Settlements and stresses of multi‐layered grounds and improved grounds by equivalent elastic method

Hirai, Hisao

doi:10.1002/nag.636

Cited by 48 publications

(35 citation statements)

References 22 publications

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“…Research study Method adopted Burmister (1945aBurmister ( , 1945bBurmister ( , 1945c Theory of elasticity Davis and Poulos (1972) Diffusion theory of consolidation Davies and Banerjee (1978) Theory of elasticity, integral transform technique Gazetas (1980) Analytical-numerical method for static and dynamic analysis Rowe and Booker (1984) Numerical inversion of the Fourier transforms Small and Booker (1984) Exact finite-layer flexibility matrix Maier and Novati (1986), Ahmad and Bharadwaj (1991), Bharadwaj and Ahmad (1992) Boundary element method Chow (1987), Azam et al (1991), Zhu and Yin (1999) Finite element method Leonards and Frost (1988) Experimental results and Schmertmann (1970) method Jommi and Novati (1989) Approach based on boundary integral equation Conte and Dente (1993) Stiffness method Shvets et al (2003) Boussinesq's method and experimental study Thomé et al (2005), Anderson et al (2007) Experimental study and finite element analysis Maheshwari and Madhav (2006), Maheshwari and Viladkar (2007) Theory of elasticity and finite difference method Hirai (2008) Equivalent elastic method Dhar and Tarefder (2011) Equivalent depth and Boussinesq's solution VOL 9 NO 1 Sheu (2011), Maheshwari and Kashyap (2011), etc. In view of non-negativity in the values of soil parameters, most of the studies considered soil parameters to follow lognormal distribution.…”

Section: Stochastic Analysismentioning

confidence: 99%

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Settlement of shallow footings on layered soil: state-of-the-art

Maheshwari

2014

International Journal of Geotechnical Engineering

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Shallow footings form the foundations of conventional structures like residential as well as industrial framed buildings and also other industrial structures like silos, chimneys, cooling towers, overhead tanks, etc. The foundations are checked both for shear failure and settlement criterion. Most of the conventional analyses consider the soil to be homogeneous, however, soil strata comprise of different soil layers with inherent variability. Several analytical, numerical, and experimental research works are available for the analysis of shallow footings on layered soil system. This paper presents comprehensive overview of literature pertaining to the settlement analysis of shallow foundations on layered soil system. It was aimed to provide all the references at one place to facilitate the research workers in this area. Deterministic as well as probabilistic studies have been compiled and it is felt that deterministic methods should be used in conjunction with the stochastic approaches for more rational analysis of shallow foundations on layered soils.

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Section: Stochastic Analysismentioning

confidence: 99%

“…An equivalent elastic method was proposed by Hirai (2008) to estimate settlements and stresses in layered and improved earth beds. The proposed method considered nonhomogeneous elastic properties of different soil layers in both directions by introducing equivalent elastic modulus and the equivalent thickness.…”

Section: Deterministic Analysismentioning

confidence: 99%

Settlement of shallow footings on layered soil: state-of-the-art

Maheshwari

2014

International Journal of Geotechnical Engineering

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“…Hirai proposed the relationship between settlement and load for the circular pile base on multilayered soils on the basis of both the equivalent thickness and the equivalent elastic modulus for layers in the equivalent elastic method. Considering that the pile base is represented as a rigid punch acting on the surface of soils ignoring the pile shaft and surrounding soil depth and taking into account the Mindlin solution and the equivalent elastic method, the relationship between the settlement w kb on the pile base and the base load P Pkb and that between the vertical pressure p Pkb and the base load P Pkb for the rigid base of circular pile are obtained as follows:

\begin{matrix} left \\ w_{k b} = {F_{P}}_{k b} \cdot P_{P k b} \\ p_{{_{P}}_{k b}} = \frac{P_{P k b}}{{((), {d_{B}}^{2} true/ 4 - r^{2})}^{1 / 2} π d_{B}} \end{matrix}

where

\begin{matrix} left \\ F_{P k b} = \{\frac{J_{P} ((, H_{k b e}) (),' ν_{n})}{E_{k b}} + \sum_{k = k b + 1}^{n} \frac{J_{P} ((, \sum_{j = k b}^{k} H_{j e}) (),' ν_{n}) - J_{P} ((, \sum_{j = k b}^{k - 1} H_{j e}) (),' ν_{n})}{E_{k}}\} / (π, d_{B}) \\ J_{P} (h^{'}, ν_{n}) = K (0, ν_{n}) - K (h^{'}, ν_{n}) \\ K (h^{'}, ν_{n}) = ... \end{matrix}

…”

Section: Formulation Of Settlement Of Piled Raft With Nodular Pilementioning

confidence: 99%

“…For the case where the pile head is subjected to external load P P 1 and the vertical stress acting on the rigid pile base is p Pkb , the settlement w Pj ″ of the point j is expressed as follows:

{w_{P j}}^{''} = {F_{P j}}^{''} \cdot P_{P 1}

where

\begin{matrix} left \\ {F_{P j}}^{''} = I_{j B} \cdot F_{P_{P k b} P_{P 1}} / (π d_{B} E_{b e q}) \\ I_{j B} = I_{j B} (x_{0}, y_{0}, h, c) \\ \begin{array}{c} center \end{array} = \int_{0}^{d_{B} true/ 2} \int_{0}^{2 π} A_{1} \cdot r \cdot dϕdr \\ F_{P_{P k b} P_{P 1}} = {P_{P}}_{k b} / P_{P 1} \end{matrix}

where E beq is the equivalent elastic modulus for layers beneath the pile base in the equivalent elastic method and P Pkb is the vertical force acting on the rigid base of the pile subjected to the load P P 1 .…”

