Assessment of sliding block methods performance considering energy-representative parameters

Soil Dynamics and Earthquake Engineering 114 (2018) 520–533

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Assessment of sliding block methods performance considering energyrepresentative parameters

T

⁎

Mohammad Hassan Baziar , Reza Karimi Moghaddam Geotechnical/Earthquake Enginee ring, School of Civil Engineering, Iran University of Science and Technology, Tehran, Islamic Republic of Iran

A R T I C LE I N FO

A B S T R A C T

Keywords: Sliding block Near-field Energy density Response ratio Case study Slippage

In this research, permanent deformation of ten real earth dams were estimated using all the sliding block models and then, the errors between calculated deformations by each model and observed deformations of earth dams were presented and discussed in detail. The applied motion for estimating displacement of each dam was the recorded acceleration in the dam site. It was indicated that, conservative and non-conservative estimations of each model can be separated by Specific Energy Density and Response Ratio parameters in the time and frequency domains, respectively. It was also shown that, there is a logical relationship between the occurred earthquake-induced displacements and the specific energy density.

1. Introduction Sliding block method, originally proposed by Newmark [1], for the prediction of the earthquake-induced permanent deformation of earthen structures has been implemented by many researchers during last five decades (e.g [2–4]). Three major approaches of Rigid, Decoupled and Coupled have been considered using Newmark sliding block model. Advantages and disadvantages of each approach and related derived models as well as progressive development of the approaches from Rigid to Coupled have been discussed by previous studies in detail (e.g [5,6]). However, after it was proved that Near-Field ground motions were capable of causing much higher level of damage for a wide range of earthen structures, only a few researchers considered the Near-Field concept, using sliding block models. More recently, Garini and Gazetas [7] focused on near-field issue and discussed the sequence of high-duration pulses importance. Afterward, Voyagaki et al. [8] studied the sliding block system by applying near-field normalized pulses. They concluded that for constant values of PGA and material shear strength, existence of half-cycle pulse in velocity time history, may result in larger permanent deformation compared to full-cycle pulse. This conclusion contradicted the common understanding (e.g. [9,10]) of increase in permanent deformation due to increase in the number of shaking record cycles. Later, Gazetas et al. [11], by analyzing a number of near-field records containing forward directivity and fling step effects, indicated that the slip nature of sliding block may be affected not only by PGV and dominant period of the pulse, but also by some other unpredictable parameters such as pulse

⁎

sequence details and polarity of the velocity pulse. Their study also revealed that the vertical component of the applied strong motion did not have significant effect on the sliding systems even when it had a large values of PGV in its velocity time history. It is worth noting that some of these finding had been mentioned by previous researchers such as Franklin and Chang [12]; Yegian et al.[10]; and Kramer and Lindwall [13]. Following previous studies, considering various parameters of a record containing forward directivity and/or fling step effects, Garini and Gazetas [14,15] indicated that the damage potential of the nearfield strong motion records may be much greater than what was previously considered. So, they defined an upper bound for permanent deformation of sliding systems under near-field ground motions using rigid approach. However, while the accuracy of this method has not been examined using real case studies, it is consistent with the study performed by Rodriguez-Marek and Song [16] which expressed that the earthquake-induced deformations of earthen structures increased when they experienced a pulse-like forward directivity motion compared with experiencing a non-pulse motions. In the present study, the calculated deformation of ten earth dams obtained by various approaches of Newmark method, are discussed in detail. These case studies included a total of 10 real dams which each of them experienced an earthquake with a reported measured displacement, with recorded motions at the dam site and with known characteristics. The selected cases were such that, they received a vast range of energy, without having significant changes in their motion frequency content due to the wave travelling. In other words, all the selected cases were located in near-field regions during the related earthquakes, while

Corresponding author. E-mail address: [email protected] (M.H. Baziar).

https://doi.org/10.1016/j.soildyn.2018.06.009 Received 1 February 2018; Received in revised form 18 May 2018; Accepted 9 June 2018 0267-7261/ © 2018 Elsevier Ltd. All rights reserved.

Soil Dynamics and Earthquake Engineering 114 (2018) 520–533

M.H. Baziar, R.K. Moghaddam

3. Calculating the motions at the crest of the dam, using the scaled motions as the input motions at the base of the dam 4. A comparison between calculated motions at the crest of the dam and the recorded real motion during the earthquake, in terms of Peak Crest Acceleration (PCA), Peak Crest Velocity (PCV) and response spectrum parameters such as Peak Spectrum acceleration (PSA) and Mean Shaking Period (Tm). These values are shown in Table 3. 5. Selecting the appropriate scaling method which produced the closest calculated motion to the recorded motion. As it is obvious in Table 3, the values related to the scaled motion to fit the target response spectrum are in good agreement with the values related to the real recorded motion.

only some of them had experienced pulse like motions at their site. The applied motion for estimating displacement of each dam was the recorded acceleration at the dam site. Also, all the required parameters including yield acceleration, strong motion parameters such as PGA, PGV and Intensity, Initial fundamental period (Ts), earthquake Magnitude and Distance, and other parameters such as Sa(1.5Ts) were available or calculated. In other words, permanent deformations of the selected cases (10 earth dams) were estimated by 32 values of 26 models, derived from the five approaches of Rigid, Decoupled, Coupled, Unified and Near-Field. The predicted values were compared with the recorded slippage of the cases to determine conservatism and nonconservatism predictions of each model in both time and frequency domains. Consequently, the Specific Energy Density (SED) as a separator parameter in the time domain and the Response Ratio as a separator parameter in the frequency domain are introduced. Furthermore, it is proved that, SED may act as a major displacement predictive parameter as well as the other fundamental parameters such as yield coefficient (Ky) and initial fundamental period (Ts).

