Visco-elastic finite element formulation for isolated foundations on clays

Viladkar, M.N.; Sharma, Richi Prasad; Ranjan, Gopal

doi:10.1016/0045-7949(92)90148-s

Cited by 4 publications

(3 citation statements)

References 5 publications

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“…The constitutive relation between the incremental effective stress and the displacement for a viscoelastic material using the Voigt model (Bardet, ; Viladkar et al ., ) can be written as

{σ_{i j}^{'}}^{e} = G ((), \frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}}) + λ ((), \frac{\partial u_{k}}{\partial x_{k}}) δ_{i j} + G^{'} \frac{\partial}{\partial t} ((), \frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}}) + λ^{'} \frac{\partial}{\partial t} ((), \frac{\partial u_{k}}{\partial x_{k}}) δ_{i j} i, j, k = x, y, z

where G and are the Lame's constants, and G ' and λ ' are viscous moduli. Substituting Equation into Equation and applying

n^{e} = ((), 1 - n^{0}) \nabla \cdot \vec{u}

(Tsai et al ., ) yields the force equilibrium in the incremental state

\frac{\partial}{\partial x_{i}} ([], ((), G + λ) \frac{\partial u_{j}}{\partial x_{j}}) + \frac{\partial}{\partial x_{j}} ([], G \frac{\partial u_{i}}{\partial x_{j}}) + \frac{\partial}{\partial x_{i}} ([], ((), G^{'} + λ^{'}) \frac{\partial^{2} u_{j}}{\partial t \partial x_{j}}) + \frac{\partial}{\partial x_{j}} ([], G^{'} \frac{\partial^{2} u_{i}}{\partial t \partial x_{j}}) + normalΔ ρ g_{i} ((), 1 -)

…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…The constitutive relation between the incremental effective stress and the displacement for a viscoelastic material using the Voigt model (Bardet, 1992;Viladkar et al, 1992) can be written as…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Expanding Terzaghi's elastic consolidation theory to include soil plasticity, the uncoupled one‐dimensional elastic–plastic consolidation model was proposed to calculate aquitard consolidation due to hydraulic head variations in neighbouring aquifers by tracking the preconsolidation stress and setting distinct volume compressibilities in normally consolidated and overconsolidated soils (Gambolati and Freeze, ; Gambolati et al ., , ; Helm, , ; Neuman et al ., ; Liu and Helm, , ). In addition, extending elastic consolidation theory (Verruijt, ) to consider soil creep, the viscoelastic consolidation model (Bardet, ; Viladkar et al ., ) was applied to calculate aquitard consolidation in multilayered aquifer system (Tsai, ). Further, the uncoupled one‐dimensional viscoelastic–plastic consolidation model has been used to simulate land subsidence (Shi et al ., ; Ye et al ., ).…”

Section: Introductionmentioning

confidence: 99%

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A coupled one-dimensional viscoelastic-plastic model for aquitard consolidation caused by hydraulic head variations in aquifers

Tsai

2015

Hydrol. Process.

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Abstract:Accurate and practical calculation of aquitard consolidation is required for a reliable analysis of land subsidence caused by groundwater overexploitation in a multilayered aquifer system because aquitards are generally more compressible than aquifers are. This study proposes a coupled one-dimensional viscoelastic-plastic consolidation model that considers the combined effect of changes in soil parameters and body force to simulate aquitard consolidation caused by hydraulic head variations in neighbouring aquifers. The proposed model uses variable total stress and simultaneously solves hydraulic head and vertical soil displacement. The constitutive relation based on the Voigt model with different elastic moduli of the spring in normally consolidated and overconsolidated soils is used to describe the viscoelastic-plastic deformation mechanism of aquitards. In addition, the proposed model considers the combined effect of variations in hydraulic conductivity, elastic moduli, and body force on the calculation of aquitard consolidation. Three hypothetical scenarios with various hydraulic head variations in aquifers are used to examine the coupled one-dimensional viscoelastic-plastic consolidation model. The results show that neglecting plasticity and viscosity of soil causes aquitard consolidation to be respectively underestimated and overestimated. In addition, ignoring body force variation underestimates aquitard consolidation, whereas neglecting soil parameters variation overestimates aquitard consolidation. Two real case scenarios are also studied to further demonstrate the applicability of the coupled onedimensional viscoelastic-plastic consolidation model.