Section: Formulation Of Settlement Of Piled Raft With Nodular Pilementioning

confidence: 99%

Analysis of piled raft with nodular pile subjected to vertical load using a Winkler model approach

Hirai

2016

Num Anal Meth Geomechanics

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Summary An investigation is made to present analytical solutions provided by a Winkler model approach for analysis of piled rafts with nodular pile subjected to vertical loads in nonhomogeneous soils. The vertical stiffness coefficient along a piled raft with the nodular pile in nonhomogeneous soils is derived from the displacement given by the Mindlin solution for elastic continuum analysis. The vertical stiffness coefficients for the bases of the raft and the nodular part in the nodular pile in a soil are expressed by the Muki solution for the 3‐D elastic analysis. The relationship between settlement and vertical load on the pile base is presented considering the Mindlin solution and the equivalent thickness in the equivalent elastic method. The interaction factor between the shaft of the nodular pile and the soil is expressed taking into account the Mindlin solution and the equivalent elastic modulus. The relationship between settlement and vertical load for a piled raft with the nodular pile in nonhomogeneous soils is obtained by using the recurrence equation of influence factors of the pile for each layer. The percentage of each load carried by both nodular pile and raft subjected to vertical load is represented through the vertical influence factors proposed here. Comparison of the results calculated by the present method for piled rafts with nodular piles in nonhomogeneous soils has shown good agreement with those obtained from the finite element method and a field test. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Hirai proposed the relationship between settlement and load for the circular pile base on multilayered soils on the basis of both the equivalent thickness and the equivalent elastic modulus for layers in the equivalent elastic method. Considering that the pile base with a rectangular cross section is represented as a rigid punch acting on the surface of soils ignoring the pile shaft and surrounding soil depth and taking into account Mindlin's solution in a homogeneous soil and the equivalent elastic method proposed by Hirai , the relationship between the settlement w B ( mb −1) on the pile base and the base load P B ( mb −1) and that between the vertical pressure p B ( mb −1) and the base load P B ( mb −1) for the rigid base of a rectangular pile are obtained as follows:

\begin{matrix} left \\ w_{B (mb - 1)} = F_{italicmb} \cdot P_{B (mb - 1)} \\ p_{B (mb - 1)} = \frac{P_{B ((), italicmb - 1)}}{{((), R^{2} - r^{2})}^{1 / 2} A_{1}} \end{matrix}

where

\begin{matrix} left \\ F_{italicmb} = \frac{1}{A_{1}} \{\frac{I_{P} ({H_{italicmbe}}^{'}, ν_{n})}{E_{mb}} + \sum_{m = mb + 1}^{n} \frac{I_{P} ((), \sum_{j = mb}^{m}, {H_{italicje}}^{'}, ν_{n}) - I_{P} ((), \sum_{j = mb}^{m - 1}, {H_{italicje}}^{'}, ν_{n})}{E_{m}}\} \\ I_{P} (h^{'}, ν_{n}) = K (0, ν_{n}) - K (h^{'}, ν_{n}) \\ K (h^{'}, ν_{n}) = ... \end{matrix}

…”

Section: Formulation Of Settlement Of a Rectangular Pile Subjected Tomentioning

confidence: 99%

Settlement analysis of rectangular piles in nonhomogeneous soil using a Winkler model approach

Hirai

2014

Num Anal Meth Geomechanics

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SUMMARY An analytical approach using a Winkler model is investigated to provide analytical　solutions of settlement of a rectangular pile subjected to vertical loads in nonhomogeneous soils. For a vertically loaded pile with a rectangular cross section, the settlement influence factor of a normal pile in nonhomogeneous soils is derived from Mindlin's solution for elastic continuum analysis. For short piles with rectangular and circular cross sections, the modified forms of settlement influence factors of normal piles are produced taking into account the load transfer parameter proposed by Randolph for short circular piles. The modulus of subgrade reaction along a rectangular pile in nonhomogeneous soils is expressed by using the settlement influence factor related to Mindlin's solution to combine the elastic continuum approach with the subgrade‐reaction approach. The relationship between settlement and vertical load for a rectangular pile in nonhomogeneous soils is available in the form of the recurrence equation. The formulation of settlement of soils surrounding a rectangular pile subjected to vertical loads in nonhomogeneous soils is proposed by taking into account Mindlin's solution and both the equivalent thickness and the equivalent elastic modulus for layers in the equivalent elastic method. The difference of settlement between square and circular piles is insignificant, and the settlement of a rectangular pile decreases as the aspect ratio of the rectangular pile cross section increases. The comparison of results calculated by the present method for a rectangular pile in nonhomogeneous soils has shown good agreement with those obtained from the analytical methods and the finite element method. Copyright © 2014 John Wiley & Sons, Ltd.

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Settlements and stresses of multi‐layered grounds and improved grounds by equivalent elastic method

Cited by 48 publications

References 22 publications

Settlement of shallow footings on layered soil: state-of-the-art

Settlement of shallow footings on layered soil: state-of-the-art

Analysis of piled raft with nodular pile subjected to vertical load using a Winkler model approach

Settlement analysis of rectangular piles in nonhomogeneous soil using a Winkler model approach

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