asintermediate Clay ( CI ). Consolidated Undrained (CU)triaxial tests with pore pressure measurements wereconducted on cylindrical soil specimens of 3.8 cmdiameter and 7.6 cm height. Casing soil ( murrum )was remolded to the field dry density of 17.5 KN/m3

and at 5.0 % moisture content were tested.Undisturbed soil samples of core soil ( black soil )were tested at dry density of 15.5 KN/m3 and 20.0 %moisture content. Remolded foundation soil ( sand )was tested. All the tests were conducted with fullsaturation achieved by Back Pressure method. Theshear strength parameters are given in Table1.

740 M.V. Chhatre and B. Muralidhar

Table 1: Shear Strength Parameters Used in the StabilityAnalysis

Zo

ne

So

il t

ype

Dry

densi

ty,

KN

/m2

Mois

ture

co

nte

nt

(%)

Co

hesi

on

C

, K

Pa

Fri

ctio

n

an

gle

, Φ

0

Casing SP 17.5 5.0 0.0 32.0

Core CI 15.5 20.0 85.0 6.5

Foundation

SP 16.5 8.0 0.0 25.0

Resonant Column Test

Shear Modulus (G) and Damping Ratio (D) of core, casingand foundation soils were determined in the laboratory,using the Resonant Column test equipment. In this test,the top end of the cylindrical soil specimen ( 38 mmdiameter x 76 mm high ) is vibrated in torsional modewhile the other end of the specimen is fixed at the bottompedestal. A torsional driver, attached to the top of thespecimen is used to vibrate the specimen in torsional mode.The vibration of the soil column is measured by anaccelerometer mounted on the soil top. Test is conductedto determine Resonant frequency (f

R) of the soil. Figure 2

shows the schematic diagram of the experimental setupfor resonant column test.

Fig. 2 : Experimental Setup for Resonant Column Test

4. DYNAMIC SHEAR MODULUS OF SOIL

In the resonant column tests the Resonant Frequency (fR)

and Acceleration of vibration were measured. The relationsbased on the theory of elasticity were used to calculate shearwave velocity, shear modulus and shear strain. Shear wavevelocity was determined from Eq. (1) and Shear modulusfrom Eq. (2) as given below :

⋅

=

SSD

S

V

L

V

L

I

I ωωtan (1)

2S

VG ρ= (2)

Where IS , I

D are moment of Inertia of soil column and

torsional driver, ù= angular resonant frequency, L = lengthof the specimen, Vs = shear wave velocity. The range of

shear strain (ã) obtained in the test is 10-4 to 1.0 %. TheG

max is the Shear Modulus value of the soil at the lowest

strain level of vibration (= 10-4 %). Figure 3 gives thevariation of G

max with that of shear strain.

Fig. 3: Variation of Gmax

with Shear Strain (%)

Evaluation of Damping Ratio

When the soil specimen is vibrating at Resonancefrequency, the power supply to the torsional driver isswitched off. The vibrating soil continues to vibrate andcomes to rest after certain time. During this period, theamplitude of vibration goes on decreasing and becomeszero. This is the amplitude decay curve of the soil sampleat a particular shear strain level of vibration. The amplitudedecay of free vibrations of a system with viscous dampingis described by logarithmic decrement (d), which is definedas the ratio of the natural logarithm of two successiveamplitudes of motion. Damping ratio was calculated byusing the relationship in (Eq. 3) and is shown in Figure 4.:

D = (d2/(4p2 + d2)) 0.5 (3) where δ = logarithmic decrement.

Fig. 4: Variation of Damping with Shear Strain (%)

Evaluation of Modulus, K2max

The variation of Gmax

with effective mean stress (��m

)depends on type of soil , density, degree of saturation etc.G

max is determined at different confining pressure (1.0 to

4.0 Kg/cm2 ) in the Resonant column test. The relationbetween G

max and σ

m is given as under (Eq. 4) :

PK x P x 21.7

0.5

a

m'

2maxamax

=

σG (4)

Dynamic Analysis of Matatila Earthern Dam... 741

where Pa = Atmospheric Pressure. The values of modulusK

2max for Casing soil and core soil samples as determined

f r o m t h e t e s t s a r e 80 and 45 respectively.

4. SLOPE STABILITY ANALYSIS

The stability of the upstream and downstream slopes wasdetermined by using Bishop’s modified slip circle method.In this method a potential failure circle passing throughthe slope of the dam was considered for the analysis. Atthe equilibrium condition, resisting moment and disturbingmoment were summed up for all vertical slices. The ratioof Resisting moment to Disturbing moment is the Factorof Safety (FoS) for that circle.

The slope stability analysis was carried out withpotential slip circles at different higher elevations. The basicsesmic coefficient for the full height circle is 0.07 g . Theseismic coefficient that is to be applied for slip circles athigher elevations was varied according to the relation givenin IS: 1893 – 1984. The FoS with seismic loading for thedownstream slope ranged from 1.28 to 1.83 for shallowcircle to deep circles. The FoS for upstream slope rangedfrom 0.74 to 0.88. The FoS less than 1.0 for upstreamindicate a likely slope failure. The Figure 5 show the deepcircular slip surfaces on the upstream slope.

Fig. 5: Critical Slip Surface on Upstream Slope

5. EARTHQUAKE INDUCED DEFORMATION

Studies were carried out to determine the earthquakeinduced deformation in Matatila earthen dam, by themethod proposed by Prof. B. Seed and F Makdisi (1978) .This method is based on the concept originally proposedby Newmark, which assumes that failure occurs on a welldefined slip surface and that the material behaves elasticallyat stress levels below failure but develops a perfectly plasticbehavior above yield.

