STATIC AND DYNAMIC ANALYSIS OF EARTH AND ROCKFILL DAMS

Abstract

The frequent occurrence of destructive earthquakes in the past in various places such as, Santa Barbara, USA (1906); Koyna, India (1967); San Fernando, USA (1971); Chile (1985) and other places, causing loss of thousands of lives and damage to dams and earth structures has demons trated the need for earthquake resistant design of these structures. Failure of a dam during an earthquake would be very catastrophic and hence extreme care should be exercised in their design with respect to earthquake resistance. An earth and rockfill dam is considered to be a desirable type of dam in seismic regions due to its flexibility. Nevertheless, its design needs numerous considerations due to complex stress-strain characteristics of soil and rock which is generally not applicable for,other types of dam. This has amply been demonstrated by the total collapse of the Sheffield Dam during the Santa Barbara earthquake of 1906 (Seed, Lee and Idriss, 1968), and the deformations and settlement that occured in the near catastrophic failure of the Lower San Fernando Dam in California (USA), during the San Fernando earthquake of February 9, 1971 (Seed et al., 1973). In recent years, high rockfill dams of height of the • order of more than 250 m are being increasingly constructed all over the world in regions of moderate to very strong seismicity. With the increase in the height of the rockfill (i) (ii) dam, proneness to failure and complexity in design also increase. This is due to the increase in height with an increase in the magnitude of confining pressure and due to the strength-deformation characteristics of the fill materials becoming nonlinear. In such cases, the stressstrain behaviour of the materials constituting the dam is essentially nonlinear (Dibaj and Penzien, 1969) and any attempt to evaluate the safety of a rockfill dam, based on a linear analysis, either in the static or dynamic condition, will only be misleading about the actual behaviour. In general, an embankment dam is a three-dimensional continuum composed of anisotropic, nonhomogenous, nonlinear, inelastic materials with rather complicated geometry, that is difficult to model accurately. The analysis of the dam becomes more complicated, when it is subjected to a severe earthquake with a peak ground acceleration of the order of 0.25g (g is the acceleration due to gravity) and above, since, its behaviour depends on the dynamic response of the different materials constituting the dam and the characteristics of the input motion. The shear modulus and damping ratios of the fill materials are strain dependent (Hardin and Drnevich, 1970a, 1970b; Seed and Idriss, 1970; Ishihara, 1971, 1982). Therefore, for a rational dynamic response evaluation of an earth and rockfill dam, the strain dependency of all the materials constituting the dam should effectively be implemented in a computer program using the finite element method, based on eight-noded isoparametric elements with (iii) reduced integration technique (Ergatoudis, Irons and Zienkiewicz, 1968). This computer coding should be capable of modelling the nonlinear stress-strain behaviour of each of the materials as a function of strain. The nonlinear model adopted should predict the behaviour of the dam as closely as possible to the actual situation for an event of a strong ground shaking. The nonlinear stress-strain characteristics — ft of each soil, as a function of strain, ranging between 10 to 1.0 percent or more could be achieved by carrying out extensive tests in the field and in the laboratory. To achieve this, the following procedures have been suggested/recommended in the available literature: 1 Using empirical equations proposed by Hardin and Drnevich (1970a, 1970b) for cohesive and cohesionless fill materials. 2 Determining the low-amplitude shear modulus in the field or in the laboratory and using modulus reduct ion factors as proposed by Seed and Idriss (1970), and Seed et al. (1984), to extrapolate high-amplitude shear modulii for clay, sand and cohesionless soils and using the normalized shear modulus curve for silty soils as proposed by Grant and Brown (1981). 3 Assuming the dynamic properties of gravels and boulders, based on the properties of sand (Seed and Idriss, 1970). 4 Classifying the different materials constituting the dam into two categories only, namely, clay and sand, (iv) and arriving at the dynamic properties of these two type of materials (Seed and Idriss, 1970). 