• Geomechanics and Engineering
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• v.24 no.4
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• pp.371-388
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• 2021

A novel flexibility-based beam-foundation model for inelastic analyses of beams resting on foundation is presented in this paper. To model the deformability of supporting foundation media, the Winkler-Pasternak foundation model is adopted. Following the derivation of basic equations of the problem (strong form), the flexibility-based finite beam-foundation element (weak form) is formulated within the framework of the matrix virtual force principle. Through equilibrated force shape functions, the internal force fields are related to the element force degrees of freedom. Tonti's diagrams are adopted to present both strong and weak forms of the problem. Three numerical simulations are employed to assess validity and to show effectiveness of the proposed flexibility-based beam-foundation model. The first two simulations focus on elastic beam-foundation systems while the last simulation emphasizes on an inelastic beam-foundation system. The influences of the adopted foundation model to represent the underlying foundation medium are also discussed.

• Geomechanics and Engineering
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• v.24 no.1
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• pp.15-28
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• 2021

Digging well foundation has been widely used in railway bridges due to its good economy and reliability. In other instances, bridges with digging well foundation still have damage risks during earthquakes. However, there is still a lack of knowledge of lateral behavior of digging well foundation considering the soil-foundation interaction. In this study, scaled models of bridge pier-digging well foundation system are constructed for quasi-static test to investigate their lateral behaviors. The failure mechanism and responses of the soil-foundation-pier interaction system are analyzed. The testing results indicate that the digging foundations tend to rotate as a rigid body under cyclic lateral load. Moreover, the depth-width ratio of digging well foundation has a significant influence on the failure mode of the interaction system, especially on the distribution of foundation displacement and the failure of pier. The energy dissipation capacity of the interaction system is discussed by using index of the equivalent viscous damping ratio. The damping varies with the depth-width ratio changing. The equivalent stiffness of soil-digging well foundation-pier interaction system decreases with the increase of loading displacement in a nonlinear manner. The absolute values of the interaction system stiffness are significantly influenced by the depth-width ratio of the foundation.

• Earthquakes and Structures
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• v.21 no.6
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• pp.641-652
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• 2021

Digging well foundation has been widely used in railway bridges due to its good economy and reliability. In other instances, bridges with digging well foundation still have damage risks during earthquakes. In this study, a new type of digging well foundation with prefabricated roots was proposed to reduce earthquake damage of these bridges. Quasi-static tests were conducted to investigate the failure mechanism of the root digging well foundation, and then to analyze seismic behaviors of the new type well foundation. The testing results indicated that these prefabricated roots could effectively limit the rotation and uplift of the digging well foundation and increase the lateral bearing capacity of the digging well foundation. The elastic critical load and ultimate load can be increased by 69% and 36% if prefabricated roots were added in the digging well foundation. The prefabricated roots drived more soil around the foundation to participate in working, the stiffness of the bridge pier with root digging well foundation was improved. Moreover, the root participation could improve the energy dissipation capacity of soil-foundation-pier interaction system. The conclusions obtained in this paper had important guiding significance for the popularization and application of the digging well foundation with prefabricated roots in earthquake-prone zones.

• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.505-511
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• 2018

Recently, a new foundation model called "Dynamic foundation model" was proposed for the dynamic analysis of structures on the foundation. This model includes a linear elastic spring, shear layer, viscous damping and the special effects of mass density parameter of foundation during vibration. However, the relationship of foundation property parameters with the experimental parameter of the influence of foundation mass also has not been established in previous research. Hence, the purpose of the paper presents a simple experimental model in order to establish relationships between foundation properties such as stiffness, depth of foundation and experimental parameter of the influence of foundation mass. The simple experimental model is described by a steel plate connected with solid rubber layer as a single degree of freedom system including an elastic spring connected with lumped mass. Based on natural circular frequencies of the experimental models determined from FFT analysis plots of the time history of acceleration data, the experimental parameter of the influence of foundation mass is obtained and the above relationships are also discussed.

• Geomechanics and Engineering
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• v.36 no.4
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• pp.329-341
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• 2024

Retaining structures are one of the most important elements in the stabilization of excavations and slopes in various engineering projects. Mechanically stabilized earth (MSE) walls are widely used as retaining structures due to their flexibility, easy and economical construction. These benefits are especially prominent for projects built on soft and weak foundation soils, which have relatively low resistance and high compressibility. For high retaining walls on weak foundations, conventional design methods are not cost-effective. Therefore, two alternative solutions for different foundation weakness are proposed in this research: optimized multi-tiered MSE walls and single tier wall with foundation improvement. The cost optimization considers both the construction components and the land price. The results show that the optimal solution depends on several factors, including the foundation strength and more importantly, the land price. For low land price, the optimized multi-tiered wall is more economical, while for high land price (urban areas), the foundation improvement is preferable. As the foundation strength decreases, the foundation improvement becomes inevitable.

