earthquake-induced displacements of earth dams and embankments

Australian Geomechanics Vol 45 No 3 September 2010 65

EARTHQUAKE-INDUCED DISPLACEMENTS OF EARTH DAMS AND EMBANKMENTS

Hendra Jitno1 and Richard Davidson2

1 Group Geotechnical Engineer, Harmony Gold, Brisbane. 2 Senior Principal and Vice President, URS Corporation, Denver, Colorado, USA.

ABSTRACT This paper presents an overview of some of the available methods to estimate earth dam displacements due to earthquakes, from the simple Newmark one-dimensional displacement method to a complex coupled effective stress dynamic analysis. It discusses the assumptions used, advantages and limitations of each method. The use of pseudo-static analysis for assessing seismic stability of earth structures is critically reviewed. An example on the use of total stress dynamic analysis in the seismic upgrade work of Yarrawonga Weir in Victoria is presented. The dynamic analyses were very useful in providing an indication of possible flow failure, crack development during earthquake shaking and the potential for loss of freeboard of the earth dam. The method was also very useful to assess the most efficient remedial method that satisfies all the imposed requirements from the community and the client.

1 INTRODUCTION Over the last five decades, a number of man-made earth structures have suffered catastrophic failure due to earthquake-induced liquefaction. Eleven tailings dams failed during and after the 28 March 1965 Chilean earthquake. The most devastating were the failures of El-Cobre dams which destroyed part of the town of El-Cobre and claimed more than 200 lives, Figure 1 (Dobry and Alvarez, 1967). Similar failures also occurred in Japan in 1978. Two tailings dams associated with the Mochikoshi gold mine failed causing a release of large volume of tailings materials (Ishihara, 1984).

Figure 1: Cerro Negro Tailings Dams, Chile 1964

On 9 February 1971, an earthquake of magnitude 6.6 on the Richter scale hit the San Fernando Valley in Southern California. One of the major effects of this earthquake was the damage inflicted on the Lower and the Upper San Fernando Dams due to liquefaction induced deformations (Seed et al., 1973). Liquefaction of the hydraulic fill materials within the body of the dam caused a flow slide to occur on the upstream part of the Lower Dam, leaving only about 1.5 m of freeboard (Figure 2). In the Upper Dam, the slide movements resulting from liquefaction of the hydraulic fill within the dam were not as severe as those in the Lower Dam. However,

EARTHQUAKE-INDUCED DISPLACEMENTS OF EARTH DAMS AND EMBANKMENTS JITNO & DAVIDSON

Australian Geomechanics Vol 45 No 3 Septrmber 2010 66

the crest of the dam moved about 5m downstream and settled about 0.8 m. Fortunately in both cases, no water was released from the reservoir (Figure 3). Earlier this year an inactive upstream method tailings dam in Chile failed due to liquefaction demonstrating their vulnerability if saturated loose tailings remain within the exterior portion of the impoundment, Figure 4 from GEER (2010).

Figure 2: Lower San Fernando Dam after the 1971 earthquake.

Figure 3.: Upper San Fernando Dam after the 1971 earthquake.



Figure 4: Los Palmas March 2010 Tailings Dam Failure, Chile (GEER, 2010)

We are fortunate in Australia and New Zealand to have been spared such an event, but is it only a matter of time?

2 MAIN ISSUES IN SEISMIC ASSESSMENT OF EARTH DAMS There are two major issues that need to be resolved in assessing the seismic performance of earth and tailings dams under earthquakes:

1. Stability: Is dam stable during and after earthquake? 2. Deformation: How much deformation will occur in the dam?

The stability of an earth or tailings dam under earthquake loading condition will depend on the dam geometry, level of earthquake shaking and the materials comprising the dam and foundation. The dam geometry will control the level of driving stresses acting on the dam during and after earthquakes, the level of earthquake shaking will control how much deformation or strains will be developed during the shaking, and the material type will govern whether or not the embankment will experience liquefaction or significant strength loss due to earthquake.

If the embankment and foundation materials are not susceptible to liquefaction or strength reduction due to earthquake shaking, then the dam will generally be stable and catastrophic failure is not expected (Seed, 1979). However, if the dam or/and foundation comprise liquefiable materials, it may experience flow failure depending on post-earthquake factor of safety against instability (FOSpe).

For high initial driving stress (steep geometry), the FOSpe will likely be much less than unity, and flow failure may occur, as depicted by strain path A-B-C in Figure 5. Path A-B is the deformations during earthquake and path B-C indicates deformations after the cessation of earthquake. Note that the higher the difference between the initial driving stress and the residual strength, the larger the deformations. An example of this is the failure of the Lower San Fernando Dam.



Shear Strain, γ

Shea

r Str

ess,

τA

QPC

B

RDeformations during EQ

High initial driving stress

Low initial driving stress

Residual Strength, Sr

FOSpe = Residual Strength/Driving Stress

Shear Strain, γ

Shea

r Str

ess,

τA

QPC

B

RDeformations during EQ

High initial driving stress

Low initial driving stress

Residual Strength, Sr

FOSpe = Residual Strength/Driving Stress

Figure 5.: Effects of initial driving stress on post-liquefaction stability and deformations.

However, for low initial driving stress, the FOSpe may still be larger than one and the dam will remain stable. It is also possible that the FOSpe is slightly less than unity but the dam is still stable after new equilibrium is achieved when the driving stress reduces to a value similar to the soil residual strength (Sr), as depicted by strain path P-Q-R. Since the initial driving stress here is smaller and almost the same as the residual strength, the additional deformation after the cessation of the earthquake (path Q-R) is relatively small.

For dams comprising liquefiable materials that do not fail under seismic shaking, the next question would be: would the earth dams undergo significant deformations that may jeopardize the structure’s integrity? Potential safety hazards after the earthquake include overtopping due to loss of freeboard and internal erosion (piping) due to cracks within the dam.

In addition to the deformations due to the shaking and loss of soil stiffness and strength, dams especially tailings dams may also experience significant settlement after all earthquake-induced pore pressures dissipate. The magnitude of settlement depends on the thickness and compressibility of vulnerable layers and shear strains developed during the shaking.

3 PSEUDO-STATIC SEISMIC STABILITY ASSESSMENT One of the earliest available methods to assess seismic stability of earth structures is pseudo-static analysis. Due mainly to its simplicity, it is still being used in the engineering community, in particular for cases which do not involve liquefaction or strength reduction due to earthquake shaking.

The method uses a limit equilibrium approach incorporating a horizontal seismic coefficient to simulate inertia forces due to the earthquake. The seismic coefficient is expressed as the ratio between the earthquake forces and the gravity acceleration. Similar to the concept of static failure, a factor of safety (FOS) of less than unity is considered unstable and FOS of greater than unity represents seismically stable slopes.