5 Assuming arbitrary and constant values for dynamic properties and neglecting the associated level of strain therein (Chandrasekaran, Paul and Suppiah, 1984, 1985; Chandrasekaran and Prakash, 1989b). In the dynamic analysis, evaluating the dynamic properties of different soils, as mentioned above would never represent the true situation. The very few cases of nonlinear dynamic analyses performed in the recent years are limited to hydraulic fill dams (Seed, Lee and Idriss, 1968; Seed et al. , 1973; Marcuson 'and Krinitzsky, 1976) and rockfill dams of medium height (Lai and Seed, 1985) only. Further, in these studies, the level of strain considered lies in the medium range and at the threshold values of large strain levels only. A limited number of dynamic analyses carried out in India (Chandrasekaran, Paul and Suppiah, 1984, 1985; Chandrasekaran and Prakash, 1989b), are based on linear and strain independent material characteristics only. When a high rockfill dam is subjected to a strong earthquake, the induced level of strain would be in the range of large to failure strain values. Thus, an appropriate model, which could predict the actual behaviour of a high rockfill dam, supplemented by field tests is essential. In view of the numerous shortcomings as mentioned above it was decided to carry out different types of tests in (v) the field, such as wave propagation test, block vibration test and cyclic plate load test, to establish the in-situ shear modulus values as a function of strain varying from low-strain level to medium strain level and then to large strain values for four different types of soils, namely, silt, clay, sand and gravel. Out of these four different types of materials, the last three types of soils typically represent the materials constituting a rockfill dam. These different types of field test are frequently carried out in India, to establish the strain dependent dynamic material properties (Prakash and his co-workers, 1968a, 1968b, 1970, 1971, 1972, 1973, 1974, 1975, 1976a, 1976b, 1980; IS: 5249, 1977; Nandakumaran et al., 1977, 1979, 1980; Prakash, 1981). Shear modulus values have also been determined in the laboratory at high-amplitude strain levels only. The influence of secondary time effects on shear modulus values of three different types of soils has been established. Due to secondary time effects, an appreciable increase in the shear modulus values has been observed for clay and silty soils. The increase in shear modulii, due to secondary time effects is of the order of 4 to 28 percent, depending upon the type of soil. The percentage increase in shear modulii is higher for fine grained soils. The reported values are in close agreement with the values reported by other researchers (Affifi and Richart, 1973; Woods and Affifi, 1976; Anderson and Stokoe, 1978). The high-amplitude shear modulus values obtained (vi) in the field and in the laboratory corresponding to a partiy cular value of strain have been compared and a relationship between these two values r.s a function of strain is presented. Based on this relationship, a factor, named as the disturbance factor (Suppiah, 1986) has been established. Using this factor, high-amplitude field shear modulus has been predicted for a particular site consisting of sand, for which in-situ shear modulus value is not available. The predicted value of shear modulus using the disturbance factor has been compared with the values obtained using other methods of prediction, presently used -in the Geotechnical- Earthquake Engineering profession, such as the arithmatic method and the percentage method (Richart, Anderson and Stokoe, 1977; Anderson and Stokoe, 1978). The merits and demerits of the disturbance factor method have also been presented. Using the field and laboratory determined shear modulii, shear modulus curves as a function of shear strain for the four different types of soils have been presented. Further, from these shear modulii, the Ramberg-Osgood model (Ramberg and Osgood, 1943) constants have been evaluated for all the four different types of soil based on the method originally proposed by Jennings (1964). The Ramberg-Osgood model parameters thus evaluated have been used to obtain modulus reduction curves as a function of strain for all the soils, through a computer program based on the Newton-Raphson root finding technique (Hinton and Owen, 1986). Using the (vii) same constants of the Ramberg-Osgood model, damping ratio curves have also been presented, independent of the experimentally determined values of damping. The null value of damping obtained at the normalized shear modulus ratio (G/Gmax =1) in the Ramberg-Osgood model, has been replaced by the experimentally determined value of damping, which had been interpolated from the medium strain levels to low strain values. The modulus reduction curves and the damping ratio curves presented for clay and sandy soils have been compared with the corresponding curves proposed by Seed and Idriss (1970), and with the modulus reduction curve of silty soil, as proposed by Grant and Brown (1981). From the comparison, it has been observed that the method proposed by Seed and Idriss (1970), which is widely being used in today's Geotechnical-Earthquake Engineering profession, yields low values of modulus reduction factors and low values of damping compared to the experimentally determined values reported in this thesis. Nevertheless, a close agreement has been noticed between the modulus reduction curve for silt as presented by Grant and Brown (1981), and the normalized shear modulus curve obtained for silty soil in the present study. From the curve fitting of experimental data, it has been observed that the Ramberg-Osgood model can be best utilized for deriving the parameters for the curve that simulates the field determined values of shear modulus as closely as possible. Using