The selected scaling method for scaling the main record of Whittier Narrows dam was also used for scaling the main record of Coyote Lake Dam. It is worth noting that the best scaling method due to results of this study (Table 3) was the method which scaled the motion to fit the target response spectrum. As mentioned previously, the target response spectrum were obtained from attenuation relationship developed by Ambraseys & Douglas [21] for Near-Field Regions (R < 15 kM, M > 5.8). However, another evidence for the selected scaling method to be appropriate is that, the calculated max settlements by numerical models of the two dams using mentioned scaled records were in good agreement with the observed settlements via earthquake for these two dams. The calculated settlements for Whittier Narrows dam was 3 mm and for Coyote Lake dam was 73 mm which were in good agreement with the observed settlement of < 5 mm and 67 mm for these two dams, respectively.

2. Case studies (10 Earth Dams) The selected case studies, presented in Table 1, were located up to 15 km from the related fault and were shaken with an earthquake of Mw > 5.8. In addition, none of them have experienced liquefaction or failure phenomenon during the related earthquake and hence, all the deformations which were recorded during and after the earthquakes were earthquake-induced deformations. Also, all the properties of these 10 dams such as recorded strong motion, material properties, geometry and etc. were available. In other words, their deformations can be predicted using all the rigorous and simplified models. For these cases, the required parameters for the deformation analysis such as yield acceleration, ground motion parameters and etc., were obtained in this study using the same method. The details of the studied earth dams are presented in Table 1. As mentioned above, the strong motions used for estimating displacements of these earth dams, were the recorded motion at the dam site during related earthquake which are presented in Table 2. It is needed to mention that, for the cases with an intermediate depth or shallow sliding wedge, the input motions for Newmark analysis were obtained at the base of sliding blocks by performing numerical analysis. Furthermore, it should be mentioned that, the recorded motion at the south-west abutment station of Coyote Lake dam was used to analyze this dam during Morgan Hill 1984 earthquake with special considerations [20] regarding the recorded motion scaling. Also, the strong motion used for analyzing Whittier Narrows dam was the recorded strong motion at the crest of the dam. However, both above mentioned records were scaled to an associated target response spectrum which were obtained from the attenuation relationship developed by Ambraseys and Douglas [21] for Near-Field Regions (R < 15 kM, M > 5.8), considering each site features during related earthquake. For selecting an appropriate scaling method for Whittier Narrows dam, the following steps were taken:

3. Discussion of fundamental concepts 3.1. Newmark family models In this research, a total of 32 predicted displacement values can be resulted from all 26 (rigorous and simplified) Newmark models within five approaches, which are categorized and introduced in Table 4. Some important expressions mentioned in Table 4, are defined as below: – Rigorous Analysis: Rigorous analysis calculates displacements using real ground motions. – Simplified Analysis: Simplified analysis calculates displacements using parameters related to the associated ground motion. – Simplified models: Simplified models usually can be developed utilizing rigorous analysis with special technics and considerations. They eliminate the need to use real ground motions. – Rigid Approach: Rigid Block approach, first developed by Newmark [1], treats a potential landslide block as a rigid mass (no internal deformation) that slides in a perfectly plastic manner on an inclined plane. – Near-Field Approach: This is a new approach derived from rigid approach. Analyzing near-field strong motion utilizing rigid method, led to a simplified possible upper bound for cases located in near-field regions [14]. – Decoupled Approach: Decoupled approach is a modification of traditional Newmark Rigid approach that does not require the potential landslide mass to behave as a rigid block but rather models its dynamic response. Decoupled sliding block analysis originally computes the dynamic response of sliding mass without considering changes due to sliding and then, uses the computed response in a Rigid-block analysis. – Unified Approach: Actually, this approach is based on decoupled equivalent linear analysis of layered systems. However, in this approach, the initial values of displacements are calculated using rigid

1. Scaling the mentioned main recorded motion using following five different approaches: – – – –

scaling the motion to the target PGA scaling the motion to fit the target response spectrum matching the motion to fit the target response spectrum matching the motion to fit the target response spectrum and the target PGV – scaling the motion to fit the target response spectrum at the site period

2. Applying the scaled motions as the input motion at the base of the dam via a numerical model 521

522

Coyote Lake La Villita Lexington

Long Valley Los Angles

Matahina Oroville Whittier Narrows

3 4 5

6 7

8 9 10

Earth Dam Earth Dam (asphalt liner) Earth-Rock-fill Earth Dam Earth Dam

Earth-Rock-fill Concrete faced Rockfill Earth-Rock-fill Earth-Rock-fill Earth Dam

Dam Type

86 235 29

38 40

43 60 63

72 81

Height (m)

EDGECUMBE 1987 Oroville 1975 Whittier Narrows 1987

Mammoth Lake 1980 Northridge 1994

Morgan Hill 1984 Mexico 1975 Loma Prieta 1989

Morgan Hill 1984 Sierra Madre 1991

Earthquake

12 8 7

15 6

1.5 10 5

3.3 4

Distance (KM)

F.D N/A F.D (4)

F.D (P.L) & H.W F.D (P.L) & H.W

F.D (P.L) UN F.D (P.L)

F.D F.D

Located zone during earthquake(2)

102 10

90

Minor(1) 55 253 15 Minor(1)

67 24 259

15 16

Vertical

37 16 76

9 41

Horizontal

271 17 6

1 70

52 22 153

13 44

(5)

Calc. Obs.B.Def

Observed Displacements (mm)

– – Bray & Travasarou [17] (Calculated) – –

– – 150

268 – –

Butcher et al. [18] (Observed) – –

– –

– –

– –

Ref.

Def.

Slippage Calculated or Observed By other Studies

Minor Means < 5 mm. F.D: Located in forward directivity zone (3) / (P.L): at least a Pulse Like motion has been recorded in dam site / H.W: Located also in Hanging Wall zone / UN: Unknown zone. Forward directivity zones are defined as recommended by Somerville et al. [19] Oroville dam made its own earthquake on an unknown fault. So, directivity zone is not valid for this case. Calculated Observed Slippage using Observed Max Horizontal and Max Vertical Deformations.

Anderson Cogswell

1 2

(1) (2) (3) (4) (5)

Dam name

Case Number

Table 1 The details of case studies.

