## What is/are Foundation Model?

Foundation Model - A series of soil-foundation models were prepared in a laminar shear box with a dimension of 1.^{[1]}The second model has the same characteristics of the first; however, it is included in it a foundation modeled like a spring with bidirectional rotational stiffness.

^{[2]}We validated the model in four additional studies, testing replication of the 7-foundation model in data including from US, Australia, and China (total N = 9,225).

^{[3]}The results of this test are used in the foundation model test.

^{[4]}As the boundary condition of jack-up systems, the foundation model of offshore structures affects the vibration mode and structural behavior of leg structure.

^{[5]}Elliptical, trapezoidal and inverted folded bottom of foundation models are tested and compared with the reference conventional square flat ones.

^{[6]}A novel flexibility-based beam-foundation model for inelastic analyses of beams resting on foundation is presented in this paper.

^{[7]}The substrate is represented by a foundation model.

^{[8]}As the boundary condition, the foundation model of offshore structures affects the vibration mode of a structure and, consequently, the behavioral and structural analysis results as well.

^{[9]}Finally, the effects of non-coaxiality on the bearing capacity of foundation are analyzed and the results show that the introduction of non-coaxial plasticity reduces the overall stiffness of the foundation model, and neglecting the non-coaxial influences may lead to unsafe designs.

^{[10]}Sway-Rocking (SR) spring system is a foundation modelling method in which a 2 × 2 spring stiffness matrix represents the foundation stiffness at seabed level.

^{[11]}The modified beam-on-foundation model is then established and verified and the model indicates that the polyurea coatings mainly influence the displacements of the tanks by increasing the area density and bending moments of the tanks.

^{[12]}5 on Anatomy, FMA-NCI (Foundation Model of Anatomy-National Cancer Institute), and FMA-SNOMED data sets, respectively.

^{[13]}Through the advance of computational technology, the use of an integrated soil and foundation model may suggest a behavioral trend to obtain a more realistic modeling for the structural element being studied.

^{[14]}The type and spacing of reinforced materials also have a significant influence on the uplift bearing capacity of the foundation model in reinforced aeolian sand, and the effect of reinforcement works until the end of the loading process.

^{[15]}The model is based on the support vector machine regression algorithm (SVR) combined with multiple variables, and then the foundation model is integrated by the weighted average integration method.

^{[16]}stl format), with a total of 313 763 375 polygons, including 10 times more information than the foundation model.

^{[17]}It provides a brief overview of the foundation models based on Winkler's original foundation model, as well as a detailed analysis of beams resting on Winkler’s foundation using the finite element method.

^{[18]}

## two parameter elastic

In this paper, based on the two-parameter elastic foundation model, a representative volume element (RVE) method is used to establish the deflection curve equation of the cutting fiber as the thickness of the uncut material changes.^{[1]}In this paper, based on the refined two-parameter elastic foundation model, the bending problem for a finite-length beam on Gibson elastic soil is solved.

^{[2]}According to the force characteristic of lattice beam, used the Two-parameter elastic foundation model to deduce the answer of internal forces of concentrated force on the finite-length beam, and calculate load distribution coefficient of node, then get the internal forces of lattice beam, used the analytical solution combined with practical engineering, and compared with numerical solution of simulation of ABAQUS finite element software, to verify the correctness of theoretical solution, and analyze its deficiency.

^{[3]}Elastic matrix is formulated with a two-parameter elastic foundation modelled by combining Winkler and Pasternak assumptions.

^{[4]}

## finite element software

By studying the safety performance of the jacking tower under the condition of uneven foundation settlement in the mined-out area, this paper uses the finite element software Midas GTS NX to establish the jacked-up transmission tower-foundation model and the jacked-up transmission tower line-foundation model.^{[1]}This study uses ABAQUS finite element software to establish a composite bucket foundation model for finite element analysis.

^{[2]}

## Elastic Foundation Model

The beam on elastic foundation model, previously developed for timber-to-concrete connections, was extended to consider the flexibility of both media where the screw is inserted.^{[1]}A two-stage method of modified Peck formula and Winkler elastic foundation model was used to investigate the additional displacement and internal force of pile.

