Analytical evaluation of the dynamic distress of rigid fixed-base retaining systems

Seismic pressures on rigid cantilever walls retaining linear poroelastic soil: An exact solution

“…2 shows the normalized base shear Q B versus L/H for an elastic soil with v ¼ 0.30, ρ s ¼2660 kg/m 3 , G ¼ 2:76 Â 10 7 N=m 2 , H ¼8.00 m and ω n ¼ω/ω 1 (with ω 1 ¼ 200 rad/s). It is observed that the results of the present analysis are very close to the "exact" elastic soil ones obtained by Wood [9], especially if one takes into account that the latter results were taken graphically from [10,12] Fig. 3 shows the normalized base shear Q B versus frequency ω for the same elastic soil as above obtained by the present analysis for various values of L/H.…”

“…3 shows the normalized base shear Q B versus frequency ω for the same elastic soil as above obtained by the present analysis for various values of L/H. The maximum values of Q B are from left to right 3.89, 5.50, 5.30, 4.52, 4.14 and 2.41 which are very close to the corresponding "exact" elastic soil values 3.80, 5.40, 5.40, 4.60, 4.04 and 2.44 obtained by Papazafeiropoulos and Psarropoulos [12], especially if one takes into account that the latter results were taken graphically from [12].…”

“…Thus, one can mention here Mononobe and Matsuo [6], Okabe [7] and Seed and Whitman [8] from the first category, Wood [9], Veletsos and Younan [10,11], Papazafeiropoulos and Psarropoulos [12] and Brandenberg et al [13] from the second category and Wu and Finn [14], Al Atik and Sitar [15], and Wilson and Elgamal [16] from the third category.…”

“…In doing so, the present paper utilizes the idea of Papazafeiropoulos and Psarropoulos [12] to expand the unknown displacement and pressure functions in Fourier sine and cosine series along the horizontal direction to reduce the problem to a system of ordinary differential equations in the frequency domain, which can be solved analytically in an exact manner. The authors of [12] used this idea to solve the easier case of elastic soil and thus obtain its exact solution. Their exact solution is less complicated than the exact analytical solution of Wood [9] obtained by modal superposition, which would be extremely difficult to be applied to the present poroelastic case.…”

Influence of Wall Flexibility on Seismic Earth Pressures in Vertically Homogeneous Soil

“…Furthermore, the retained soil is taken as an elastic soil layer resting on a rigid base, and the soil layer thickness is the same as the wall height (i.e., the "bathtub" configuration). Notable examples of this method are Wood (1973), Arias et al (1981), Veletsos and Younan (1994), Younan and Veletsos (2000), Ostadan (2005), Papazafeiropoulos and Psarropoulos (2010), Kloukinas et al (2012) and Vrettos et al (2016). These methods tend to produce seismic earth pressures that are higher than M-O pressures because: (1) the wall is usually assumed to be rigid, (2) the soil layer is excited at its first-mode frequency, producing significant depth-variations in ground motions, which in turn produce large relative wall-soil displacements.…”