Yield Acceleration

The yield acceleration, Ky,

is defined as that horizontalacceleration producing a horizontal inertia force on apotential sliding mass so as to produce a Factor of Safety

equal to unity and thus cause it to experience permanentdisplacement. It is determined from the slope stabilityanalysis by considering the undrained shear strengthproperties of the soil. The value of undrained shear strengthparameters for the casing soil from tests are c =0.0 KN/m2

and Φ = 24.00 . In the slope stability analysis Φ = 19.00

was used. The yield acceleration for the upstream slipsurface was found to be 0.022g. The downstream slope theyield acceleration computed with Φ =32 degrees formurrum, was found to be 0.315 g.

Maximum Crest Acceleration

The dynamic response of the dam was evaluated using acomputer program QUAD-4. The program uses a step-by-step integration procedure with variable Rayleigh damping.The program uses four noded, isoparametric, plane strainelements. The finite element idealization of the Matatilaearthen dam was done with 447 nodes and 427 elements(Fig. 6).

Fig. 6: Finite Element Idealization of the Matatila Earthen Dam

Site specific Horizontal and Vertical acceleration-timehistory corresponding to site specific Earthquake are appliedto the base of the dam. The Maximum Credible Earthquake(MCE) has maximum horizontal and vertical accelerationsas 0.124 g and 0.118 g respectively (Fig. 7). The DesignBasis Earthquake (DBE) which are taken as half of theMCE level.

Fig. 7: Horizontal Acceleartion-Time History (MCE)

The dynamic response analysis gives maximumhorizontal and vertical acceleration that are likely to beinduced at each nodal point (Fig. 8). The maximum crestacceleration is found to be 0.107g.

742 M.V. Chhatre and B. Muralidhar

Fig. 8: Acceleration Response Along the Central Line of the Dam

CREST DISPLACEMENT

Seed and Makdisi carried out dynamic analysis on differentearthen dams that were subjected to earthquakes of differentmagnitudes to determine permanent displacements likelyto be developed in the body of the dam. Based on theseanalyses two design curves were prepared.

The first design curve as shown in Figure 9, gives acorrelation between the ratio of ‘Maximum accelerationratio’ ( K

max / Ü

max ) and ‘Depth ratio of sliding mass’

( y / H ) , where Kmax

- maximum acceleration of the vibratingsliding mass, Ü

max - maximum Crest acceleration , y - the

depth of sliding mass, H - the height of the rockfill dam, y/H - Depth ratio of the sliding mass. The average value of(K

max/Ü

max) is found to be 0.35 for the sliding mass that is

passing through the full height of the dam. The computedvalue of K

max is found to be 0.037 g , for Ü

max of 0.107 g.

This is the maximum acceleration of the sliding mass duringthe earthquake motion.

Fig. 9: Variation of Ratio Kmax

/Ümax

With Depth Ratio (y/H) ofSliding Mass

The second design curve (Fig. 10) shows the variationof ratio (K

y / K

max) with ‘Normalized permanent

displacement’ (U / Kmax

.g .To) for different magnitudes of

earthquakes ( 6¼,7 ½ and 8 ¼ ), where ‘U’ is the actualpermanent displacement. (Fig. 9). It is mentioned thatpermanent displacement of the sliding mass occurs only ifthe ratio (K

y / K

max) is less than 1.0. For a given ratio of

(Ky/K

max), normalized displacement could be found out for

a given magnitude of earthquake. The actual displacement(U) of the sliding mass is determined from the value

normalized displacement. The ratio of Ky/K

max ranged from

0.26 to 0.58 for u/s slope. The permanent displacementevaluated for earthquake Magnitude of 6½ was in the rangeof 0.2 to 2.9 cm. The permanent displacement computedwith MCE ranged from 0.53 to 6.6 cm.

Fig. 10: Variation of Normalized Displacement withRatio of K

y / K

max

CONCLUSIONS

The slope stability analysis with seismic coefficientindicated Factor of Safety of the upstream slope of Matatilaearthen dam is in the range of 0.78 to 0.88, which is lessthan 1.0, indicating there is likely failure of slope by circularslip surface. However, the likely permanent crestdisplacement computed by the method of Makdisi and Seed,ranged from 0.53 cms to 6.6 cms, with MCE and 0.2 to 2.9by DBE, which is insignificant. There would not be loss offreeboard. Analysis indicated that Matatila earthen dam issafe against site specific design basis earthquake.

ACKNOWLEDGEMENT

The authors are grateful to Dr.I D Gupta, Director for givingpermission to publish the paper and Shri. R K Kamble,Joint Director for his valuable suggestions.

REFERENCES

CWPRS (2008). Estimation of site specific design seismicground motion for dynamic analysis of Matatila damU.P.Technical Report No.4575.

Idriss I. M., Lysmer, J., Hwang, R. and Seed, H. B. (1973).Seismic response of soil structures by variable dampingfinite element procedure. Earthquake Engineering

Research Center, Report No.EERC 73-16. Universityof California, Berkeley.

IS: 1893-1984: (1984). Criteria for earthquake resistantdesign of structures, Bureau of Indian Standards, NewDelhi.

Makdisi, F. I., Seed, H. B. (1978). Simplified procedurefor estimating dam and embankment – earthquakeinduced deformation, ASCE Journal of

GeotechnicalEngineering Division. Vol.104.

Seed, H. B.(1979). Considerations in the earthquakeresistant design of earth and rock fill dams, 19th Rankine

lecture, British Geotechnical Society.