Analysis of Newmark method on type 1 semi-gravity reinforsced. concrete cantilever retaining walls with and without sound wall.

Transcription

1 Analysis of Newmark method on type semi-gravity reinforsced concrete cantilever retaining walls with and without sound wall Xiaozang Chen University of California-Davis REU Institution: University of California-San Diego/Englekirk Shake Table REU Advisor: Dr. Lijuan Dawn Cheng Graduate Student Mentors: Erin Mock

2 I. Abstract This research report illustrates the engineering formulas developed for the seismic reaction of retaining walls to earthquake ground motions. The study focuses on the Newmark sliding block methods of seismic analysis and design. Newmark sliding block method is a permanent sliding block displacement analysis adopted by American Association of State Highway and Transportation Officials (ASSHTO). (ASSHTO 005) Step by step calculation is conducted and examined on Type semi-gravity reinforced concrete cantilever retaining walls with and without sound wall. The Newmark method will be computed by given Northridge and Kocaeli earthquake acceleration time-histories. Two of the Newmark methods will be applied on the design project specimens. The AASHTO Newmark method (965) and simplified Newmark method (008) conducted and investigated by National Cooperative Highway Research Program (NCHRP). Since the overall project (Cheng 008) was funded by Caltrans, Mononobe-Okabe Method (adopted by Caltrans) was also considered in the study and compared with the Newmark methods. Later, results of the study will be analyzed and confronted with the real time experiment measurements which conducted on the UC San Diego Englekirk Shake table. II. Introduction Seismic design of retaining walls had been overlooked by the civil engineers as compare to other seismic structures. Results of the negligence lead to a lack of precise, reliable, and authorized guideline in the existing design codes and specifications. One explanation of the inattention could be the lack of wall collapses in the recent US-California earthquakes (Loma-Prieta, and North Ridge). The devastating bridge collapses had overshadowed the retaining wall failure. As of now, Caltrans had not addressed detail guidelines for the rational seismic design guideline of the retaining walls. However, damage and collapse of the retaining walls can pose an extensive life and property loss. Failure and rapture of the retaining wall can lead to bridge failure, high way traffic, land slide, etc. This research project is part of the Caltran Seismic Design Guidelines of Retaining Walls with/without Sound Wall project. In this project, available seismic design methods are used to investigate the seismic motions of the retaining wall. Caltran uses Monoable-Okabe method to calculate the dynamic motion of retaining wall under earthquake. American Association of State Highway and Transportation Officials (AASHTO) adopt Newmark

3 method (displacement-based) to predict retaining wall seismic deformation. Newmark method will be used to predict the residual deformation and displacement of the type I semi-gravity reinforced concrete cantilever retaining walls with and without sound wall. Northridge and Kocaeli (Yagi and Kikuchi 999) earthquake data and time history will be used in the calculation and estimation. III. Background The objective of this overall research project (Cheng 008), S079, Seismic Design Guidelines of Retaining Walls with or without Sound Wall, is to develop and improve new guideline and tools for the seismic design of retaining wall on the firm soil. Numerical tools such as finite-element method and soil-structure interaction principal will be used to develop new sets of models. Two full size retaining walls (6 ft high Type Semi-Gravity Reinforced Concrete Cantilever Walls with and without sound wall) will be constructed and tested on the University of California San Diego s Englekirk shake table. Walls will be placed in the soil box and backfilled with Caltrans specified soil. Within the soil box, the wall will not be anchored and will be stabilizes with its own weight and joint seals. All designs of the retaining walls, soil foundation and soil backfills are composed according to the Caltrans guidelines and specifications. Analysis of Newmark method on type semi-gravity reinforced concrete cantilever retaining walls with and without sound wall is part of the overall research project. It applies Newmark methods to project dynamic seismic motion before the experiment. Calculations and examinations are leveraged by using Department and the National Cooperative Highway Research Program NCHRP Project -70 on Seismic Analysis and Design of Retaining Walls, Buried Structures, Slopes, and Embankments. (Anderson et al 008) ASSHTO adopted Newmark method will also be practiced in this study. 3