Despite its popularity, this method suffers from serious limitations as follows:

• It inherently assumes that the earthquake loading acting on the potentially unstable slope mass is permanent and in one direction only. In reality, earthquake loading is multi-direction and cyclic which involves stress reversal. Therefore, the calculated FOS of less than unity does not necessarily mean failure. It may only be an indication of limited slope movement, with magnitude depending on the soil strength and earthquake intensity as will be discussed in the next section. Similarly, for cases involving strength reduction due to shaking, a FOS of greater than unity does not always mean the slope is stable because it may fail in post-earthquake undrained loading.

• Neither peak drained nor undrained strengths are suitable in pseudo static analyses for slopes comprised of materials that may undergo earthquake-induced strength loss.

• Difficulties in selecting an appropriate seismic coefficient. The use of a seismic coefficient that equals the Peak Ground Acceleration (PGA) is an overly conservative assumption. This assumption implies that the slope is a perfectly rigid body, which will move together as one block. This is clearly not true as the slope mass is generally deformable and tends to attenuate the earthquake shaking depending on the ratio between its natural period and the predominant period of the earthquake.

• The method only considers earthquake acceleration but fails to consider earthquake duration and frequency. Thus, the method will give the same results for a given acceleration, regardless of the



magnitude and distance of the earthquake. This is misleading as the bigger earthquakes will have longer duration and therefore will be more devastating than small earthquakes. Also, far distant earthquakes will have lower frequencies and may cause ground amplification if the frequency is close to the slope natural period.

Because of its limitations, this method is only used as a screening tool to assess if further analysis is required, as recommended in ANCOLD Guidelines (1998). ANCOLD recommend the use of pseudo-static analysis method developed by US Army Corps of Engineers (Hynes-Griffin and Franklin, 1984) as a screening method for well constructed earth and rockfill dams, which are not susceptible to liquefaction or significant strength loss due to earthquakes. This method has been calibrated against a large number of deformation analyses with deformations of up to 1 m.

Procedures to use this method are as follows:

1. Determine the appropriate Peak Ground Acceleration (PGA) at the site; 2. Use undrained strength for cohesive soils and drained strength for free-draining materials; 3. Apply 20% strength reduction for both cohesive and free-draining soils (Note that the free draining

materials must not be liquefiable because otherwise this method is not applicable); 4. Apply seismic coefficient equal to 50% of the PGA.

Slopes with calculated FOS greater than unity are considered stable. However, more detailed analyses including deformation analysis are required for slopes with computed FOS less than one.

There are some other screening methods available, but the methods were specifically developed for landfills (Bray et al., 1998) and residential development (Stewart et al., 2003) with smaller tolerable seismic displacements (15 cm to 30 cm).

Because the pseudo static method does not correctly simulate the actual slope behaviour in an earthquake, the authors do not advocate its use except as an intermediate step in a simplified Newmark-type deformation analysis. Far superior screening can be accomplished using post earthquake undrained stability analyses discussed below.

4 POST EARTHQUAKE UNDRAINED STABILITY ANALYSES The most useful method available to assess the risk of earthquake-induced instability is post earthquake undrained stability analyses. This approach does correctly simulate the process of slope instability observed in many earthquake case histories. It recognises that fact that slopes generally fail at the end of or after earthquake shaking has ceased as excess pore pressures induced during shaking redistribute within liquefied soil mass and the residual strength is mobilised. The first step is to assess the level of earthquake ground motions at the site. Either using simplified methods or attenuating the ground motions through the embankment section, the degree of strength reduction is evaluated ranging from relatively small strength loss in materials that behave in a “clay-like” manner to liquefaction in contractive “sand-like” material. Very useful methods of liquefaction evaluation have been summarized by Idriss and Boulanger (2008). From these methods the post earthquake undrained shear strength can be interpreted Supe as a total stress value or a strength ratio Su/σv ‘, and can be as low as the residual strength Sr.

With the appropriate post earthquake strength selection, then undrained strength analysis static limit equilibrium slope stability calculations can be completed for the appropriate pre-shaking effective stress conditions. Factors of safety less than 1.0 would be indicative of failure conditions and depending on the size of the earthquake and zone of liquefaction could result in uncontrolled flow failure. The next question is what the quantum of seismically-induced deformations is.

5 METHODS FOR PREDICTING EARTHQUAKE-INDUCED DEFORMATIONS OF EARTH DAMS

Various methods for predicting seismic deformation of earth structures have been developed. These methods include the simplified one-dimensional Newmark’s method and its modified versions by Sarma (1975) and Makdisi-Seed (1978), the simplified two dimensional finite element (FE) stiffness reduction method proposed by Lee (1974), the more involved Seed’s strain potential approach (Seed et al., 1973, Seed, 1979), FE stiffness reduction method incorporating inertia effects (Byrne, 1991; Jitno, 1995) and the sophisticated total and effective stress dynamic analysis methods (e.g.. Finn et al., 1977, 1986; Byrne et al., 2004).



5.1 ONE DIMENSIONAL SIMPLIFIED METHOD The stability of earth structures has been traditionally assessed based on the factor of safety of a potential sliding mass using a pseudo-static limit equilibrium analysis. The term factor of safety is defined as the ratio of shear strength of soil to the driving shear stress acting at the points on the potential sliding surface. A factor of safety less than unity implies that the soil-structures are not stable since the sliding mass will accelerate and large displacement will occur. However, under seismic shaking where the loads act only for a finite duration of time and cyclic in nature, a factor of safety less than unity may still be acceptable. Newmark (1965) was the first to advance a concept that the stability of an embankment during earthquake should be assessed on the basis of the deformation produced instead of the traditional pseudo-static factor of safety.

5.1.1 Newmark’s method Newmark proposed a simple method for evaluating the potential deformation of earth-structures due to earthquake shaking. He modelled a potential sliding block of the dam as a rigid plastic single degree of freedom system which can be viewed as a rigid mass resting on an inclined plane and subjected to earthquake ground acceleration (a), as shown in Figure 6.

Figure 6. Potential sliding block under earthquake shaking.

Newmark assumed that the soil behaves in a rigid-perfectly-plastic manner in which the movement will only occur when the driving forces due to earthquake base acceleration are sufficient to overcome the yield resistance of the block. As shown in Figure 6, the block will only move if the acceleration is higher than the ay (yield acceleration).

Several models have been proposed based on the concept that Newmark (1965) developed for calculating the deformation of earth dams during earthquakes.

Yegian et al. (1991) proposed that the amplitude D of permanent displacement is:

(Equation 1) where Neq is the number of cycles equivalent uniform base motion, T the period (s), ay the yield acceleration, ap the peak acceleration (g), and f the dimensionless function depending on base motion.

Baziar et al. (1992) proposed that D depends on peak velocity:

(Equation 2) where amax is the peak acceleration, and vmax the peak velocity.

Jibson (1993) proposed that D (cm) depends on the Aria intensity:

Log D = 1.46 log Ia - 6.642 ay + 1.546 (Equation 3)



where Ia the Aria intensity (m/s), and ay the yield acceleration (g). Plot between Ia and displacement computed using Jibson’ method is presented in Figure 7. Arias intensity is a single numerical measure of the shaking intensity of the record calculated by integrating the squared acceleration values (Arias, 1970) as shown below:

(Equation 4) This method is not necessarily founded on a theoretical basis given that the deformation of a slope is only a result of acceleration values that exceed the critical acceleration value.