M.H. Baziar, R.K. Moghaddam

Soil Dynamics and Earthquake Engineering 114 (2018) 520–533

Soil Dynamics and Earthquake Engineering 114 (2018) 520–533

5.538 48.49

Note that, all 5 above mentioned approaches can be performed using rigorous or simplified analysis. It is obvious that the models can be also categorized in other ways such as separating them into rigorous and simplified models. However, since fundamentally, the various models from the same root of analysis have followed each other during their development, categorizing the models due to the ways that they were developed is more methodological compared with other types of categories. It should be noted that, the mean values of all 26 models (Except Garini and Gazetas [14] method which include just an upper bound) and the possible upper bound and lower bound for the best model of each approach were considered (Table 4). Also, the mentioned upper bound and lower bound values were calculated as defined by the related models or their associated standard deviation (σ). Note that, all the models mentioned in Table 4, consider yield acceleration as a constant value during their analysis. Therefore, the models such as Baziar et al. [36] (a modified decoupled model) and Jafarian and Lashgari [37] (a modified coupled model) which account in the variations of Ky in their relationship during analysis were not considered in this study. In addition, the sliding block models such as Baziar et al. [38] which have been developed for calculating lateral spreading-induced deformations, or the processes such as Kishida et al. [39], which was calibrated just for levees, were not considered in this study. Also, the earthquake-induced displacements of the selected earth dams were not large enough to cause a significant effect on the deformations due to the rotation of sliding block, as described by Stamatopoulos et al. [40].

3.0

213.67 (749.9) – 1289.53 (9216.1) 1.36 (15.10) Not recorded

0.088 (0.102) 0.208 Scaled by the same way which was applied for case number 3

Horizontal Transverse Component (Perpendicular to the dam axis in horizontal direction). Vertical Component. Values in brackets are related to the records at the base of sliding blocks (for the cases: block height ‡ dam height: Table 5).

3.2. Yield coefficient (Ky) The yield acceleration, conceptually, is an acceleration when related factor of safety for sliding block is equal to unit. This concept is a basis for calculating yield acceleration in the pseudo-static analysis. In this study, the pseudo-static analysis was used for all the cases to obtain yield acceleration. The Morgenstern-Price's method was used as a limit equilibrium method in pseudo-static analysis for predicting the sliding block. All the properties of the dams were obtained from their real conditions (reservoir level, geometry and material, site condition and etc.) during experienced earthquake and the analysis were performed in the total stress or undrained condition as recommended by Newmark [1]. Finally, due to the effect of cyclic loading, the calculated yield accelerations were reduced by 10% [32]. Therefore, all the yield accelerations, used in this study, were the same theoretical yield accelerations that authors obtained from the above procedure and are expressed in this research as a coefficient of acceleration of gravity (g). It is worth noting that, originally, the near-field Pulse-Like motions have small number of cycles in their content. However, in this study, although the selected earth dams were located in near-field regions for the related earthquakes, just two cases experienced pulse-like motions in the direction perpendicular to the dam axis. The calculated yield coefficients are presented in Table 5. As it is clear in this table, the calculated yield accelerations in this study are in good agreement with the yield acceleration calculated in other studies. 3.3. Observed slippage As noted previously, the predicted values by all the models have been compared with the observed slippage in this study. Observed slippage, which included both the deformation related to sliding block

c

b

a

303 Crest 10

N37E 9

Seismological Station

0.120

0.14 (0.20) 0.240 (0.26) – 8

353

–

0.084 0.130 – – 90 334

Down-Stream toe Foundation (on free field) Down-Stream Toe 6 7

S05E 0 Berm (Near the Toe) Left Abutment 4 5

approach. Then, the calculated initial displacements are enhanced using decoupled analysis. The only two models of this approach are simplified models [31]. – Coupled Approach: An extension of decoupled approach, it also considers the interaction of sliding-limited shear stresses on the dynamic response of the sliding mass.

20.6 (63.50) 2.25 (4.03) 11.3

8.4 (18.3) –

3.99 754.78 (812.02) 28.053 496.19 24.40 3102.42 (3215.6) 135.44 3209.95 0.060 0.143 (0.14)

0.071 0.440 (0.443)c 0.187 0.279

5.11 84.7 (86.03) 17.8 62.2

1.8 27.0 (28.4) 5.9 16.9

88.9 27.50 44.80 322.35 34.02 491.8 0.208 0.228 0.182 250 60 195 1 2 3

Down-Stream toe Right Abutment South-West Abutment

– – Scaled to the target response spectrum which obtained from attenuation relationship recommended by Ambraseys & Douglas [21] for Near-Field Regions (D < 15 kM) – –

0.420 0.264 0.43

27.6 9.55 32.2

9.6 6.6 7.3

Ver. H.T H.T H.Ta

Operations On Record Horizontal Transverse (H.T) Component {Perpendicular to Dam Axis} Applied Station for Analysis Case Number due to the Table 1

Table 2 Characteristics of recorded motions at the dam site which were applied in the study.

Ver.b

PGV (cm/s) PGA (g)

Ver.

SED (cm2/s)

M.H. Baziar, R.K. Moghaddam

523

Soil Dynamics and Earthquake Engineering 114 (2018) 520–533

M.H. Baziar, R.K. Moghaddam

Table 3 Comparison of recorded motion at the crest of Whittier Narrows dam with calculated motions at the same point applying scaled records as the input motion of numerical model of the dam, for the sake of selecting the appropriate scaling method. Origin of the motion at the Crest

PCA (g)

PCV (cm/ s)

PSA (g)

Sa(0.6) (g)

Tm (Sec)

Recorded motion during the earthquake at the crest of the dam Calculated motion at the crest of the dam using scaled record as input base record (Scaling the motion to the target PGA) Calculated motion at the crest of the dam using scaled record as input base record (Scaling the motion to fit the target response spectrum) Calculated motion at the crest of the dam using scaled record as input base record (Matching the motion to fit the target response spectrum) Calculated motion at the crest of the dam using scaled record as input base record (matching the motion to fit the target response spectrum and the target PGV) Calculated motion at the crest of the dam using scaled record as input base record (scaling the motion to fit the target response spectrum at site period)