the Ramberg-Osgood model parameters, damping values can also be obtained as a function (viii) of strain without conducting experiments to evaluate damping. To verify the applicability of the shear modulus reduction curves and damping ratio curves obtained based on the Ramberg-Osgood model parameters of the present study, a casehistory study has been performed. For the case-history analysis, the extensively instrumented El Infiernillo rock fill Dam (Mexico) of height 146 m has -been chosen and the dynamic stress-strain characteristics have been simulated based on the Ramberg-Osgood model as proposed in the present thesis. Prior to the dynamic analysis, the pre-earthquake stresses in the El Infiernillo Dam have been evaluted using the nonlinear model based on the hyperbolic law (Kondner, 1963; Kondner and Zelasko, 1963), as proposed by Duncan and Chang, 1970; Duncan et al. (1980). This model has been implemented in a computer coding based on the finite element method, with the versatile, stable eight-noded isoparametric elements and reduced integration (2x2) technique as proposed by Ergatoudis, Irons and Zienkiewicz (1968). This computer coding can account for layer-wise construction sequence operation as well. The computed nonlinear static stresses have been used as the initial condition for the dynamic analysis (Kulhawy, Duncan and Seed, 1969; Lai and Seed, 1985). For the dynamic analysis of the El Infiernillo Dam, three different accelerograms, namely, GM1, GM2 and GM3 have been selected as the base input motion. Accelerogram, (ix) GM1 has been recorded during a recent earthquake in the North-Eastern Region of India (Chandrasekaran and Das, 1989) , GM2 is an artificially generated record (Srivastava et al., 1983) and GM3 is the Taft (Kern County) earthquake record of 1952 (Idriss et al., 1973). The total durations of the three ground motions are 120, 38 and 30 seconds respectively. In the literature, an accelerogram with a total duration of 120 seconds has not been used till today for the dynamic analysis of an embankment dam (Prater and Studer, 1979). All the three ground motions have been normalized to a peak ground acceleration value of 0.25g. This has been done since the intensity of the base input motion of the March 14, 1979, Mexico earthquake record was also of the order of 0.2 5g only. For performing the dynamic analysis, a computer coding based on the finite element method using the same type of eight-noded elements with reduced integration technique has been developed. The Ramberg-Osgood model, Hardin- Drnevich model and the Seed-Idriss method of simulating the stress-strain characteristics have been implemented in this computer coding. This program performs the dynamic analysis in the time domain based on the step-by-step integration scheme, as proposed by Newmark (1959). The variable damping technique, as proposed by Idriss et al. (1973), has also been implemented in the same computer program. From the case-history study of the El Infiernillo Dam, based on the strain dependent modulus reduction curves obtained from experiments and the Ramberg-Osgood model (x) parameters as evaluated in the present thesis, the resulting values of crest accelerations, for the three ground motions, GM1, GM2 and GM3 are respectively of "the order of 0.13g, 0.34g and 0.35g. Whereas, the recorded value of acceleration at the crest of the El Infiernillo Dam, due to the March 14, 1979, Mexico earthquake (Resendiz, Romo and Moreno, 1980) is of the order of 0.36g only. The peak ground acceleration value of the March 14, 1979, Mexico earthquake was 0.25g only. This demonstrates that the dynamic analysis as performed in the present thesis based on the Ramberg-Osgood model, predicts a behaviour that is very close to the actual situation in the event of a strong ground shaking. The material properties used in the present analysis are the same as that adopted by Romo et al. (1980). Similar to the acceleration values, the computed displacement by the present analysis and the measured displacement at the crest, during the March 14, 1979, Mexico earthquake have been compared. For the Taft earthquake wave form, the computed displacement value at the crest by the analysis based on the Ramberg-Osgood model is 13.13 cm. On the other hand, the measured value of crest displacement during the March 14, 1979, Mexico earthquake was approximately, 13 cm only (Resendiz, Romo and Moreno, 1980). The close agreement between the computed value of crest displacement (= 13.13 cm) from the analysis based on the Ramberg-Osgood model and the measured displacement value (approximately, 13 cm) at the crest of the El Infiernillo (xi) Dam, during the March 14, 1979, Mexico earthquake merits comments and demonstrates that the Ramberg-Osgood model is the most appropriate model to simulate nonlinear stressstrain characteristics of different soils subjected to seismic forces. Using the Ramberg-Osgood model the displacement at the crest is of the order of 5.20 and 20.37 cm respectively for the other two ground motions (GM1 and GM2) adopted in the analysis. For the purpose of comparison, the nonlinear dynamic analysis of the El Infiernillo Dam has been carried out by