Figure 7.: Plot between Arias Intensity and Newmark’s displacement.

The models based on Newmark sliding blocks assume that the deformation takes place on a well defined failure surface, the yield acceleration remains constant during shaking, and the soil is perfectly plastic. However, these assumptions do not hold in the case of liquefied soils and lateral spreads, because of the following:

• Shear strain in liquefied soil does not concentrate within a well defined surface; • Shear strength (and yield acceleration) of saturated soils varies during cyclic loading as pore pressure

varies and • Soils are generally not perfectly plastic materials, but commonly harden or soften.

Therefore, while this method is very useful for predicting seismic displacement of earth structures, it generally does not give satisfactory results for predicting liquefaction-induced ground deformations.

5.1.2 Makdisi-Seed Method One of the assumptions used in Newmark’s analysis is that the ground acceleration is constant along the sliding block. This may not necessarily true for earth slopes which may deform during the shaking. To account for the variability of ground accelerations along the potential sliding block, Makdisi and Seed (1978) refined the Newmark’s method by using average accelerations applied to the slopes. Makdisi and Seed then computed the variation of permanent displacement with ratio of yield acceleration (ay) and peak ground acceleration (amax) and earthquake magnitude (M), by subjecting several real and hypothetical dams to several recorded and synthetic earthquake ground motions for given magnitudes.

The permanent displacements computed by Makdisi-Seed method for different ay/amax ratio and earthquake magnitudes are presented in Figure 8.

The procedure to estimate the seismic deformations using Makdisi-Seed method are as follows:

1. Determine the design peak ground acceleration of the dam (ümax). This can be obtained from deterministic or probabilistic seismic hazard analysis, or any other sources.

2. Determine the natural period of the dam. The first natural period of the dam with constant modulus can be computed using To=2.61*h/vs. (vs.= shear wave velocity of dam material, h = dam height).



3. Determine the yield acceleration of the dam by carrying out pseudo-static analysis with different accelerations. Yield acceleration is the acceleration that gives a factor of safety of unity.

4. Determine the height of potential sliding mass (y) from above step and calculate y/h ratio, where h is the maximum dam height.

5. Using Figure 8a, determine the average maximum acceleration, kmax. 6. Compute ky/kmax and using Figure 8b, determine the normalised displacements (g = gravity acceleration).

Knowing g and To, the displacement can then be computed.

(a)

(b)

Figure 8: (a).Variation of average maximum acceleration with depth of potential failure surface and (b) Normalised permanent displacement with yield acceleration for earthquakes with different magnitudes (right) (Makdisi and Seed, 1978). Note: U = displacement; To = natural period of embankment.

5.1.3 Empirical methods Swaisgood (2003) has carried out an extensive study of case histories of embankment dam behaviour during earthquakes, particularly those which are not susceptible to liquefaction problems. The objectives of the study were to determine if there is a “normal” trend of seismic deformation that can be predicted and if there are certain factors that consistently have an effect on the amount of damage and deformation incurred during earthquakes. Nearly 70 case histories have been reviewed, compared and statistically analysed in this effort. The results of this empirical study have shown that the most important factors that appear to affect dam crest settlement during earthquake include (a) the peak ground acceleration at the site and (b) the earthquake magnitude. The relationship between the magnitude of measured settlement and the peak ground accelerations during earthquake were plotted and presented in Figure 9.

This finding supports one of the findings of an earlier investigation in which it was concluded that “there is ample evidence that well-built dams can withstand moderate shaking with peak accelerations up to at least 0.2 g with no harmful effects” (Seed, 1979).



Figure 9. Empirical relationship between the peak ground acceleration and crest settlement (Swaisgood, 2003).

In addition, an empirical equation was formulated as an aid in estimating the amount of dam crest settlement as follows:

S (%) = e (6.07 PGA + 0.57 M -8.00) Equation 5 In which, s = crest settlement in percent; PGA = Peak Ground Acceleration at the foundation rock and M = earthquake magnitude.

Pells and Fell (2002) also collected data from 305 dams in which 95 of them suffered cracks due to earthquake shaking. They plot the data as a function of peak ground acceleration and earthquake magnitude, and classified the damage based on the crack width and crest settlement. More detailed discussion of this method can be found in Fell et al. (2005).

5.2 TWO-DIMENSIONAL SIMPLIFIED METHOD The two-dimensional simplified method generally uses the finite element or finite difference method to calculate deformations due to earthquakes. However, the seismic loadings are not directly used as part of the input. Below are some of the methods available.

5.2.1 Strain Potential Method One of the earliest two-dimensional FE methods was developed by Seed et al. (1973) by combining the results of linear or equivalent linear analysis and the laboratory data. The procedure can generally be described as follows:

1. Compute the cyclic shear stresses in each element of the dam using linear or equivalent linear analysis. 2. Assign each soil element in the dam a strain potential in terms of shear strain, as a function of cyclic shear

stresses obtained from the above step in combination with the results of cyclic laboratory tests. 3. Compute dam deformations based on the prescribed shear strain for each soil element.

One of the major assumptions used here is that the shear strain developed during earthquake will be similar to the strain developed from triaxial laboratory tests, and the maximum shear stress acts in horizontal direction in all elements. This assumption is only valid for a small portion of the dam, whereas the majority of the soil elements within the dam experience stress conditions similar to those developed in simple shear tests. Therefore, the results of deformation analysis using this method are very approximate and tend to underestimate the



observed deformations in the field. In addition, this simplified method is not simple or practical. It is quite time consuming and expensive due to relatively large number of laboratory cyclic tests required.

5.2.2 Stiffness Reduction Method Another method developed by Seed and his co-workers is stiffness reduction approach (Lee, 1974 and Serff et al., 1976). In this method, the soil is assumed to lose part of its stiffness in the earthquake. The method can be described as follows:

1. Compute the initial static shear stresses in the dam using initial soil moduli (before earthquake). Set the displacement to zero.

2. Using the pre-earthquake static shear stresses, compute the deformations of the dam due to earthquake by using the reduced soil stiffness.

This method is also very approximate but it is not as time consuming as the strain potential method. This method does not consider any inertia effects due to earthquake shaking and can only be used to estimate the dam deformations due to strong earthquake with short duration. This method can be applied using commercial finite element/differnce software such as SIGMA/w, PLAXIS or FLAC.

5.2.3 Pseudo-dynamic Method Based on the work of Byrne (1991), Jitno (1995) developed a method that combines the effects of stiffness reduction and the inertia forces due to earthquake shaking. This method is essentially an extension of Newmark's method from a rigid-plastic single-degree-of-freedom system to a flexible multi-degree of- freedom system. In addition to the softening of the liquefied soil, it takes into account the effects of inertia forces from the earthquake and the post-liquefaction settlement. The method is based on the concept that the deformation prior to liquefaction is small and can be neglected compared to those which occur after liquefaction. A key aspect of the method is the post-liquefaction stress-strain response for which there is now considerable laboratory data available.