4 Figure Section view of the retaining walls with and without of sound wall Figure : Section view of the laminar soil box 4

5 Figure 3: Top view of the laminar soil box Figure 4: Detail Specific of the Retaining wall and soil box set up The above graphs present the experimental design of the Seismic Design Guidelines of Retaining Walls with/without Sound Wall project. Newmark method will be used to predict the seismic motion, displacement of the retaining wall be estimated. 5

6 IV. Methodology Newmark method is known as the Newmark sliding block method. It s the conservative displacement approach method at calculating the seismic deformation of the retaining walls. Newmark method analogy proposes of a block resting on a plane and rough horizontal surface then subjected to a horizontal acceleration motion (Wartman et al 003). As the earthquake induces inertia force into the block (retaining wall), the inertia moves the block to the direction opposite to the acceleration of the base. The block will shift when the sum of static and dynamic forces excess the yield resistance. Newmark method assumes that by double integrate the base yield acceleration; an accumulated displacement can be computed (Rauch 993). The first integration gives velocity of the block, the velocity reaches its peak when the acceleration reverses its direction and the acceleration reaches zero. Results of second integration produce the net displacement. Weight and size of the block is an important factor within the calculation. Newmark s sliding block model had been proved to be quite appropriate when considering with the permanent deformation results from the internal and external sliding and the sliding between the facing units (Cai and Bathurst 996). Newmark method seeks for the yield acceleration, which is the horizontal earthquake coefficient (k h ), when the safety factor of the sliding is.0. As the permanent deformation increase, the coefficient (k h ) will also increase. During the Newmark stability analysis, the k h will be adjusted according to the safety factor estimation. The study uses the Goal Seek function in the Microsoft-Excel to determine the most reasonable safety factor. The Mononobe-Okabe method had been developed in the 90s and is the extension of the Coulomb-Rankine sliding-wedge theory. Additional earthquake effects of horizontal and vertical inertia forces are introduced in the Coulomb-Rankine sliding-wedge theory. Pseudo-statis Mononobe-Okabe method is a forces approach method at determining the effects of lateral active soil pressure on the seismic structure (Cornell 970). Caltrans uses Mononobe-Okabe method at predicting the seismic deformation of the retaining wall (BDA Caltrans). Calculation of seismic earth pressure by Mononobe-Okabe method is required during internal stability check. The earth pressure equation used by this method is related to the direction and position of the soils. Based on the direction of soil and wall interaction, the earth pressure is divided into three types: Active earth pressure, Passive earth pressure and at rest earth pressure. Both M-O method and Newmark method required the calculation of the active earth pressure coefficient (Ka), the dynamic active earth pressure coefficient (Kae), and active earth pressure in both x-&y- direction(p) (Day 00). 6