the Hardin-Drnevich model and the very widely used Seed-Idriss method as well. The computed values of the crest acceleration for the El Infiernillo rockfill Dam using the Hardin-Drnevich model and the Seed-Idriss method for the three ground motions respectively are 0.14g, 0.17g and 0.20g, and 0.79g, 0.41g and 0.51g. From the crest acceleration values obtained for the three ground motions, it can be noticed, that the Hardin-Drnevich model predicts extremely low values. This is perhaps, because the Hardin-Drnevich model converges to an excessively large value of damping of the order of 63.7 percent at large and failure levels of strain (Ishihara, 1982; Shamoto, 1984). On the other hand, the Seed-Idriss method yields very high values of crest acceleration for all the three ground motions. This could possibly be due to the usage of low values of damping. Identically, the Hardin-Drnevich model yields (xii) crest displacement of the order of 3.22, 14.17 and 7.39 cm respectively corresponding to the three ground motions. The Seed-Idriss method gives displacement values at the crest of the order of 8.38, 13.22 and 11.12 cm respectively, for the three ground motions. As can be seen from the computed and the measured displacement values, the Hardin-Drnevich model and the Seed-Idriss method do not predict the behaviour that is close to the actual situation. Therefore, as mentioned earlier the Ramberg-Osgood model is the most suitable method for the evaluation of dynamic response analysis of earth and earthfill structures. In the dynamic analysis of the El Infiernillo Dam, the peak values of dynamic shear strain obtained using the Ramberg-Osgood model for the three ground motions are of the order of 1.097, 3.247 and 2.435 percent respectively and the values of total (= static + dynamic) shear strain are respectively of the order of 2.425, 4.434 and 3.734 percent, and occuring at 135.7 m from the base, under the postulated ground motion of 0.25g as the peak ground acceleration value. Using the Hardin-Drnevich model the maximum values of dynamic shear strain for the three ground motions are 1.93 0, 2.021 and 1.707 percent and the values of total shear strain are 2.450, 2.865 and 2.551 percent respectively. Based on the Seed-Idriss method the maximum values of dynamic shear strain are of the order of 1.782, 2.419 and 2.170 percent and the total values of shear strain are 2.459, 3.096 and 2.847 percent respectively, for the three ground motions and (xiii) occuring at element 242. From the dynamic analysis of El Infiernillo Dam, it is seen that the artificial accelerogram is more severe followed by the Taft earthquake waveform and the North- Eastern earthquake record. Under the postulated three ground motions with a peak ground acceleration of 0.25g, it has been observed that no portion of the El Infiernillo Dam reaches a five percent shear strain value which is the threshold level of failure (Marcuson and Krinitzsky, 1976) . Therefore, the intensity of the artificial waveform has been modified to yield higher peak ground acceleration value of the order of 0.40g. Subsequently, dynamic analysis- has been carried out with the re-generated ground motion as the base input motion. In the revised dynamic analysis, it has been observed, that the El Infiernillo Dam reaches a maximum value of dynamic shear strain of 13.016 percent and the peak value of total shear strain of the order of 13.860 percent and occuring at element 241. These values of shear strain lie in the threshold level of failure criteria based on the 5 to 15 percent shear strain phenomenon. This conclusion is gualitative in nature, since for an accurate prediction of the failure criteria, the laboratory determined cyclic shear stress values are inevitable and these values were not available for comparison. To investigate the influence of the foundation on the stability of the El Infiernillo Dam, the initial maximum (xiv) section of this dam has been appended with a stiffer foundav- tion of depth equal to 6.0 m. This modified section of the El Infiernillo Dam has subsequently been analysed to obtain the dynamic response using the artificial (GM2) accelerogram with a peak ground acceleration of 0.25g. The modified section inclusive of the foundation, resulted in marginally lower values of shear strain, in comparison to the shear strain values obtained from the analysis based on the dam without the foundation. Neglecting the minor differences in the values of shear strain between the two cases (with and without the foundation) of analyses, it was concluded, that the presence of a stiff foundation, practically has no influence on the stability of the dam. The previously mentioned nonlinear static and nonlinear dynamic methods of analysis have been extended to evaluate the dynamic response of two other rockfill dams of height 108 m (Dam DB) and 336 m (Dam DC) inclusive of their respective foundations. These two rockfill dams (DB and DC) were proposed to be built in India, in two different regions with moderate and high seismicity respectively. The base of the dam DB has been extended in the upstream and in the downstream by one time the width of the dam at the base (without the