The proposed method employs a pseudo-dynamic finite element method in which the additional displacements due to liquefaction and inertia forces are accounted for by applying additional forces that satisfy energy principles. The procedure has been validated by applying it to field case histories involving both one-dimensional sloping ground as well as two-dimensional cases. These case histories include the Wildlife and the Heber Road sites, the Lower and Upper San Fernando dams (Seed et al., 1973), the Mochikoshi tailings dams (Ishihara, 1984), the La Marquesa and La Palma dams in Chile (De Alba et al., 1988). It was found that the predicted and observed results in those case histories are in reasonable agreement in terms of both the magnitude and pattern of displacements.

The method has been working quite well for liquefaction cases due to medium earthquakes but it might underestimate deformations for liquefaction cases due to bigger earthquakes (magnitude>M8).

5.2.4 Dynamic Runout Method (DRUM) Tan et al. (2000) developed the Dynamic Runout Method (DRUM) to estimate the run-out distance of an unstable sliding mass that moves due to its inertia, which normally occurs on cases with drastic strength reduction (e.g. liquefaction). The DRUM program analyses a series of sliding rigid-body masses, gradually changing from an initial embankment configuration to a final stable configuration. The driving force acting on the sliding block is the down slope component of its weight, and the resisting force is the shear strength resistance along the postulated shear surface.

Using Newton’s equation of motion, the unbalanced forces in the initial configuration are used to calculate an initial acceleration of the initial rigid-body sliding mass. The analysis is then continued in small increments of time in which the acceleration, velocity, and displacement of the rigid-body sliding mass are computed based on the available unbalanced forces. At each time increment, the volume/area of the sliding mass is kept the same (undrained), but the shape is changed to regularize the sliding mass. In the early time increments, when the static factor of safety is less than 1.0, the acceleration of the mass is positive, which produces increasing velocity and displacement. As the rigid body is displaced and the resulting equivalent slope flattens, the factor of safety increases. Eventually the factor of safety exceeds 1.0, after which the acceleration of the mass is negative. The negative accelerations reduce the velocity of the mass in succeeding time increments, until the velocity is reduced to zero, at which time movement of the mass stops and the configuration is stable. The method has been calibrated against two liquefaction case histories – the Lower San Fernando (Seed et al., 1973) and La Marquesa Dam (De Alba et al., 1988), and provided reasonable calculated run-out distance when compared to the observed distances.



The DRUM program is applicable only to cases with static factors of safety less than 1.0 and can be used to estimate only the deformations resulting from the unbalanced static forces. The DRUM program does not provide an estimate of deformations from the earthquake shaking itself. Consequently, the DRUM program underestimates the total deformations from earthquake loading. However, because the displacements prior to liquefaction are generally small, we believe the method can give reasonable estimates on the run-out distance of earth dams failed due to liquefaction.

5.3 TOTAL STRESS FULLY DYNAMIC ANALYSIS The method utilises the time history of acceleration as direct input to the analysis. The dynamic analysis is carried out either in the time domain, or in the frequency domain using an equivalent non-linear method. The method does not directly analyse the zone of liquefaction for cases involving liquefiable soils as it does not calculate the pore pressure development during earthquake. The liquefaction zone must be determined separately either using a simplified approach (Youd et al, 2001) or by carrying out site response analysis such as SHAKE (Idriss and Sun, 1992), QUAD4 or FLUSH (Lysmer et al., 1975). The procedure can be briefly described as follows:

1. Determine the time history of acceleration for a given design earthquake. Selection of the time history of acceleration depends on the Peak Ground Acceleration (PGA), distance from the earthquake source, earthquake magnitude and geological condition at the site.

2. Determine zone of liquefaction within the dam and foundation and estimate the time required (number of cycles) to cause liquefaction (tliq).

3. Carry out stress deformation analysis using non-liquefied soil properties for t less than tliq, and use the post-liquefaction soil properties for t ≥ tliq.

4. Estimate the settlement due to pore pressure dissipation using the method proposed by Tokimatsu and Seed (1987) or Ishihara & Yoshimine (1992).

5. Add the settlement computed from step (4) to the dam deformations computed by steps (1) to (3).

It is usually very time consuming to carry out analysis in the time domain for any finite element programs, as each digitised earthquake load will be treated as a separate static load and the program must process the matrix of equations for the entire mesh. Because of this, the commercial finite element programs usually adopt frequency domain solution to analyse earthquake loads. Examples of the programs that use this method are PLAXIS and QUAKE/w. For finite difference programs, however, this is not a problem. Both time domain and frequency domain solutions can be processed relatively fast (e.g. FLAC).

The results of deformation analysis are quite sensitive to the results of liquefaction analysis, which is done separately using a simplified approach. The results are also sensitive to the estimate of time required to cause liquefaction. Therefore, although the method and the software are readily available in the marketplace, judgement must be exercised during the analysis and understanding the soil behaviour under dynamic loading is required to obtain meaningful results.

5.4 EFFECTIVE STRESS FULLY DYNAMIC ANALYSIS The effective stress analysis is the most comprehensive approach for estimating dam deformations due to earthquake loading. The effective stress approach computes pore pressure development during the earthquake shaking. The method takes into account the strength and stiffness reduction due to pore pressure increase during the shaking and it is also able to incorporate the residual strength after liquefaction. Post-liquefaction settlement can be calculated by analysing the pore pressure dissipation after the cessation of earthquake.

There are basically two approaches available:

1. Uncoupled effective stress approach. The pore pressure response due to earthquake is estimated from an empirical formula based on the calculated shear-strains during earthquake shaking (Martin, Finn and Seed, 1975, Byrne, 1991) or from post cyclic laboratory testing. This method has been implemented in the most recent version of the dynamic FLAC software (Itasca, 2008) and has been used more extensively in practice.

2. Coupled effective stress approach. This method utilises the more rigorous approach based on an elastic plastic stress strain law for the sand skeleton that includes shear- induced plastic volumetric strains. It is these strains under the constraint of the pore fluid stiffness that generate pore water pressure changes. Such an approach allows coupled dynamic stress-flow analyses to be carried out in which both generation and dissipation of pore water pressures and their effects are considered for a specific base motion.

Fully coupled effective stress approaches have been developed by many researchers including Dafalias (1986), Prevost (1981, 1989), Zienkiewicz et al. (1990), Byrne et al. (1995), Beaty and Byrne (1999), Elgamal et al.



(1999), and Kramer and Arduino (1999), and Byrne et al. (2004). At the moment, due to various reasons, analyses of this level of complexity are relatively rare in practice. An example of the application of this approach in practice is presented by Jitno (2011) utilising the UBCSAND model developed by Byrne et al. (2004).

