A 2D semi-analytical analysis of the time-dependent settlement of a shallow foundation placed near the soil slope

نوع مقاله : مقاله پژوهشی

نویسندگان

1 Department of Mining Engineering, Tehran University, Tehran, Iran

2 Rock Mechanics Specialist, Thurber Engineering Ltd., Vancouver, British Columbia, Canada

چکیده

To assess the safety of the foundation, the ultimate bearing capacity, as well as the settlement of the footing, should be studied. The bearing capacity of a footing built near the slope has been widely investigated. However, the published research work which focused on the settlement of the footing close to the slope is very limited. In many cases, the foundations should be built adjacent to a slope. Since geomaterial behavior is usually time-dependent, and due to the limited published research work on the time-dependent settlement of the foundation on a slope, in this study, a semi-analytical method has been used to obtain the elastic and viscoelastic settlement of a foundation rested on a slope. The proposed method has been developed based on the theory of elasticity by combining a transformed Airy stress function and finite difference method. To facilitate the use of the proposed solution, as well as investigating the effect of slope characteristics and footing geometry on the settlement, a set of elastic and time-dependent settlement charts have been proposed. The results indicate that the slope angle, the normalized footing distance from the crest, and the slope height play a prominent role in the settlement behavior of footing. By increasing the normalized footing distance or decreasing the slope angle, the settlement of the edges of the foundation tends to be equal and the behavior like a footing rested on a horizontal ground surface can be observed. Also, by decreasing the height of the slope, this behavior, i.e. behave like a footing on half-space, will happen in the smaller normalized footing distance.

کلیدواژه‌ها

عنوان مقاله [English]

A 2D semi-analytical analysis of the time-dependent settlement of a shallow foundation placed near the soil slope

نویسندگان [English]

  • Hadi Haghgouei 1
  • Ali Reza Kargar 1
  • Mohammad Hossein Khosravi 1
  • Mehdi Amini 2
1 Department of Mining Engineering, Tehran University, Tehran, Iran
2 Rock Mechanics Specialist, Thurber Engineering Ltd., Vancouver, British Columbia, Canada
چکیده [English]

To assess the safety of the foundation, the ultimate bearing capacity, as well as the settlement of the footing, should be studied. The bearing capacity of a footing built near the slope has been widely investigated. However, the published research work which focused on the settlement of the footing close to the slope is very limited. In many cases, the foundations should be built adjacent to a slope. Since geomaterial behavior is usually time-dependent, and due to the limited published research work on the time-dependent settlement of the foundation on a slope, in this study, a semi-analytical method has been used to obtain the elastic and viscoelastic settlement of a foundation rested on a slope. The proposed method has been developed based on the theory of elasticity by combining a transformed Airy stress function and finite difference method. To facilitate the use of the proposed solution, as well as investigating the effect of slope characteristics and footing geometry on the settlement, a set of elastic and time-dependent settlement charts have been proposed. The results indicate that the slope angle, the normalized footing distance from the crest, and the slope height play a prominent role in the settlement behavior of footing. By increasing the normalized footing distance or decreasing the slope angle, the settlement of the edges of the foundation tends to be equal and the behavior like a footing rested on a horizontal ground surface can be observed. Also, by decreasing the height of the slope, this behavior, i.e. behave like a footing on half-space, will happen in the smaller normalized footing distance.

کلیدواژه‌ها [English]

  • Shallow foundation settlement
  • Creep
  • Time-dependent behavior
  • Soil bearing capacity
  • 2D semi-analytical method
  • Finite difference method
  • Differential Settlement