0.31 0.24

17.5 10.9

1.24 0.77

0.25 0.21

0.28 0.21

0.30

19.9

1.31

0.28

0.22

0.32

21.4

1.42

0.30

0.22

0.32

20.8

1.45

0.30

0.22

0.30

20.5

1.35

0.28

0.22

inclination angle of the base of the sliding surface (Thrust angle), using F.S, Ky and below relationship which has been proposed by Newmark [1]:

movement on the inclined slip surface and the deformation related to volumetric contraction of sliding block, were calculated for each case by distributing the values of the observed maximum horizontal and maximum vertical deformations on the related inclined slip surface. It is worth noting that, the obtained slippage by this procedure were mainly related to horizontal component of observed deformations [58]. Schematic of slippage is shown in Fig. 1. Slippage, which is defined as the deformation of the sliding block along the slip surface, has been calculated in the present study using below procedure:

Ky ⎞ ϴ ≈ Sin−1 ⎜⎛ ⎟ ⎝ F. S − 1 ⎠

(1)

Note: ϴ was also checked by the inclined angle of sliding block which was drawn in pseudo-static analysis. – Taking the dot product of the vertical and horizontal components of the observed displacement vectors and a unit vector aligned along the average inclination of the base of the sliding surface:

– Estimating Static Factor of Safety (F.S) using limit-equilibrium Analysis (Morgenstern-Price's Method) – Estimating Yield Coefficient (Ky) using pseudo-static analysis (Morgenstern-Price's Method) – Estimating Thrust Angle of sliding block (ϴ) as the average

̇ Vj )̇ .|ϴ|̇ Observed Max Slippage = (Hi +

(2)

Note: in Eq. (2), H is the maximum observed horizontal and V is the maximum observed vertical deformations. Also, |ϴ|̇ is the unit vector oriented parallel to the direction of slope movement. The direction of

Table 4 Newmark sliding block various approaches (including 26 models with 32 values). Rigid approach 1. Rigorous Method (Newmark Original Method) [1] 4. Franklin & Chang [12] 7. Jibson et al. [25] 10. Jibson [26] (c) 13. Saygili & Rathje [28] (a) 16. Saygili & Rathje (Upper Bound.) [29]

2. Newmark Simplified (mean): by Newmark [1] 5. Ambraseys & Menu (Median) [23] 8. Jibson [26] (a) 11. Jibson [26] (d) 14. Saygili & Rathje [28] (b) 17. Ebling et al. (Mean) [30]

3. Newmark Simplified (mean): by Cai and Bathurst [22] 6. Jibson [24] 9. Jibson [26] (b) 12. Watson-Lamprey and Abrahamson [27] 15. Saygili & Rathje [28] (c) Note: Relationships 2–17 are simplified models.

Unified approach Simplified Models 18. Rathje and Antonakos (PGA,M) [31]

19. Rathje and Antonakos (PGA,PGV) [31] Near-field-based approach Simplified Models

20. Garini and Gazetas– Upper Bound [14] Decoupled approach Chart-Based Models

Simplified Models 24. Hynes-Griffin & Franklin [33]

Seed & Makdisi [32] 21. Upr. Bnd

22. Mean (Gazetas)

23. Lwr. Bnd.

Rigorous Models 25. Bray et al. [34]

Rathje & Bray [35] 26. Linear Elastic

27. Equivalent Linear

Coupled approach Rigorous Models Bray & Rathje [35] 28. Linear Elastic

Simplified Models Bray & Travasarou [17] 29. Equivalent Linear

30. Upper bnd.

524

31. Mean

32. Lower bnd.

Soil Dynamics and Earthquake Engineering 114 (2018) 520–533

M.H. Baziar, R.K. Moghaddam

Table 5 Characteristics of Sliding Block of case studies. Case Number due to the Table 1

Static Factor of Safety

Thrust Angle (ϴ) {Degree}

Calculated Ky (g)

Ts

By This Study

By Other Studies

Ky by PseudoStatic

Ky

Ref.

b

(Sec)

Sa(1.5Ts) (g)

Block Height When Sliding Is Triggered (m)

Geometry and Material Properties of Dam, References

1

1.197

19.4

0.059

0.03a

Ryan et al. [41]

0.40

0.46

72

2

1.465

21.0

0.150

0.15

0.55

0.10

81

3 4

2.346 1.808

13.8 15.8

0.288 0.200

– 0.2

Singh & Debasis [44] – -Singh & Debasis [44] -Bray & Travasarou [17] TERRA Report No. LN-4 [47] Singh & Debasis [44] Singh & Debasis [44]

1.AMEC- Technical memorandum No.7 [42] 2.Tepel et al. [43] Boulanger et al. [45]

0.40 0.33

0.76 0.10

43 60

Tepel et al. [43] 1.Elgamal [46]

5

1.814

18.3

0.230

0.23

6

2.046

15.0

0.243

0.23

7

2.269

10.0

0.198

0.15

8

1.641

15.4

0.153

0.17

9

1.692

18.5

0.198

0.21

10

2.386

14.6

0.315

–

2.Gazetas & Uddin [47] c

0.20

0.72

25

0.31

0.44

38

0.25

0.37

40

Singh & Debasis [44]

0.13

0.59

15

Singh & Debasis [44] –

0.76

0.0

106

0.27

0.40

29

TERRRA Report No. LN-4 [48] Griffiths [49]

c

c

Los Angeles Department of Water and Power [50] 1.Mejia [51] 2.Finn [52] 3.Gillon [53] California State Water Project [54] 1.US Army Corps of Engineering [55] 2.Horowitz and Ehasz [56] 3. Rickerd [57]

a

The Ky value has been calculated by Ryan et al. [41] for Upstream of the Leroy Anderson Dam The values are related to expression Ts =2.61 H/Vs. c For the cases with an intermediate depth or shallow sliding wedge, the input motions for Newmark analysis were obtained at the base of sliding blocks by performing numerical analysis. b

from existed information for each dam which were extracted from insitu tests or using developed relationship for calculating maximum shear modulus by Seed [59] (for fine grained materials) and Seed et al. [60] (for coarse grained materials), depending on the type of material and available data. The values of Initial Fundamental Period (Ts) and block height for each case are introduced in Table 5. In addition, the effect of applying the expression Ts = 2 H/Vs, as suggested by Dakoulas and Gazetas [61] for realistic inhomogeneous earth dams, instead of the expression Ts = 2.61 H/Vs is also considered in this study.

