Earthquake Design and Evaluation of Concrete Hydraulic Structures

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4-7. Permanent Sliding Displacement EM 1110-2-6053 1 May 2007 a. Retaining walls and dams that are stable under static loading conditions may slide under severe earthquake ground motions, if the combined static plus seismic shear demands exceed sliding resistance along any potential sliding planes. The acceleration that generates sufficient force to initiate sliding is termed the critical acceleration (ac). Every time the ground acceleration exceeds the critical acceleration the structure will slide. The ratio of the critical acceleration to the acceleration of gravity (ac/g), is termed the yield coefficient (ky). The ratio of the peak ground acceleration (am) to the acceleration of gravity (am/g), is termed the seismic coefficient (A). The expected permanent displacement of a retaining wall or dam treated as a rigid block can be estimated using the Newmark sliding block analogy (Newmark, 1965). b. As shown in Figure 4-9, each time the ground acceleration exceeds the critical acceleration (ac), some displacement at the structure-foundation interface will occur, and these will add up throughout the ground shaking and result in a final sliding permanent displacement. The total permanent sliding displacement will be a function of the earthquake characteristics such as duration and intensity, with the major factor being the number of times the critical acceleration is exceeded. As a part of extensive parametric studies, Richards and Elms have suggested the following equation for estimating permanent displacement, (Richards and Elms, 1977). Where: Δ = 0. 087 2 vg ⎡k y Ag ⎢ ⎣ A ⎤ ⎥ ⎦ −4 vg = The peak ground velocity of the earthquake. (4-8) For preliminary design purposes the peak ground acceleration can be assumed equal to: vg = 0.30A (distance in inches) vg = 0.75 A (distance in meters) The relationship described above then can be simplified to: 5 A Δ = 0. 2 (inches) (4-9a) k 4 y 4 y 5 A Δ = 5 (mm) (4-9b) k A plot of the above relationship is shown in Figure 4-10. This plot can be used as a preliminary evaluation tool for estimating permanent displacement in retaining walls and dams. Additional information relative to the sliding displacement of dams can be found in Zhang and Chopra (1991). 4-17
EM 1110-2-6053 1 May 2007 4-18 Acceleration Permanent Displacemen Time Time Figure 4-9. Permanent Sliding Displacement Permanent Displacement, D (inches) 10 9 8 7 6 5 4 3 2 1 0 Ky/A = 0.3 Ky/A = 0.4 Ky/A = 0.5 Ky/A = 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Peak Ground Acceleration, A (in g's) Figure 4-10. Permanent Displacement as a Function of ky and A ac Δ am
Page 1: US Army Corps Of Engineers Earthqua
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Page 8 and 9: Appendix A References EM 1110-2-605
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Page 20 and 21: EQ V EQ c) Shear (diagonal tension)
Page 22 and 23: ⎛ h − a ⎞ M r = P⎜ ⎟ ⎝
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Page 30 and 31: Force F FY Equal Areas δy δE δU
Page 32 and 33: Chapter 4 Methods of Seismic Analys
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Page 42 and 43: F - FORCE LINEAR - INITIAL TANGENT
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Earthquake Design and Evaluation of Concrete Hydraulic Structures

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