foundation). Thus the ratio of the width of the dam DB at the base (without the foundation) to that of the width at the bottom inclusive of the found ation was 1:3 (Franklin, 1987). Identically, the same pro portion was adopted in the case of the dam DC as well. The (XV) two dams DB and DC have been analysed using the Ramberg- Osgood model with the previously mentioned three ground motions as the earthquake load vectors. As before, for comparison purposes, the dynamic analysis has been done using the Hardin-Drnevich model and the Seed-Idriss method as well. Out of these two dams (DB and DC), the dam DC was the tallest (336 m) and was proposed to be constructed in a region with severe seismicity. The existing literature on the dynamic analysis of such a high rockfill dam is scanty, therefore, this dam has been subjected to an extensive dynamic response evaluation by computing the time-histories of acceleration, displacement and shear stress at a few important locations, using only the synthetic accelerogram as the base input motion, since, the artificial earthquake record was more severe than the other two actual earthquake records. As mentioned earlier, the dynamic analysis has been done using the Ramberg-Osgood and the Hardin-Drnevich models and the Seed-Idriss method. From the dynamic analysis of the dam DB the values ^\„ of the crest acceleration obtained using the Ramberg-Osgood model corresponding to the three ground motions are 0.39g, 0.42g and 0.40g respectively. Using the Hardin-Drnevich model the acceleration values obtained at the crest are 0.28g, 0.31g and 0.27g and that for the Seed-Idriss method of analysis these values are 0.46g, 0.50g and 0.56g respectively for the three ground motions. The maximum values of dynamic shear strain (xvi) obtained using the Ramberg-Osgood model for the dam DB are 0.175, 0.342 and 0.242 percent and the total values of shear strain are 1.875, 2.042 and 1.942 percent, respectively and taking place at element 84, for the three ground motions. Using the Hardin-Drnevich model the maximum dynamic shear strain values are 0.140, 0.308 and 0.201 percent and the total values of shear strain are 1.840, 2.008 and 1.901 percent respectively, for the three ground motions and occuring at the same location as in the case of the Ramberg- Osgood model. Using the Seed-Idriss method the maximum values of dynamic shear strain are of the order of 0.200, 0.324 and 0.198 percent and the total values of shear strain are 1.854, 1.978 and 1.852 percent respectively, corresponding to the three ground motions and occuring at element 94, unlike in the other two models. The displacement at the crest of the dam DB by the Ramberg-Osgood model using the three ground motions are 7.10, 12.27 and 10.59 cm respectively. Using the Hardin-Drnevich model and the Seed-Idriss method, the displacement at the crest for the three ground motions are 4.11, 8.42 and 6.57 cm and 9.83, 17.43 and 11.72 cm respectively. In all the three ground motions, except in one case (the Seed-Idriss method and the Ta-ft accelerogram) , it was noticed that the maximum value of acceleration, maximum value of shear strain and the maximum displacement value are obtained corresponding to the artificial waveform as the base (xvii) input motion with a peak ground acceleration of 0.2 5g. Since the dam DB did not undergo any excessive deformation at any part under the postulated three ground motions with a peak ground acceleration of 0.25g and the artificial accelerogram is more stronger than the other two actually recorded accelerograms, as before a revised dynamic analysis has been performed using the Ramberg-Osgood model and the modified artificial waveform as the base input motion with a peak ground acceleration of 0.40g. From the revised dynamic analysis the peak values of dynamic shear strain and the total shear strain are of the order of 3.680 and 5.380 percent respectively and taking place at element 84. Thus, it has been observed that the dam DB is generally safe under the postulated peak ground acceleration of 0.40g as well, based on the 5 percent shear strain failure criteria (Marcuson and Krinitzsky, 1976). However, this conclusion is qualitative only, since for an exact prediction of failure criterion, the laboratory determined cyclic shear stress values were not available. Similarly, from the dynamic analysis of dam DC the maximum values of crest acceleration using the Ramberg-Osgood model for the three ground motions with peak ground accelera tion as 0.25g are 0.17g, 0.33g and 0.32g respectively, obtained at node 48 which is lying along the axis of the dam and is just below the crest. For the Hardin-Drnevich model these values are 0.12g, 0.16g and 0.17g respectively for the (xviii.) three ground motions occuring at the same location as in the case of the Ramberg-Osgood model. Using the Seed-Idriss method, the crest acceleration values are of the order of 0.32g, 0.37g and 0.36g respectively for the three ground motions, obtained at node 23 lying along the crest (downstream). The maximum values of dynamic shear strain using the Ramberg-Osgood model for the three ground motions with peak ground acceleration as 0.25g are of the order of 0.542, 