^{[2]}In this paper, based on the two-parameter elastic foundation model, a representative volume element (RVE) method is used to establish the deflection curve equation of the cutting fiber as the thickness of the uncut material changes.

^{[3]}In this study, the crack lengths in adhesively bonded double cantilever beam (DCB) test specimens have been determined using the digital image correlation technique in combination with an elastic foundation model.

^{[4]}In addition, the paper establishes a thin plate on a nonlinear elastic foundation model by adopting semianalytical and seminumerical method and obtains the relational expression between roof deflection, roof stress, and backfilling material’s compressive deformation.

^{[5]}In this paper, based on the refined two-parameter elastic foundation model, the bending problem for a finite-length beam on Gibson elastic soil is solved.

^{[6]}The twoparameter elastic foundation model is selected as Pasternak foundation that takes into account a shear layer at the end of linear springs of Winkler foundation.

^{[7]}The estimate of failure probability on the inclined section from the action of transverse forces, as well as the total probability of the limit States of reinforced concrete beams with probabilistic strength parameters lying on an elastic Foundation model V.

^{[8]}According to the force characteristic of lattice beam, used the Two-parameter elastic foundation model to deduce the answer of internal forces of concentrated force on the finite-length beam, and calculate load distribution coefficient of node, then get the internal forces of lattice beam, used the analytical solution combined with practical engineering, and compared with numerical solution of simulation of ABAQUS finite element software, to verify the correctness of theoretical solution, and analyze its deficiency.

^{[9]}However, across all simulations, the Hunt-Crossley model produced a greater proportion of accurate finger-tip force simulations than the Elastic Foundation model, suggesting that the Hunt-Crossley contact model may be preferable for modeling the fingerpad.

^{[10]}Elastic matrix is formulated with a two-parameter elastic foundation modelled by combining Winkler and Pasternak assumptions.

^{[11]}The interactions between nanowires and medium are simulated by the Winkler elastic foundation model.

^{[12]}Given the combined sidewall multi-stiffness function of the membrane feature and structural deformation, the elastic foundation model acts as an independent module to enrich the flexible belt beam model.

^{[13]}Double and multiple-Beam System (BS) models are structural models that idealize a system of beams interconnected by elastic layers, where beam theories are assumed to govern the beams and elastic foundation models are assumed to represent the elastic layers.

^{[14]}For each separation rate, the interfacial properties were extracted by a beam on elastic foundation model and an iterative method, assuming a bilinear traction-separation relation.

^{[15]}This paper describes the effects of soil non-homogeneity, the soil–structure interaction and the two-parameter elastic foundation model on the free vibration of Euler–Bernoulli beams.

^{[16]}The deflection-differential equation of the roof rock beam is established based on the Pasternak elastic foundation model.

^{[17]}The elastic foundation model (EFM) and stick–slip friction model are used to describe the normal contact and tangential friction force between bushing and pin, respectively.

^{[18]}Based on the theory of the Winkler elastic foundation model, a mechanical model of a prestressed anchor cable lattice beam at the tension stage was established.

^{[19]}

## Pasternak Foundation Model

Parameter identification of Pasternak foundation models (PFM) is never satisfactory, which discourages the application and popularization of PFM.^{[1]}The present work is a pioneering study on the contact mechanics including Pasternak foundation model.

^{[2]}In this paper, an analytical approach is proposed to investigate the nonlinear dynamic analysis of porous eccentrically stiffened (PES) double curved shallow auxetic shells with negative Poisson’s ratio (NPR) subjected to blast, mechanical and thermal loads resting on Visco-Pasternak foundation model.

^{[3]}In this study, a mechanical model of the bottom lining under the nonuniform frost heave deformation is built based on the Euler–Bernoulli beam and the Pasternak foundation model, and the analytical solution of the model is obtained.

^{[4]}The research results show that for certain working conditions and soil parameters, there will be an optimal pipeline diameter D, which minimizes the deformation of the buried pipeline under the rockfall impact; based on Pasternak foundation model and Winker foundation model to calculate the rockfall impact load on buried pipe deformation respectively, it is found that the difference between these two foundation models on pipe deformation is small.