7 The M-O method and Newmark method have some similarity and difference Table. Comparison of Mononobe-Okabe Method and Newmark Method Mononobe-Okabe Method Newmark Method Year Mononobe-Okabe 96 Kramer 996 Newmark 965, Richard-Elms 979 Approach Force Based approach Displacement Based approach Type of Method Pseudo-static limit equilibrium Sliding-block method Simplifying Assumptions. Mobilized soil Strength and active pressure.. Backfill is cohesionless 3. No water table present in the soil 4. Active wedge of Soil is homogenous cohesionless materials. Input Parameters a) kh = horizontal acceleration coefficient b) kv = vertical acceleration coefficient c) φ = friction angle of soil d) δ = angle of friction between wall and soil e) i = backfill slope angle f) Batter of retaining wall g) Unit weight of backfill soil h) Unit weight of weight of retaining wall i) Dimensions of retaining wall (H, W, C, B, F, thickness of the top of the stem) Output Data/Results a) Maximum moment, shear, and axial load demands b) Factor of Safety for sliding and overturning (want factor of safety >.5) Limitation/Draw back a) Horizontal seismic acceleration cannot exceed around 0.3 g b) Backfill slope cannot become greater than approximately 5 Adopted by Caltrans ASSHTO. The soil treated in a rigid, perfectly plastic manner;. Displacements of retaining wall occur along a single, well defined slip surface; 3. The soil does not undergo strength loss as a result of shaking 4. No water table present in the soil 5. Soil us homogenous and cohesion less materials. 6. Backfill is cohesive a) kh = horizontal acceleration coefficient b) kv = vertical acceleration coefficient c) φ = friction angle of soil d) δ = angle of friction between wall and soil e) i = backfill slope angle f) Batter of retaining wall g) Unit weight of backfill soil h) Unit weight of weight of retaining wall i) Dimensions of retaining wall (H, W, C, B, F, thickness of the top of the stem) j) PGA (peak ground acceleration) k) PGV (peak ground velocity) a) ky = yield acceleration (where factor of safety is equal to.0) b) Ground motion displacement of retaining wall a) Design motion time history is not often available, it rely on the PGA and PGV to calculate the displacement b) Show insensitivity to earthquake magnitude by using average acceleration time history 7

8 ASSHTO had adopted Newmark method in 99 (BDA Caltrans). ASSHTO Newmark method combines the Mononobe-Okabe method to find the yield acceleration (Kh) and further calculate the displacement of retaining wall seismic deformations. ASSHTO Newmark formulas generate the wall displacement based on the peak ground acceleration. Seismic deformation is estimated and compared by using the past earthquake acceleration time-history and ground motions. Newmark method overcomes Mononobe-Okabe s limitations. To find the displacement, Newmark method takes given yield accerations and set the safety factor in sliding to.0. To estimate seismic deformation, the Newmark method procedures are (ASSHTO 005, Tayatli and Li 008, Towhata 008, Cheng 008):. Determine the weight per unit foot for each component of the sliding block. The sliding block combines the retaining wall and the backfill soil which is on the heel of the retaining wall. The entire block has been seen as one ridge body.. Determine the lever arm about the toe of the retaining wall. The lever arm is the distance of the center of back fill soil and sections of retaining wall to the retaining wall toe. 3. Calculate the active earth pressure coefficient (Ka) and the dynamic active earth pressure coefficient (Kae) using the soil parameters and the M-O equations. The two equations can be found in the NCHRP Report-6. Active Earth pressure coefficient (Ka): cos ( φ β ) K a =, (Eq. ) sin( φ+ δ )sin( φ i) cos β cos( δ + β ) + cos( δ + β )cos( i β ) Dynamic active earth pressure coefficient (Kae): K ae = cosθ cos cos ( φ θ β ) β cos( δ + β + θ ) + sin( φ+ δ )sin( φ θ i) cos( δ + β + θ ) cos( i β ), (Eq. ) Where k θ = tan h ( ), (Eq. 3) k v k h &kv = horizontal and vertical ground accelerations respectively. 8

9 φ = angle of internal friction of soil δ = angle of wall friction ( / 3).φ i = Slope of ground surface behind wall β = slope of back of wall to vertical 4. Determine Kae. Kae = Kae Ka, (Eq. 4) To check your calculation, Kae need to be positive number. 5. Find active earth pressure P a and the seismic active earth pressure Pae in both x- and y- directions. Also, determine their Lever Arms to the toe of the retaining wall. Pa Pae = kaeγ sh, (Lever Arm Applied at 0.6H), (Eq. 6) = kaγ s H, (Lever Arm Applied at /3 H), (Eq. 5) Where, H = Height of the Retaining Wall 6. Calculate the sum of the soil resistance (Q) in the seismic state (x-, y- direction). Q = Σ weights of sliding block + P a + Pae, (Eq.7) 7. Determine the distance from the center of the footing to the resultant force. e = w Q + P ax L Pax + P aex L Paex P Q ay L Pay P Where, w = Width of the footing W = Weight of the sections of the retaining wall L Pax Paex Pay Paey aey L Paey q i= W L & L & L & L = Lever arm of the earth pressure i i, (Eq. 8) L i = Lever arm of the weight of the sections to the toe of retaining wall If e > (Width of footing)/6, then it s unsafe. Torque and moment will cause the wall 9