Fig. 1. Schematic of Earthquake-Induced Slippage. Note: Observed slippage includes both the deformation related to sliding block movement on the inclined slip surface and also the deformation related to volumetric contraction of sliding block.

3.5. Forward directivity

slope movement is the same thrust angle introduced by Newmark [1]. Also, i and j are the unit vectors in the horizontal (x) and vertical (y) directions, respectively. The amounts of observed slippage, thrust angle and factor of safety for each case are presented in Table 5. Also, the references which are needed to model the analyzed case studies are introduced in this table.

Somerville et al. [19] parameterized forward directivity effect, for the first time, and accounted directivity effect in the attenuation relation as the broad band method. They defined forward directivity zones and excluded zones for both dip-slip and strike slip faulting considering site orientation toward fault plane. According to their definition, when a site is located in the forward directivity zone, it may experience twosided pulse cycles which emerge in the velocity time history of the faultnormal component. However, in addition to being in the forward directivity zone, existence of such pulse also is depended on other important parameters such as fault rupture velocity. In summary, when the fault rupture velocity is close to the site shear wave velocity, the highest accumulated energy can be observed. In the present study, the dam sites locations regarding forward directivity zones were defined as recommended by Somerville et al. [19]. The located zones of selected cases are introduced in Table 1.

3.4. Initial fundamental period (Ts) The expression: Ts = 2.61 H/Vs̅ , obtained from shear beam analysis, is used to estimate initial fundamental period of sliding wedge, where H is the height (depth) of triggered sliding block, obtained by pseudo-static analysis as mentioned in Section 3.2. Vs̅ is the average shear wave velocity of the sliding block mass which was obtained by averaging the shear wave velocity in each part of the sliding mass. Also, shear wave velocity in each part of the sliding block mass was obtained 525

Soil Dynamics and Earthquake Engineering 114 (2018) 520–533

M.H. Baziar, R.K. Moghaddam

Fig. 2. The error of different rigid, Unified and Near-Field models for estimating max slippage versus specific energy density of the selected 10 case studies. Note1: SED values are related to the base of the sliding blocks. Note2: The Points related to Lexington and Los Angeles dams may have overlapping because of their almost equal SED values. Also, the points with relative error > 500% are not appeared in the figures.

526

Soil Dynamics and Earthquake Engineering 114 (2018) 520–533

M.H. Baziar, R.K. Moghaddam

Fig. 3. The error of different decoupled and coupled models for estimating max slippage versus specific energy density of the selected 10 case studies. Note1: SED values are related to the base of the sliding blocks. Note2: The Points related to Lexington and Los Angeles dams may have overlapping because of their almost equal SED values. Also, the points with relative error > 500% are not appeared in the figures.

b. Extracted pulse should reach 10% of its total CSV, before the original ground motion reaches 20% of its CSV. c. The original ground motion has a PGV of greater than 30 cm/sec.

3.6. Pulse like ground motions Backer [62] introduced a procedure to distinguish pulse-like strong motions based on wavelet analysis. In this procedure, the main extracted pulse and the residual record were derived from the original velocity record using continuous wavelet analysis (10 times repeating extracting). It should be noted that, the Daubechies wavelet of Order 4 was used as the mother wavelet in the analysis process. Then, two predictor variables, PGV ratio and Energy ratio, were identified as the peak ground velocity (PGV) of the residual record divided by the original record's PGV, and the energy of the residual record divided by the original record's energy, respectively. Note that the energy for both original and residual records were obtained from cumulated squared velocity (CSV) which is known also as the record specific energy density:

All of the Pulse-Like strong motions, mentioned in this study (Table 1), meet all the above requirements. 4. Discussion of results Having the needed informations for all the earth dams, their deformation can be estimated using all the Newmark models, and the results can be discussed in both Time and Frequency domains. 4.1. Time domain view

t

CSV =

∫ V 2 (u) d (u) 0

The energy, generated by an earthquake source, is depreciated due to the earthquake wave travelling from the source to the far-field. Therefore, one of the main differences between Near-Field and FarField zones is the level of energy reaching to each site. The orientation of the site toward the wave emission direction as well as fault rupture velocity have also their own impact on the accumulation of energy in the near-field regions. In fact, the accumulation of energy in a site is a generic parameter for defining effect of an earthquake in any site and hence, it is anticipated that, CSV (Eq. (3)) can present the effect of an earthquake at a site better than other parameters such as PGA or PGV. To express energy concept in the time domain, the cumulative

(3)

Finally, the Pulse Indicator was defined using below equation:

PI =

1 1+e−23.3 + 14.6(PGV ratio) +20.5(Energy ratio)

(4)

A fault-normal ground motion is Pulse-Like when it meets all the three of below criteria: a. The pulse indicator value, as defined in Eq. (4), is greater than 0.85. 527

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Fig. 4. The errors of the upper bound values of Bray and Travasarou [17] non-linear coupled model, for estimating max slippage versus SED of the selected 10 case studies: (a) relative error Vs SED; (b) absolute error Versus SED. Note1: SED values are related to the base of the sliding blocks. Note2: The Bray and Travasarou model [17] resulted in non-conservative predictions for low and high values of SED, and conservative predictions for the medium values of SED.