^{[5]}The panel and the foundation respectively are modeled based on the third-order shear deformation theory (TSDT) and the Winkler-Pasternak foundation model.

^{[6]}In the second stage, the additional stress calculated using the greenfield displacement is imposed on the existing tunnel resting on Pasternak foundation model.

^{[7]}Second, the shear-displacement method and improved Pasternak foundation model incorporating the impact of lateral soil displacement are introduced to investigate the pile-soil interaction.

^{[8]}The Brinson model, nonlocal elasticity and Pasternak foundation model are used to take into account shape memory alloy effects, the influences of being size-dependent and the effects of the elastic matrix on the vibrational behavior, respectively.

^{[9]}In order to effectively predict the pipeline displacement induced by water leakage during tunnel construction, based on the Pasternak foundation model, a two-stage analysis method was used to establish the equilibrium differential equations of pipeline.

^{[10]}For modeling surrounding elastic medium, the nonlinear Winkler–Pasternak foundation model is employed.

^{[11]}A nonlinear Pasternak foundation model (NPFM), considering the nonlinear deformation of the ground as well as the interaction between adjacent springs and upward tunnel displacement, is proposed for modelling the tunnel-soil interaction associated with unloading stress.

^{[12]}The structural formulation is based on the classical beam theory along with the Winkler-Pasternak foundation model, the MRF is modeled as a first order Kelvin-Voigt material, and the quasi-steady first order supersonic piston theory is employed to define the aerodynamic loading.

^{[13]}The granular fill and the soft soil foundation were both modelled using two-parameter Pasternak foundation models.

^{[14]}In order to consider the elastic substrate, Winkler and Pasternak foundation models are used.

^{[15]}The plate is assumed to resting on Pasternak foundation model and subjected to mechanical and thermal loads.

^{[16]}

## Winkler Foundation Model

Verification of pipe integrity against such actions and design of mitigation measures is based on analyses with nonlinear beam-on-non-linear Winkler foundation models, where the soil reaction developing on a pipe as result of differential ground movements is modelled by means of elastoplastic springs.^{[1]}In this paper, the tunnel face stability under the advanced pipe was analyzed using the Winkler foundation model and rigid limit equilibrium.

^{[2]}Based on the beam-on-a-nonlinear Winkler foundation model, this study develops a practical approach to simulate the seismic responses of bridge columns with spread footings, including the footing settlement and rotation and the accelerations of the structure, by employing structural elements that are readily available in most commercial structural analysis software.

^{[3]}The elastic foundation was considered in the framework of inertial Winkler foundation model.

^{[4]}Interaction between the beam and its underlying substrate medium is described by the Winkler foundation model.

^{[5]}A Winkler foundation model is used to describe the contact deformation of the third-body layer.

^{[6]}In the analysis, Euler-Bernoulli beam theory and Winkler foundation model are used.

^{[7]}In the present study, to investigate the structural performance and failure mode of RC column-isolated footing substructures on foundation, a test device using rubber-wooden composite blocks to simulate elastic foundation based on Winkler foundation model was designed.

^{[8]}Existing analytical method to predict tunneling-induced pile deformation is generally based on the Winkler foundation model that neglects shear effects of soil, which is not sufficient for engineering practice.

^{[9]}For this purpose, nonlinear time history analyses were carried out for the pipeline considering soil-pipeline interaction represented by beam on nonlinear Winkler foundation model.

^{[10]}

## Viscoelastic Foundation Model

A nonlinear viscoelastic foundation model under a moving load is established.^{[1]}The viscoelastic foundation model for gangue mechanical response is different from the traditionally used elastic foundation model, as it considers the time factor and viscoelasticity.

^{[2]}This paper presents a comprehensive review on different theoretical elastic and viscoelastic foundation models in oscillatory systems.

^{[3]}

## Spring Foundation Model

It was found that the ratio between fundamental frequency for the fixed base model of the building and elastic spring foundation model is the decisive parameter for selecting the building part to be monitored.^{[1]}The developed model resembles the traditional two-parameter spring foundation model but the analysis shows that the traditional foundation spring parameters cannot be prescribed a priori but determined as part of the solution.