10 to shift and creates seismic deformations. 8. Determine the earth pressure below the footing (q and q ) and ignoring the effect of the footing key. q q Q w+ 6e = *, w w (Eq. 9) Q w 6e = *, w w (Eq. 0) If q is positive and q is negative, since the soil tensile strength is almost zero, there for earth pressure need be redistributed. ( q can not be zero) So, Lx = (3w 6e), (Eq. ) New q and q are, (Eq. ) q = Q 4Lx 3w+ 6e *, (Eq. 3) L L x x q = 0, (Eq. 4) Else, if both q and q are positive, redistribute the trapezoidal pressure graph to triangle shape. 9. Determine Q and Q, the earth pressures below the footing multiplied by their lever arms about the toe of the retaining wall. q Q = * L x, (Eq. 5) Q = 0, (Eq. 6) 0. Determine the Maximum Resisting force between the wall footing base and the foundation soil (R max ) R max = Q tanϕ + B c) + ( Q tanδ + ( B' B ) Ca), (Eq. 7) ( Where, 0

11 B = width of footing actually in compression c = cohesion of foundation soil (assume zero) Ca = adhesion between wall footing and foundation (assume zero) B = width of footing subtracting the width of the key. Set the Factor safety equation (Factor of safety need to be.0) and find the yield acceleration by changing the horizontal acceleration coefficient (k h ). Microsoft Excel is needed for this process. F Sliding Rmax + 0.5PPx =, (Eq. 8) P Where, P px = vertical component of passive earth pressure (assume zero) P = Pa + Pae So, in the Excel sheet, set the F equal to and use the Goal Seek function to seek for yield acceleration (N).. Last step. Using the ASSHTO and NCHRP Equation, determine the seismic deformation displacement of the retaining wall (d). ASSHTO use the equation: ASSHTO LRFD: V Ag N A 4 d = ( ), (Eq. 9) Where, V = 30 in/s (recommended by AASHTO) A = 0.5 g (recommended by AASHTO) g = 386 in/s² N = yield acceleration (k h when F sliding =.0) In NCHRP report -70, a new and adjusted logarithm equation was used. log( d) = log( k y / kmax ) log( k y / kmax ) 0.80log( PGA) +.59log( PGV ), Where, k y = yield acceleration k max = maximum seismic acceleration in the sliding block PGA = peak ground acceleration PGV = peak ground velocity (Eq. 0)

12 Result displacements from both ASSHTO and NCHRP are estimation of the seismic deformation. All results need to compare with experimental results and history data. V. Results The research project focuses on the seismic deformation of the retaining walls with and with out sound wall. California-Northridge and Turkey-Kocaeli earthquake recorded historic data set are used in this study. Table. Retaining Wall Dimension Width Lever Soil 7.75 ft 5.75 ft Area soil 4 ft Length Horizontal ft Area Horizontal ft Length Vertical 3.5 ft Area Vertical 6 ft Height of R.W 7.5 ft Table 3. Northridge and Kocaeli Earthquake Parameter Parameter Unit Parameter Unit γsoil 0 lbf/ft 3 V 30 in/s γwall 50 lbf/ft 3 A 0.5 g φ 30 Degree g 386 in/s² β 0 Degree N δ 0 Degree PGV 3.5 in/s, Kocaeli i 0 Degree PGA g, Kocaeli Kv 0 Northridge Kh Northridge PGV in/s, N.R K real max 0.6 Northridge PGA g, N.R Kh Kocaeli K real max 0.6 Northridge