As illustrated in Figs. 2 and 3, all the models result in non-conservative predictions for low values of SED (i.e. SED < 50 cm2/s) and high values of SED (i.e. SED > 1000 cm2/s). On the other hand, all the models generally result in conservative predictions for medium values of SED. Although Figs. 2 and 3 depict only the errors of max slippage predictions, but the conclusion is also valid for max horizontal and max overall deformations. Note that, the expression Ts= 2.61 H/Vs was used to estimate initial fundamental period of sliding wedge. However, using the expression Ts= 2 H/Vs as suggested by Dakoulas and Gazetas [61] for realistic inhomogeneous earth dams revealed that the same trend were observed despite having some changes in the values of calculated deformations. One notable phenomenon is that, none of the models can properly predict the deformation related to the cases which experienced very low values of SED (i.e. SED < 50 cm2/s) so that all the predicted values for these cases were zero using all the models (which it meant −100% error). However, this error is perceptible for the rigid block based models, since for these cases the PGA of the base record of the block is smaller than the related yield acceleration. It should be mentioned that for any Newmark model which takes into account the response of the sliding system, this phenomenon is unperceptible with the concept of sliding block. Yet, since the low values of SED are related to the small values of occurred deformations, the accepted concept which states that when deformation is very small the Newmark Models does not predict the deformations correctly, may be restated by the expression of “for the cases which experience low values of energy, the Newmark models does not predict the deformation correctly”. The results of this study indicate that the conservative results are correspond to the medium values of SED. In other words, a small observed deformation may be predicted conservatively or non-conservatively, depends on its related SED value. Hence, despite having a little importance in practice, small deformations are theorically usefull to explain the effectiveness of energy effect. As seen in Figs. 2 and 3, among all the Newmark models, the model developed by Bray and Travasarou [17] has the highest number of positive errors (conservative results) and the lowest rate of negative errors (non-conservative results) for the prediction of permanent deformation of the selected case studies. Note that, the method developed by Garini and Gazetas [14] has also equal number of acceptable (conservative) predictions compared with Bray and Travasarou [17] model

squared velocity (CSV) of the recorded strong motion in the dam site was presented. This parameter is also known as the recorded specific energy density which is derived from the site specific energy density defined by Sarma [63]. It should be mentioned that, since the site effect, path effect, faulting effect, orientation effect and other related parameters are emerged in a recorded motion of a site, the recorded SED (CSV) can appropriately express the nature of motions.

Site Specific Energy Density =

βs. ρs 4

∫ v2 (t ) dt

(5)

In this equation, βs and ρs are the shear wave velocity and the mass density of the recording site, respectively.

Recorded S. E. D = Cumulative Squared Velocity(CSV) =

∫ v 2 (t ) dt (6)

In this research, recorded specific energy density values are computed for ten selected case studies using velocity time histories of the recorded motions at the dam sites and, are indicated in Table 2. Hence, all the SED values, discussed or mentioned in this research, are related to the Recorded SED calculated by Eq. (6). The predicted displacement errors for each model versus SED are depicted in Figs. 2 and 3 by implementing the below expression:

Relative Error(%) =

D , calculated − D, observed × 100 D , observed

(7)

Note that the vertical axis of Figs. 2 and 3 are relative error which are calculated by Eq. (7). It is obvious that positive errors are related to the conservative prediction and negative errors are related to the nonconservative prediction for each model. Hence, the positive parts of diagrams may gain high values (For example > 500%) for very conservative results while, the negative part of diagrams can have maximum of − 100% errors when the calculated deformations are equal to zero and the values of deformations have been measured in the field. The horizontal axis of these figures are SED which are calculated for each dam record using Eq. (6). Note that the Eq. (6) is a different representation of Eq. (3). The velocity time histories, used in the Eq. (6), were obtained from the recorded strong motion accelerations at the base of related sliding blocks. The relative error, instead of absolute error, is used in order to normalize the differences between the observed and calculated displacements. 528

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regarding conservative and non-conservative predictions, the convergent of the results using SED and ΔPGV are more than the convergent of the results using PGV. In other words, the polarity of velocity time history (ΔPGV), the same way as SED, is able to provide a clear relation for errors.

4.1.1. Specific energy density as a predictor parameter Although SED acts as a separator parameter between conservative and non-conservative results in time domain, it has also direct impact on the occurring of earthen structures permanent deformation during an earthquake, as it is shown in Fig. 8. The vertical axis of this figure presents the observed slippage of the case studies and the horizontal axis presents the SEDs related to the transverse component of the earth dams’ base record. Fig. 8 also indicates that, the observed slippage increases with increasing SED of the base record. For the cases with low and medium values of SED, small values of slippage occur (for example < 5 cm), despite of having values of Ky in the wide range of 0.06–0.32. On the other hand, large values of permanent deformations occur for large values of SED. Furthermore, when three cases which have experienced large values of energy are compared with each other, it can be said that Matahina dam with lower Ky and larger SED at the horizontal component of the motion at the base of the sliding block, has experienced larger slippage compared with Lexington and Los Angeles (LA) dams. However, between Lexington and Los Angeles dams with almost equal values of Ky and SED at the base of related sliding block, Lexington dam which had larger SED value in the vertical component, experienced larger slippage compared with Los Angeles dam (While both of them had almost equal PGA in the vertical component). In addition, as it is illustrated in Fig. 9, the settlement of the case studies (Vertical axis of Fig. 9) increases with increasing the specific energy density values of the vertical record at the base of sliding block (Horizontal axis of Fig. 9). Hence, it is again confirmed that the SED, obtained from the horizontal or vertical component, controls the deformations. The SED values for vertical records of the earth dams are also presented in Table 2. From directivity perspective, the selected cases (Table 1) meet all the requirements for being considered as Near-Field sites. All of these dams had a maximum distance of 15 km from the fault with a minimum earthquake magnitude of 5.8. As mentioned previously, the selected cases were such that, they received a vast range of SED values from 1 cm2/s to 9216 cm2/s during earthquakes (Table 2). As it is obvious, the records with forward directivity effect have larger values of specific energy density. It is worth noting that eight dams of Table 1 were located in the forward directivity zones and two of these eight dams were also located in the hanging wall zones. The other two dams were located in the neutral or unknown zones. Four cases which were located in the forward directivity zones, have experienced at least a pulse like motion in the dam site, while others have not experienced pulse like in their motion (Table 1). However, since the transverse component of a base motion is needed to apply Newmark sliding block models for an earth dam, it is