^{[2]}Moreover, the paper presents a two-parameter spring foundation model applied to realistically capture the continuity in the supporting medium.

^{[3]}

## Parameter Foundation Model

On the basis of comprehensive consideration of the continuity of the deformation of the filling behind the reinforced retaining wall, if the filling behind the wall is regarded as the Pasternak two-parameter foundation model, then the retaining wall panels can be considered as Bernoulli–Euler beams.^{[1]}Secondly, the Pasternak’s two-parameter foundation model is employed for the time-domain deformation response of adjacent pile caused by excavation unloading stress, which accounts for rheological effects in viscoelastic soil.

^{[2]}A nonlinear three-parameter foundation model was employed to estimate the plate-foundation interactions.

^{[3]}

## Linear Foundation Model

Secant rotational stiffness is used to represent the value of rotational stiffness of linear foundation model when the soil changes from elastic to elasto-plastic and then to plastic.^{[1]}Beam is assumed to be resting on an elastic foundation and in this linear foundation model, foundation modulus is assumed to vary axially with respect to space variable in a non-linear manner ignoring the effect of mass density of foundation on the behavior of micro-beam.

^{[2]}It is considered that mechanical behavior of elastic media is supposed to be like linear foundation model.

^{[3]}

## Simplified Foundation Model

Based on the response spectra of WFEM of hydropower house and a constructed energy error objective function, the optimal equivalent parameters of the simplified foundation model are then determined by using the genetic algorithm.^{[1]}Subsequently, the treated data is used to calibrate the dynamic impedances of the simplified foundation model using an iterative curve fitting procedure.

^{[2]}

## Raft Foundation Model

In this research, the raft foundation modeling combined with deep-mixing columns is performed using FLAC3D with the mixing parameters obtained using experimental uniaxial and triaxial tests.^{[1]}This paper presents the preparing, executing, data acquisition, and result presentation for an experimental work concerns with five scale-down mini-piled raft foundation models.

^{[2]}

## Two Foundation Model

Results from series of centrifuge experiments on a foundation-structure model, and two foundation models revealed that: (1) inertial interaction significantly affects the lateral and rocking transfer functions around structural flexible-base natural frequencies; (2) while amplitudes of the lateral transfer functions of the foundation-structure model are smaller than those of the two other the physical models, amplitudes of the rocking transfer functions are larger; thus, using available models may lead to over-reduction and over-introduction of lateral and rocking foundation motions, respectively; (3) the effect of foundation mass is not significant; (4) increasing the motion intensity decreases the incoherence parameters; and (5) incoherence parameters had good correlations with ground motion parameters and soil shear wave velocity.^{[1]}In addition, this research also compares the calculation results of two foundation models and investigates the change of plate height ratio to plate size.

^{[2]}

## Hybrid Foundation Model

Hybrid foundation models with different dimensions were installed on both dry and saturated loose sand deposits and subjected to dynamic geotechnical centrifuge tests.^{[1]}Five hybrid foundation models are tested by considering the influence of the foundation thicknesses and diameters, and a monopile foundation is tested for comparison.

^{[2]}

## Shallow Foundation Model

Then, using the optimum PP addition, the bearing capacity of the soil was estimated through a series of loading tests on a shallow foundation model placed in a test box.^{[1]}The prospects of a shallow foundation model with a variable cross section or a beam of finite length with variable stiffness, which is accepted as one of the options for modifying a typical structural solution of a strip foundation, are shown.

^{[2]}

## Type Foundation Model

Further, the use of the Kerr-type foundation model can improve the vibration suppression characteristics.^{[1]}Some new results are obtained by applying different thermal loadings to the plate according to the GOPs’ negative coefficient of thermal expansion and considering both Winkler-type and Pasternak-type foundation models.

^{[2]}

## Different Foundation Model

A comparative analysis of the effectiveness of damping foundation vibrations using different foundation models, including the model of an elastic, homogeneous half-space and a system of semi-infinite rods, the modulus of elasticity of which increases with depth according to the quadratic law, shows a fairly close agreement.^{[1]}The paper presents the implementation and comparison of two different foundation modeling methods, referred to as the simplified apparent fixity method and the improved apparent fixity method.

^{[2]}