Inclined retaining walls with slopes less than perpendicular are appropriate candidates in several

engineering problems. Yet, to the knowledge of authors, only a few analytical solution for calculation of active earth

pressure on such walls, which will be usually smaller than the same pressure on vertical ones, has been presented

neither in research papers nor in design codes. Considering limit equilibrium concept in current research, a new

formulation is proposed for determination of active earth pressure, angle of failure wedge and application point of

resultant force for inclined walls. Necessary parameters are extracted assuming the pseudo-static seismic coefficient

to be valid in earthquake conditions. Moreover, based on Horizontal Slices Method (HSM) a new formulation is

obtained for determining the characteristics of inclined walls in granular and or frictional cohesive soils. Findings of

present analysis are then compared with results from other available methods in similar conditions and this way, the

validity of proposed methods has been proved. Finally according to the results of this research, a simplified relation

for considering the effect of slope in reduction of active earth pressure and change in failure wedge in inclined

retaining walls has been proposed.

For calculating the natural frequency of structures such as buildings, chimneys, bridges and silos appropriate analytical

formulas exist. However, in the case of retaining walls undergoing the soil pressure at one side, calculating the natural frequency

is not a straightforward task and requires the effects of soil-structure interactions to be considered. By modeling the soil as series

of linear springs, a new formulation is presented in this article, to calculate the natural frequency of retaining walls. This formula

considers the vertical cross sectional width change, and hence, enables us to calculating the natural frequency of retaining walls

with different types of backfill. The geometrical properties of the retaining walls and its bending rigidity together with the soil’s

modulus of elasticity and its Poisson’s ratio are the most important parameters to calculate. A comparison of the results for

retaining walls with constant cross section obtained from the suggested method with those of the software analyses was carried

out and good agreement was detected. A second comparison of the results with those of other researchers revealed that the natural

frequency of flexible retaining wall is an upper bound for natural frequency of rigid walls. The Selected shape function is also

very close to the real shape mode.

Most of the proposed methods for obtaining the free vibration natural frequency of the retaining wall have been presented, assuming the behavior of the wall in two-dimensional domain, and they are not able to express the three-dimensional behavior of these structures in a satisfying manner. In this paper, the plate theory is employed to analyze the free vibration of wall-soil system in three-dimensional domain. So the retaining wall is modeled as a clamped-free plate and the stiffness of the soil existing behind the wall is modeled as a set of springs. Using the approximate Rayleigh method, new analytical expression for obtaining the free vibration natural frequencies for the three first modes of the wall is represented. The results of the proposed model are compared with both the results of the other researchers and the ones from finite element method (FEM). They are also compared with the results of a full-scale experiment and it shows a good agreement. The comparison shows that modeling the wall in two-dimensional form is not accurate enough to calculate all the natural frequencies of the wall. The results of this paper show that there is a considerable difference between two- and three-dimensional behavior of the walls. The proposed method also gives the free vibration natural frequencies of the wall extensional modes with an acceptable accuracy. Finally, the effect of tensile and compressive behavior of the soil on the fundamental frequency is studied. This research can be considered as a new field in three-dimensional calculation of the retaining walls.