مراجع

[1] Meyerhof G. The ultimate bearing capacity of foudations. Geotechnique. 1951;2(4):301-32.
[2] Chen YF, Ai ZY. Viscoelastic analysis of transversely isotropic multilayered porous rock foundation by fractional Poyting-Thomson model. Eng Geol. 2020;264(105327.
[3] Fisher K. Zur Berechnung der setzung Von Fundamenten in der form einer Kreisformigen Ringflache. Der Bauingenieur. 1957;32(5):172-4.
[4] Egorov K, Nichiporovich A. Research on the deflection of foundations.  Proceedings of the 5th international conference on soil mechanics and foundation engineering1961. p. 861-6.
[5] Gazetas G, Tassoulas J, Dobry R, O'Rourke M. Elastic settlement of arbitrarily shaped foundations embedded in half-space. Geotechnique. 1985;35(3):339-46.
[6] Choobbasti A, Hesami S, Najafi A, Pirzadeh S, Farrokhzad F, Zahmatkesh A. Numerical evaluation of bearing capacity and settlement of ring footing; case study of Kazeroon cooling towers. International Journal of Research and Reviews in Applied Sciences. 2010;4(2).
[7] Naseri M, Hosseininia ES. Elastic settlement of ring foundations. Soils and Foundations. 2015;55(2):284-95.
[8] Gunerathne S, Seo H, Lawson WD, Jayawickrama PW. Analysis of edge-to-center settlement ratio for circular storage tank foundation on elastic soil. Computers and Geotechnics. 2018;102(136-47.
[9] Díaz E, Brotons V, Tomás R. Use of artificial neural networks to predict 3-D elastic settlement of foundations on soils with inclined bedrock. Soils and Foundations. 2018;58(6):1414-22.
[10] Taylor DW, Merchant W. A theory of clay consolidation accounting for secondary compression. Journal of Mathematics and Physics. 1940;19(1-4):167-85.
[11] Biot MA. Theory of deformation of a porous viscoelastic anisotropic solid. Journal of Applied physics. 1956;27(5):459-67.
[12] Booker JR, Small J. Finite layer analysis of viscoelastic layered materials. International Journal for Numerical and Analytical Methods in Geomechanics. 1986;10(4):415-30.
[13] Xie KH, Xie XY, Li XB. Analytical theory for one‐dimensional consolidation of clayey soils exhibiting rheological characteristics under time‐dependent loading. International journal for numerical and analytical methods in geomechanics. 2008;32(14):1833-55.
[14] Yin Z-Y, Chang CS, Karstunen M, Hicher P-Y. An anisotropic elastic–viscoplastic model for soft clays. International Journal of Solids and Structures. 2010;47(5):665-77.
[15] Zou S-F, Li J-Z, Xie X-Y. A semi-analytical solution for one-dimensional elasto-viscoplastic consolidation of layered soft clay. Applied Clay Science. 2018;153(9-15.
[16] Meyerhof G. The ultimate bearing capacity of foundations on slopes.  Proc, 4th Int Conf on Soil Mechanics and Foundation Engineering1957. p. 384-6.
[17] Kusakabe O, Kimura T, Yamaguchi H. Bearing capacity of slopes under strip loads on the top surfaces. Soils and foundations. 1981;21(4):29-40.
[18] Narita K, Yamaguchi H. Bearing capacity analysis of foudations on slopes by use of log-spiral sliding surfaces. Soils and Foundations. 1990;30(3):144-52.
[19] Georgiadis K. Undrained bearing capacity of strip footings on slopes. Journal of geotechnical and geoenvironmental engineering. 2010;136(5):677-85.
[20] Leshchinsky B. Bearing capacity of footings placed adjacent to c′-ϕ′ slopes. Journal of geotechnical and geoenvironmental engineering. 2015;141(6):04015022.
[21] Zhou H, Zheng G, Yin X, Jia R, Yang X. The bearing capacity and failure mechanism of a vertically loaded strip footing placed on the top of slopes. Computers and Geotechnics. 2018;94(12-21.
[22] Haghgouei H, Kargar AR, Amini M, Khosravi MH. Semianalytical Solution for Evaluating Bearing Capacity of a Footing Adjacent to a Slope. International Journal of Geomechanics. 2020;21(2):06020041.
[23] Ni P, Wang S, Zhang S, Mei L. Response of heterogeneous slopes to increased surcharge load. Computers and Geotechnics. 2016;78(99-109.