6 TOLERABLE SEISMIC DISPLACEMENTS The final step in the analysis is to decide if the calculated displacement is tolerable. Ideally, allowable displacements for analyses should be established from a database in which observed slope displacements from earthquakes are correlated to damage and loss of integrity in structures associated with the slope displacements. Unfortunately, however, such data is quite limited or was destroyed when the structure failed, and hence there is limited empirical data from which to serve as a rational basis for selecting allowable displacements. Accordingly, allowable displacement levels are established from engineering judgment. Some of the parameters to be considered are as follows:

• Maintaining freeboard - The freeboard will control how much settlement is allowable without overtopping after the earthquake.

• Filter thickness - This will govern how much lateral deformation is allowed before the filter protection is disrupted by cracking leading to potential piping problems through the embankment.

• Thickness of core - In old dams, a relatively narrow puddle clay core may extend into the foundation, where the liquefiable layers are found. If the dam core is sheared during earthquake, the risk of piping though dam foundation will increase.

• Stability assessment– if the deformation analysis comes to equilibrium with movement stabilising after shaking has ceased, then the model indicates an uncontrolled flow failure has not occurred. On the other hand, if the model continues to deform after shaking or can not converge during shaking, flow failure is indicated. As a rule of thumb with FLAC, if the maximum lateral displacement remains below about 3 m to 4 m and is stable, then flow failure would not be expected.

7 APPLICATIONS OF THE SEISMIC DEFORMATION ANALYSIS METHODS IN AUSTRALIA

The methods discussed above have been applied to assess the seismic stability of a number of dams in Australia and New Zealand. The following case history is presented to give an example on the use of available seismic stability assessment methods. Over the last 10 years, URS Australia has applied the total and effective stress dynamic analyses for assessing seismic deformations of several dams, whose foundations are prone to potential liquefaction concerns (eg. Yarrawonga Weir, Waranga Basin, Lance Creek and Hindmarsh Valley). In this paper, one case history from Victoria (Davidson et al., 2003) will be presented.

7.1 DAM GEOMETRY Yarrawonga Weir is located approximately 240 km north of Melbourne, on the River Murray near Yarrawonga at the Victoria/New South Wales border. The weir was constructed in the 1930's and consists of a southern (main) embankment, a northern embankment and concrete regulating structures at the north and south of the facility. The southern (main) embankment is a zoned earthfill structure approximately 7 m high and extends for a length of about 275 m. The embankment has a centrally located steel sheet pile cutoff wall that extends from RL 123.1 m to bedrock and is encased in a clay core which extends from just below the crest to the base of the embankment. The remainder of the embankment generally comprises a low plasticity silty clay fill material that has been placed with side slopes of 4H:1V. The embankments are founded on alluvial soils comprised of clean sands and clayey / sandy silt overlying stiff clays and then siltstone / sandstone bedrock.

7.2 SEISMIC HAZARD ASSESSMENT The site specific seismic hazard assessment comprised several tasks, including data review and collection, fault mapping and trenching, earthquake source characterisation, ground motion attenuation, probabilistic seismic hazard analysis (PSHA) and ground motion assessment. A probabilistic seismic hazard analysis (PSHA) was performed for Yarrawonga Weir, using the refined source characterisation and the recently developed ground motion attenuation relations proposed by Sadigh et al. (1997), Idriss (1994) and Toro et al. (1997). The resultant average seismic hazard curve (Figure 10) illustrates the increase in ground motion level with increasing earthquake recurrence interval.



0.001

0.01

0.1

1

10

1 10 100 1000 10000 100000

Return Period (Years)

Ave

rage

Pea

k G

roun

d A

ccel

erat

ion

(PG

A, g

)

Figure 10: Probabilistic seismic hazard for Yarrawonga Weir

Based on the ANCOLD (1998) and the New South Wales Dams Safety Committee guidelines, the appropriate design seismic loading depends on the downstream population at risk and the expected level of damage should the dam fail. After conducting a dam-break analysis that considered the likely consequences of each mode of failure, the Maximum Design Earthquake (MDE) for the ogee crest was assigned the 1:1000 AEP while the remainder of the structures and embankment were assigned a 1:5000 AEP.

De-aggregation analysis was used to identify the earthquake magnitude and distance combination most likely to contribute to a given level of acceleration at each site. The results indicated that the largest contribution to the seismic hazard (measured by the 2.5 Hz spectral acceleration) comes from the earthquakes located on average at least 53 km from the site for Operating Basis Earthquake (OBE) events (Mw 6.2), and at least 25 km for MDE events (Mw 6.4).

Table 1. Site Specific Seismic Hazard Study Results for Yarrawonga Weir embankment

Earthquake OBE MDE AEP 1:475 1:5,000 Magnitude, Mw 6.2 6.4 Distance (km) 53 25 Peak Ground Acceleration (g) 0.07 0.28

On the basis of the earthquake distance, magnitude and the shear wave velocity of the top 30 m of the soil/rock layer (vs30), time history of ground motions were selected from the Griffith Park record of the 1971 San Fernando earthquake and scaled to match the response spectra for Yarrawonga Weir, for both OBE and MDE. These ground motion parameters were used as the design basis for seismic analysis of Yarrawonga Weir embankment.

7.3 LIQUEFACTION ASSESSMENT Geotechnical investigations including numerous sampled drill holes, test pits and CPT soundings revealed two layers of recent alluvial, fine to medium sand (SP), identified as 2A and 2C with corrected SPT blow counts N = 2 to 13, within the foundation. Results of liquefaction assessment based on Seed method outlined in ANCOLD guidelines (1998) indicate that these layers were susceptible to liquefaction, even under OBE earthquake loading conditions. Figure 11 illustrates the typical embankment section showing geotechnical profile beneath the embankment.



1A, 1B : EMBANKMENT FILL2A : ALLUVIAL SAND, LOOSE2B : ALLUVIAL CLAY SANDY SILT2C : ALLUVIAL SAND2D : SHEPARTON FORMATION CLAY

2C

1B1A

2A

BEDROCK

Reservoir level 124.90 m

2D

2B2A

Distance (m)20 30 40 50 60 70 80 90 100 110 120 130 140

100

105

110

115

120

125

130

135

140

145

15020 30 40 50 60 70 80 90 100 110 120 130 140

Ele

vatio

n (m

)

100

105

110

115

120

125

130

135

140

145

150

Figure 11. Typical embankment section showing zones of liquefiable materials.

Interbedded clayey silt and sandy silt (layer 2B) was found between the two clean sand layers 2A and 2C. This layer contained some relatively soft and loose zones which would experience strength loss on shaking. These alluvial layers are underlain by Shepparton formation clays (layer 2D), which were generally of medium to high plasticity clay (CH) of a stiff to hard consistency. The siltstone/sandstone bedrock was found under this layer. The embankment fill (layer 1A and 1B) was typically comprised of low plasticity clay, although a thin layer of loose sand was encountered upstream at several locations.

The analysis indicated that layer 2A (loose sand) located at the downstream and upstream embankment is liquefiable under both OBE and MDE. The Factors of Safety against liquefaction (FOSL) for each layer under MDE are presented in Table 2.