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“…The constitutive relation between the incremental effective stress and the displacement for a viscoelastic material using the Voigt model (Bardet, ; Viladkar et al ., ) can be written as

{σ_{i j}^{'}}^{e} = G ((), \frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}}) + λ ((), \frac{\partial u_{k}}{\partial x_{k}}) δ_{i j} + G^{'} \frac{\partial}{\partial t} ((), \frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}}) + λ^{'} \frac{\partial}{\partial t} ((), \frac{\partial u_{k}}{\partial x_{k}}) δ_{i j} i, j, k = x, y, z

where G and are the Lame's constants, and G ' and λ ' are viscous moduli. Substituting Equation into Equation and applying

n^{e} = ((), 1 - n^{0}) \nabla \cdot \vec{u}

(Tsai et al ., ) yields the force equilibrium in the incremental state

\frac{\partial}{\partial x_{i}} ([], ((), G + λ) \frac{\partial u_{j}}{\partial x_{j}}) + \frac{\partial}{\partial x_{j}} ([], G \frac{\partial u_{i}}{\partial x_{j}}) + \frac{\partial}{\partial x_{i}} ([], ((), G^{'} + λ^{'}) \frac{\partial^{2} u_{j}}{\partial t \partial x_{j}}) + \frac{\partial}{\partial x_{j}} ([], G^{'} \frac{\partial^{2} u_{i}}{\partial t \partial x_{j}}) + normalΔ ρ g_{i} ((), 1 -)

…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A coupled one-dimensional viscoelastic-plastic model for aquitard consolidation caused by hydraulic head variations in aquifers

Tsai

2015

Hydrol. Process.

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Soil structure interaction in framed structure on a hilly area: a case study

Paknahad¹,

Hejazi

Jaafar

et al. 2019

IOP Conf. Ser.: Earth Environ. Sci.

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There are many problems in civil engineering which are involving some kind of structural element in straight connection with the land. When there is some forces are applied to the structural element, both component (structural element and soil/ground) must deform and move in compatible manner. These types of problems are referred as Soil-Structure Interaction (SSI) problem. In this project, an analysis of a building on the slope (10˚) with 5 stories was carried out. The soil under the building are make up by 8 layers consist different type of material. The study in this project is focusing on development of finite element model in order to analysis of a framed structure foundation comprised of a pile system and soil media resting on a hilly area. A beam bending element that calculate the outcome of transverse shear deformation and the axial interaction is then formulated. Based on the interaction behavior of the superstructure foundation soil system, bending moment in the superstructure is found to increase in the external beam and decrease in the inner beams. The effect of hill slope influences the displacements, and subsequently, the forces in the superstructure. This study also compares the result from SSI program and conventional analysis to find out the weakness of the conventional analysis.

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Numerical simulation of soil-structure interaction in framed and shear-wall structures

Dalili¹,

Al-Karni²,

Noorzaei³

et al. 2011

Interaction and multiscale mechanics

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This paper deals with the modeling of the plane frame structure-foundation-soil system. The superstructure along with the foundation beam is idealized as beam bending elements. The soil medium near the foundation beam with stress concentrated is idealized by isoparametric finite elements, and infinite elements are used to represent the far field of the soil media. This paper presents the modeling of shear wall structure-foundation and soil system using the optimal membrane triangular, super and conventional finite elements. Particularly, an alternative formulation is presented for the optimal triangular elements aimed at reducing the programming effort and computational cost. The proposed model is applied to a plane framecombined footing-soil system. It is shown that the total settlement obtained from the nonlinear interactive analysis is about 1.3 to 1.4 times that of the non-interactive analysis. Furthermore, the proposed model was found to be efficient in simulating the shear wallfoundation-soil system, being able to yield results that are similar to those obtained by the conventional finite element method.

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Visco-elastic finite element formulation for isolated foundations on clays

Cited by 4 publications

References 5 publications

A coupled one-dimensional viscoelastic-plastic model for aquitard consolidation caused by hydraulic head variations in aquifers

A coupled one-dimensional viscoelastic-plastic model for aquitard consolidation caused by hydraulic head variations in aquifers

Soil structure interaction in framed structure on a hilly area: a case study

Numerical simulation of soil-structure interaction in framed and shear-wall structures

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