8.491 and 3.265 percent respectively and the values of total shear strain are 4.013, 10.162 and 4.936 percent respectively occuring at the same elevation. Using the Hardin-Drnevich model the maximum values of dynamic shear strain for the three ground motions are 1.829, 2.739 and 2.251 percent respectively and the total values of shear strain are 3.918, 4.757 and 4.269 percent respectively. Based on the Seed-Idriss method of analysis the maximum values of dynamic shear strain are 2.712, 6.137 and 3.067 percent and the total values of shear strain are 4.383, 7.808 and 4.738 percent respectively for'the three base input motions and occuring at element 199 which is at a height of 328.0 metres from the base. The displacement at the crest of the dam DC, using the Ramberg-Osgood model for the three ground motions with peak ground acceleration as 0.25g are 6.91, 49.26 and 20.50 cm respectively. For the Hardin-Drnevich model using the three ground motions the crest displacement is of the order i (xix) of 5.99, 27.55 and 13.66 cm respectively. The displacement using the Seed-Idriss method of analysis is of the order of 9.02, 20.85 and 15.69 cm for the three ground motions respectively. From the dynamic analysis of the dam DC irrespect ive of the method of analysis adopted, it is seen that the artificial accelerogram is more severe than the other two actually recorded waveforms. Since the dam DC did not reach the threshold level of failure under the postulated peak ground acceleration value of 0.25g for the three ground motions and as before the artificial waveform was more severe than the other two acce lerograms, to evaluate the stability of the dam DC a revised dynamic analysis has been performed using the Ramberg-Osgood model and the synthetic accelerogram as base input motion modified to yield a peak ground acceleration value of 0.40g. In this revised analysis the peak values of dynamic shear strain and total shear strain obtained are of the order of 12.325 and 13.996 percent respectively and taking place at the same elevation as before (element 199) . In this dynamic analysis, it has been observed that under the postulated artificial accelerogram with the peak ground acceleration value of 0.4 0g, a major portion of the dam DC reaches the threshold level of failure (value of shear strain is between 5 to 15 percent, Marcuson and Krinitzsky, 1976). From the extensive dynamic analysis performed on three different dam sections of varying geometry, three diff( XX) erent ground motions of varying durations and three, different methods of analysis, it is again demonstrated that the Hardin-Drnevich model yields very low values of crest acceleration and the Seed-Idriss method of analysis gives excessively high values of acceleration as compared to the proposed method of analysis based on the Ramberg-Osgood model which predicts crest acceleration values and displacement values which are in close agreement with the actually recorded/measured values of acceleration/displacement during the March 14, 1979, Mexico earthquake as demonstrated in the case-history analysis of the El Infiernillo Dam. Also, as far as the cost of the computer time is concerned, the Ramberg-Osgood and Hardin-Drnevich models need approximately 50 percent less time than the Seed-Idriss method, which shows that the latter method is uneconomical as well. From the extensive dynamic analysis carried out, it has been observed that the Hardin-Drnevich model which is based on the hyperbolic law is not suitable for the dynamic response evaluation of embankment dams and as well the Seed- Idriss method based on empirical equations for predicting the strain dependent shear modulii and damping ratios does not provide a rational solution. The Ramberg-Osgood model represents the nonlinear • material properties, such as the strain dependent shear modulus and damping values in a functional form which is very essential for a nonlinear dynamic analysis based on the step( xxi) by-step integration technique. However, the Seed-Idriss method does not employ a functional expression to represent these dynamic properties and therefore, may not be utilized efficiently for a nonlinear dynamic analysis of an earth or earthfill structure. As noticed previously, the response of an earth and rockfill dam is a function of the geometry of the structure, nature of the foundation material, zoning of the dam body, strain dependent dynamic properties of the various constituting materials and the characteristics of the base f input motion. Thus, to outline an approach that could predict the response of a complicated structure, such as an earth and rockfill dam as closely as possible to the actual situation, in the event of a severe ground shaking is a tedious effort. The investigation presented in this thesis demonstrates that in the event of a strong ground motion, the proposed method based on the versatile Ramberg-Osgood model can predict the dynamic behaviour of an earth and rockfill dam as closely as possible to the actual condition. Therefore, in view of the findings of the present thesis, for a rational dynamic response evaluation of an earth structure, only the Ramberg-Osgood model should be used.