7.4 SEISMIC STABILITY ASSESSMENT The OBE and MDE earthquake loadings were used to assess the post earthquake performance of the embankment by using limit equilibrium analysis. The stability analysis was performed on sections RD 300, RD 345 and RD 405. Section RD 345 was identified in earlier work as the overall critical foundation section for the embankment. The phreatic surface adopted was obtained from seepage analysis with the downstream water table set to approximately two metres below ground level (119 m AHD). The post-earthquake soil strengths were determined based on the results of liquefaction assessment. For liquefiable sand layers (FOS against liquefaction, FOSL ≤ 1.0), the post-earthquake undrained strength was assigned an undrained strength ratio (Su/σvo’) according to the chart proposed by Stark and Mesri (1992). For sand layers with FOSL >1.0, the undrained strength ratio was estimated based on the pore pressure development due to shaking, using the chart proposed by Seed and Harder (1990). The non liquefiable sand layers were assigned undrained strength ratio equal to the tangent of their drained friction angle (Su/σvo’=tan φ’). Summary of the post-earthquake soil strength properties used in the analysis are presented in Table 2, and the results of post earthquake stability and seismic deformation analyses are shown in Figure 12 and Figure 13.

Table 2. Post-earthquake Soil Strength Parameters used in the analysis under MDE loading.

Soil Type FOS against liquefaction, FOSL

(N1)60-cs Su/σvo’

2A-dry-D/S Dry (NL) 24 0.70 2A-sat-loose-D/S 0.47 6 0.04 2A-sat-loose-U/S 0.41 10 0.05 2A-sat-MD-U/S 1.15 22 0.34 2B-D/S 0.95 15 0.08 2B-U/S 1.21 21 0.32 2C 2.90 (NL) 29 0.70



9

FOS = 0.733

Distance (m)20 30 40 50 60 70 80 90 100 110 120 130 140

100

105

110

115

120

125

130

135

140

145

15020 30 40 50 60 70 80 90 100 110 120 130 140

Ele

vatio

n (m

)

100

105

110

115

120

125

130

135

140

145

150

Figure 12: Results of post earthquake stability analysis of embankment under MDE loading.

Pre-remedial work geometry.

For pre-remedial works geometry, the post MDE stability and deformation of the embankments was unacceptable and catastrophic failure of the embankments and loss of the reservoir was predicted. The computed post earthquake undrained stability factor of safety was significantly less than unity (FOS=0.7), indicating that the residual strength is much less than the driving stress and excessive deformation was predicted in the model.

Figure 13. Results of FLAC total stress dynamic deformation analysis under MDE loading. Pre-remedial work

geometry. Displacement pattern and magnitude of deformations.

As can be seen in Figure 13, the upstream crest moved about 3.4 m and the downstream crest only moved about 3.0 m, suggesting tension cracks would have developed at the dam crest. The crest also settled about 1.3 m at the downstream and only 0.8 m at the upstream. The large deformations experienced by the dam reduced the driving stress to some degree but the residual strength was still lower than the driving stress, causing the dam to keep deforming. The time – deformation plot shown in Figure 14 demonstrates that the deformations do not stabilise with time after the cessation of earthquake indicating a potential for an uncontrolled breach and release of the storage.



0 10 20 30 40 50Time - sec

-0.3

0

0.3

Inpu

t Acc

eler

atio

n - g

0 10 20 30 40 50Time - sec

-500

0

500

1000

1500

2000

2500

3000

3500

4000

Hor

isoa

ntal

Dis

plac

emen

t - m

m

Point BPoint CPoint D

Figure 14: Plot of horizontal deformation vs. time obtained from the results of FLAC total stress dynamic

deformation analysis. Pre-remedial work geometry.

7.5 EMBANKMENT REMEDIAL WORKS DESIGN The primary criterion for the design of remedial works for the embankment was to increase stability under earthquake loading conditions. The selection of a FOS was dependent upon the level of uncertainty with regard to embankment and foundation design parameters, as well as uncertainty about embankment performance. Under OBE loading, the embankment must be able to sustain shaking without loss of serviceability, and under MDE loading, the embankment should withstand shaking without uncontrolled loss of storage.

Since no filters were present in the original embankment, two stage filters were incorporated in the design of the downstream stabilising berm. The filters were designed to be compatible with the clay core and the embankment fill to prevent piping of the embankment materials and crack migration, particularly where seismically-induced tension cracks of the core or embankment fill is expected to be most severe.

There were several key constraints on the embankment construction:

• The storage had to remain in operation at full supply level for most of the construction period, with a draw down of the storage only possible in the 2002 winter period towards the end of the first year of construction. The available duration of the draw down was limited to about ten weeks.

• For dam safety reasons the downstream embankment construction had to be completed before the upstream works could be constructed.

• The construction could not adversely affect the riverine environment and construction methods had to meet planning guidelines and community expectations, as the construction site was located within a sizeable rural centre.



The following remedial works were implemented to upgrade the embankments to satisfy the above design criteria:

• Foundation improvement beneath the embankment both upstream and downstream; • Construction of a downstream stabilising berm and an upstream rock blanket; • Installation of a filter layer into the new downstream stabilising berm and within the embankment

transition zones adjacent to the regulating structures, to reduce the risk of post-earthquake piping of embankment materials and

• Addition of erosion protection blocks on the upstream and downstream face of the embankment.

Because of the requirement that full supply level must be maintained during remedial works, an innovative foundation improvement program at the upstream of the dam was adopted as shown in Figure 15.

Figure 15: Upgraded embankment design section.

Several options were considered for the foundation improvement included (1) excavation and replacement of the liquefiable foundation materials, (2) construction of stone columns, (3) jet grouting and (4) both deep and shallow soil mixing of the foundation materials. Stone columns were finally selected because of their ability to increase the density of the loose foundation soils, to drain excess pore pressures during earthquake shaking, and to add composite strength and stiffness from the compacted gravel. There also were several successful precedents in Australia and overseas (Davidson and Perez, 1984; Hayden and Welch, 1991).

A series of geotechnical analyses was carried out to confirm satisfactory performance of the upgraded embankment against seepage, stability, static and seismic deformation criteria. Stability analyses provided a post earthquake stability factor of safety in excess of the required 1.3 (Figure 16) and maximum seismic lateral deformation of less than 200 mm (Figure 17) except for some localised deformations (slumping) at the downstream toe of the stabilising berm.

FOS =1.333

Distance (m)20 30 40 50 60 70 80 90 100 110 120 130 140

100

105

110

115

120

125

130

135

140

145

15020 30 40 50 60 70 80 90 100 110 120 130 140

Ele

vatio

n (m

)

100

105

110

115

120

125

130

135

140

145

150

Figure 16: Results of post earthquake stability analysis of embankment under MDE loading.

Upgraded embankment.



Figure 17: Results of FLAC total stress dynamic deformation analysis under MDE loading. Upgraded embankment. Displacement pattern and magnitude of deformations.

The proposed remedial work was implemented and constructed successfully, within budget and time. Details of the soil improvement process and the other aspects of the seismic upgrade at Yarrawonga Weir are provided in the paper by Davidson et al. (2003).