13 Table 4. Newmark Method Calculation Results and Variables. Variables Northridge with Real Kh without soundwall Kocaeli with real Kh with out sound wall Adjusted Northridge With Sound wall Adjusted Northridge with out Sound wall Adjusted Kocaeli With Sound wall Adjusted Kocaeli With Sound wall θ Degree Ka Kae Kae Pa lbf/ft Pae lbf/ft L Pa ft L Pae Q lbf/ft e Unsafe q psf q psf Lx ft qx psf q' q' Units Q Q Rmax lbf/ft Fsliding D, ASSHTO LRFD in d, NCHRP N/A N/A in 3

14 By using the ASSHTO and NCHRP Newmark method in the calculation, the calculated seismic deformation displacement of Northridge earthquake is about 0.806in (ASSHTO) and in (NCHRP) for both trials both and without retaining wall. The Turkey Kocaeli earth quake s yield acceleration resulted displacement of 0.806in (ASSHTO) for both trials with and without retaining wall. By using the Goal seek function in the Microsoft Excel software, the closest Factor of safety is for all trials. All four trial shows sum of soil resistance equal to lbf/ft. Without the sound wall weight, both Northridge and Kocaeli data set resulted e (Distance from the center of the footing to the resultant force.) equal to.6866ft. With the sound wall on top, e equal to.6866ft. Weight of the retaining wall decreased the distance from the center of the footing to the resultant force and the earth pressure below the footing. The extra sound wall weight also changes Lx the lever arm of earth pressure to the toe. However, resulting earth pressures below the footing multiplied by their lever arms about the toe of the retaining wall is the same for both retaining walls with or without the sound wall. VI. Discussion Newmark block-on-plane models available in ASSHTO and NCHRP give two different estimations of the permanent earthquake induced displacements. The two answers are fairly small compare to the specimen scale. ASSHTO Newmark estimated 0.806in for both Northridge and Kocaeli earthquake. And NCHRP Newmark predicted in for Northridge earthquake. The estimations do not match. Experimental permanent earthquake induced displacements is needed for future comparison and confirmation. ASSHTO Model: This equation was derived from limited studies with earthquake accelerations. d V N = ( ) Ag A 4 ASSHTO model contains four parameters in the equation, in the ASSHTO report of structure of retaining wall, variable V, A, and g is given, the only unknown variable is N. AASHTO gives suggested values of 0.5g for A and 30 in/s for V to be used in the equation (ASSHTO 005). N is the yield acceleration k h when F sliding equal to.0. Calculating Yield acceleration can propose large range of error and multiple assumptions. M-O method features the Active earth pressure coefficient and Dynamic active earth pressure coefficient which are important for earth pressure estimations. However, by 4

15 change the Kh, denominator in the active earth pressure coefficient equation equal to zero and coefficient equation becomes default. Since the yield acceleration is limited by the earth pressure coefficients, the goal seek function find the closest resulting Kh to be 0.587g and the factor of safety equal to.9, which is large than.0. NCHRP Model: log( d) = log( k y / kmax ) log( k y / kmax ) 0.80log( PGA) +.59log( PGV ) For the NCHRP model, PGV and PGA is record from the each past earthquake. The important parameters are Ky and Kmax. For Northridge earthquake, Kmax is given by the report as.6. However, for the Kocaeli earthquake, since we do not have the critical PGV and PGA values, it was not calculated. For now, NCHRP method can only apply with U.S earthquake data history. PGV and PGA are only recorded in recent U.S. earthquake. Since NCHRP published the method on 008, the equation needs to be further studied and approved. Sound wall: Base on the data results and predictions from the study, weight of the sound wall does not affect the induced displacement of the retaining walls. However, the prediction is false according to the AASHTO Newmark method principal (ASSHTO 005). In the ASSHTO Newmark estimation, weight of the specimen is the primary variable in the Newmark method estimation. The weight of the specimen directly affects the result of the permanent induce displacement. From this study, by adding the sound wall on top, the resulting soil resistant (Q) had increased. However, the permanent displacements had not changed. Other important factors such as adjusted coefficient of horizontal acceleration, Maximum Resisting force between the wall footing base and the foundation soil, and factor of safety also did not change. The reason is because when applying the Goal-Seeking function, the safety factor was roughly estimated to be.95 (Goal is ). Application has also set the Kh to be and K real maximum to be 0.6 for both specimens with or without sound wall. Active earth pressure coefficient equation is the main cause of this invariable. When sequencing the parameters in the related equations, estimation is stopped when the denominator of the Active earth pressure coefficient equation reaches 0. 5