• Coupled systems mechanics
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• v.12 no.1
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• pp.83-102
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• 2023

First introduced in 2016, the dynamic foundation model is an interesting topic in which the foundation is described close to reality by taking into account the influence of the foundation mass in the calculation of oscillation and is an important parameter that should be considered. In this paper, a follow-up investigation is conducted with the object of the Mindlin plate on a nonlinear dynamic foundation under moving loads. The base model includes nonlinear elastic springs, linear Pasternak parameters, viscous damping, and foundation mass. The problem is formulated by the finite element analysis and solved by the Newmark-β method. The displacement results at the center of the plate are analyzed and discussed with the change of various parameters including the nonlinear stiffness, the foundation mass, and the load velocity. The dynamic response of the plate sufficiently depends on the foundation mass.

• Earthquakes and Structures
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• v.15 no.2
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• pp.215-225
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• 2018

To reach a better foundation treatment project, an optimized analysis of composite foundation was studied in the field of hydraulic engineering. Its unique characteristics in hydraulic engineering were concluded. And, the overall and detailed analysis of the composite foundation model established was carried out. The index parameters of the vertical reinforced rigid pile composite foundation were formulated. Further, considering the unique role of cushion in hydraulic engineering, its penetration and regularity were analyzed. Then, comparative and optimized analyses of cushion multistage physical dimensions and multistage material characteristics were established. The parameters of the piles distance were optimized and the multilevel scientific and reasonable parameters information was obtained. Based on the information of these parameters, the practical application was verified. It effectively supported the effective application of vertical reinforcement rigid pile composite foundation in hydraulic engineering. The service mechanism of composite foundation was fully analyzed.

• Structural Engineering and Mechanics
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• v.27 no.5
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• pp.555-574
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• 2007

Static response of an elastic beam on a two-parameter tensionless foundation is investigated by assuming that the beam is symmetrically subjected to a uniformly distributed load and concentrated edge loads. Governing equations of the problem are obtained and solved by pointing out that a concentrated edge foundation reaction in addition to a continuous foundation reaction along the beam axis in the case of complete contact and a discontinuity in the foundation reactions in the case of partial contact come into being as a direct result of the two-parameter foundation model. The numerical solution of the complete contact problem is straightforward. However, it is shown that the problem displays a highly non-linear character when the beam lifts off from the foundation. Numerical treatment of the governing equations is accomplished by adopting an iterative process to establish the contact length. Results are presented in figures to demonstrate the linear and non-linear behavior of the beam-foundation system for various values of the parameters of the problem comparatively.

• Geomechanics and Engineering
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• v.34 no.6
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• pp.649-664
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• 2023

Structural inertial interaction is a representative the effect of dynamic soil-foundation-structure interaction (SFSI), which leads to a relative displacement between soil and foundation, period lengthening, and damping increasing phenomena. However, for a system with a significantly heavy foundation, the dynamic inertia of the foundation influences and interacts with the structural seismic response. The structure-to-foundation mass ratio (MR) quantifies the distribution of mass between the structure and foundation for a structure on a shallow foundation. Although both systems exhibit the same vertical factor of safety (FS_v), the MR and corresponding seismic responses attributed to the structure and foundation masses may differ. This study explored the influence of MR on the permanent deformation and seismic response of soil-foundation-structure system considering SFSI via numerical simulations. Given that numerous dimensionless parameters of SFSI described its influence on the structural seismic response, the parameters, except for MR and FS_v, were fixed for the sensitivity analysis. The results demonstrated that the foundation inertia of heavier foundations induced more settlement due to sliding behavior of heavily-loaded systems. Moreover, the structural inertia of heavier structures evidently exhibited foundation rocking behavior, which results in a more elongated natural period of the structure for lightly-loaded systems.

• Structural Engineering and Mechanics
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• v.38 no.5
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• pp.573-592
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• 2011

Comprehensive and accurate analysis of a finite foundation beam is a challenging engineering problem and an important subject in foundation design. One of the limitation of the traditional Winkler elastic foundation model is that the model neglects the effect of the interface resistance between the beam and the underneath foundation soil. By taking the beam-soil interface resistance into account, a deformation governing differential equation for a finite beam resting on the Winkler elastic foundation is developed. The coupling effect between vertical and horizontal displacements is also considered in the presented method. Using Galerkin method, semi-analytical solutions for vertical and horizontal displacements, axial force, shear force and bending moment of the beam under symmetric loads are presented. The influences of the interface resistance on the behavior of foundation beam are also investigated.