Fig. 5. Relationship between SED and PGV for case studies of the 10 case studies with the base records. Note1: SED values are related to the base of the earth dams. Note2: The Points related to Lexington and Los Angeles dams may have overlapping because of their almost equal SED values.

while, the absolute values of negative errors of Garini and Gazetas [14] model are higher than Bray and Travasarou [17] model. This means that, when two models result in underestimated predictions, Garini and Gazetas [14] model is more non-conservative than Bray and Travasarou [17] model. For this reason, Bray and Travasarou [17] model is selected for further analysis in this study. The above conclusion, regarding the non-conservatism of the models in low and high values of SED is more evident especially in Fig. 4, associated with the upper bound of Bray and Travasarou [17] model. Furthermore, it can be noticed that, the upper bound of Makdisi and Seed [32] method and the upper bound of Saygili and Rathje [29] method have the best results among decoupled and rigid models, respectively. Since for any earthquake motion, SED is directly calculated from a velocity time history and hence, it is proportional with PGV (SED α PGV2). As seen in Fig. 5, SED has a direct relationship with PGV, such that SED increases with increasing PGV. It is therefore expected that the same trend to be obtained when PGV, instead of SED, is depicted against permanent deformation. Also, since SED considers the amount of PGV in positive and negative positions, it is expected that the velocity time history polarity (ΔPGV) to have more effect on SED than the PGV and therefore, it is logic to say that PGV does not present the full content of SED. The definition of PGV polarity is illustrated in Fig. 6, originally reported by Garini and Gazetas [7]. Fig. 7 presents the errors between predicted displacements by the upper bound of Bray and Travasarou [17] model and the observed slippage for the selected dams, against PGV, ΔPGV and SED values which have been recorded during the related earthquakes at the base of all ten dams. It should be mentioned that, since Fig. 7 is a comparative figure, it is preferred to utilize the recorded values of SED, PGV and ΔPGV at the base of the dams instead of calculated values of SED, PGV and ΔPGV at the base of the related sliding block, in the horizontal axis of the included graphs of this figure, to minimize the possible unintendedly errors associated with the calculations. As seen in this figure,

Fig. 6. Velocity time history polarity (ΔPGV) concept in Near-Fault records - Garini and Gazettas [7]: (a) Fling Step record; (b) Forward Directivity record. 529

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Fig. 7. (a) Relative error Versus PGV; (b) Relative Error Versus ΔPGV; (c) Relative Error Versus SED. Note1: PGV, ΔPGV and SED values are related to the base of the earth dams. Note2: Relative errors are related to the upper bound of the Bray and Travasarou [17] model for estimating max slippage of the selected 10 case studies: Note 3: Compared with PGV, the polarity of velocity time history (ΔPGV), the same way as SED, is able to provide a clear relation for errors.

Fig. 10. Schematics of directions and orientations in a dam site. Fig. 8. Observed slippage versus Specific energy density (SED) for the selected 10 case studies. Note: SED values are related to the base of sliding blocks.

experienced pulse like at the transverse component of the dam during Loma Prieta 1989 earthquake and consequently its deformations have been affected by a high level of energy. The above mentioned components (directions) are presented in Fig. 10, schematically. Another important observation is that, the vertical component of the dams which had forward directivity effect in the transverse components presented higher SED values, despite of having even smaller values of PGA (for example, comparison of Lexington and Los Angeles dams with Anderson and Cogswell dams). Furthermore, on a similar conditions for two earth dams, the case with larger value of SED in the vertical component experienced larger vertical deformation and slippage (for example, comparison of Lexington dam and LA dam with each other). Also, it seems that the energy value at the base of sliding block is more important than the energy at the base of dam, for calculating permanent deformation of an earth dam under earthquake shaking. For example, energy value at the base of Matahina dam was equal to 1290 cm2/s, while the energy value at the base of sliding block was equal to 9216 cm2/s (Table 2), which is more consistent with the observed deformation of this dam. Athanasopoulos-Zekkos et al. [64] conducted an investigation and stated that the seismic slope displacements were better correlated to PGV than PGA and other conventional parameters, which their conclusion is in good agreement with the observations of the present study. Actually, PGA cannot explain the occurred deformation, the same way as SED can. For example, Ky and PGA values for the sliding block of Anderson dam during Morgan Hill 1984 earthquake were equal to 0.06 g and 0.42 g respectively, while for Los Angeles dam during Northridge 1994 earthquake, these values were equal to 0.2 g and 0.28 g respectively. It is anticipated that the permanent deformation of Anderson dam to be larger than the permanent deformation of Los Angeles dam. While in reality, the slippage of LA dam (70 mm) was larger than the slippage of Anderson dam (13 mm). However, this

Fig. 9. Observed settlement versus energy values of vertical records of the selected 10 case studies. Note1: SED values are related to the base of sliding blocks. Note2: The Vertical motion for Oroville dam has not been recorded during Oroville earthquake of 1975.

important to investigate the cases which have experienced forward directivity effect in the transverse component of their base record, as Lexington and LA Dams were in this situation. It should be noted that when the axis of a dam length is perpendicular to the related fault plane, the forward directivity effect emerges in the longitudinal direction of the dam. Therefore, despite having pulse-like in the recorded strong motion of Long Valley dam, it has not experienced pulse like in the transverse component of base record during Mammoth Lake 1980 earthquake and consequently, its deformations have been affected by a medium level of energy. On the other hand, Lexington dam has

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bound values of the Bray and Travasarou [17] model is non-conservative. Although Fig. 11 only depicts the errors of max slippage predictions, but this conclusion is also valid for max horizontal and max overall deformations. The same way, this conclusion is valid about the mean values of Bray and Travasarou [17] model.

difference in the deformation values can be logically explained by energy concept, when SED value for Los Angeles Dam was equal to 3210 cm2/s and while for Anderson dam was equal to 322 cm2/s. Overall, it can be concluded that, for calculating earthquake-induced permanent deformation of earthen structures, considering energy (SED), can lead to more realistic values than using other parameters such as PGA and PGV in the time domain. Also, when SED is accounted for estimation of occurred deformations, it is no need to separate far and near field strong motion records with and without directivity pulse.