16 Limitations: Newmark method has a lot of limitations at calculating the permanent induced displacement. The Design motion time history is often not available, such as the Kocaeli earthquake (Yagi and Kikuchi 999). Earthquakes outside of the US often do not have a measured and clarified data. Parameters often need to be estimated or assumed in the calculations (Anderson et al 008). The ASSHTO method shows insensitivity to earthquake magnitude by using average acceleration time history. Other limitation of the ASSHTO model include Natural frequency is not considered, rotation is not considered, vertical acceleration is neglected, fill and foundation soil are not subject to significant build up of pore pressure due to shaking (Wartman et al 003, Rauch 993). From the study, it s notice that the retaining will yield faster at smaller acceleration and lower frequency. However, the frequency factor is not considered in the equations. Under real earthquake, the vertical acceleration can be critical and the retaining wall can be sensitive to the up lifting force and pressure. ASSHTO method is also assumed to have no water table on the backfill. The assumption limited the pore pressure against the wall. Pore pressure can increase the distance of the permanent displacement. Future study For future study and analysis, other earthquake cases are needed to apply with larger yield acceleration. Caltrans M-O method needed to be applied to compare with the ASSHTO and NCHRP Newmark models. Since the calculated permanent induce displacement is small, horizontal acceleration of both Northridge and Kocaeli will be doubled for ASSHTO estimation. VII. Conclusion By adopting the Northridge and Kocaeli earthquake Acceleration Time-History, Newmark methods predicted the minor permanent displacement of the retaining wall with and with out sound wall. Since the horizontal yield accelerations of both earthquakes were fairly small (Northridge-0.387g, Kocaeli-0.05g) and been predicted not to cause extreme permanent earthquake induced displacement, calculations of other massive earthquake acceleration time-histories are needed. The goal of the Caltrans project is to develop and examine seismic guidelines and designs for the retaining wall. To make the estimations reliable, study results need to compare with the experimental outcomes. 6

17 VIII. Acknowledgements This research was sponsored by California Department of Transportation (Caltrans) and supported by the George E. Brown, Jr. Network for Earthquake Engineering Simulation (NEES), Research Experience for Undergraduate (REU) Program; The National Science Foundation (NSF); NEES Englekirk Center; University of California Davis (UCD); University of California San Diego (UCSD). Thanks gratefully to the PI mentor Prof. Lijuan Dawn Cheng; Graduate student Erin Mock; REU program advisor Tezeswi Tadepalli; Tess Kinderman, Lelli Van Den Einde; and Englekirk shake table center faculties and staffs. 7