8 SUMMARY Several methods to estimate seismic deformations of earth dams have been presented. The available methods range from the simple one-dimensional Newmark or Makdisi-Seed analysis to complex two-dimensional effective stress dynamic analysis, which considers the development of pore water pressures with earthquake shaking. Each of the methods has been briefly discussed and limitations of the method have been highlighted. The practice of earthquake engineering is evolving and is not without significant controversy at present. However, the methods discussed in this paper can provide the design engineer and dam owner with some confidence in tackling this most difficult geotechnical engineering challenge.

An example has been provided where a process including liquefaction assessment, post earthquake stability analysis and total stress dynamic analysis has been successfully applied in a significant dam safety seismic upgrade project in Victoria. The dynamic analyses were very useful in providing an indication of possible flow failure, crack development during the shaking and the potential for loss of freeboard in a critical irrigation control structure on the River Murray. The method was also very useful to assess the most efficient remedial method that satisfies all the imposed requirements from the community and the client (e.g. the remedial work must be carried out with the lake level at full supply level most of the time).

9 ACKNOWLEDGEMENT The authors would like to express their sincere gratitude to G-MW (Goulburn-Murray Water) and the MDBA (Murray Darling Basin Authority) for the permission to publish information on the seismic upgrade of the Yarrawonga Weir. G-MW manages the Weir on behalf of the Murray Darling Basin Authority.

10 REFERENCES ANCOLD (1998), “Guidelines for Design of Dams for Earthquakes”. Baziar, M.H., and Dobry, R. (1995) Residual Strength and Large Deformation Potential of Loose Silty Sands, J.

Geotech. Engineering Div., ASCE, 121(12): 896-906. Beaty M., H. and Byrne, P. M. (1999) A Synthesized Approach for Modeling Liquefaction and Displacements,

FLAC and Numerical Modeling in Geomechanics, 339-347. Bray, J. D., Rathje, E.M., Augello, A.J., and Merry, S.M., (1998).”Simplified Seismic Design Procedure for

Geosynthetic-lined, solid-waste Landfills”, Geosynthetics Int. 5, 203-235. Byrne, P. M. (1991) “A Cyclic Shear-Volume Coupling and Pore Pressure Model for Sand”. 2nd Int. Conf.,

Recent Advances in Geotechnical Earthquake Engg., and Soil Dynamics, St. Louis, Missouri, 2: 47-55. Byrne, P.M., H. Jitno, and F. Salgado. (1992). “Earthquake Induced Displacements of Soil-structures Systems,”

Proc. 10th World Conf. on Earthquake Engineering, A.A. Balkema. pp. 1407-1412. Byrne, P.M., H. Jitno, D.L. Anderson, and J. Haile. (1994). “A Procedure for Predicting Seismic Displacements

of Earth Dams,” Proc. of the 13th International Conference on Soil Mechanics and Foundation Engineering, New Delhi, India. 1047-1052.

Byrne, P.M., Phillips, R., and Zang, Y. 1995. Centrifuge tests and analysis of CANLEX field event, 48th Canadian Geotechnical Conference, Vancouver, British Columbia.

Byrne, P.M., Park, S., Beaty, M., Sharp, M., Gonzalez, L., Abdoun, T. (2004) “Numerical Modeling of Liquefaction and Comparison With Centrifuge Tests”. Can Geotechnical Journal, 41:193-211.



Dafalias, Y.F. 1986. Bounding surface plasticity. I: mathematical foundation and the concept of hypoplasticity. Journal of Engineering Mechanics, ASCE, 112 (9), 966-987.

Davidson, R.R. and Perez, J.-Y. (1984), “Treatment of Recent Sediments Using Compacted Gravel Columns, Tablachaca Landslide Peru”, Paper presented at the Symposium on Remedial Treatment of Liquefiable Soils Beneath Existing Structures, Waterways Experiment Station, Vicksburg, MS, September.

Davidson, R.R., Fox, S.D and Cooper, B.R. (2003). “Seismic Upgrade of Yarrawonga Weir,” ICOLD Conference, Montreal.

De Alba, P., Seed, H.B., Retamal, E. and Seed, R.A (1988). “Analyses of Dam Failures in 1985 Chilean Earthquake” Journal of Geotechnical Engineering, Vol. 114, No. 12, December 1988, pp. 1414-1434

Dobry,R and Alvarez,L. (1967). “Seismic failures of Chilean tailings dams,” J. Soil. Mech. Foundation Div. 93 (1967) 237–260.

Elgamal, A.-W., Parra, E., Yang, Z, Dobry, R., and Zeghal M. 1999. Liquefaction constitutive model. In Proc., Physics and Mechanics of Soil Liquefaction Symposium, Balkema, Rotterdam.

Farrar, J.A., Wirkus, K.E. and McClain, J.A. (1990), “Foundation Treatment Methods for the Jackson Lake Dam Modification”, Proc. of the US Comm. on Large Dams Annual Meeting, New Orleans.

Fell, R., MacGregor, P., Stapledon, D. and Bell, G. (2005). “Geotechnical Engineering of Dams,” Taylor & Francis, London.

Finn WD, Liam, Yogendrakumar M, Yoshida N, Yoshida H. (1986) Tara-3: A program for Nonlinear Static and Dynamic Effective Stress Analysis, Soil Dynamics Group, University of British Columbia, Vancouver, BC, Canada.

Finn, W.D.L., K.W. Lee, and G.R. Martin. (1977). “An Effective Stress Model For Liquefaction,” Journal of the Geotechnical Engineering Division 103(6):517-533.

Geo-Engineering Extreme Events Reconnaissance Association (2010) Geo-engineering Reconnaissance of the 2010 Maule Chile Earthquake, GEER Association Report No. GEER-022, April

Hayden, R.F. and Welch, J.P. (1991), “Design and Installation of Stone Columns at Naval Air Station," in M. Esrig and R.C. Baachus, eds., Deep Foundation Improvement: Design, Construction, and Testing, ASTM STP 1089, ASTM, Philadelphia, 172-184.

Idriss, I.M. and Boulanger, R.W. 2008. “Soil Liquefaction During Earthquakes”. Earthquake Engineering Research Institute.

Idriss, I.M. and Sun, J.I. (1992) "User's Manual for SHAKE91," Center for Geotechnical Modeling, Department of Civil and Environmental Engineering, University of California, Davis, California, 13 p. (plus Appendices).

Ishihara, K. (1984). “Post-earthquake failure of a tailings dam due to liquefaction of the pond deposit,” Proc. Int. Conf. on Case Histories in Geotechnical Eng., St. Louis, Vol. 3, pp. 1129-1143.

Ishihara, K., and M. Yoshimine. (1992). “Evaluation of Settlements in Sand Deposits Following Liquefaction During Earthquakes,” Soils and Foundations, Japanese Society of Soil Mechanics and Foundation Engineering 32(1):173-188.

