Lateral stress caused by horizontal and vertical surcharge strip loads on a cross-anisotropic backfill

SUMMARYThis article derives the closed-form solutions for estimating the vertical surface displacements of crossanisotropic media due to various loading types of batter piles. The loading types include an embedded point load for an end-bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The planes of cross-anisotropy are assumed to be parallel to the horizontal ground surface. The proposed solutions are never mentioned in literature and can be developed from Wang and Liao's solutions for a horizontal and vertical point load embedded in the cross-anisotropic half-space. The present solutions are identical with Wang's solutions when batter angle equals to 0 • . In addition, the solutions indicate that the surface displacements in cross-anisotropic media are influenced by the type and degree of material anisotropy, angle of inclination, and loading types. An illustrative example is given at the end of this article to investigate the effect of the type and degree of soil anisotropy (E/E , G /E , and / ), pile inclination ( ), and different loading types (a point load, a uniform skin friction, and a linear variation of skin friction) on vertical surface displacements. Results show that the displacements accounted for pile batter are quite different from those estimated from plumb piles, both driven in cross-anisotropic media.

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“…• A 11 , A 13 , A 33 , A 44 are the elastic moduli or elasticity constants of the medium and can be expressed as follows [20]:…”

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confidence: 99%

Surface displacements due to batter piles driven in cross‐anisotropic media

Wang

Chen

Lee

2007

Num Anal Meth Geomechanics

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“…The solutions derived in this work can be combined with previous lateral stress solutions [16] for complete analysis of a retaining wall structure with a cross-anisotropic backfill subjected to any conceivable surcharge strip load. The proposed solutions demonstrate that the type and degree of material anisotropy, loading distance from the retaining wall, dimension of the loading strip, and loading directions and types significantly influence induced lateral force and centroid location.…”

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confidence: 95%

“…case [16] with respect to the z direction can yield the closed-form solutions for lateral force and centroid location caused by horizontal and vertical surcharge loads (point, line, and strip loads) on a cross-anisotropic backfill. The solutions derived in this work can be combined with previous lateral stress solutions [16] for complete analysis of a retaining wall structure with a cross-anisotropic backfill subjected to any conceivable surcharge strip load.…”

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confidence: 99%

“…Wang's paper [16], conducted a detailed survey of studies that investigated lateral stress. Table I presents a summary of the proposed solutions [16], and lists loading Cases A-G with respect to lateral stress solutions.…”

mentioning

confidence: 99%

“…Table I presents a summary of the proposed solutions [16], and lists loading Cases A-G with respect to lateral stress solutions. According to Table I, lateral stress resulting from any conceivable surcharge strip load can be examined by superimposing loading Cases C-G.…”

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confidence: 99%

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Lateral force and centroid location caused by horizontal and vertical surcharge strip loads on a cross‐anisotropic backfill

Wang

2007

Num Anal Meth Geomechanics

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SUMMARYThis work presents analytical solutions for determining lateral force (force per unit length) and centroid location caused by horizontal and vertical surcharge surface loads acting on a cross-anisotropic backfill. The surcharge loading types are point load, line load, uniform strip load, upward linear-varying strip load, upward nonlinear-varying strip load, downward linear-varying strip load, and downward nonlinearvarying strip load. The planes of cross-anisotropy are assumed parallel to the backfill ground surface. The proposed solutions, derived by integrating the lateral stress solutions (Int. J. Numer. Anal. Meth. Geomech. 2005; 29:1341-1361), do not exist in literature. Clearly, the type and degree of material anisotropy, loading distance from the retaining wall, and loading types markedly impact the proposed solutions. Two examples are utilized to illustrate the type and degree of soil anisotropy, and the loading types on the lateral force and centroid location in the isotropic/cross-anisotropic backfills generated by the horizontal and vertical uniform, upward linear-varying and upward nonlinear-varying strip loads. The parametric study results demonstrate that the lateral force and centroid location accounting for soil anisotropy, loading distance from the retaining wall, dimension of the loading strip, and loading directions and types differ significantly from those estimated using existing isotropic solutions. The derived solutions can be added to other lateral pressures, such as earth pressure or water pressure, required for stability and structural analysis of a retaining wall. Additionally, they can simulate realistically actual surcharge loading problems in geotechnical engineering when backfill materials are cross-anisotropic.

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Simplified analytical solution for point load acting behind a cantilever wall

Iskander

2011

Num Anal Meth Geomechanics

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SUMMARYThe analysis of earth pressure resulting from an applied point load behind a retaining wall is to be carried out in three dimensions as the earth pressure distribution varies both in vertical and horizontal directions. In this research, the semi-empirical expressions developed by Terzaghi [Trans. ASCE 1954; 119] for earth pressure due to point load are integrated and a correction factor is introduced to develop equivalent equations for two-dimensional analyses. A new parameter referred to as the design width, which is the horizontal distance retained by the individual vertical retaining element is introduced. As retaining structures are used to retain soil and to support adjacent structures, reliable prediction of the effect of external loads on the retaining structure is very important to achieve a safe and economic design. The supporting wall should be designed to limit ground movement [1].There are a number of methods to estimate the effect of external loads on the adjacent retaining wall. The elasticity solution developed by Boussinesq has been commonly adopted to estimate the earth pressure due to external loads. Many of the external loads can be represented by point and line loads. Researchers investigated the lateral earth pressure on a retaining wall due to point and line loads; Kim Analytical closed-form solutions have the great advantage of providing easy, direct, and powerful tool for the design process. Terzaghi [9] developed semi-empirical solutions for the cases of point and line loads, based on experimental work. These expressions are widely used and given in different geotechnical design manuals as NAVFAC [10]. In this research, a new attempt has been performed and discussed to achieve an easier analytical procedure for analyzing the problem of a point load based on Terzaghi solution.

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Lateral stress caused by horizontal and vertical surcharge strip loads on a cross-anisotropic backfill

Cited by 11 publications

References 23 publications

Surface displacements due to batter piles driven in cross‐anisotropic media

Surface displacements due to batter piles driven in cross‐anisotropic media

Lateral force and centroid location caused by horizontal and vertical surcharge strip loads on a cross‐anisotropic backfill

Simplified analytical solution for point load acting behind a cantilever wall

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