5. Conclusions Following Conclusions can be drawn from present study: a. Applying all the 26 simplified and rigorous Newmark models (with 32 predicted values) for 10 real earthen structures has indicated that the Bray and Travasarou [17] model which was a simplified nonlinear fully coupled model, predicted the occurred displacements better than other models. This model had the highest number of acceptable (conservative) predictions and the lowest absolute values of negative errors among all of the Newmark sliding block family models. It should be mentioned that, Garini and Gazetas [14] method also performed well, but due to the absolute values of negative erros, the previous model was preferred. This preference was due to the fact that, when two models resulted in underestimated predictions, the Bray and Travasarou [17] model was more conservative than the Garini and Gazetas [14] model. b. Specific Energy Density (SED), obtained from recorded velocity time history, was introduced as the separator parameter in the time domain so that the predictions of almost all models were underestimated for low and high levels of SED, and were overestimated only for medium levels of SED. It was concluded that SED had a key role in the prediction or occurrence of the permanent deformation of earthen structures. c. While PGV was an important parameter for defining an earthquake motion, the Polarity of the velocity time history (ΔPGV) was more important parameter for calculation of SED. However, this is due to the fact that, SED depends on many other unknown parameters such as the number of half-cycles, duration and etc., in addition to the PGV of each half-cycle. Furthermore, convergence level of the errors of ΔPGV compared to the errors of PGV was an indicator that the polarity of a velocity time history (ΔPGV) was more effective parameter than PGV (Fig. 7).

4.2. Frequency domain view Somerville et al. [19] showed that forward directivity caused a larger response at the periods greater than 0.6 s. Similarly, Seneviratna [65] compared the average response of 15 far-field ground motions records with the response of several near-field ground motions and confirmed the Somerville et al. [19] conclusion about the response at the period of 0.6 s. In the present study, response ratio for each case-record is defined as the ratio of response of a SDOF system with a period of 1.5Ts seconds (with 5% damping) subjected to the input motion over the response of a SDOF system with a period of 0.6 s (with 5% damping) subjected to the same input motion, where Ts is the initial fundamental period of the sliding block. In other words, the ratio of Sa(1.5Ts)/Sa(0.6) is considered as the goal parameter to scrutinize different sliding block models in the frequency domain. Then, the errors between observed slippage and calculated deformation by the upper bound values of the simplified non-linear coupled model developed by Bray and Travasarou [17] versus response ratio are drawn in Fig. 11. Note that, the vertical axis of Fig. 11 is related to the absolute error and the horizontal axis of this figure is related to the response ratio. So, it is clear that the positive errors indicate the conservative predictions and the negative errors are related to the non-conservative predictions. As it is clear from Fig. 11, the below law is established between response ratios and errors: When Sa(1.5Ts)/Sa(0.6) < 1 → Error (%) < 0 (Non-Conservative) When Sa(1.5Ts)/Sa(0.6) > 1 → Error (%) > 0 (Conservative) It can be said that, for any input motion, when the response of a system with the period of 1.5Ts seconds is larger than the response of a system with the period of 0.6 s, (i.e. when the response ratio is larger than one), the upper bound of the Bray and Travasarou [17] model for the prediction of max slippage is conservative. On the contrary, when the response of a system with the period of 1.5Ts seconds is smaller than the response of the system with the period of 0.6 s, the upper

Such importance of SED, as an energy representative parameter, was proved because of the following observations: – SED separates conservative and non-conservative predictions of the sliding block models – The values of PGV and ΔPGV are included in SED content – Deformations of earth dams increase with increasing SED values and hence, large values of permanent deformations occur when large values of SED from the earthquake motion reach to the earth dams. In other words, although permanent deformations of earth dams depend on some other parameters such as Ky and Ts, which are related to dam properties, SED is a key parameter of input motion since there is a direct relationship between occurred deformations and SED values. – Large values of vertical displacements also occur for large values of vertical SED. In other words, there is a direct relationship between settlement of dams and SED values of vertical components of strong motions. – Large values of SED occur when an earthquake produces the pulselike motions in a dam site and consequently, large values of deformation are resulted from such motions.

Fig. 11. Absolute error of Bray and Travasarou [17] non-linear coupled model for prediction of max slippage versus Response Ratio {Sa(1.5Ts)/Sa(0.6)} of the case studies. Note 1: The expression 2.61 H/Vs were used for estimation of initial fundamental period (Ts). Note 2: When Sa(1.5Ts)/Sa(0.6) < 1 → Error (%) < 0 (Non-Conservative Predictions), When Sa(1.5Ts)/Sa(0.6) > 1 → Error (%) > 0 (Conservative Predictions).

a. Response ratio {Sa(1.5Ts)/Sa(0.6)}, defined as the ratio of response of a SDOF system with the period of 1.5Ts seconds to the response of a SDOF system with the period of 0.6 s, was introduced as the separator of conservative and non-conservative predictions in the 531

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frequency domain. In addition to being separator, response ratio was also a Near-Field Seismo-Structure depended parameter which simultaneously can consider some of the Near-Field effects (Sa (0.6)), Seismic characteristics (Sa(1.5Ts)) and also earthen structure properties (Ts). b. All the results, mentioned above, are also valid for the prediction of the observed max slippage, max horizontal and max overall earthquake-induced deformations. Also, while the occurred deformations were compared with the mean values of all the models (and with the lower bound and the upper-bound values of the best models of each approach), the trend of results are also valid for the possible lowerbound and upper-bound values of all the models.

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