ITASCA, 2008. FLAC -Fast Langrangian Analysis of Continua, Version 6.0 ITASCA Consulting Group Inc., Minneapolis, Minnesota.

Jibson, R.W. (1993). “Predicting Earthquake-Induced Landslide Displacements Using Newmark’s Sliding Block Analysis.” Transportation Research Record, No. 1411-Earthquake-Induced Ground Failure Hazards. Transportation Research Board. National Research Council. Washington, D.C. pp. 9-17.

Jitno, H. (1995). “Liquefaction induced deformation of earth structures,” Ph.D. Thesis, Department of Civil Engineering, The University of British Columbia, Canada.

Jitno, H. (2011). “Effective stress dynamic analysis of Hamata Tailings Dam”, accepted for publication in 2nd International FLAC/DEM Symposium, Melbourne.

Kramer, S., and Arduino, P. 1999. Constitutive modeling of cyclic mobility and implications for site response. In Proceedings of the 2nd International Conference on Earthquake Geotechnical Engineering, Balkema, Rotterdam, The Netherlands, 1029-1034.

Lee, K.L. (1974).”Seismic permanent deformations of earth dams,” Report No UCLA-ENG-7497, School of Engineering and Applied Science, University of California Los Angeles.

Lysmer, J. et al. (1975). “FLUSH – A Computer Program for Approximate 3-D Analysis of Soil-Structure Interaction Problems,” EERC-UCB Report 75-30, Earthquake Engineering Research Center, Univ. of California, Berkeley.

Makdisi, F.I., and Seed, H.B. (1978), "Simplified Procedure for Estimating Dam and Embankment Earthquake-Induced Deformations," Journal of Geotechnical Engineering, American Society of Civil Engineers, Vol. 104, No. 7, 849-867.

Martin, G.R., Finn, W.D.L. and Seed, H.B., 1975. “Fundamentals of Liquefaction under Cyclic Loading,” ASCE, J., Geotechnical Engineering Division, V. 101(GT5), Proc. Paper 11284, 423-438.



Newmark, N.M. 1965. "Effects of Earthquakes on Dams and Embankments," J., Geotechnique, 15, No. 2, 139-160.

Prevost, J.H. DYNAFLOW, 1981. A nonlinear transient finite element analysis program, Princeton University, Department of Civil Engineering, Princeton, N J.

Prevost, J.H. 1989. DYNA1D: A computer program for nonlinear site response analysis. Technical Report No. NCEER-89-0025, National Center for Earthquake Engineering Research, SUNY at Buffalo, NY.

Puebla, H., Byrne, P.M., Phillips, R., 1997. Analysis of CANLEX liquefaction embankment: prototype and centrifuge models. Canadian Geotechnical J., 34, 641-654.

Sadigh, K., Chang, C-Y., Egan, J.A., Makdisi, F. and Youngs, R.R. 1997. Attenuation relations for shallow crustal earthquakes based on California strong motion data. Seismological Research Letters, 68(1): 180-189.

Sarma, S.K. (1975). “Seismic stability of earth dams and embankments”, Geotechnique 25, 743-761 (1975). Seed, H.B. (1979), "Considerations in the earthquake-resistant design of earth and rockfill dams," Geotechnique,

29(3), 215-263. Seed, H.B., Lee, K.L., Idriss, I.M., and Makdisi, F., 1973. Analysis of the slides in the San Fernando Dams

during the earthquake of Feb. 9, 1971. Earthquake Engineering Research Center, Rpt. EERC 73-2. Seed, H.B., Seed, R.B., Harder, L.F., and Jong, H.L., 1989. Re-evaluation of the Lower San Fernando Dam, Rpt.

2, US Army Engineer Waterways Experiment Station, Contract Rpt. GL-89-2. Seed, H.B., Seed, R.B., Harder, L.F., Jr and Jong, Hsing-Lian (1988).”Re-evaluation of the Slide in the Lower

San Fernando Dam in the Earthquake of February 9, 1971.” Report No UCB/EERC-88/04, University of California, Berkeley, CA.

Seed, R.B., and Harder, L.F., Jr. 1990. SPT-based analysis of cyclic pore pressure generation and undrained residual strength. In Proceedings of the H.B. Seed Memorial Symposium, Bi-Tech Publishing Ltd., Vol. 2, 351–376.

Serff, N., Seed, H.B., Makdisi, F.I., and Chang, C-Y. (1976).”Earthquake-induced deformations of earth dams,” EERC 76-4, University of California, Berkeley, 140 pp.

Stark, T.D. and Mesri, G. (1992), “Undrained Shear Strength of Sands for Stability Analysis”, Journal of Geotechnical Engineering, ASCE, Vol. 118, No. 11, 1727-1747.

Stewart, J.P., Blake, T.F., and Hollingsworth, R.A. (2003).”A Screen Analysis Procedure for Seismic Slope Stability,” Earthquake Spectra, Vol. 19, No 3, 697-712.

Swaisgood, (2003).” Embankment dam deformations caused by earthquakes,” 2003 Pacific Conference on Earthquake Engineering.

Tan, P., Moriwaki, Y., Seed, R.B., and Davidson, R.R. 2000. “Dynamic Run-out Analysis Methodology (DRUM)”. Tailings and Mine Waste ’00. Balkema, Rotterdam.

Tokimatsu, K. and H.B. Seed. (1987). “Evaluation of Settlements in Sands Due to Earthquake Shaking,” Journal of Geotechnical Engineering 113(8):861-878.

Toro, G.R., Abrahamson, N.A., Schneider, J.F. 1997. Model of strong ground motions from earthquakes in Central and Eastern North America: best estimates and uncertainties. Seismological Research Letters, 68(1): 41-57.

URS (2000). “Yarrawonga Weir Embankment and Foundation Remedial Options Study”, Final Report, August 2000.

Yegian, M.K., E.A. Marciano and V.G. Ghahraman. (1991). “Earthquake-Induced Permanent Deformations: Probabilistic Approach,” Journal of Geotechnical Engineering 117(1):35-50.

Youd, T.L., Idriss, I.M., Andrus, R., Arango, I., Castro, G., Christian, J., Dobry, J., Finn, L., Harder Jr., L., Hynes, H.M., Ishihara, K., Koester, J., Liao, S.S., Marcuson III, W.F., Martin, G., Mitchell, J.K., Moriwaki, Y., Power, M.S., Robertson, P.K., Seed, R.B., and Stokoe II, K.H., 2001. Liquefaction Resistance of Soils: Summary Report from the 1996 NCEER and 1998 CEER/NSF Workshops on Evaluation of Liquefaction Resistance of Soils, Journal of Geotechnical and Geoenvironmental Engineering., ASCE, 127: 817-833.

Zienkiewicz, O.C., Chan, A.H.C., Pastor, M., Paul, D.K., and Shiomi, T. 1990. Static and dynamic behavior of soils: a rational approach to quantitative solutions. Part I: fully saturated problems. In Proceeding, Research Society London, A429, pp. 28

earthquake-induced displacements of earth dams and embankments

Documents