18 IX. Appendices. Variables and Parameters γs = Unit weight of soil δ = Angle of friction range from (f/) to (f/3) for dry sand φ = Slope of ground surface behind wall (34 degrees for sand) θ Kv = Coefficient of vertical acceleration Kh = Coefficient of Horizontal acceleration γw = Unit weight of retaining wall i NCEL) = Seismic inertia angle q = tan- [Kh/(-Kv)] = Slope of ground surface behind wall (b in β = Slope of back of the wall to vertical (q in NCEL) Ka = Active earth pressure coefficient Kae = Dynamic active earth pressure coefficient k h &kv = horizontal and vertical ground accelerations respectively. φ = angle of internal friction of soil δ = angle of wall friction ( / 3).φ i = Slope of ground surface behind wall β = slope of back of wall to vertical P a = active earth pressure P ae = seismic active earth pressure H = Height of the Retaining Wall Q = the soil resistance w = Width of the footing W = Weight of the sections of the retaining wall L Pax & L & L & L = Lever arm Paex Pay of the earth pressure Paey the toe of retaining wall e = distance from the center of the footing to the resultant force. q and q = earth pressure below the footing Lx = Lever of earth pressure Q and Q = the earth pressures below the footing multiplied by their lever arms about the toe of the retaining wall. R max = Maximum Resisting force between the wall footing base and the foundation soil B = width of footing actually in compression c = cohesion of foundation soil (assume zero) Ca = adhesion between wall footing and foundation (assume zero) B = width of footing subtracting the width of the key Fsilding = Factor of safety need to be.0 P px = vertical component of passive earth pressure (assume zero) P = Pa + Pae d = deformation displacement of the retaining wall. V = 30 in/s (recommended by AASHTO) A = 0.5 g (recommended by AASHTO) g = 386 in/s² N = yield acceleration (k h when F sliding =.0) k y = yield acceleration k max = maximum seismic acceleration in the sliding block PGA = peak ground acceleration PGV = peak ground velocity L i = Lever arm of the weight of the sections to 8

19 X. Reference Anderson, Donald G., Geoffrey R. Martin, Ignatius Lam, and Joe Wang. Seismic Analysis and Design of Retaining Walls, Buried Structures, Slopes, and Embankments. Publication. National Cooperative Highway Research Program, 008. Print. ASSHTO. ASSHTO LRFD Bridge DESIGN specifications. Publication no.. ASSHTO, 005. Print. Bridge Design Specification, California Department of Transportation, Structure Design Manual Bridge Design Aids Manual (BDA), California Department of Transportation, Structure Design Manual Cai, Z., and R.J. Bathurst. "Seismic-induced permanent displacement of geosynthetic-reinforced segmental retaining walls." Can. Geotech 33 (996): Print. Cornell University. Lateral stresses in the ground and design of earth-retaining structures. Tech. no.. New York: American Society of Civil Engineers, 970. Print. Day, Robert W. Geotechnical earthquake engineering handbook. New York: McGraw-Hill, 00. Print. Lijuan Dawn Cheng, Seismic Design Guidelines of Retaining Walls with/without Sound Wall, University of California Davis, March 3, 008 Rauch, Alan F. "Review of methods for predicting displacement in Lateral Spreads." EPOLLS: An Empirical Method for Predicting Surface Displacements Due to Liquefaction-Induced Lateral Spreading in Earthquake. National Sicnce Fundation, Print. Seco e Pinto, Pedro S. Seismic behavior of ground and geotechnical structures proceedings of a discussion special technical session on earthquake geotechnical engineering during fourteenth International Conference on Soil Mechanics and Foundation Engineering, Hamburg, Germany, 6- September 997. Rotterdam: A.A. Balkema, 997. Print. 9

20 Tavatli, Dary, and Jane Li. Seismic analysis of Semi-Gravity Retaining Walls. Thesis. University of California Davis, 008. Print. Tonias, Demetrios E., and Jim J. J. Zhao. Bridge engineering. nd ed. McGraw-Hill Professional, 006. Print. Towhata, Ikuo. Geotechnical Earthquake Engineering. New York: Springer, 008. Print. Wartman, Joseph, Jonathan D. Bray, and Raymond B. Seed. "JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING." Inclined Plane Studies of the Newmark Sliding Block Procedure (003): Print. Wieland, Martin, Qingwen Ren, and John S. Y. Tan. New developments in dam engineering. 4th ed. Taylor & Francis. Google Book. Google, 8 Oct Web. 5 Aug < lse>. Yagi, Yuji, and Masayuki Kikuchi. "Source rupture process of the Kocaeli, Turkey, earthquake of August7, 999, obtained by joint inversion of near-field data and teleseismic data." Earthquake Research Institute, The University of Tokyo: -. Print. 0