[24] Saran S, Sud V, Handa S. Bearing capacity of footings adjacent to slopes. Journal of geotechnical engineering. 1989;115(4):553-73.
[25] Graham J, Andrews M, Shields D. Stress characteristics for shallow footings in cohesionless slopes. Canadian Geotechnical Journal. 1988;25(2):238-49.
[26] Shields D, Chandler N, Garnier J. Bearing capacity of foundations in slopes. Journal of geotechnical engineering. 1990;116(3):528-37.
[27] Bungenstab FC, Bicalho KV. Settlement predictions of footings on sands using probabilistic analysis. Journal of Rock Mechanics and Geotechnical Engineering. 2016;8(2):198-203.
[28] Deng Q, Zhu Z, Cui Z, Wang X. Mass rock creep and landsliding on the Huangtupo slope in the reservoir area of the Three Gorges Project, Yangtze River, China. Eng Geol. 2000;58(1):67-83.
[29] Cong L, Hu X. Triaxial rheological property of sandstone under low confining pressure. Eng Geol. 2017;231(45-55.
[30] Malan D. Time-dependent behaviour of deep level tabular excavations in hard rock. Rock Mech Rock Eng. 1999;32(2):123-55.
[31] Zeng Z, Kou X. Application of viscoelasticity to study the time-dependent surface subsidence caused by underground mining. Eng Geol. 1992;32(4):279-84.
[32] Omar MN, Abbiss CP, Taha MR, Nayan KAM. Prediction of long-term settlement on soft clay using shear wave velocity and damping characteristics. Eng Geol. 2011;123(4):259-70.
[33] Zhou X, Cheng H. The long-term stability analysis of 3D creeping slopes using the displacement-based rigorous limit equilibrium method. Eng Geol. 2015;195(292-300.
[34] Yao Y-P, Qi S-J, Che L-W, Chen J, Han L-M, Ma X-Y. Postconstruction settlement prediction of high embankment of silty clay at Chengde airport based on one-dimensional creep analytical method: case study. International Journal of Geomechanics. 2018;18(7):05018004.
[35] Christie I. A re-appraisal of Merchant's contribution to the theory of consolidation. Geotechnique. 1964;14(4):309-20.
[36] Kaliakin VN, Dafalias YF. Theoretical aspects of the elastoplastic-viscoplastic bounding surface model for cohesive soils. Soils and foundations. 1990;30(3):11-24.
[37] Yin J-H, Graham J. Equivalent times and one-dimensional elastic viscoplastic modelling of time-dependent stress–strain behaviour of clays. Canadian Geotechnical Journal. 1994;31(1):42-52.
[38] Justo J, Durand P. Settlement‐time behaviour of granular embankments. International journal for numerical and analytical methods in geomechanics. 2000;24(3):281-303.
[39] Zhu H-H, Liu L-C, Pei H-F, Shi B. Settlement analysis of viscoelastic foundation under vertical line load using a fractional Kelvin-Voigt model. Geomechanics and Engineering. 2012;4(1):67-78.
[40] Haghgouei H, Kargar AR, Amini M, Esmaeili K. An analytical solution for analysis of toppling-slumping failure in rock slopes. Eng Geol. 2020;265(105396.
[41] Goodman L, Brown C. Dead load stresses and the instability of slopes. Journal of the Soil Mechanics and Foundations Division. 1963;89(3):103-36.
[42] Filon LNG. III.—On a Quadrature Formula for Trigonometric Integrals. Proceedings of the Royal Society of Edinburgh. 1930;49(38-47.
[43] Pellet FL. Large Time-Dependent Convergences In A Tunnel Excavated In A Carboniferous Rock Mass.  ISRM International Symposium-6th Asian Rock Mechanics Symposium: International Society for Rock Mechanics and Rock Engineering, 2010.
[44] Paraskevopoulou C, Perras M, Diederichs M, Loew S, Lam T, Jensen M. Time-dependent behaviour of brittle rocks based on static load laboratory tests. Geotechnical and Geological Engineering. 2018;36(1):337-76.
[45] Paraskevopoulou C. Time-dependency of rocks and implications associated with tunnelling: Queen's University (Canada), 2016.

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  • تاریخ دریافت: 13 مرداد 1400
  • تاریخ بازنگری: 11 آذر 1400
  • تاریخ پذیرش: 06 دی 1400

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