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.

In this paper, the probabilistic seismic performance of vertically irregular steel buildings, considering soil-structure interaction effects, is evaluated. Various irregular distributions of structural properties, including mass, stiffness and strength along the height of three-dimensional moment resisting steel frames were intended. The finite element model of soil medium was created with solid elements below the structure. The nonlinear material behavior of soil was considered as well. Nonlinear incremental dynamic analysis was performed to evaluate the flexible-base structural performance in the framework of probabilistic performance-based earthquake engineering. According to the median curves of intensity-demand of structures, it is concluded that non-uniform height-wise distribution of lateral resistance properties of steel structures varies the displacement demand and the seismic capacity of the irregular frames, compare to the regular structure. The capacity variation of most irregular frames is more obvious at the nonlinear phase of structural behavior. Due to the foundation flexibility, the damage concentration raises in the bottom floor and the irregularity increase the seismic demands of the lower floors of the system. Among all the irregular steel frames, the average increase of the displacement demand and reduction of the seismic capacity are maximal for the strength and concurrent variation of stiffness and strength irregularity models, respectively. Additionally, mass irregularity shows minor influence in the seismic demand and capacity variations of the steel frames. The predominant influence of stiffness and strength irregularities (soft and weak story) is observed in reduction of the structural ductility factor and the mean annual frequency of exceeding limit states.

It is vital to control the settlement of ultra-high voltage and long span tower foundation because of the difficult construction and strict deformation control. Based on the thinking of deformation compatibility, the mechanical model of deformation compatibility between pile and soil is established. Relying on the long span tower project Lingzhou–Shaoxing ±800 kV DC transmission lines across the Yangtze River, through checking ultimate bearing capacity of existing pile foundation, it can be obtained that the present design foundation can effectively meet the upper 200–220 t load, but it cannot meet the load requirements about 300 t in the construction. The failures of tower foundation mainly display that piles cut into the soil with penetration type in the early condition. With the load increasing, the shallow soil and infrastructure gradually damage with the whole cap sinking, cushion layer destruction and the surrounding soil uplifting. As a result, tower foundation is unable to withstand the effect of upper overload and the whole tower becomes shear failure. The treatment scheme was proposed that it can improve the cushion thickness and strength combined with grouting consolidation to soil around the piles. Thus, the stability of tower foundation improves significantly and settlement was controlled within the permitted range of below 10 mm, which can meet the structure requirements. The results of numerical simulation based on deformation compatibility between pile and soil coincide well with field measured results.

This paper proposes a modified strain wedge (MSW) model for nonlinear analysis of laterally loaded single piles in clays. The MSW model is used to calculate the soil resistance under increasing pile deflection. The stress–strain behavior of clays in the MSW, which is needed to calculate the soil resistance, is described in terms of both hyperbolic and bilinear stress–strain relationships. The subgrade reaction modulus of soil below the MSW is assumed to equal the conventional subgrade reaction modulus and to remain constant under the lateral loading of the pile. The applicability of the proposed model was verified by eight case histories. The results indicate that (1) the predicted results are consistent with the measurements for all eight full-scale tested piles; (2) the bilinear stress–strain relationship is not recommended for clays because the clays usually have a large ε50 and, thus, they exhibit a linear behavior in the MSW during loading; (3) the predicted pile response is less sensitive to the effective friction angle than to the undrained shear strength; and (4) the proposed MSW model applies to normally consolidated clays and to overconsolidated clays until they reach their peak strength.